Sieve methods: what are they, and what are they good for?

Given the nature of the lecture it was difficult to come up with relevant links to include in this post, but these seemed relevant enough to include them here:

Sieve theory.
Inclusion–exclusion principle.
Fundamental lemma of sieve theory.
Parity problem (sieve theory).
Viggo Brun (the lecturer mentions along the way that many of the things he talks about in this lecture are things this guy figured out, but the wiki article is unfortunately very short).

As he notes early on, when working with sieves we’re: “*Interested in objects which are output of some inclusion-exclusion process & *Rather than counting precisely, we want to gain good bounds, but work flexibly.”

‘Counting’ should probably be interpreted loosely here, in the general scheme of things; sieves are mostly used in number theory, but as Maynard mentions presumably similar methods can be used in other mathematical contexts – thus the deliberate use of the word ‘objects’. It seems to be all about trying to ascertain some properties about some objects/sets/whatever, without necessarily imposing much structure (‘are we within the right order of magnitude?’ rather than ‘did we get them all?’). The basic idea behind restricting the amount of structure imposed is, as far as I gathered from the lecture, to make the problem you’re faced with more tractable.


February 24, 2018 Posted by | Lectures, Mathematics | Leave a comment

Some things you need to know about machine learning but didn’t know whom to ask (the grad school version)

Some links to stuff related to the lecture’s coverage:
An overview of gradient descent optimization algorithms.
Rectifier (neural networks) [Relu].
Escaping From Saddle Points – Online Stochastic Gradient for Tensor Decomposition (Ge et al.).
How to Escape Saddle Points Efficiently (closely related to the paper above, presumably one of the ‘recent improvements’ mentioned in the lecture).
Linear classifier.
Concentration inequality.
A PAC-Bayesian Approach to Spectrally-Normalized Margin Bounds for Neural Networks (Neyshabur et al.).
Off the convex path (the lecturer’s blog).

February 19, 2018 Posted by | Computer science, Lectures, Mathematics | Leave a comment


Complexity theory is a topic I’ve previously been exposed to through various channels; examples include Institute for Advanced Studies comp sci lectures, notes included in a few computer science-related books like Louridas and Dasgupta, and probably also e.g. some of the systems analysis/-science books I’ve read – Konieczny et al.’s text which I recently finished reading is another example of a book which peripherally covers content also covered in this book. Holland’s book pretty much doesn’t cover computational complexity theory at all, but some knowledge of computer science will probably still be useful as e.g. concepts from graph theory are touched upon/applied in the coverage; I am also aware that I derived some benefit while reading this book from having previously spent time on signalling models in microeconomics, as there were conceptual similarities between those models and their properties and some of the stuff Holland includes. I’m not really sure if you need to know ‘anything’ to read the book and get something out of it, but although Holland doesn’t use much mathematical formalism some of the ‘hidden’ formalism lurking in the background will probably not be easy to understand if you e.g. haven’t seen a mathematical equation since the 9th grade, and people who e.g. have seen hierarchical models before will definitely have a greater appreciation of some of the material covered than people who have not. Obviously I’ve read a lot of stuff over time that made the book easier for me to read and understand than it otherwise would have been, but how easy would the book have been for me to read if I hadn’t read those other things? It’s really difficult for me to say. I found the book hard to judge/rate/evaluate, so I decided against rating it on goodreads.

Below I have added some quotes from the book.

“[C]omplex systems exhibits a distinctive property called emergence, roughly described by the common phrase ‘the action of the whole is more than the sum of the actions of the parts’. In addition to complex systems, there is a subfield of computer science, called computational complexity, which concerns itself with the difficulty of solving different kinds of problems. […] The object of the computational complexity subfield is to assign levels of difficulty — levels of complexity — to different collections of problems. There are intriguing conjectures about these levels of complexity, but an understanding of the theoretical framework requires a substantial background in theoretical computer science — enough to fill an entire book in this series. For this reason, and because computational complexity does not touch upon emergence, I will confine this book to systems and the ways in which they exhibit emergence. […] emergent behaviour is an essential requirement for calling a system ‘complex’. […] Hierarchical organization is […] closely tied to emergence. Each level of a hierarchy typically is governed by its own set of laws. For example, the laws of the periodic table govern the combination of hydrogen and oxygen to form H2O molecules, while the laws of fluid flow (such as the Navier-Stokes equations) govern the behaviour of water. The laws of a new level must not violate the laws of earlier levels — that is, the laws at lower levels constrain the laws at higher levels. […] Restated for complex systems: emergent properties at any level must be consistent with interactions specified at the lower level(s). […] Much of the motivation for treating a system as complex is to get at questions that would otherwise remain inaccessible. Often the first steps in acquiring a deeper understanding are through comparisons of similar systems. By treating hierarchical organization as sine qua non for complexity we focus on the interactions of emergent properties at various levels. The combination of ‘top–down’ effects (as when the daily market average affects actions of the buyers and sellers in an equities market) and ‘bottom–up’ effects (the interactions of the buyers and sellers determine the market average) is a pervasive feature of complex systems. The present exposition, then, centres on complex systems where emergence, and the reduction(s) involved, offer a key to new kinds of understanding.”

“As the field of complexity studies has developed, it has split into two subfields that examine two different kinds of emergence: the study of complex physical systems (CPS) and the study of complex adaptive systems (CAS): The study of complex physical systems focuses on geometric (often lattice-like) arrays of elements, in which interactions typically depend only on effects propagated from nearest neighbours. […] the study of CPS has a distinctive set of tools and questions centring on elements that have fixed properties – atoms, the squares of the cellular automaton, and the like. […] The tools used for studying CPS come, with rare exceptions, from a well-developed part of mathematics, the theory of partial differential equations […] CAS studies, in contrast to CPS studies, concern themselves with elements that are not fixed. The elements, usually called agents, learn or adapt in response to interactions with other agents. […] It is unusual for CAS agents to converge, even momentarily, to a single ‘optimal’ strategy, or to an equilibrium. As the agents adapt to each other, new agents with new strategies usually emerge. Then each new agent offers opportunities for still further interactions, increasing the overall complexity. […] The complex feedback loops that form make it difficult to analyse, or even describe, CAS. […] Analysis of complex systems almost always turns on finding recurrent patterns in the system’s ever-changing configurations. […] perpetual novelty, produced with a limited number of rules or laws, is a characteristic of most complex systems: DNA consists of strings of the same four nucleotides, yet no two humans are exactly alike; the theorems of Euclidian geometry are based on just five axioms, yet new theorems are still being derived after two millenia; and so it is for the other complex systems.”

“In a typical physical system the whole is (at least approximately) the sum of the parts, making the use of PDEs straightforward for a mathematician, but in a typical generated system the parts are put together in an interconnected, non-additive way. It is possible to write a concise set of partial differential equations to describe the basic elements of a computer, say an interconnected set of binary counters, but the existing theory of PDEs does little to increase our understanding of the circuits so-described. The formal grammar approach, in contrast, has already considerably increased our understanding of computer languages and programs. One of the major tasks of this book is to use a formal grammar to convert common features of complex systems into ‘stylized facts’ that can be examined carefully within the grammar.”

“Many CPS problems (e.g. the flow of electrons in superconductive materials) […] involve flows — flows that are nicely described by networks. Networks provide a detailed snapshot of CPS and complex adaptive systems (CAS) interactions at any given point in their development, but there are few studies of the evolution of networks […]. The distinction between the fast dynamic of flows (change of state) and the slow dynamic of adaptation (change of the network of interactions) often distinguishes CPS studies from CAS studies. […] all well-studied CAS exhibit lever points, points where a small directed action causes large predictable changes in aggregate behaviour, as when a vaccine produces long-term changes in an immune system. At present, lever points are almost always located by trial and error. However, by extracting mechanisms common to different lever points, a relevant CAS theory would provide a principled way of locating and testing lever points. […] activities that are easy to observe in one complex system often suggest ‘where to look’ in other complex systems where the activities are difficult to observe.”

“Observation shows that agents acting in a niche continually undergo ‘improvements’, without ever completely outcompeting other agents in the community. These improvements may come about in either of two ways: (i) an agent may become more of a generalist, processing resources from a wider variety of sources, or (ii) it may become more specialized, becoming more efficient than its competitors at exploiting a particular source of a vital resource. Both changes allow for still more interactions and still greater diversity. […] All CAS that have been examined closely exhibit trends toward increasing numbers of specialists.”

“Emergence is tightly tied to the formation of boundaries. These boundaries can arise from symmetry breaking, […] or they can arise by assembly of component building blocks […]. For CAS, the agent-defining boundaries determine the interactions between agents. […] Adaptation, and the emergence of new kinds of agents, then arises from changes in the relevant boundaries. Typically, a boundary only looks to a small segment of a signal, a tag, to determine whether or not the signal can pass through the boundary. […] an agent can be modelled by a set of conditional IF/THEN rules that represent both the effects of boundaries and internal signal-processing. Because tags are short, a given signal may carry multiple tags, and the rules that process signals can require the presence of more than one tag for the processing to proceed. Agents are parallel processors in the sense that all rules that are satisfied simultaneously in the agent are executed simultaneously. As a result, the interior of an agent will usually be filled with multiple signals […]. The central role of tags in routing signals through this complex interior puts emphasis on the mechanisms for tag modification as a means of adaptation. Recombination of extant conditions and signals […] turns tags into building blocks for specifying new routes. Parallel processing then makes it possible to test new routes so formed without seriously disrupting extant useful routes. Sophisticated agents have another means of adaptation: anticipation (‘lookahead’). If an agent has a set of rules that simulates part of its world, then it can run this internal model to examine the outcomes of different action sequences before those actions are executed.”

“The flow of signals within and between agents can be represented by a directed network, where nodes represent rules, and there is a connection from node x to node y if rule x sends a signal satisfying a condition of rule y. Then, the flow of signals over this network spells out the performance of the agent at a point in time. […] The networks associated with CAS are typically highly tangled, with many loops providing feedback and recirculation […]. An agent adapts by changing its signal-processing rules, with corresponding changes in the structure of the associated network. […] Most machine-learning models, including ‘artificial neural networks’ and ‘Bayesian networks’, lack feedback cycles — they are often called ‘feedforward networks’ (in contrast to networks with substantial feedback). In the terms used in Chapter 4, such networks have no ‘recirculation’ and hence have no autonomous subsystems. Networks with substantial numbers of cycles are difficult to analyse, but a large number of cycles is the essential requirement for the autonomous internal models that make lookahead and planning possible. […] The complexities introduced by loops have so far resisted most attempts at analysis. […] The difficulties of analysing the behaviour of networks with many interior loops has, both historically and currently, encouraged the study of networks without loops called trees. Trees occur naturally in the study of games. […] because trees are easier to analyse, most artificial neural networks constructed for pattern recognition are trees. […] Evolutionary game theory makes use of the tree structure of games to study the ways in which agents can modify their strategies as they interact with other agents playing the same game. […] However, evolutionary game theory does not concern itself with the evolution of the game’s laws.”

“It has been observed that innovation in CAS is mostly a matter of combining well-known components in new ways. […] Recombination abets the formation of new cascades. […] By extracting general mechanisms that modify CAS, such as recombination, we go from examination of particular instances to a unified study of characteristic CAS properties. The mechanisms of interest act mainly on extant substructures, using them as building blocks for more complex substructures […]. Because signals and boundaries are a pervasive feature of CAS, their modification has a central role in this adaptive process.”

February 12, 2018 Posted by | Books, Computer science, Mathematics | Leave a comment

Random stuff

I have almost stopped posting posts like these, which has resulted in the accumulation of a very large number of links and studies which I figured I might like to blog at some point. This post is mainly an attempt to deal with the backlog – I won’t cover the material in too much detail.

i. Do Bullies Have More Sex? The answer seems to be a qualified yes. A few quotes:

“Sexual behavior during adolescence is fairly widespread in Western cultures (Zimmer-Gembeck and Helfland 2008) with nearly two thirds of youth having had sexual intercourse by the age of 19 (Finer and Philbin 2013). […] Bullying behavior may aid in intrasexual competition and intersexual selection as a strategy when competing for mates. In line with this contention, bullying has been linked to having a higher number of dating and sexual partners (Dane et al. 2017; Volk et al. 2015). This may be one reason why adolescence coincides with a peak in antisocial or aggressive behaviors, such as bullying (Volk et al. 2006). However, not all adolescents benefit from bullying. Instead, bullying may only benefit adolescents with certain personality traits who are willing and able to leverage bullying as a strategy for engaging in sexual behavior with opposite-sex peers. Therefore, we used two independent cross-sectional samples of older and younger adolescents to determine which personality traits, if any, are associated with leveraging bullying into opportunities for sexual behavior.”

“…bullying by males signal the ability to provide good genes, material resources, and protect offspring (Buss and Shackelford 1997; Volk et al. 2012) because bullying others is a way of displaying attractive qualities such as strength and dominance (Gallup et al. 2007; Reijntjes et al. 2013). As a result, this makes bullies attractive sexual partners to opposite-sex peers while simultaneously suppressing the sexual success of same-sex rivals (Gallup et al. 2011; Koh and Wong 2015; Zimmer-Gembeck et al. 2001). Females may denigrate other females, targeting their appearance and sexual promiscuity (Leenaars et al. 2008; Vaillancourt 2013), which are two qualities relating to male mate preferences. Consequently, derogating these qualities lowers a rivals’ appeal as a mate and also intimidates or coerces rivals into withdrawing from intrasexual competition (Campbell 2013; Dane et al. 2017; Fisher and Cox 2009; Vaillancourt 2013). Thus, males may use direct forms of bullying (e.g., physical, verbal) to facilitate intersexual selection (i.e., appear attractive to females), while females may use relational bullying to facilitate intrasexual competition, by making rivals appear less attractive to males.”

The study relies on the use of self-report data, which I find very problematic – so I won’t go into the results here. I’m not quite clear on how those studies mentioned in the discussion ‘have found self-report data [to be] valid under conditions of confidentiality’ – and I remain skeptical. You’ll usually want data from independent observers (e.g. teacher or peer observations) when analyzing these kinds of things. Note in the context of the self-report data problem that if there’s a strong stigma associated with being bullied (there often is, or bullying wouldn’t work as well), asking people if they have been bullied is not much better than asking people if they’re bullying others.

ii. Some topical advice that some people might soon regret not having followed, from the wonderful Things I Learn From My Patients thread:

“If you are a teenage boy experimenting with fireworks, do not empty the gunpowder from a dozen fireworks and try to mix it in your mother’s blender. But if you do decide to do that, don’t hold the lid down with your other hand and stand right over it. This will result in the traumatic amputation of several fingers, burned and skinned forearms, glass shrapnel in your face, and a couple of badly scratched corneas as a start. You will spend months in rehab and never be able to use your left hand again.”

iii. I haven’t talked about the AlphaZero-Stockfish match, but I was of course aware of it and did read a bit about that stuff. Here’s a reddit thread where one of the Stockfish programmers answers questions about the match. A few quotes:

“Which of the two is stronger under ideal conditions is, to me, neither particularly interesting (they are so different that it’s kind of like comparing the maximum speeds of a fish and a bird) nor particularly important (since there is only one of them that you and I can download and run anyway). What is super interesting is that we have two such radically different ways to create a computer chess playing entity with superhuman abilities. […] I don’t think there is anything to learn from AlphaZero that is applicable to Stockfish. They are just too different, you can’t transfer ideas from one to the other.”

“Based on the 100 games played, AlphaZero seems to be about 100 Elo points stronger under the conditions they used. The current development version of Stockfish is something like 40 Elo points stronger than the version used in Google’s experiment. There is a version of Stockfish translated to hand-written x86-64 assembly language that’s about 15 Elo points stronger still. This adds up to roughly half the Elo difference between AlphaZero and Stockfish shown in Google’s experiment.”

“It seems that Stockfish was playing with only 1 GB for transposition tables (the area of memory used to store data about the positions previously encountered in the search), which is way too little when running with 64 threads.” [I seem to recall a comp sci guy observing elsewhere that this was less than what was available to his smartphone version of Stockfish, but I didn’t bookmark that comment].

“The time control was a very artificial fixed 1 minute/move. That’s not how chess is traditionally played. Quite a lot of effort has gone into Stockfish’s time management. It’s pretty good at deciding when to move quickly, and when to spend a lot of time on a critical decision. In a fixed time per move game, it will often happen that the engine discovers that there is a problem with the move it wants to play just before the time is out. In a regular time control, it would then spend extra time analysing all alternative moves and trying to find a better one. When you force it to move after exactly one minute, it will play the move it already know is bad. There is no doubt that this will cause it to lose many games it would otherwise have drawn.”

iv. Thrombolytics for Acute Ischemic Stroke – no benefit found.

“Thrombolysis has been rigorously studied in >60,000 patients for acute thrombotic myocardial infarction, and is proven to reduce mortality. It is theorized that thrombolysis may similarly benefit ischemic stroke patients, though a much smaller number (8120) has been studied in relevant, large scale, high quality trials thus far. […] There are 12 such trials 1-12. Despite the temptation to pool these data the studies are clinically heterogeneous. […] Data from multiple trials must be clinically and statistically homogenous to be validly pooled.14 Large thrombolytic studies demonstrate wide variations in anatomic stroke regions, small- versus large-vessel occlusion, clinical severity, age, vital sign parameters, stroke scale scores, and times of administration. […] Examining each study individually is therefore, in our opinion, both more valid and more instructive. […] Two of twelve studies suggest a benefit […] In comparison, twice as many studies showed harm and these were stopped early. This early stoppage means that the number of subjects in studies demonstrating harm would have included over 2400 subjects based on originally intended enrollments. Pooled analyses are therefore missing these phantom data, which would have further eroded any aggregate benefits. In their absence, any pooled analysis is biased toward benefit. Despite this, there remain five times as many trials showing harm or no benefit (n=10) as those concluding benefit (n=2), and 6675 subjects in trials demonstrating no benefit compared to 1445 subjects in trials concluding benefit.”

“Thrombolytics for ischemic stroke may be harmful or beneficial. The answer remains elusive. We struggled therefore, debating between a ‘yellow’ or ‘red’ light for our recommendation. However, over 60,000 subjects in trials of thrombolytics for coronary thrombosis suggest a consistent beneficial effect across groups and subgroups, with no studies suggesting harm. This consistency was found despite a very small mortality benefit (2.5%), and a very narrow therapeutic window (1% major bleeding). In comparison, the variation in trial results of thrombolytics for stroke and the daunting but consistent adverse effect rate caused by ICH suggested to us that thrombolytics are dangerous unless further study exonerates their use.”

“There is a Cochrane review that pooled estimates of effect. 17 We do not endorse this choice because of clinical heterogeneity. However, we present the NNT’s from the pooled analysis for the reader’s benefit. The Cochrane review suggested a 6% reduction in disability […] with thrombolytics. This would mean that 17 were treated for every 1 avoiding an unfavorable outcome. The review also noted a 1% increase in mortality (1 in 100 patients die because of thrombolytics) and a 5% increase in nonfatal intracranial hemorrhage (1 in 20), for a total of 6% harmed (1 in 17 suffers death or brain hemorrhage).”

v. Suicide attempts in Asperger Syndrome. An interesting finding: “Over 35% of individuals with AS reported that they had attempted suicide in the past.”

Related: Suicidal ideation and suicide plans or attempts in adults with Asperger’s syndrome attending a specialist diagnostic clinic: a clinical cohort study.

“374 adults (256 men and 118 women) were diagnosed with Asperger’s syndrome in the study period. 243 (66%) of 367 respondents self-reported suicidal ideation, 127 (35%) of 365 respondents self-reported plans or attempts at suicide, and 116 (31%) of 368 respondents self-reported depression. Adults with Asperger’s syndrome were significantly more likely to report lifetime experience of suicidal ideation than were individuals from a general UK population sample (odds ratio 9·6 [95% CI 7·6–11·9], p<0·0001), people with one, two, or more medical illnesses (p<0·0001), or people with psychotic illness (p=0·019). […] Lifetime experience of depression (p=0·787), suicidal ideation (p=0·164), and suicide plans or attempts (p=0·06) did not differ significantly between men and women […] Individuals who reported suicide plans or attempts had significantly higher Autism Spectrum Quotient scores than those who did not […] Empathy Quotient scores and ages did not differ between individuals who did or did not report suicide plans or attempts (table 4). Patients with self-reported depression or suicidal ideation did not have significantly higher Autism Spectrum Quotient scores, Empathy Quotient scores, or age than did those without depression or suicidal ideation”.

The fact that people with Asperger’s are more likely to be depressed and contemplate suicide is consistent with previous observations that they’re also more likely to die from suicide – for example a paper I blogged a while back found that in that particular (large Swedish population-based cohort-) study, people with ASD were more than 7 times as likely to die from suicide than were the comparable controls.

Also related: Suicidal tendencies hard to spot in some people with autism.

This link has some great graphs and tables of suicide data from the US.

Also autism-related: Increased perception of loudness in autism. This is one of the ‘important ones’ for me personally – I am much more sound-sensitive than are most people.

vi. Early versus Delayed Invasive Intervention in Acute Coronary Syndromes.

“Earlier trials have shown that a routine invasive strategy improves outcomes in patients with acute coronary syndromes without ST-segment elevation. However, the optimal timing of such intervention remains uncertain. […] We randomly assigned 3031 patients with acute coronary syndromes to undergo either routine early intervention (coronary angiography ≤24 hours after randomization) or delayed intervention (coronary angiography ≥36 hours after randomization). The primary outcome was a composite of death, myocardial infarction, or stroke at 6 months. A prespecified secondary outcome was death, myocardial infarction, or refractory ischemia at 6 months. […] Early intervention did not differ greatly from delayed intervention in preventing the primary outcome, but it did reduce the rate of the composite secondary outcome of death, myocardial infarction, or refractory ischemia and was superior to delayed intervention in high-risk patients.”

vii. Some wikipedia links:

Behrens–Fisher problem.
Sailing ship tactics (I figured I had to read up on this if I were to get anything out of the Aubrey-Maturin books).
Anatomical terms of muscle.
Phatic expression (“a phatic expression […] is communication which serves a social function such as small talk and social pleasantries that don’t seek or offer any information of value.”)
Three-domain system.
Beringian wolf (featured).
Subdural hygroma.
Cayley graph.
Schur polynomial.
Solar neutrino problem.
Hadamard product (matrices).
True polar wander.
Newton’s cradle.

viii. Determinant versus permanent (mathematics – technical).

ix. Some years ago I wrote a few English-language posts about some of the various statistical/demographic properties of immigrants living in Denmark, based on numbers included in a publication by Statistics Denmark. I did it by translating the observations included in that publication, which was only published in Danish. I was briefly considering doing the same thing again when the 2017 data arrived, but I decided not to do it as I recalled that it took a lot of time to write those posts back then, and it didn’t seem to me to be worth the effort – but Danish readers might be interested to have a look at the data, if they haven’t already – here’s a link to the publication Indvandrere i Danmark 2017.

x. A banter blitz session with grandmaster Peter Svidler, who recently became the first Russian ever to win the Russian Chess Championship 8 times. He’s currently shared-second in the World Rapid Championship after 10 rounds and is now in the top 10 on the live rating list in both classical and rapid – seems like he’s had a very decent year.

xi. I recently discovered Dr. Whitecoat’s blog. The patient encounters are often interesting.

December 28, 2017 Posted by | Astronomy, autism, Biology, Cardiology, Chess, Computer science, History, Mathematics, Medicine, Neurology, Physics, Psychiatry, Psychology, Random stuff, Statistics, Studies, Wikipedia, Zoology | Leave a comment

The history of astronomy

It’s been a while since I read this book, and I was for a while strongly considering not blogging it at all. In the end I figured I ought to cover it after all in at least a little bit of detail, though when I made the decision to cover the book here I also decided not to cover it in nearly as much detail as I usually cover the books in this series.

Below some random observations from the book which I found sufficiently interesting to add here.

“The Almagest is a magisterial work that provided geometrical models and related tables by which the movements of the Sun, Moon, and the five lesser planets could be calculated for the indefinite future. […] Its catalogue contains over 1,000 fixed stars arranged in 48 constellations, giving the longitude, latitude, and apparent brightness of each. […] the Almagest would dominate astronomy like a colossus for 14 centuries […] In the universities of the later Middle Ages, students would be taught Aristotle in philosophy and a simplified Ptolemy in astronomy. From Aristotle they would learn the basic truth that the heavens rotate uniformly about the central Earth. From the simplified Ptolemy they would learn of epicycles and eccentrics that violated this basic truth by generating orbits whose centre was not the Earth; and those expert enough to penetrate deeper into the Ptolemaic models would encounter equant theories that violated the (yet more basic) truth that heavenly motion is uniform. […] with the models of the Almagest – whose parameters would be refined over the centuries to come – the astronomer, and the astrologer, could compute the future positions of the planets with economy and reasonable accuracy. There were anomalies – the Moon, for example, would vary its apparent size dramatically in the Ptolemaic model but does not do so in reality, and Venus and Mercury were kept close to the Sun in the sky by a crude ad hoc device – but as a geometrical compendium of how to grind out planetary tables, the Almagest worked, and that was what mattered.”

“The revival of astronomy – and astrology – among the Latins was stimulated around the end of the first millennium when the astrolabe entered the West from Islamic Spain. Astrology in those days had a [‘]rational[‘] basis rooted in the Aristotelian analogy between the microcosm – the individual living body – and the macrocosm, the cosmos as a whole. Medical students were taught how to track the planets, so that they would know when the time was favourable for treating the corresponding organs in their patients.” [Aaargh! – US]

“The invention of printing in the 15th century had many consequences, none more significant than the stimulus it gave to the mathematical sciences. All scribes, being human, made occasional errors in preparing a copy of a manuscript. These errors would often be transmitted to copies of the copy. But if the works were literary and the later copyists attended to the meaning of the text, they might recognize and correct many of the errors introduced by their predecessors. Such control could rarely be exercised by copyists required to reproduce texts with significant numbers of mathematical symbols. As a result, a formidable challenge faced the medieval student of a mathematical or astronomical treatise, for it was available to him only in a manuscript copy that had inevitably become corrupt in transmission. After the introduction of printing, all this changed.”

“Copernicus, like his predecessors, had been content to work with observations handed down from the past, making new ones only when unavoidable and using instruments that left much to be desired. Tycho [Brahe], whose work marks the watershed between observational astronomy ancient and modern, saw accuracy of observation as the foundation of all good theorizing. He dreamed of having an observatory where he could pursue the research and development of precision instrumentation, and where a skilled team of assistants would test the instruments even as they were compiling a treasury of observations. Exploiting his contacts at the highest level, Tycho persuaded King Frederick II of Denmark to grant him the fiefdom of the island of Hven, and there, between 1576 and 1580, he constructed Uraniborg (‘Heavenly Castle’), the first scientific research institution of the modern era. […] Tycho was the first of the modern observers, and in his catalogue of 777 stars the positions of the brightest are accurate to a minute or so of arc; but he himself was probably most proud of his cosmology, which Galileo was not alone in seeing as a retrograde compromise. Tycho appreciated the advantages of heliocentic planetary models, but he was also conscious of the objections […]. In particular, his inability to detect annual parallax even with his superb instrumentation implied that the Copernican excuse, that the stars were too far away for annual parallax to be detected, was now implausible in the extreme. The stars, he calculated, would have to be at least 700 times further away than Saturn for him to have failed for this reason, and such a vast, purposeless empty space between the planets and the stars made no sense. He therefore looked for a cosmology that would have the geometrical advantages of the heliocentric models but would retain the Earth as the body physically at rest at the centre of the cosmos. The solution seems obvious in hindsight: make the Sun (and Moon) orbit the central Earth, and make the five planets into satellites of the Sun.”

“Until the invention of the telescope, each generation of astronomers had looked at much the same sky as their predecessors. If they knew more, it was chiefly because they had more books to read, more records to mine. […] Galileo could say of his predecessors, ‘If they had seen what we see, they would have judged as we judge’; and ever since his time, the astronomers of each generation have had an automatic advantage over their predecessors, because they possess apparatus that allows them access to objects unseen, unknown, and therefore unstudied in the past. […] astronomers [for a long time] found themselves in a situation where, as telescopes improved, the two coordinates of a star’s position on the heavenly sphere were being measured with ever increasing accuracy, whereas little was known of the star’s third coordinate, distance, except that its scale was enormous. Even the assumption that the nearest stars were the brightest was […rightly, US] being called into question, as the number of known proper motions increased and it emerged that not all the fastest-moving stars were bright.”

“We know little of how Newton’s thinking developed between 1679 and the visit from Halley in 1684, except for a confused exchange of letters between Newton and the Astronomer Royal, John Flamsteed […] the visit from the suitably deferential and tactful Halley encouraged Newton to promise him written proof that elliptical orbits would result from an inverse-square force of attraction residing in the Sun. The drafts grew and grew, and eventually resulted in The Mathematical Principles of Natural Philosophy (1687), better known in its abbreviated Latin title of the Principia. […] All three of Kepler’s laws (the second in ‘area’ form), which had been derived by their author from observations, with the help of a highly dubious dynamics, were now shown to be consequences of rectilinear motion under an inverse-square force. […] As the drafts of Principia multiplied, so too did the number of phenomena that at last found their explanation. The tides resulted from the difference between the effects on the land and on the seas of the attraction of Sun and Moon. The spinning Earth bulged at the equator and was flattened at the poles, and so was not strictly spherical; as a result, the attraction of Sun and Moon caused the Earth’s axis to wobble and so generated the precession of the equinoxes first noticed by Hipparchus. […] Newton was able to use the observed motions of the moons of Earth, Jupiter, and Saturn to calculate the masses of the parent planets, and he found that Jupiter and Saturn were huge compared to Earth – and, in all probability, to Mercury, Venus, and Mars.”

December 5, 2017 Posted by | Astronomy, Books, History, Mathematics, Physics | Leave a comment


i. “The party that negotiates in haste is often at a disadvantage.” (Howard Raiffa)

ii. “Advice: don’t embarrass your bargaining partner by forcing him or her to make all the concessions.” (-ll-)

iii. “Disputants often fare poorly when they each act greedily and deceptively.” (-ll-)

iv. “Each man does seek his own interest, but, unfortunately, not according to the dictates of reason.” (Kenneth Waltz)

v. “Whatever is said after I’m gone is irrelevant.” (Jimmy Savile)

vi. “Trust is an important lubricant of a social system. It is extremely efficient; it saves a lot of trouble to have a fair degree of reliance on other people’s word. Unfortunately this is not a commodity which can be bought very easily. If you have to buy it, you already have some doubts about what you have bought.” (Kenneth Arrow)

vii. “… an author never does more damage to his readers than when he hides a difficulty.” (Évariste Galois)

viii. “A technical argument by a trusted author, which is hard to check and looks similar to arguments known to be correct, is hardly ever checked in detail” (Vladimir Voevodsky)

ix. “Suppose you want to teach the “cat” concept to a very young child. Do you explain that a cat is a relatively small, primarily carnivorous mammal with retractible claws, a distinctive sonic output, etc.? I’ll bet not. You probably show the kid a lot of different cats, saying “kitty” each time, until it gets the idea. To put it more generally, generalizations are best made by abstraction from experience. They should come one at a time; too many at once overload the circuits.” (Ralph P. Boas Jr.)

x. “Every author has several motivations for writing, and authors of technical books always have, as one motivation, the personal need to understand; that is, they write because they want to learn, or to understand a phenomenon, or to think through a set of ideas.” (Albert Wymore)

xi. “Great mathematics is achieved by solving difficult problems not by fabricating elaborate theories in search of a problem.” (Harold Davenport)

xii. “Is science really gaining in its assault on the totality of the unsolved? As science learns one answer, it is characteristically true that it also learns several new questions. It is as though science were working in a great forest of ignorance, making an ever larger circular clearing within which, not to insist on the pun, things are clear… But as that circle becomes larger and larger, the circumference of contact with ignorance also gets longer and longer. Science learns more and more. But there is an ultimate sense in which it does not gain; for the volume of the appreciated but not understood keeps getting larger. We keep, in science, getting a more and more sophisticated view of our essential ignorance.” (Warren Weaver)

xiii. “When things get too complicated, it sometimes makes sense to stop and wonder: Have I asked the right question?” (Enrico Bombieri)

xiv. “The mean and variance are unambiguously determined by the distribution, but a distribution is, of course, not determined by its mean and variance: A number of different distributions have the same mean and the same variance.” (Richard von Mises)

xv. “Algorithms existed for at least five thousand years, but people did not know that they were algorithmizing. Then came Turing (and Post and Church and Markov and others) and formalized the notion.” (Doron Zeilberger)

xvi. “When a problem seems intractable, it is often a good idea to try to study “toy” versions of it in the hope that as the toys become increasingly larger and more sophisticated, they would metamorphose, in the limit, to the real thing.” (-ll-)

xvii. “The kind of mathematics foisted on children in schools is not meaningful, fun, or even very useful. This does not mean that an individual child cannot turn it into a valuable and enjoyable personal game. For some the game is scoring grades; for others it is outwitting the teacher and the system. For many, school math is enjoyable in its repetitiveness, precisely because it is so mindless and dissociated that it provides a shelter from having to think about what is going on in the classroom. But all this proves is the ingenuity of children. It is not a justifications for school math to say that despite its intrinsic dullness, inventive children can find excitement and meaning in it.” (Seymour Papert)

xviii. “The optimist believes that this is the best of all possible worlds, and the pessimist fears that this might be the case.” (Ivar Ekeland)

xix. “An equilibrium is not always an optimum; it might not even be good. This may be the most important discovery of game theory.” (-ll-)

xxi. “It’s not all that rare for people to suffer from a self-hating monologue. Any good theories about what’s going on there?”

“If there’s things you don’t like about your life, you can blame yourself, or you can blame others. If you blame others and you’re of low status, you’ll be told to cut that out and start blaming yourself. If you blame yourself and you can’t solve the problems, self-hate is the result.” (Nancy Lebovitz & ‘The Nybbler’)

December 1, 2017 Posted by | Mathematics, Quotes/aphorisms, Science, Statistics | 4 Comments

The mystery of over-parametrization in neural networks

October 6, 2017 Posted by | Computer science, Mathematics | Leave a comment

Interactive Coding with “Optimal” Round and Communication Blowup

The youtube description of this one was rather longer than usual, and I decided to quote it in full below:

“The problem of constructing error-resilient interactive protocols was introduced in the seminal works of Schulman (FOCS 1992, STOC 1993). These works show how to convert any two-party interactive protocol into one that is resilient to constant-fraction of error, while blowing up the communication by only a constant factor. Since these seminal works, there have been many follow-up works which improve the error rate, the communication rate, and the computational efficiency. All these works assume that in the underlying protocol, in each round, each party sends a *single* bit. This assumption is without loss of generality, since one can efficiently convert any protocol into one which sends one bit per round. However, this conversion may cause a substantial increase in *round* complexity, which is what we wish to minimize in this work. Moreover, all previous works assume that the communication complexity of the underlying protocol is *fixed* and a priori known, an assumption that we wish to remove. In this work, we consider protocols whose messages may be of *arbitrary* lengths, and where the length of each message and the length of the protocol may be *adaptive*, and may depend on the private inputs of the parties and on previous communication. We show how to efficiently convert any such protocol into another protocol with comparable efficiency guarantees, that is resilient to constant fraction of adversarial error, while blowing up both the *communication* complexity and the *round* complexity by at most a constant factor. Moreover, as opposed to most previous work, our error model not only allows the adversary to toggle with the corrupted bits, but also allows the adversary to *insert* and *delete* bits. In addition, our transformation preserves the computational efficiency of the protocol. Finally, we try to minimize the blowup parameters, and give evidence that our parameters are nearly optimal. This is joint work with Klim Efremenko and Elad Haramaty.”

A few links to stuff covered/mentioned in the lecture:

Coding for interactive communication correcting insertions and deletions.
Efficiently decodable insertion/deletion codes for high-noise and high-rate regimes.
Common reference string model.
Small-bias probability spaces: Efficient constructions and applications.
Interactive Channel Capacity Revisited.
Collision (computer science).
Chernoff bound.

September 6, 2017 Posted by | Computer science, Cryptography, Lectures, Mathematics | Leave a comment

Quantifying tumor evolution through spatial computational modeling

Two general remarks: 1. She talks very fast, in my opinion unpleasantly fast – the lecture would have been at least slightly easier to follow if she’d slowed down a little. 2. A few of the lectures uploaded in this lecture series (from the IAS Mathematical Methods in Cancer Evolution and Heterogeneity Workshop) seem to have some sound issues; in this lecture there are multiple 1-2 seconds long ‘chunks’ where the sound drops out and some words are lost. This is really annoying, and a similar problem (which was likely ‘the same problem’) previously lead me to quit another lecture in the series; however in this case I decided to give it a shot anyway, and I actually think it’s not a big deal; the sound-losses are very short in duration, and usually no more than one or two words are lost so you can usually figure out what was said. During this lecture there was incidentally also some issues with the monitor roughly 27 minutes in, but this isn’t a big deal as no information was lost and unlike the people who originally attended the lecture you can just skip ahead approximately one minute (that was how long it took to solve that problem).

A few relevant links to stuff she talks about in the lecture:

A Big Bang model of human colorectal tumor growth.
Approximate Bayesian computation.
Site frequency spectrum.
Identification of neutral tumor evolution across cancer types.
Using tumour phylogenetics to identify the roots of metastasis in humans.

August 22, 2017 Posted by | Cancer/oncology, Evolutionary biology, Genetics, Lectures, Mathematics, Medicine, Statistics | Leave a comment

How Species Interact

There are multiple reasons why I have not covered Arditi and Ginzburg’s book before, but none of them are related to the quality of the book’s coverage. It’s a really nice book. However the coverage is somewhat technical and model-focused, which makes it harder to blog than other kinds of books. Also, the version of the book I read was a hardcover ‘paper book’ version, and ‘paper books’ take a lot more work for me to cover than do e-books.

I should probably get it out of the way here at the start of the post that if you’re interested in ecology, predator-prey dynamics, etc., this book is a book you would be well advised to read; or, if you don’t read the book, you should at least familiarize yourself with the ideas therein e.g. through having a look at some of Arditi & Ginzburg’s articles on these topics. I should however note that I don’t actually think skipping the book and having a look at some articles instead will necessarily be a labour-saving strategy; the book is not particularly long and it’s to the point, so although it’s not a particularly easy read their case for ratio dependence is actually somewhat easy to follow – if you take the effort – in the sense that I believe how different related ideas and observations are linked is quite likely better expounded upon in the book than they might have been in their articles. The presumably wrote the book precisely in order to provide a concise yet coherent overview.

I have had some trouble figuring out how to cover this book, and I’m still not quite sure what might be/have been the best approach; when covering technical books I’ll often skip a lot of detail and math and try to stick to what might be termed ‘the main ideas’ when quoting from such books, but there’s a clear limit as to how many of the technical details included in a book like this it is possible to skip if you still want to actually talk about the stuff covered in the work, and this sometimes make blogging such books awkward. These authors spend a lot of effort talking about how different ecological models work and which sort of conclusions these different models may lead to in different contexts, and this kind of stuff is a very big part of the book. I’m not sure if you strictly need to have read an ecology textbook or two before you read this one in order to be able to follow the coverage, but I know that I personally derived some benefit from having read Gurney & Nisbet’s ecology text in the past and I did look up stuff in that book a few times along the way, e.g. when reminding myself what a Holling type 2 functional response is and how models with such a functional response pattern behave. ‘In theory’ I assume one might argue that you could theoretically look up all the relevant concepts along the way without any background knowledge of ecology – assuming you have a decent understanding of basic calculus/differential equations, linear algebra, equilibrium dynamics, etc. (…systems analysis? It’s hard for me to know and outline exactly which sources I’ve read in the past which helped make this book easier to read than it otherwise would have been, but suffice it to say that if you look at the page count and think that this will be an quick/easy read, it will be that only if you’ve read more than a few books on ‘related topics’, broadly defined, in the past), but I wouldn’t advise reading the book if all you know is high school math – the book will be incomprehensible to you, and you won’t make it. I ended up concluding that it would simply be too much work to try to make this post ‘easy’ to read for people who are unfamiliar with these topics and have not read the book, so although I’ve hardly gone out of my way to make the coverage hard to follow, the blog coverage that is to follow is mainly for my own benefit.

First a few relevant links, then some quotes and comments.

Lotka–Volterra equations.
Ecosystem model.
Arditi–Ginzburg equations. (Yep, these equations are named after the authors of this book).
Nicholson–Bailey model.
Functional response.
Monod equation.
Rosenzweig-MacArthur predator-prey model.
Trophic cascade.
Underestimation of mutual interference of predators.
Coupling in predator-prey dynamics: Ratio Dependence.
Michaelis–Menten kinetics.
Trophic level.
Advection–diffusion equation.
Paradox of enrichment. [Two quotes from the book: “actual systems do not behave as Rosensweig’s model predict” + “When ecologists have looked for evidence of the paradox of enrichment in natural and laboratory systems, they often find none and typically present arguments about why it was not observed”]
Predator interference emerging from trophotaxis in predator–prey systems: An individual-based approach.
Directed movement of predators and the emergence of density dependence in predator-prey models.

“Ratio-dependent predation is now covered in major textbooks as an alternative to the standard prey-dependent view […]. One of this book’s messages is that the two simple extreme theories, prey dependence and ratio dependence, are not the only alternatives: they are the ends of a spectrum. There are ecological domains in which one view works better than the other, with an intermediate view also being a possible case. […] Our years of work spent on the subject have led us to the conclusion that, although prey dependence might conceivably be obtained in laboratory settings, the common case occurring in nature lies close to the ratio-dependent end. We believe that the latter, instead of the prey-dependent end, can be viewed as the “null model of predation.” […] we propose the gradual interference model, a specific form of predator-dependent functional response that is approximately prey dependent (as in the standard theory) at low consumer abundances and approximately ratio dependent at high abundances. […] When density is low, consumers do not interfere and prey dependence works (as in the standard theory). When consumers density is sufficiently high, interference causes ratio dependence to emerge. In the intermediate densities, predator-dependent models describe partial interference.”

“Studies of food chains are on the edge of two domains of ecology: population and community ecology. The properties of food chains are determined by the nature of their basic link, the interaction of two species, a consumer and its resource, a predator and its prey.1 The study of this basic link of the chain is part of population ecology while the more complex food webs belong to community ecology. This is one of the main reasons why understanding the dynamics of predation is important for many ecologists working at different scales.”

“We have named predator-dependent the functional responses of the form g = g(N,P), where the predator density P acts (in addition to N [prey abundance, US]) as an independent variable to determine the per capita kill rate […] predator-dependent functional response models have one more parameter than the prey-dependent or the ratio-dependent models. […] The main interest that we see in these intermediate models is that the additional parameter can provide a way to quantify the position of a specific predator-prey pair of species along a spectrum with prey dependence at one end and ratio dependence at the other end:

g(N) <- g(N,P) -> g(N/P) (1.21)

In the Hassell-Varley and Arditi-Akçakaya models […] the mutual interference parameter m plays the role of a cursor along this spectrum, from m = 0 for prey dependence to m = 1 for ratio dependence. Note that this theory does not exclude that strong interference goes “beyond ratio dependence,” with m > 1.2 This is also called overcompensation. […] In this book, rather than being interested in the interference parameters per se, we use predator-dependent models to determine, either parametrically or nonparametrically, which of the ends of the spectrum (1.21) better describes predator-prey systems in general.”

“[T]he fundamental problem of the Lotka-Volterra and the Rosensweig-MacArthur dynamic models lies in the functional response and in the fact that this mathematical function is assumed not to depend on consumer density. Since this function measures the number of prey captured per consumer per unit time, it is a quantity that should be accessible to observation. This variable could be apprehended either on the fast behavioral time scale or on the slow demographic time scale. These two approaches need not necessarily reveal the same properties: […] a given species could display a prey-dependent response on the fast scale and a predator-dependent response on the slow scale. The reason is that, on a very short scale, each predator individually may “feel” virtually alone in the environment and react only to the prey that it encounters. On the long scale, the predators are more likely to be affected by the presence of conspecifics, even without direct encounters. In the demographic context of this book, it is the long time scale that is relevant. […] if predator dependence is detected on the fast scale, then it can be inferred that it must be present on the slow scale; if predator dependence is not detected on the fast scale, it cannot be inferred that it is absent on the slow scale.”

Some related thoughts. A different way to think about this – which they don’t mention in the book, but which sprang to mind to me as I was reading it – is to think about this stuff in terms of a formal predator territorial overlap model and then asking yourself this question: Assume there’s zero territorial overlap – does this fact mean that the existence of conspecifics does not matter? The answer is of course no. The sizes of the individual patches/territories may be greatly influenced by the predator density even in such a context. Also, the territorial area available to potential offspring (certainly a fitness-relevant parameter) may be greatly influenced by the number of competitors inhabiting the surrounding territories. In relation to the last part of the quote it’s easy to see that in a model with significant territorial overlap you don’t need direct behavioural interaction among predators for the overlap to be relevant; even if two bears never meet, if one of them eats a fawn the other one would have come across two days later, well, such indirect influences may be important for prey availability. Of course as prey tend to be mobile, even if predator territories are static and non-overlapping in a geographic sense, they might not be in a functional sense. Moving on…

“In [chapter 2 we] attempted to assess the presence and the intensity of interference in all functional response data sets that we could gather in the literature. Each set must be trivariate, with estimates of the prey consumed at different values of prey density and different values of predator densities. Such data sets are not very abundant because most functional response experiments present in the literature are simply bivariate, with variations of the prey density only, often with a single predator individual, ignoring the fact that predator density can have an influence. This results from the usual presentation of functional responses in textbooks, which […] focus only on the influence of prey density.
Among the data sets that we analyzed, we did not find a single one in which the predator density did not have a significant effect. This is a powerful empirical argument against prey dependence. Most systems lie somewhere on the continuum between prey dependence (m=0) and ratio dependence (m=1). However, they do not appear to be equally distributed. The empirical evidence provided in this chapter suggests that they tend to accumulate closer to the ratio-dependent end than to the prey-dependent end.”

“Equilibrium properties result from the balanced predator-prey equations and contain elements of the underlying dynamic model. For this reason, the response of equilibria to a change in model parameters can inform us about the structure of the underlying equations. To check the appropriateness of the ratio-dependent versus prey-dependent views, we consider the theoretical equilibrium consequences of the two contrasting assumptions and compare them with the evidence from nature. […] According to the standard prey-dependent theory, in reference to [an] increase in primary production, the responses of the populations strongly depend on their level and on the total number of trophic levels. The last, top level always responds proportionally to F [primary input]. The next to the last level always remains constant: it is insensitive to enrichment at the bottom because it is perfectly controled [sic] by the last level. The first, primary producer level increases if the chain length has an odd number of levels, but declines (or stays constant with a Lotka-Volterra model) in the case of an even number of levels. According to the ratio-dependent theory, all levels increase proportionally, independently of how many levels are present. The present purpose of this chapter is to show that the second alternative is confirmed by natural data and that the strange predictions of the prey-dependent theory are unsupported.”

“If top predators are eliminated or reduced in abundance, models predict that the sequential lower trophic levels must respond by changes of alternating signs. For example, in a three-level system of plants-herbivores-predators, the reduction of predators leads to the increase of herbivores and the consequential reduction in plant abundance. This response is commonly called the trophic cascade. In a four-level system, the bottom level will increase in response to harvesting at the top. These predicted responses are quite intuitive and are, in fact, true for both short-term and long-term responses, irrespective of the theory one employs. […] A number of excellent reviews have summarized and meta-analyzed large amounts of data on trophic cascades in food chains […] In general, the cascading reaction is strongest in lakes, followed by marine systems, and weakest in terrestrial systems. […] Any theory that claims to describe the trophic chain equilibria has to produce such cascading when top predators are reduced or eliminated. It is well known that the standard prey-dependent theory supports this view of top-down cascading. It is not widely appreciated that top-down cascading is likewise a property of ratio-dependent trophic chains. […] It is [only] for equilibrial responses to enrichment at the bottom that predictions are strikingly different according to the two theories”.

As the book does spend a little time on this I should perhaps briefly interject here that the above paragraph should not be taken to indicate that the two types of models provide identical predictions in the top-down cascading context in all cases; both predict cascading, but there are even so some subtle differences between the models here as well. Some of these differences are however quite hard to test.

“[T]he traditional Lotka-Volterra interaction term […] is nothing other than the law of mass action of chemistry. It assumes that predator and prey individuals encounter each other randomly in the same way that molecules interact in a chemical solution. Other prey-dependent models, like Holling’s, derive from the same idea. […] an ecological system can only be described by such a model if conspecifics do not interfere with each other and if the system is sufficiently homogeneous […] we will demonstrate that spatial heterogeneity, be it in the form of a prey refuge or in the form of predator clusters, leads to emergence of gradual interference or of ratio dependence when the functional response is observed at the population level. […] We present two mechanistic individual-based models that illustrate how, with gradually increasing predator density and gradually increasing predator clustering, interference can become gradually stronger. Thus, a given biological system, prey dependent at low predator density, can gradually become ratio dependent at high predator density. […] ratio dependence is a simple way of summarizing the effects induced by spatial heterogeneity, while the prey dependent [models] (e.g., Lotka-Volterra) is more appropriate in homogeneous environments.”

“[W]e consider that a good model of interacting species must be fundamentally invariant to a proportional change of all abundances in the system. […] Allowing interacting populations to expand in balanced exponential growth makes the laws of ecology invariant with respect to multiplying interacting abundances by the same constant, so that only ratios matter. […] scaling invariance is required if we wish to preserve the possibility of joint exponential growth of an interacting pair. […] a ratio-dependent model allows for joint exponential growth. […] Neither the standard prey-dependent models nor the more general predator-dependent models allow for balanced growth. […] In our view, communities must be expected to expand exponentially in the presence of unlimited resources. Of course, limiting factors ultimately stop this expansion just as they do for a single species. With our view, it is the limiting resources that stop the joint expansion of the interacting populations; it is not directly due to the interactions themselves. This partitioning of the causes is a major simplification that traditional theory implies only in the case of a single species.”

August 1, 2017 Posted by | Biology, Books, Chemistry, Ecology, Mathematics, Studies | Leave a comment

Melanoma therapeutic strategies that select against resistance

A short lecture, but interesting:

If you’re not an oncologist, these two links in particular might be helpful to have a look at before you start out: BRAF (gene) & Myc. A very substantial proportion of the talk is devoted to math and stats methodology (which some people will find interesting and others …will not).

July 3, 2017 Posted by | Biology, Cancer/oncology, Genetics, Lectures, Mathematics, Medicine, Statistics | Leave a comment

Harnessing phenotypic heterogeneity to design better therapies

Unlike many of the IAS lectures I’ve recently blogged this one is a new lecture – it was uploaded earlier this week. I have to say that I was very surprised – and disappointed – that the treatment strategy discussed in the lecture had not already been analyzed in a lot of detail and been implemented in clinical practice for some time. Why would you not expect the composition of cancer cell subtypes in the tumour microenvironment to change when you start treatment – in any setting where a subgroup of cancer cells has a different level of responsiveness to treatment than ‘the average’, that would to me seem to be the expected outcome. And concepts such as drug holidays and dose adjustments as treatment responses to evolving drug resistance/treatment failure seem like such obvious approaches to try out here (…the immunologists dealing with HIV infection have been studying such things for decades). I guess ‘better late than never’.

A few papers mentioned/discussed in the lecture:

Impact of Metabolic Heterogeneity on Tumor Growth, Invasion, and Treatment Outcomes.
Adaptive vs continuous cancer therapy: Exploiting space and trade-offs in drug scheduling.
Exploiting evolutionary principles to prolong tumor control in preclinical models of breast cancer.

June 11, 2017 Posted by | Cancer/oncology, Genetics, Immunology, Lectures, Mathematics, Medicine, Studies | Leave a comment

The Mathematical Challenge of Large Networks

This is another one of the aforementioned lectures I watched a while ago, but had never got around to blogging:

If I had to watch this one again, I’d probably skip most of the second half; it contains highly technical coverage of topics in graph theory, and it was very difficult for me to follow (but I did watch it to the end, just out of curiosity).

The lecturer has put up a ~500 page publication on these and related topics, which is available here, so if you want to know more that’s an obvious place to go have a look. A few other relevant links to stuff mentioned/covered in the lecture:
Szemerédi regularity lemma.
Turán’s theorem.
Quantum graph.

May 19, 2017 Posted by | Computer science, Lectures, Mathematics, Statistics | Leave a comment

Quantifying tradeoffs between fairness and accuracy in online learning

From a brief skim of this paper, which is coauthored by the guy giving this lecture, it looked to me like it covers many of the topics discussed in the lecture. So if you’re unsure as to whether or not to watch the lecture (…or if you want to know more about this stuff after you’ve watched the lecture) you might want to have a look at that paper. Although the video is long for a single lecture I would note that the lecture itself lasts only approximately one hour; the last 10 minutes are devoted to Q&A.

May 12, 2017 Posted by | Computer science, Economics, Lectures, Mathematics | Leave a comment

Biodemography of aging (IV)

My working assumption as I was reading part two of the book was that I would not be covering that part of the book in much detail here because it would simply be too much work to make such posts legible to the readership of this blog. However I then later, while writing this post, had the thought that given that almost nobody reads along here anyway (I’m not complaining, mind you – this is how I like it these days), the main beneficiary of my blog posts will always be myself, which lead to the related observation/notion that I should not be limiting my coverage of interesting stuff here simply because some hypothetical and probably nonexistent readership out there might not be able to follow the coverage. So when I started out writing this post I was working under the assumption that it would be my last post about the book, but I now feel sure that if I find the time I’ll add at least one more post about the book’s statistics coverage. On a related note I am explicitly making the observation here that this post was written for my benefit, not yours. You can read it if you like, or not, but it was not really written for you.

I have added bold a few places to emphasize key concepts and observations from the quoted paragraphs and in order to make the post easier for me to navigate later (all the italics below are on the other hand those of the authors of the book).

Biodemography is a multidisciplinary branch of science that unites under its umbrella various analytic approaches aimed at integrating biological knowledge and methods and traditional demographic analyses to shed more light on variability in mortality and health across populations and between individuals. Biodemography of aging is a special subfield of biodemography that focuses on understanding the impact of processes related to aging on health and longevity.”

“Mortality rates as a function of age are a cornerstone of many demographic analyses. The longitudinal age trajectories of biomarkers add a new dimension to the traditional demographic analyses: the mortality rate becomes a function of not only age but also of these biomarkers (with additional dependence on a set of sociodemographic variables). Such analyses should incorporate dynamic characteristics of trajectories of biomarkers to evaluate their impact on mortality or other outcomes of interest. Traditional analyses using baseline values of biomarkers (e.g., Cox proportional hazards or logistic regression models) do not take into account these dynamics. One approach to the evaluation of the impact of biomarkers on mortality rates is to use the Cox proportional hazards model with time-dependent covariates; this approach is used extensively in various applications and is available in all popular statistical packages. In such a model, the biomarker is considered a time-dependent covariate of the hazard rate and the corresponding regression parameter is estimated along with standard errors to make statistical inference on the direction and the significance of the effect of the biomarker on the outcome of interest (e.g., mortality). However, the choice of the analytic approach should not be governed exclusively by its simplicity or convenience of application. It is essential to consider whether the method gives meaningful and interpretable results relevant to the research agenda. In the particular case of biodemographic analyses, the Cox proportional hazards model with time-dependent covariates is not the best choice.

“Longitudinal studies of aging present special methodological challenges due to inherent characteristics of the data that need to be addressed in order to avoid biased inference. The challenges are related to the fact that the populations under study (aging individuals) experience substantial dropout rates related to death or poor health and often have co-morbid conditions related to the disease of interest. The standard assumption made in longitudinal analyses (although usually not explicitly mentioned in publications) is that dropout (e.g., death) is not associated with the outcome of interest. While this can be safely assumed in many general longitudinal studies (where, e.g., the main causes of dropout might be the administrative end of the study or moving out of the study area, which are presumably not related to the studied outcomes), the very nature of the longitudinal outcomes (e.g., measurements of some physiological biomarkers) analyzed in a longitudinal study of aging assumes that they are (at least hypothetically) related to the process of aging. Because the process of aging leads to the development of diseases and, eventually, death, in longitudinal studies of aging an assumption of non-association of the reason for dropout and the outcome of interest is, at best, risky, and usually is wrong. As an illustration, we found that the average trajectories of different physiological indices of individuals dying at earlier ages markedly deviate from those of long-lived individuals, both in the entire Framingham original cohort […] and also among carriers of specific alleles […] In such a situation, panel compositional changes due to attrition affect the averaging procedure and modify the averages in the total sample. Furthermore, biomarkers are subject to measurement error and random biological variability. They are usually collected intermittently at examination times which may be sparse and typically biomarkers are not observed at event times. It is well known in the statistical literature that ignoring measurement errors and biological variation in such variables and using their observed “raw” values as time-dependent covariates in a Cox regression model may lead to biased estimates and incorrect inferences […] Standard methods of survival analysis such as the Cox proportional hazards model (Cox 1972) with time-dependent covariates should be avoided in analyses of biomarkers measured with errors because they can lead to biased estimates.

“Statistical methods aimed at analyses of time-to-event data jointly with longitudinal measurements have become known in the mainstream biostatistical literature as “joint models for longitudinal and time-to-event data” (“survival” or “failure time” are often used interchangeably with “time-to-event”) or simply “joint models.” This is an active and fruitful area of biostatistics with an explosive growth in recent years. […] The standard joint model consists of two parts, the first representing the dynamics of longitudinal data (which is referred to as the “longitudinal sub-model”) and the second one modeling survival or, generally, time-to-event data (which is referred to as the “survival sub-model”). […] Numerous extensions of this basic model have appeared in the joint modeling literature in recent decades, providing great flexibility in applications to a wide range of practical problems. […] The standard parameterization of the joint model (11.2) assumes that the risk of the event at age t depends on the current “true” value of the longitudinal biomarker at this age. While this is a reasonable assumption in general, it may be argued that additional dynamic characteristics of the longitudinal trajectory can also play a role in the risk of death or onset of a disease. For example, if two individuals at the same age have exactly the same level of some biomarker at this age, but the trajectory for the first individual increases faster with age than that of the second one, then the first individual can have worse survival chances for subsequent years. […] Therefore, extensions of the basic parameterization of joint models allowing for dependence of the risk of an event on such dynamic characteristics of the longitudinal trajectory can provide additional opportunities for comprehensive analyses of relationships between the risks and longitudinal trajectories. Several authors have considered such extended models. […] joint models are computationally intensive and are sometimes prone to convergence problems [however such] models provide more efficient estimates of the effect of a covariate […] on the time-to-event outcome in the case in which there is […] an effect of the covariate on the longitudinal trajectory of a biomarker. This means that analyses of longitudinal and time-to-event data in joint models may require smaller sample sizes to achieve comparable statistical power with analyses based on time-to-event data alone (Chen et al. 2011).”

“To be useful as a tool for biodemographers and gerontologists who seek biological explanations for observed processes, models of longitudinal data should be based on realistic assumptions and reflect relevant knowledge accumulated in the field. An example is the shape of the risk functions. Epidemiological studies show that the conditional hazards of health and survival events considered as functions of risk factors often have U- or J-shapes […], so a model of aging-related changes should incorporate this information. In addition, risk variables, and, what is very important, their effects on the risks of corresponding health and survival events, experience aging-related changes and these can differ among individuals. […] An important class of models for joint analyses of longitudinal and time-to-event data incorporating a stochastic process for description of longitudinal measurements uses an epidemiologically-justified assumption of a quadratic hazard (i.e., U-shaped in general and J-shaped for variables that can take values only on one side of the U-curve) considered as a function of physiological variables. Quadratic hazard models have been developed and intensively applied in studies of human longitudinal data”.

“Various approaches to statistical model building and data analysis that incorporate unobserved heterogeneity are ubiquitous in different scientific disciplines. Unobserved heterogeneity in models of health and survival outcomes can arise because there may be relevant risk factors affecting an outcome of interest that are either unknown or not measured in the data. Frailty models introduce the concept of unobserved heterogeneity in survival analysis for time-to-event data. […] Individual age trajectories of biomarkers can differ due to various observed as well as unobserved (and unknown) factors and such individual differences propagate to differences in risks of related time-to-event outcomes such as the onset of a disease or death. […] The joint analysis of longitudinal and time-to-event data is the realm of a special area of biostatistics named “joint models for longitudinal and time-to-event data” or simply “joint models” […] Approaches that incorporate heterogeneity in populations through random variables with continuous distributions (as in the standard joint models and their extensions […]) assume that the risks of events and longitudinal trajectories follow similar patterns for all individuals in a population (e.g., that biomarkers change linearly with age for all individuals). Although such homogeneity in patterns can be justifiable for some applications, generally this is a rather strict assumption […] A population under study may consist of subpopulations with distinct patterns of longitudinal trajectories of biomarkers that can also have different effects on the time-to-event outcome in each subpopulation. When such subpopulations can be defined on the base of observed covariate(s), one can perform stratified analyses applying different models for each subpopulation. However, observed covariates may not capture the entire heterogeneity in the population in which case it may be useful to conceive of the population as consisting of latent subpopulations defined by unobserved characteristics. Special methodological approaches are necessary to accommodate such hidden heterogeneity. Within the joint modeling framework, a special class of models, joint latent class models, was developed to account for such heterogeneity […] The joint latent class model has three components. First, it is assumed that a population consists of a fixed number of (latent) subpopulations. The latent class indicator represents the latent class membership and the probability of belonging to the latent class is specified by a multinomial logistic regression function of observed covariates. It is assumed that individuals from different latent classes have different patterns of longitudinal trajectories of biomarkers and different risks of event. The key assumption of the model is conditional independence of the biomarker and the time-to-events given the latent classes. Then the class-specific models for the longitudinal and time-to-event outcomes constitute the second and third component of the model thus completing its specification. […] the latent class stochastic process model […] provides a useful tool for dealing with unobserved heterogeneity in joint analyses of longitudinal and time-to-event outcomes and taking into account hidden components of aging in their joint influence on health and longevity. This approach is also helpful for sensitivity analyses in applications of the original stochastic process model. We recommend starting the analyses with the original stochastic process model and estimating the model ignoring possible hidden heterogeneity in the population. Then the latent class stochastic process model can be applied to test hypotheses about the presence of hidden heterogeneity in the data in order to appropriately adjust the conclusions if a latent structure is revealed.”

The longitudinal genetic-demographic model (or the genetic-demographic model for longitudinal data) […] combines three sources of information in the likelihood function: (1) follow-up data on survival (or, generally, on some time-to-event) for genotyped individuals; (2) (cross-sectional) information on ages at biospecimen collection for genotyped individuals; and (3) follow-up data on survival for non-genotyped individuals. […] Such joint analyses of genotyped and non-genotyped individuals can result in substantial improvements in statistical power and accuracy of estimates compared to analyses of the genotyped subsample alone if the proportion of non-genotyped participants is large. Situations in which genetic information cannot be collected for all participants of longitudinal studies are not uncommon. They can arise for several reasons: (1) the longitudinal study may have started some time before genotyping was added to the study design so that some initially participating individuals dropped out of the study (i.e., died or were lost to follow-up) by the time of genetic data collection; (2) budget constraints prohibit obtaining genetic information for the entire sample; (3) some participants refuse to provide samples for genetic analyses. Nevertheless, even when genotyped individuals constitute a majority of the sample or the entire sample, application of such an approach is still beneficial […] The genetic stochastic process model […] adds a new dimension to genetic biodemographic analyses, combining information on longitudinal measurements of biomarkers available for participants of a longitudinal study with follow-up data and genetic information. Such joint analyses of different sources of information collected in both genotyped and non-genotyped individuals allow for more efficient use of the research potential of longitudinal data which otherwise remains underused when only genotyped individuals or only subsets of available information (e.g., only follow-up data on genotyped individuals) are involved in analyses. Similar to the longitudinal genetic-demographic model […], the benefits of combining data on genotyped and non-genotyped individuals in the genetic SPM come from the presence of common parameters describing characteristics of the model for genotyped and non-genotyped subsamples of the data. This takes into account the knowledge that the non-genotyped subsample is a mixture of carriers and non-carriers of the same alleles or genotypes represented in the genotyped subsample and applies the ideas of heterogeneity analyses […] When the non-genotyped subsample is substantially larger than the genotyped subsample, these joint analyses can lead to a noticeable increase in the power of statistical estimates of genetic parameters compared to estimates based only on information from the genotyped subsample. This approach is applicable not only to genetic data but to any discrete time-independent variable that is observed only for a subsample of individuals in a longitudinal study.

“Despite an existing tradition of interpreting differences in the shapes or parameters of the mortality rates (survival functions) resulting from the effects of exposure to different conditions or other interventions in terms of characteristics of individual aging, this practice has to be used with care. This is because such characteristics are difficult to interpret in terms of properties of external and internal processes affecting the chances of death. An important question then is: What kind of mortality model has to be developed to obtain parameters that are biologically interpretable? The purpose of this chapter is to describe an approach to mortality modeling that represents mortality rates in terms of parameters of physiological changes and declining health status accompanying the process of aging in humans. […] A traditional (demographic) description of changes in individual health/survival status is performed using a continuous-time random Markov process with a finite number of states, and age-dependent transition intensity functions (transitions rates). Transitions to the absorbing state are associated with death, and the corresponding transition intensity is a mortality rate. Although such a description characterizes connections between health and mortality, it does not allow for studying factors and mechanisms involved in the aging-related health decline. Numerous epidemiological studies provide compelling evidence that health transition rates are influenced by a number of factors. Some of them are fixed at the time of birth […]. Others experience stochastic changes over the life course […] The presence of such randomly changing influential factors violates the Markov assumption, and makes the description of aging-related changes in health status more complicated. […] The age dynamics of influential factors (e.g., physiological variables) in connection with mortality risks has been described using a stochastic process model of human mortality and aging […]. Recent extensions of this model have been used in analyses of longitudinal data on aging, health, and longevity, collected in the Framingham Heart Study […] This model and its extensions are described in terms of a Markov stochastic process satisfying a diffusion-type stochastic differential equation. The stochastic process is stopped at random times associated with individuals’ deaths. […] When an individual’s health status is taken into account, the coefficients of the stochastic differential equations become dependent on values of the jumping process. This dependence violates the Markov assumption and renders the conditional Gaussian property invalid. So the description of this (continuously changing) component of aging-related changes in the body also becomes more complicated. Since studying age trajectories of physiological states in connection with changes in health status and mortality would provide more realistic scenarios for analyses of available longitudinal data, it would be a good idea to find an appropriate mathematical description of the joint evolution of these interdependent processes in aging organisms. For this purpose, we propose a comprehensive model of human aging, health, and mortality in which the Markov assumption is fulfilled by a two-component stochastic process consisting of jumping and continuously changing processes. The jumping component is used to describe relatively fast changes in health status occurring at random times, and the continuous component describes relatively slow stochastic age-related changes of individual physiological states. […] The use of stochastic differential equations for random continuously changing covariates has been studied intensively in the analysis of longitudinal data […] Such a description is convenient since it captures the feedback mechanism typical of biological systems reflecting regular aging-related changes and takes into account the presence of random noise affecting individual trajectories. It also captures the dynamic connections between aging-related changes in health and physiological states, which are important in many applications.”

April 23, 2017 Posted by | Biology, Books, Demographics, Genetics, Mathematics, Statistics | Leave a comment

Random stuff

It’s been a long time since I last posted one of these posts, so a great number of links of interest has accumulated in my bookmarks. I intended to include a large number of these in this post and this of course means that I surely won’t cover each specific link included in this post in anywhere near the amount of detail it deserves, but that can’t be helped.

i. Autism Spectrum Disorder Grown Up: A Chart Review of Adult Functioning.

“For those diagnosed with ASD in childhood, most will become adults with a significant degree of disability […] Seltzer et al […] concluded that, despite considerable heterogeneity in social outcomes, “few adults with autism live independently, marry, go to college, work in competitive jobs or develop a large network of friends”. However, the trend within individuals is for some functional improvement over time, as well as a decrease in autistic symptoms […]. Some authors suggest that a sub-group of 15–30% of adults with autism will show more positive outcomes […]. Howlin et al. (2004), and Cederlund et al. (2008) assigned global ratings of social functioning based on achieving independence, friendships/a steady relationship, and education and/or a job. These two papers described respectively 22% and 27% of groups of higher functioning (IQ above 70) ASD adults as attaining “Very Good” or “Good” outcomes.”

“[W]e evaluated the adult outcomes for 45 individuals diagnosed with ASD prior to age 18, and compared this with the functioning of 35 patients whose ASD was identified after 18 years. Concurrent mental illnesses were noted for both groups. […] Comparison of adult outcome within the group of subjects diagnosed with ASD prior to 18 years of age showed significantly poorer functioning for those with co-morbid Intellectual Disability, except in the domain of establishing intimate relationships [my emphasis. To make this point completely clear, one way to look at these results is that apparently in the domain of partner-search autistics diagnosed during childhood are doing so badly in general that being intellectually disabled on top of being autistic is apparently conferring no additional disadvantage]. Even in the normal IQ group, the mean total score, i.e. the sum of the 5 domains, was relatively low at 12.1 out of a possible 25. […] Those diagnosed as adults had achieved significantly more in the domains of education and independence […] Some authors have described a subgroup of 15–27% of adult ASD patients who attained more positive outcomes […]. Defining an arbitrary adaptive score of 20/25 as “Good” for our normal IQ patients, 8 of thirty four (25%) of those diagnosed as adults achieved this level. Only 5 of the thirty three (15%) diagnosed in childhood made the cutoff. (The cut off was consistent with a well, but not superlatively, functioning member of society […]). None of the Intellectually Disabled ASD subjects scored above 10. […] All three groups had a high rate of co-morbid psychiatric illnesses. Depression was particularly frequent in those diagnosed as adults, consistent with other reports […]. Anxiety disorders were also prevalent in the higher functioning participants, 25–27%. […] Most of the higher functioning ASD individuals, whether diagnosed before or after 18 years of age, were functioning well below the potential implied by their normal range intellect.”

Related papers: Social Outcomes in Mid- to Later Adulthood Among Individuals Diagnosed With Autism and Average Nonverbal IQ as Children, Adults With Autism Spectrum Disorders.

ii. Premature mortality in autism spectrum disorder. This is a Swedish matched case cohort study. Some observations from the paper:

“The aim of the current study was to analyse all-cause and cause-specific mortality in ASD using nationwide Swedish population-based registers. A further aim was to address the role of intellectual disability and gender as possible moderators of mortality and causes of death in ASD. […] Odds ratios (ORs) were calculated for a population-based cohort of ASD probands (n = 27 122, diagnosed between 1987 and 2009) compared with gender-, age- and county of residence-matched controls (n = 2 672 185). […] During the observed period, 24 358 (0.91%) individuals in the general population died, whereas the corresponding figure for individuals with ASD was 706 (2.60%; OR = 2.56; 95% CI 2.38–2.76). Cause-specific analyses showed elevated mortality in ASD for almost all analysed diagnostic categories. Mortality and patterns for cause-specific mortality were partly moderated by gender and general intellectual ability. […] Premature mortality was markedly increased in ASD owing to a multitude of medical conditions. […] Mortality was significantly elevated in both genders relative to the general population (males: OR = 2.87; females OR = 2.24)”.

“Individuals in the control group died at a mean age of 70.20 years (s.d. = 24.16, median = 80), whereas the corresponding figure for the entire ASD group was 53.87 years (s.d. = 24.78, median = 55), for low-functioning ASD 39.50 years (s.d. = 21.55, median = 40) and high-functioning ASD 58.39 years (s.d. = 24.01, median = 63) respectively. […] Significantly elevated mortality was noted among individuals with ASD in all analysed categories of specific causes of death except for infections […] ORs were highest in cases of mortality because of diseases of the nervous system (OR = 7.49) and because of suicide (OR = 7.55), in comparison with matched general population controls.”

iii. Adhesive capsulitis of shoulder. This one is related to a health scare I had a few months ago. A few quotes:

Adhesive capsulitis (also known as frozen shoulder) is a painful and disabling disorder of unclear cause in which the shoulder capsule, the connective tissue surrounding the glenohumeral joint of the shoulder, becomes inflamed and stiff, greatly restricting motion and causing chronic pain. Pain is usually constant, worse at night, and with cold weather. Certain movements or bumps can provoke episodes of tremendous pain and cramping. […] People who suffer from adhesive capsulitis usually experience severe pain and sleep deprivation for prolonged periods due to pain that gets worse when lying still and restricted movement/positions. The condition can lead to depression, problems in the neck and back, and severe weight loss due to long-term lack of deep sleep. People who suffer from adhesive capsulitis may have extreme difficulty concentrating, working, or performing daily life activities for extended periods of time.”

Some other related links below:

The prevalence of a diabetic condition and adhesive capsulitis of the shoulder.
“Adhesive capsulitis is characterized by a progressive and painful loss of shoulder motion of unknown etiology. Previous studies have found the prevalence of adhesive capsulitis to be slightly greater than 2% in the general population. However, the relationship between adhesive capsulitis and diabetes mellitus (DM) is well documented, with the incidence of adhesive capsulitis being two to four times higher in diabetics than in the general population. It affects about 20% of people with diabetes and has been described as the most disabling of the common musculoskeletal manifestations of diabetes.”

Adhesive Capsulitis (review article).
“Patients with type I diabetes have a 40% chance of developing a frozen shoulder in their lifetimes […] Dominant arm involvement has been shown to have a good prognosis; associated intrinsic pathology or insulin-dependent diabetes of more than 10 years are poor prognostic indicators.15 Three stages of adhesive capsulitis have been described, with each phase lasting for about 6 months. The first stage is the freezing stage in which there is an insidious onset of pain. At the end of this period, shoulder ROM [range of motion] becomes limited. The second stage is the frozen stage, in which there might be a reduction in pain; however, there is still restricted ROM. The third stage is the thawing stage, in which ROM improves, but can take between 12 and 42 months to do so. Most patients regain a full ROM; however, 10% to 15% of patients suffer from continued pain and limited ROM.”

Musculoskeletal Complications in Type 1 Diabetes.
“The development of periarticular thickening of skin on the hands and limited joint mobility (cheiroarthropathy) is associated with diabetes and can lead to significant disability. The objective of this study was to describe the prevalence of cheiroarthropathy in the well-characterized Diabetes Control and Complications Trial/Epidemiology of Diabetes Interventions and Complications (DCCT/EDIC) cohort and examine associated risk factors […] This cross-sectional analysis was performed in 1,217 participants (95% of the active cohort) in EDIC years 18/19 after an average of 24 years of follow-up. Cheiroarthropathy — defined as the presence of any one of the following: adhesive capsulitis, carpal tunnel syndrome, flexor tenosynovitis, Dupuytren’s contracture, or a positive prayer sign [related link] — was assessed using a targeted medical history and standardized physical examination. […] Cheiroarthropathy was present in 66% of subjects […] Cheiroarthropathy is common in people with type 1 diabetes of long duration (∼30 years) and is related to longer duration and higher levels of glycemia. Clinicians should include cheiroarthropathy in their routine history and physical examination of patients with type 1 diabetes because it causes clinically significant functional disability.”

Musculoskeletal disorders in diabetes mellitus: an update.
“Diabetes mellitus (DM) is associated with several musculoskeletal disorders. […] The exact pathophysiology of most of these musculoskeletal disorders remains obscure. Connective tissue disorders, neuropathy, vasculopathy or combinations of these problems, may underlie the increased incidence of musculoskeletal disorders in DM. The development of musculoskeletal disorders is dependent on age and on the duration of DM; however, it has been difficult to show a direct correlation with the metabolic control of DM.”

Rheumatic Manifestations of Diabetes Mellitus.

Prevalence of symptoms and signs of shoulder problems in people with diabetes mellitus.

Musculoskeletal Disorders of the Hand and Shoulder in Patients with Diabetes.
“In addition to micro- and macroangiopathic complications, diabetes mellitus is also associated with several musculoskeletal disorders of the hand and shoulder that can be debilitating (1,2). Limited joint mobility, also termed diabetic hand syndrome or cheiropathy (3), is characterized by skin thickening over the dorsum of the hands and restricted mobility of multiple joints. While this syndrome is painless and usually not disabling (2,4), other musculoskeletal problems occur with increased frequency in diabetic patients, including Dupuytren’s disease [“Dupuytren’s disease […] may be observed in up to 42% of adults with diabetes mellitus, typically in patients with long-standing T1D” – link], carpal tunnel syndrome [“The prevalence of [carpal tunnel syndrome, CTS] in patients with diabetes has been estimated at 11–30 % […], and is dependent on the duration of diabetes. […] Type I DM patients have a high prevalence of CTS with increasing duration of disease, up to 85 % after 54 years of DM” – link], palmar flexor tenosynovitis or trigger finger [“The incidence of trigger finger [/stenosing tenosynovitis] is 7–20 % of patients with diabetes comparing to only about 1–2 % in nondiabetic patients” – link], and adhesive capsulitis of the shoulder (5–10). The association of adhesive capsulitis with pain, swelling, dystrophic skin, and vasomotor instability of the hand constitutes the “shoulder-hand syndrome,” a rare but potentially disabling manifestation of diabetes (1,2).”

“The prevalence of musculoskeletal disorders was greater in diabetic patients than in control patients (36% vs. 9%, P < 0.01). Adhesive capsulitis was present in 12% of the diabetic patients and none of the control patients (P < 0.01), Dupuytren’s disease in 16% of diabetic and 3% of control patients (P < 0.01), and flexor tenosynovitis in 12% of diabetic and 2% of control patients (P < 0.04), while carpal tunnel syndrome occurred in 12% of diabetic patients and 8% of control patients (P = 0.29). Musculoskeletal disorders were more common in patients with type 1 diabetes than in those with type 2 diabetes […]. Forty-three patients [out of 100] with type 1 diabetes had either hand or shoulder disorders (37 with hand disorders, 6 with adhesive capsulitis of the shoulder, and 10 with both syndromes), compared with 28 patients [again out of 100] with type 2 diabetes (24 with hand disorders, 4 with adhesive capsulitis of the shoulder, and 3 with both syndromes, P = 0.03).”

Association of Diabetes Mellitus With the Risk of Developing Adhesive Capsulitis of the Shoulder: A Longitudinal Population-Based Followup Study.
“A total of 78,827 subjects with at least 2 ambulatory care visits with a principal diagnosis of DM in 2001 were recruited for the DM group. The non-DM group comprised 236,481 age- and sex-matched randomly sampled subjects without DM. […] During a 3-year followup period, 946 subjects (1.20%) in the DM group and 2,254 subjects (0.95%) in the non-DM group developed ACS. The crude HR of developing ACS for the DM group compared to the non-DM group was 1.333 […] the association between DM and ACS may be explained at least in part by a DM-related chronic inflammatory process with increased growth factor expression, which in turn leads to joint synovitis and subsequent capsular fibrosis.”

It is important to note when interpreting the results of the above paper that these results are based on Taiwanese population-level data, and type 1 diabetes – which is obviously the high-risk diabetes subgroup in this particular context – is rare in East Asian populations (as observed in Sperling et al., “A child in Helsinki, Finland is almost 400 times more likely to develop diabetes than a child in Sichuan, China”. Taiwanese incidence of type 1 DM in children is estimated at ~5 in 100.000).

iv. Parents who let diabetic son starve to death found guilty of first-degree murder. It’s been a while since I last saw one of these ‘boost-your-faith-in-humanity’-cases, but they in my impression do pop up every now and then. I should probably keep at hand one of these articles in case my parents ever express worry to me that they weren’t good parents; they could have done a lot worse…

v. Freedom of medicine. One quote from the conclusion of Cochran’s post:

“[I]t is surely possible to materially improve the efficacy of drug development, of medical research as a whole. We’re doing better than we did 500 years ago – although probably worse than we did 50 years ago. But I would approach it by learning as much as possible about medical history, demographics, epidemiology, evolutionary medicine, theory of senescence, genetics, etc. Read Koch, not Hayek. There is no royal road to medical progress.”

I agree, and I was considering including some related comments and observations about health economics in this post – however I ultimately decided against doing that in part because the post was growing unwieldy; I might include those observations in another post later on. Here’s another somewhat older Westhunt post I at some point decided to bookmark – I in particular like the following neat quote from the comments, which expresses a view I have of course expressed myself in the past here on this blog:

“When you think about it, falsehoods, stupid crap, make the best group identifiers, because anyone might agree with you when you’re obviously right. Signing up to clear nonsense is a better test of group loyalty. A true friend is with you when you’re wrong. Ideally, not just wrong, but barking mad, rolling around in your own vomit wrong.”

vi. Economic Costs of Diabetes in the U.S. in 2012.

“Approximately 59% of all health care expenditures attributed to diabetes are for health resources used by the population aged 65 years and older, much of which is borne by the Medicare program […]. The population 45–64 years of age incurs 33% of diabetes-attributed costs, with the remaining 8% incurred by the population under 45 years of age. The annual attributed health care cost per person with diabetes […] increases with age, primarily as a result of increased use of hospital inpatient and nursing facility resources, physician office visits, and prescription medications. Dividing the total attributed health care expenditures by the number of people with diabetes, we estimate the average annual excess expenditures for the population aged under 45 years, 45–64 years, and 65 years and above, respectively, at $4,394, $5,611, and $11,825.”

“Our logistic regression analysis with NHIS data suggests that diabetes is associated with a 2.4 percentage point increase in the likelihood of leaving the workforce for disability. This equates to approximately 541,000 working-age adults leaving the workforce prematurely and 130 million lost workdays in 2012. For the population that leaves the workforce early because of diabetes-associated disability, we estimate that their average daily earnings would have been $166 per person (with the amount varying by demographic). Presenteeism accounted for 30% of the indirect cost of diabetes. The estimate of a 6.6% annual decline in productivity attributed to diabetes (in excess of the estimated decline in the absence of diabetes) equates to 113 million lost workdays per year.”

vii. Total red meat intake of ≥0.5 servings/d does not negatively influence cardiovascular disease risk factors: a systemically searched meta-analysis of randomized controlled trials.

viii. Effect of longer term modest salt reduction on blood pressure: Cochrane systematic review and meta-analysis of randomised trials. Did I blog this paper at some point in the past? I could not find any coverage of it on the blog when I searched for it so I decided to include it here, even if I have a nagging suspicion I may have talked about these findings before. What did they find? The short version is this:

“A modest reduction in salt intake for four or more weeks causes significant and, from a population viewpoint, important falls in blood pressure in both hypertensive and normotensive individuals, irrespective of sex and ethnic group. Salt reduction is associated with a small physiological increase in plasma renin activity, aldosterone, and noradrenaline and no significant change in lipid concentrations. These results support a reduction in population salt intake, which will lower population blood pressure and thereby reduce cardiovascular disease.”

ix. Some wikipedia links:

Heroic Age of Antarctic Exploration (featured).

Wien’s displacement law.

Kuiper belt (featured).

Treason (one quote worth including here: “Currently, the consensus among major Islamic schools is that apostasy (leaving Islam) is considered treason and that the penalty is death; this is supported not in the Quran but in the Hadith.[42][43][44][45][46][47]“).

Lymphatic filariasis.

File:World map of countries by number of cigarettes smoked per adult per year.

Australian gold rushes.

Savant syndrome (“It is estimated that 10% of those with autism have some form of savant abilities”). A small sidenote of interest to Danish readers: The Danish Broadcasting Corporation recently featured a series about autistics with ‘special abilities’ – the show was called ‘The hidden talents’ (De skjulte talenter), and after multiple people had nagged me to watch it I ended up deciding to do so. Most of the people in that show presumably had some degree of ‘savantism’ combined with autism at the milder end of the spectrum, i.e. Asperger’s. I was somewhat conflicted about what to think about the show and did consider blogging it in detail (in Danish?), but I decided against it. However I do want to add here to Danish readers reading along who’ve seen the show that they would do well to repeatedly keep in mind that a) the great majority of autistics do not have abilities like these, b) many autistics with abilities like these presumably do quite poorly, and c) that many autistics have even greater social impairments than do people like e.g. (the very likeable, I have to add…) Louise Wille from the show).

Quark–gluon plasma.

Simo Häyhä.

Chernobyl liquidators.

Black Death (“Over 60% of Norway’s population died in 1348–1350”).

Renault FT (“among the most revolutionary and influential tank designs in history”).

Weierstrass function (“an example of a pathological real-valued function on the real line. The function has the property of being continuous everywhere but differentiable nowhere”).

W Ursae Majoris variable.

Void coefficient. (“a number that can be used to estimate how much the reactivity of a nuclear reactor changes as voids (typically steam bubbles) form in the reactor moderator or coolant. […] Reactivity is directly related to the tendency of the reactor core to change power level: if reactivity is positive, the core power tends to increase; if it is negative, the core power tends to decrease; if it is zero, the core power tends to remain stable. […] A positive void coefficient means that the reactivity increases as the void content inside the reactor increases due to increased boiling or loss of coolant; for example, if the coolant acts as a neutron absorber. If the void coefficient is large enough and control systems do not respond quickly enough, this can form a positive feedback loop which can quickly boil all the coolant in the reactor. This happened in the RBMK reactor that was destroyed in the Chernobyl disaster.”).

Gregor MacGregor (featured) (“a Scottish soldier, adventurer, and confidence trickster […] MacGregor’s Poyais scheme has been called one of the most brazen confidence tricks in history.”).


Irish Civil War.

March 10, 2017 Posted by | Astronomy, autism, Cardiology, Diabetes, Economics, Epidemiology, Health Economics, History, Infectious disease, Mathematics, Medicine, Papers, Physics, Psychology, Random stuff, Wikipedia | Leave a comment

Random Stuff

i. On the youtube channel of the Institute for Advanced Studies there has been a lot of activity over the last week or two (far more than 100 new lectures have been uploaded, and it seems new uploads are still being added at this point), and I’ve been watching a few of the recently uploaded astrophysics lectures. They’re quite technical, but you can watch them and follow enough of the content to have an enjoyable time despite not understanding everything:

This is a good lecture, very interesting. One major point made early on: “the take-away message is that the most common planet in the galaxy, at least at shorter periods, are planets for which there is no analogue in the solar system. The most common kind of planet in the galaxy is a planet with a radius of two Earth radii.” Another big take-away message is that small planets seem to be quite common (as noted in the conclusions, “16% of Sun-like stars have an Earth-sized planet”).

Of the lectures included in this post this was the one I liked the least; there are too many (‘obstructive’) questions/interactions between lecturer and attendants along the way, and the interactions/questions are difficult to hear/understand. If you consider watching both this lecture and the lecture below, I would say that it would probably be wise to watch the lecture below this one before you watch this one; I concluded that in retrospect some of the observations made early on in the lecture below would have been useful to know about before watching this lecture. (The first half of the lecture below was incidentally to me somewhat easier to follow than was the second half, but especially the first half hour of it is really quite good, despite the bad start (which one can always blame on Microsoft…)).

ii. Words I’ve encountered recently (…or ‘recently’ – it’s been a while since I last posted one of these lists): Divagationsperiphrasis, reedy, architravesettpedipalp, tout, togs, edentulous, moue, tatty, tearaway, prorogue, piscine, fillip, sop, panniers, auxology, roister, prepossessing, cantle, catamite, couth, ordure, biddy, recrudescence, parvenu, scupper, husting, hackle, expatiate, affray, tatterdemalion, eructation, coppice, dekko, scull, fulmination, pollarding, grotty, secateurs, bumf (I must admit that I like this word – it seems fitting, somehow, to use that word for this concept…), durophagy, randy, (brief note to self: Advise people having children who ask me about suggestions for how to name them against using this name (or variants such as Randi), it does not seem like a great idea), effete, apricity, sororal, bint, coition, abaft, eaves, gadabout, lugubriously, retroussé, landlubber, deliquescence, antimacassar, inanition.

iii. “The point of rigour is not to destroy all intuition; instead, it should be used to destroy bad intuition while clarifying and elevating good intuition. It is only with a combination of both rigorous formalism and good intuition that one can tackle complex mathematical problems; one needs the former to correctly deal with the fine details, and the latter to correctly deal with the big picture. Without one or the other, you will spend a lot of time blundering around in the dark (which can be instructive, but is highly inefficient). So once you are fully comfortable with rigorous mathematical thinking, you should revisit your intuitions on the subject and use your new thinking skills to test and refine these intuitions rather than discard them. One way to do this is to ask yourself dumb questions; another is to relearn your field.” (Terry Tao, There’s more to mathematics than rigour and proofs)

iv. A century of trends in adult human height. A figure from the paper (Figure 3 – Change in adult height between the 1896 and 1996 birth cohorts):


(Click to view full size. WordPress seems to have changed the way you add images to a blog post – if this one is even so annoyingly large, I apologize, I have tried to minimize it while still retaining detail, but the original file is huge). An observation from the paper:

“Men were taller than women in every country, on average by ~11 cm in the 1896 birth cohort and ~12 cm in the 1996 birth cohort […]. In the 1896 birth cohort, the male-female height gap in countries where average height was low was slightly larger than in taller nations. In other words, at the turn of the 20th century, men seem to have had a relative advantage over women in undernourished compared to better-nourished populations.”

I haven’t studied the paper in any detail but intend to do so at a later point in time.

v. I found this paper, on Exercise and Glucose Metabolism in Persons with Diabetes Mellitus, interesting in part because I’ve been very surprised a few times by offhand online statements made by diabetic athletes, who had observed that their blood glucose really didn’t drop all that fast during exercise. Rapid and annoyingly large drops in blood glucose during exercise have been a really consistent feature of my own life with diabetes during adulthood. It seems that there may be big inter-individual differences in terms of the effects of exercise on glucose in diabetics. From the paper:

“Typically, prolonged moderate-intensity aerobic exercise (i.e., 30–70% of one’s VO2max) causes a reduction in glucose concentrations because of a failure in circulating insulin levels to decrease at the onset of exercise.12 During this type of physical activity, glucose utilization may be as high as 1.5 g/min in adolescents with type 1 diabetes13 and exceed 2.0 g/min in adults with type 1 diabetes,14 an amount that quickly lowers circulating glucose levels. Persons with type 1 diabetes have large interindividual differences in blood glucose responses to exercise, although some intraindividual reproducibility exists.15 The wide ranging glycemic responses among individuals appears to be related to differences in pre-exercise blood glucose concentrations, the level of circulating counterregulatory hormones and the type/duration of the activity.2

August 13, 2016 Posted by | Astronomy, Demographics, Diabetes, Language, Lectures, Mathematics, Physics, Random stuff | Leave a comment

Random stuff

I find it difficult to find the motivation to finish the half-finished drafts I have lying around, so this will have to do. Some random stuff below.


(15.000 views… In some sense that seems really ‘unfair’ to me, but on the other hand I doubt neither Beethoven nor Gilels care; they’re both long dead, after all…)

ii. New/newish words I’ve encountered in books, on or elsewhere:

Agleyperipeteia, disseverhalidom, replevinsocage, organdie, pouffe, dyarchy, tauricide, temerarious, acharnement, cadger, gravamen, aspersion, marronage, adumbrate, succotash, deuteragonist, declivity, marquetry, machicolation, recusal.

iii. A lecture:

It’s been a long time since I watched it so I don’t have anything intelligent to say about it now, but I figured it might be of interest to one or two of the people who still subscribe to the blog despite the infrequent updates.

iv. A few wikipedia articles (I won’t comment much on the contents or quote extensively from the articles the way I’ve done in previous wikipedia posts – the links shall have to suffice for now):

Duverger’s law.

Far side of the moon.

Preference falsification.

Russian political jokes. Some of those made me laugh (e.g. this one: “A judge walks out of his chambers laughing his head off. A colleague approaches him and asks why he is laughing. “I just heard the funniest joke in the world!” “Well, go ahead, tell me!” says the other judge. “I can’t – I just gave someone ten years for it!”).

Political mutilation in Byzantine culture.

v. World War 2, if you think of it as a movie, has a highly unrealistic and implausible plot, according to this amusing post by Scott Alexander. Having recently read a rather long book about these topics, one aspect I’d have added had I written the piece myself would be that an additional factor making the setting seem even more implausible is how so many presumably quite smart people were so – what at least in retrospect seems – unbelievably stupid when it came to Hitler’s ideas and intentions before the war. Going back to Churchill’s own life I’d also add that if you were to make a movie about Churchill’s life during the war, which you could probably relatively easily do if you were to just base it upon his own copious and widely shared notes, then it could probably be made into a quite decent movie. His own comments, remarks, and observations certainly made for a great book.

May 15, 2016 Posted by | Astronomy, Computer science, History, Language, Lectures, Mathematics, Music, Random stuff, Russia, Wikipedia | Leave a comment

A few lectures

Below are three new lectures from the Institute of Advanced Study. As far as I’ve gathered they’re all from an IAS symposium called ‘Lens of Computation on the Sciences’ – all three lecturers are computer scientists, but you don’t have to be a computer scientist to watch these lectures.

Should computer scientists and economists band together more and try to use the insights from one field to help solve problems in the other field? Roughgarden thinks so, and provides examples of how this might be done/has been done. Applications discussed in the lecture include traffic management and auction design. I’m not sure how much of this lecture is easy to follow for people who don’t know anything about either topic (i.e., computer science and economics), but I found it not too difficult to follow – it probably helped that I’ve actually done work on a few of the things he touches upon in the lecture, such as basic auction theory, the fixed point theorems and related proofs, basic queueing theory and basic discrete maths/graph theory. Either way there are certainly much more technical lectures than this one available at the IAS channel.

I don’t have Facebook and I’m not planning on ever getting a FB account, so I’m not really sure I care about the things this guy is trying to do, but the lecturer does touch upon some interesting topics in network theory. Not a great lecture in my opinion and occasionally I think the lecturer ‘drifts’ a bit, talking without saying very much, but it’s also not a terrible lecture. A few times I was really annoyed that you can’t see where he’s pointing that damn laser pointer, but this issue should not stop you from watching the video, especially not if you have an interest in analytical aspects of how to approach and make sense of ‘Big Data’.

I’ve noticed that Scott Alexander has said some nice things about Scott Aaronson a few times, but until now I’ve never actually read any of the latter guy’s stuff or watched any lectures by him. I agree with Scott (Alexander) that Scott (Aaronson) is definitely a smart guy. This is an interesting lecture; I won’t pretend I understood all of it, but it has some thought-provoking ideas and important points in the context of quantum computing and it’s actually a quite entertaining lecture; I was close to laughing a couple of times.

January 8, 2016 Posted by | Computer science, Economics, Game theory, Lectures, Mathematics, Physics | Leave a comment


i. “By all means think yourself big but don’t think everyone else small” (‘Notes on Flyleaf of Fresh ms. Book’, Scott’s Last Expedition. See also this).

ii. “The man who knows everyone’s job isn’t much good at his own.” (-ll-)

iii. “It is amazing what little harm doctors do when one considers all the opportunities they have” (Mark Twain, as quoted in the Oxford Handbook of Clinical Medicine, p.595).

iv. “A first-rate theory predicts; a second-rate theory forbids and a third-rate theory explains after the event.” (Aleksander Isaakovich Kitaigorodski)

v. “[S]ome of the most terrible things in the world are done by people who think, genuinely think, that they’re doing it for the best” (Terry Pratchett, Snuff).

vi. “That was excellently observ’d, say I, when I read a Passage in an Author, where his Opinion agrees with mine. When we differ, there I pronounce him to be mistaken.” (Jonathan Swift)

vii. “Death is nature’s master stroke, albeit a cruel one, because it allows genotypes space to try on new phenotypes.” (Quote from the Oxford Handbook of Clinical Medicine, p.6)

viii. “The purpose of models is not to fit the data but to sharpen the questions.” (Samuel Karlin)

ix. “We may […] view set theory, and mathematics generally, in much the way in which we view theoretical portions of the natural sciences themselves; as comprising truths or hypotheses which are to be vindicated less by the pure light of reason than by the indirect systematic contribution which they make to the organizing of empirical data in the natural sciences.” (Quine)

x. “At root what is needed for scientific inquiry is just receptivity to data, skill in reasoning, and yearning for truth. Admittedly, ingenuity can help too.” (-ll-)

xi. “A statistician carefully assembles facts and figures for others who carefully misinterpret them.” (Quote from Mathematically Speaking – A Dictionary of Quotations, p.329. Only source given in the book is: “Quoted in Evan Esar, 20,000 Quips and Quotes“)

xii. “A knowledge of statistics is like a knowledge of foreign languages or of algebra; it may prove of use at any time under any circumstances.” (Quote from Mathematically Speaking – A Dictionary of Quotations, p. 328. The source provided is: “Elements of Statistics, Part I, Chapter I (p.4)”).

xiii. “We own to small faults to persuade others that we have not great ones.” (Rochefoucauld)

xiv. “There is more self-love than love in jealousy.” (-ll-)

xv. “We should not judge of a man’s merit by his great abilities, but by the use he makes of them.” (-ll-)

xvi. “We should gain more by letting the world see what we are than by trying to seem what we are not.” (-ll-)

xvii. “Put succinctly, a prospective study looks for the effects of causes whereas a retrospective study examines the causes of effects.” (Quote from p.49 of Principles of Applied Statistics, by Cox & Donnelly)

xviii. “… he who seeks for methods without having a definite problem in mind seeks for the most part in vain.” (David Hilbert)

xix. “Give every man thy ear, but few thy voice” (Shakespeare).

xx. “Often the fear of one evil leads us into a worse.” (Nicolas Boileau-Despréaux)


November 22, 2015 Posted by | Books, Mathematics, Medicine, Philosophy, Quotes/aphorisms, Science, Statistics | Leave a comment