An introduction to Invariant Theory

I was strongly considering not watching this one to the end (…such as it is – the video cuts off before the talk was completely finished, but I’m okay with missing out on the last 2 (?) minutes anyway) at several points during the lecture, mainly because this is definitely far from a ‘gentle’ introduction; this one is tough for an introductory lecture and I had to look up a lot of stuff to just sort-of-kind-of muddle along. One of the things that I recall kept me from giving the rest of the lecture a miss along the way was that some parts of the coverage made me review a few topics in group theory which I’d previously encountered, but did not remember at all well – basically I was reminded along the way that concepts X, Y, and Z existed, and that I’d forgot how they worked/what they were useful for.

I think most (…non-mathematicians? …people?) who watch this one will miss a lot of stuff and details, and although you by watching it might get some idea what this stuff’s about I’m quite sure I’d not recommend this lecture to non-mathematicians; I don’t think it’s really worth it to watch it.

I’ve posted some links below to things related to the lecture’s coverage.

Invariant (mathematics).
Loop invariant.
Knot invariant.
Jones polynomial.
Homogeneous polynomial.
Invariant polynomial.
Invariant of a binary form.
Paul Gordan.
Polynomial ring.
Indeterminate (variable).
Ideal (ring theory).
Hilbert’s basis theorem.
Hilbert’s Nullstellensatz.
Group representation.
Group action.
Permutation matrix.
Symmetric polynomial.
Hilbert’s finiteness theorem.
Irreducible representation.
Multiplicative group.
One-parameter group.
Hilbert–Mumford criterion.
Strictly Upper Triangular Matrix.
Nilpotent matrix.
Characteristic polynomial.


June 23, 2018 Posted by | Lectures, Mathematics | Leave a comment

Mathematics in Cryptography III

As she puts it herself, most of this lecture [~first 47 minutes or so] was basically “an explanation by a non-expert on how the internet uses public key” (-cryptography). The last 20 minutes cover, again in her own words, “more theoretical aspects”.

Some links:

Hypertext Transfer Protocol (HTTP). HTTPS.
Project Athena. Kerberos (protocol).
Pretty Good Privacy (PGP).
Secure Sockets Layer (SSL)/Transport Layer Security (TLS).
Cipher suite.
Elliptic Curve Digital Signature Algorithm (ECDSA).
Request for Comments (RFC).
Elliptic-curve Diffie–Hellman (ECDH).
The SSL/TLS Handshake: an Overview.
Advanced Encryption Standard.
Galois/Counter Mode.
XOR gate.
IP Header.
Time to live (TTL).
Transmission Control Protocol. TCP segment structure.
TLS record.
Security level.
Birthday problem. Birthday attack.
Handbook of Applied Cryptography (Alfred J. Menezes, Paul C. van Oorschot and Scott A. Vanstone). (§3.6 in particular is mentioned/referenced as this is stuff she talks about in the last ‘theoretical’ part of the lecture).


June 8, 2018 Posted by | Computer science, Cryptography, Lectures, Mathematics | Leave a comment

Mathematics in Cryptography II

Some links to stuff covered in the lecture:

Public-key cryptography.
New Directions in Cryptography (Diffie & Hellman, 1976).
The history of Non-Secret Encryption (James Ellis).
Note on “Non-Secret Encryption” – Cliff Cocks (1973).
RSA (cryptosystem).
Discrete Logarithm Problem.
Diffie–Hellman key exchange.
AES (Advanced Encryption Standard).
Triple DES.
Trusted third party (TTP).
Key management.
Man-in-the-middle attack.
Digital signature.
Public key certificate.
Secret sharing.
Hash function. Cryptographic hash function.
Secure Hash Algorithm 2 (SHA-2).
Non-repudiation (digital security).
L-notation. L (complexity).
ElGamal signature scheme.
Digital Signature Algorithm (DSA).
Schnorr signature.
Identity-based cryptography.
Identity-Based Cryptosystems and Signature Schemes (Adi Shamir, 1984).
Algorithms for Quantum Computation: Discrete Logarithms and Factoring (Peter Shor, 1994).
Quantum resistant cryptography.
Elliptic curve. Elliptic-curve cryptography.
Projective space.

I have included very few links relating to the topics covered in the last part of the lecture. This was deliberate and not just a result of the type of coverage included in that part of the lecture. In my opinion non-mathematicians should probably skip the last 25 minutes or so as they’re – not only due to technical issues (the lecturer is writing stuff on the blackboard and for several minutes you’re unable to see what she’s writing, which is …unfortunate), but those certainly were not helping – not really worth the effort. The first hour of the lecture is great, the last 25 minutes are, well, less great, in my opinion. You should however not miss the first part of the coverage of ECC-related stuff (in particular the coverage ~55-58 minutes in), if you’re interested in making sense of how ECC works; I certainly found that part of the coverage very helpful.

June 2, 2018 Posted by | Computer science, Cryptography, Lectures, Mathematics, Papers | Leave a comment

Computers, People and the Real World

“An exploration of some spectacular failures of modern day computer-aided systems, which fail to take into account the real-world […] Almost nobody wants an IT system. What they want is a better way of doing something, whether that is buying and selling shares on the Stock Exchange, flying an airliner or running a hospital. So the system they want will usually involve changes to the way people work, and interactions with physical objects and the environment. Drawing on examples including the new programme for IT in the NHS, this lecture explores what can go wrong when business change is mistakenly viewed as an IT project.” (Quote from the video description on youtube).

Some links related to the lecture coverage:
Computer-aided dispatch.
London Ambulance Service – computerization.
Report of the Inquiry Into The London Ambulance Service (February 1993).
Sociotechnical system.
Tay (bot).

A few observations/quotes from the lecture (-notes):

The bidder who least understands the complexity of a requirement is likely to put in the lowest bid.
“It is a mistake to use a computer system to impose new work processes on under-trained or reluctant staff. – Front line staff are often best placed to judge what is practical.” [A quote from later in the lecture [~36 mins] is even more explicit: “The experts in any work process are usually the people who have been carrying it out.”]
“It is important to understand that in any system implementation the people factor is as important, and arguably more important, than the technical infrastructure.” (This last one is a full quote from the report linked above; the lecture includes a shortened version – US) [Quotes and observations above from ~16 minute mark unless otherwise noted]

“There is no such thing as an IT project”
“(almost) every significant “IT Project” is actually a business change project that is enabled and supported by one or more IT systems. Business processes are expensive to change. The business changes take at least as long and cost as much as the new IT system, and need at least as much planning and management” [~29 mins]

“Software packages are packaged business processes
*Changing a package to fit the way you want to work can cost more than writing new software” [~31-32 mins]

“Most computer systems interact with people: the sociotechnical view is that the people and the IT are two components of a larger system. Designing that larger system is the real task.” [~36 mins]

May 31, 2018 Posted by | Computer science, Economics, Engineering, Lectures | Leave a comment

Mathematics in Cryptography

Some relevant links:

Caesar cipher.
Substitution cipher.
Frequency analysis.
Vigenère cipher.
ADFGVX cipher.
One-time pad.
Arthur Scherbius.
Enigma machine.
Cycle notation.
Permutation group.
Cyclic permutation.
Involution (mathematics).
An Application of the Theory of Permutations in Breaking the Enigma CipherMarian Rejewski.

May 23, 2018 Posted by | Cryptography, Lectures, Mathematics | Leave a comment

On the cryptographic hardness of finding a Nash equilibrium

I found it annoying that you generally can’t really hear the questions posed by the audience (which includes people like Avi Wigderson), especially considering that there are quite a few of these, especially in the middle section of the lecture. There are intermittent issues with the camera’s focus occasionally throughout the talk, but those are all transitory problems that should not keep you from watching the lecture. The sound issue at the beginning of the talk is resolved after 40 seconds.

One important take-away from this talk, if you choose not to watch it: “to date, there is no known efficient algorithm to find Nash equilibrium in games”. In general this paper – coauthored by the lecturer – seems from a brief skim to cover many of the topics also included in the lecture. I have added some other links to articles and topics covered/mentioned in the lecture below.

Nash’s Existence Theorem.
Reducibility Among Equilibrium Problems (Goldberg & Papadimitriou).
Three-Player Games Are Hard (Daskalakis & Papadimitriou).
3-Nash is PPAD-Complete (Chen & Deng).
PPAD (complexity).
On the (Im)possibility of Obfuscating Programs (Barak et al.).
On the Impossibility of Obfuscation with Auxiliary Input (Goldwasser & Kalai).
On Best-Possible Obfuscation (Goldwasser & Rothblum).
Functional Encryption without Obfuscation (Garg et al.).
On the Complexity of the Parity Argument and Other Inefficient Proofs of Existence (Papadimitriou).
Pseudorandom function family.
Revisiting the Cryptographic Hardness of Finding a Nash Equilibrium (Garg, Pandei & Srinivasan).
Constrained Pseudorandom Functions and Their Applications (Boneh & Waters).
Delegatable Pseudorandom Functions and Applications (Kiayias et al.).
Functional Signatures and Pseudorandom Functions (Boyle, Goldwasser & Ivan).
Universal Constructions and Robust Combiners for Indistinguishability Obfuscation and Witness Encryption (Ananth et al.).

April 18, 2018 Posted by | Computer science, Cryptography, Game theory, Lectures, Mathematics, Papers | Leave a comment

The Internet of Things


Some links to stuff he talks about in the lecture:

The Internet of Things: making the most of the Second Digital Revolution – A report by the UK Government Chief Scientific Adviser.
South–North Water Transfer Project.
FDA approves first smart pill that tracks drug regimen compliance from the inside.
The Internet of Things (IoT)* units installed base by category from 2014 to 2020.
Share of the IoT market by sub-sector worldwide in 2017.
San Diego to Cover Half the City with Intelligent Streetlights.
IPv4 and IPv6 (specifically, he talks a little about the IPv4 address space problem).
General Data Protection Regulation (GDPR).
Shodan (website).
Mirai botnet.
Gait analysis.
Website reveals 73,000 unprotected security cameras with default passwords. (This was just an example link – it’s unclear if the site he used to illustrate his point in that part of the lecture was actually Insecam, but he does talk about the widespread use of default passwords and related security implications during the lecture).
Strava’s fitness heatmaps are a ‘potential catastrophe’.
‘Secure by Design’ (a very recently published proposed UK IoT code of practice).

March 26, 2018 Posted by | Computer science, Engineering, Lectures | Leave a comment

Safety-Critical Systems

Some related links to topics covered in the lecture:

Safety-critical system.
Safety engineering.
Fault tree analysis.
Failure mode and effects analysis.
Value of a statistical life.
ALARP principle.
Hazards and Risk (HSA).
Software system safety.
Aleatoric and epistemic uncertainty.
N-version programming.
An experimental evaluation of the assumption of independence in multiversion programming (Knight & Leveson).
Safety integrity level.
Software for Dependable Systems – Sufficient Evidence? (consensus study report).

March 15, 2018 Posted by | Computer science, Economics, Engineering, Lectures, Statistics | Leave a comment

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

Analgesia and Procedural Sedation

I didn’t actually like this lecture all that much, in part because I obviously disagree to some extent with the ideas expressed, but I try to remember to blog lectures I watch these days even if I don’t think they’re all that great. It’s a short lecture, but why not at least add a comment about urine drug screening and monitoring or patient selection/segmentation when you’re talking about patients whom you’re considering discharging with an opioid prescription? Recommending acupuncture in a pain management context? Etc.

Anyway, below a few links to stuff related to the coverage:

Pain Management in the Emergency Department.
WHO analgesic ladder.
Nonsteroidal anti-inflammatory drug.
Fentanyl (“This medication should not be used to treat pain other than chronic cancer pain, especially short-term pain such as migraines or other headaches, pain from an injury, or pain after a medical or dental procedure.” …to put it mildly, that’s not the impression you get from watching this lecture…)
Parenteral opioids in emergency medicine – A systematic review of efficacy and safety.
Procedural Sedation (medscape).

December 22, 2017 Posted by | Lectures, Medicine, Pharmacology | Leave a comment

Concussion and Sequelae of Minor Head Trauma

Some related links:

PECARN Pediatric Head Injury/Trauma Algorithm.
Canadian CT Head Injury/Trauma Rule.
ACEP – Traumatic Brain Injury (Mild – Adult).
AANS – concussion.
Guidelines for the Management of Severe Traumatic Brain Injury – 4th edition.
Return-to-play guidelines.
Second-impact syndrome.
Repetitive Head Injury Syndrome (medscape).
Traumatic Brain Injury & Concussion (CDC).

December 1, 2017 Posted by | Lectures, Medicine, Neurology | Leave a comment

Acute Coronary Syndromes

A few quotes from the lecture, as well as some links to related stuff:

“You might say: Why doesn’t coronary stenting prevent heart attacks? You got an 80 % blockage causing some angina and you stent it, why doesn’t that prevent a heart attack? And the answer is very curious. The plaques that are most likely to rupture are mild. They’re typically less than 50 %. They have a thin fibrous cap, a lot of lipid, and they rupture during stress. This has been the real confusion for my specialty over the last 30 years, starting to realize that, you know, when you get angina we find the blockage and we fix it and your angina’s better, but the lesions that were gonna cause next week’s heart attack often are not the lesion we fixed, but there’s 25 other moderate plaques in the coronary tree and one of them is heating up and it’s vulnerable. […] ACS, the whole thing here is the idea of a vulnerable plaque rupture. And it’s often not a severe narrowing.” (3-5 minutes in)

[One of the plaque rupture triggers of relevance is inflammatory cytokines…] “What’s a good example of that? Influenza. Right, influenza releases things like, IL-6 and other cytokines. What do they do? Well, they make you shake and shiver and feel like your muscles are dying. They also dissolve plaques. […] If you take a town like Ann Arbor and vaccinate everybody for influenza, we reduce heart attacks by a lot … 20-30 % during flu season.” (~11-12 minutes in)

“What happens to your systolic function as you get older? Any ideas? I’m happy to tell you it stays strong. […] What happens to diastole? […] As your myocardial cells die, a few die every day, […] those cells get replaced by fibrous tissue. So an aging heart becomes gradually stiffer [this is apparently termed ‘presbycardia’]. It beats well because the cells that are alive can overcome the fibrosis and squeeze, but it doesn’t relax as well. So left ventricular and diastolic pressure goes up. Older patients are much more likely to develop heart failure [in the ACS setting] because they already have impaired diastole from […] presbycardia.” (~1.14-1.15)

Some links to coverage of topics covered during the lecture:

Acute Coronary Syndrome.
Unstable angina.
Pathology of Acute Myocardial Infarction.
Acute Coronary Syndrome Workup.
Acute Coronary Syndrome Treatment & Management.
The GRACE risk score.
Complications of Myocardial Infarction.
Early versus Delayed Invasive Intervention in Acute Coronary Syndromes (Mehta et al. 2009).

November 3, 2017 Posted by | Cardiology, Lectures, Medicine, Studies | Leave a comment

The mystery of over-parametrization in neural networks


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

National EM Board Review Course: Toxicology

Some links:

Alcoholic Ketoacidosis.
Gastrointestinal decontamination in the acutely poisoned patient.
Chelation in Metal Intoxication.
Mudpiles – causes of high anion-gap metabolic acidosis.
Whole-bowel irrigation: Background, indications, contraindications…
Organophosphate toxicity.
Withdrawal syndromes.
Acetaminophen toxicity.
Alcohol withdrawal.
Wernicke syndrome.
Methanol toxicity.
Ethylene glycol toxicity.
Sympathomimetic toxicity.
Disulfiram toxicity.
Arsenic toxicity.
Barbiturate toxicity.
Beta-blocker toxicity.
Calcium channel blocker toxicity.
Carbon monoxide toxicity.
Caustic ingestions.
Clonidine toxicity.
Cyanide toxicity.
Digitalis toxicity.
Gamma-hydroxybutyrate toxicity.
Hydrocarbon toxicity.
CDC Facts About Hydrogen Fluoride (Hydrofluoric Acid).
Hydrogen Sulfide Toxicity.
Isoniazid toxicity.
Iron toxicity.
Lead toxicity.
Lithium toxicity.
Mercury toxicity.
Mushroom toxicity.
Gyromitra mushroom toxicity.
Neuroleptic agent toxicity.
Neuroleptic malignant syndrome.
Oral hypoglycemic agent toxicity.
PCP toxicity.
Phenytoin toxicity.
Rodenticide toxicity.
Salicylate toxicity.
Serotonin syndrome.
TCA toxicity.

September 29, 2017 Posted by | Lectures, Medicine, Pharmacology, Psychiatry | Leave a comment

National EM Board Review Course: Environmental Emergencies

Some links to resources on stuff covered in the lecture:

Diving disorders.
Henry’s law/Boyle’s law/Dalton’s law.
Nitrogen narcosis.
Decompression Sickness.
Hyperbaric Oxygen Therapy.
Blast Injuries.
Altitude sickness.
High Altitude Flatus Expulsion (HAFE).
High-Altitude Pulmonary Edema.
Cold-induced vasodilation.
Osborn Waves.
Frostbite (‘think of this as a thermal burn equivalent caused by cold’).
Trench foot.
Heat stroke.
Heat cramps.
Thermal Burns.
Parkland formula.
Escharotomy and Burns.
Electrical Injuries in Emergency Medicine.
Lightning Injuries.
Radiation exposure.
Inhalation Anthrax.
Botulism As a Bioterrorism Agent.
Chemical weapon/vessicants/nerve agent.
Bite injuries.
Cat scratch disease.
Rattlesnake Bite.
Snakebites: First aid.
Snake bite: coral snakes.
Black widow spider bite.
Brown recluse spider bite.
Marine envenomation.

September 22, 2017 Posted by | Lectures, Medicine | Leave a comment

Ophthalmology – National EM Board Review Course

The lecture covers a lot of different stuff. Some links:

Orbital Cellulitis.
Cranial Nerves III, IV, and VI: The Oculomotor System.
Argyll Robertson pupil.
Marcus Gunn pupil.
Horner syndrome.
Third nerve palsy.
Homonymous hemianopsia.
Central Retinal Artery Occlusion.
Central Retinal Vein Occlusion.
Optic Neuritis.
Retinal detachment.
Temporal Arteritis.
Epidemic Keratoconjunctivitis (EKC).
Herpes Zoster Ophthalmicus.
Subconjunctival Hemorrhage.
Corneal Abrasion.
Corneal Laceration.
Globe Rupture.
Acute Angle-Closure Glaucoma.
Retrobulbar hemorrhage.

September 15, 2017 Posted by | Lectures, Medicine, Ophthalmology, Pharmacology | Leave a comment

Gastroenterology – Amal Mattu

If I hadn’t just read Horowitz & Samsom’s book I’m fairly sure this lecture would have been difficult to follow, but a lot of the stuff covered here is (naturally) closely related to the stuff covered in that book; this is mostly a revision lecture aimed at reminding you of stuff you already (supposedly?) know and/or dealing with topics closely related to stuff you already know, I don’t think it’s the right lecture for someone who knows very little about gastroenterology. I like Mattu’s approach to lecturing; this lecture was both fun and enjoyable to watch, despite (?) including a lot of information.

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

Boerhaave syndrome.
Does This Patient Have a Severe Upper Gastrointestinal Bleed? (JAMA).
Acute Liver Failure (NEJM review article).
Charcot’s cholangitis triad.
Ranson criteria.
Crohn’s disease.
Ulcerative colitis.
Abdominal aortic aneurysm.
Mesenteric ischemia.
Shigella infection.
Clostridium perfringens.
Pseudomembranous colitis.

September 11, 2017 Posted by | Gastroenterology, Lectures, Medicine, Microbiology | 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

Utility of Research Autopsies for Understanding the Dynamics of Cancer

A few links:
Pancreatic cancer.
Jaccard index.
Limited heterogeneity of known driver gene mutations among the metastases of individual patients with pancreatic cancer.
Tissue-specific mutation accumulation in human adult stem cells during life.
Epigenomic reprogramming during pancreatic cancer progression links anabolic glucose metabolism to distant metastasis.

August 25, 2017 Posted by | Cancer/oncology, Genetics, Immunology, Lectures, Medicine, Molecular biology, Statistics | Leave a comment