Blog Profile / Reasonable Deviations
| URL : | http://stochastix.wordpress.com/ | |
|---|---|---|
| Filed Under: | Academics / Mathematics | |
| Posts on Regator: | 165 | |
| Posts / Week: | 0.7 | |
| Archived Since: | December 12, 2008 | |
Blog Post Archive
Interview with László Lovász
On November 28, 2011, Avi Wigderson interviewed László Lovász. A total of 27 short videos can be watched at the Simons Foundation website. I particularly liked the discussion on the LLL algorithm, and also on semidefinite relaxations. Show More Summary
Der Wanderer über dem Nebelmeer
I love Der Wanderer über dem Nebelmeer (1818), by Caspar David Friedrich (1774-1840): [ source ] Filed under: Art Tagged: Art, Caspar David Friedrich
Sipser on P versus NP
On October 3, 2006 Michael Sipser was at Harvard to give the following lecture on the P versus NP problem: This talk is arguably the very best introduction to Computational Complexity I have ever come across. I highly recommend it. Filed under: Computational Complexity, Computer Science Tagged: Computational Complexity, Michael Sipser, P versus NP, Talks
Compressive Sensing for DoD Sensor Systems
JASON has just released a report on Compressive Sensing: Compressive Sensing for DoD Sensor Systems [pdf] The emphasis is on radar systems. Hat tip to Steven Aftergood. Filed under: Military Technology, Signal Processing, Technology Tagged: Compressed Sensing, Compressive Sampling, Compressive Sensing, JASON, Military Technology
Luttwak on Kissinger
Edward Luttwak on Henry Kissinger: Kissinger at 88 is writing brochures for Kissinger Associates. His last book on China is one such work written by the staff at Kissinger Associates. It is designed to curry favor with the Chinese authorities and nothing else. I know him personally very well, but he is such a deceptive [...]
Function composition via folding
Let us suppose that we are given a list of functions. We would like to compose the functions in this list (if they are composable, of course) in the order in which they are arranged in the list, i.e., we would like to create a higher-order function compose such that Here is one of many [...]
Composing an endofunction with itself
Suppose we are given an endofunction. Let us introduce a new function, where, which we define recursively as follows where is the identity function on, i.e., for all. In Haskell, it is easy to create a higher-order function compose that composes an endofunction with itself times: compose :: (a -> a) [...]
Zawinski on venture capitalists
Approximately one year ago, über-hacker Jamie Zawinski wrote the following on venture capitalists: Normally I just ignore navel-gazing tech-industry articles like this, but people keep sending it to me, so I guess this guy is famous or something. Michael Arrington posted this article, “Startups Are Hard. So Work More, Cry Less, And Quit All The [...]
Generalizing Heron’s method
Suppose we are given a positive rational number. We would like to compute an approximation of the -th root of, which we denote by. If, we can use Heron’s method to approximate, as we saw a few days ago. But, what if we have that ? Is it possible to [...]
Heron’s method using integer arithmetic
Suppose we are given a positive rational number, whose square root we would like to compute. To be more precise, we would like to compute an approximation of. Let be an approximation of. Hence, we have that is the geometric mean of and. If we replace the geometric mean of these [...]
Conservatives and Progressives
G. K. Chesterton on conservatives and progressives: The whole modern world has divided itself into Conservatives and Progressives. The business of Progressives is to go on making mistakes. The business of the Conservatives is to prevent the mistakes being corrected. Even when the revolutionist might himself repent of his revolution, the traditionalist is already defending it [...]
Freeman Dyson on Wittgenstein
[ source ] Freeman Dyson on Ludwig Wittgenstein: Wittgenstein, unlike Heidegger, did not establish an ism. He wrote very little, and everything that he wrote was simple and clear. The only book that he published during his lifetime was Tractatus Logico-Philosophicus, written in Vienna in 1918 and published in England with a long introduction by [...]
Deterministic Finite Automata in Haskell
Consider the deterministic finite automaton [1] illustrated below [ state diagram courtesy of Michael Sipser [1] ] Henceforth, we will call this automaton. Note that has three states, labeled,, and. The start state is (note the arrow coming from nowhere) and the accept state is (note the double circle). There are [...]
Generating all words over an alphabet
An alphabet is a finite set of symbols. A word (or string) over an alphabet is a sequence of symbols. Alternatively, we can view a word over as a tuple (i.e., an ordered list) over . The set of all finite words over, including the empty word, is denoted by, where is [...]
Gell-Mann on learning
Murray Gell-Mann on why being in awe inhibits learning: I said I’d rather be poor or die than be an engineer because I would be no good at it. If I designed something it would fall down. When I was admitted to Yale, I took an aptitude test, and when the counselor gave me the [...]
My implementation of (!!)
In Haskell we can easily create a list and then access its elements using the (!!) function, which is defined in the Prelude. Here is a very brief GHCi session: Prelude> let xs = [7,8,9] Prelude> xs !! 0 7 Prelude> xs !! 1 8 Prelude> xs !! 2 9 So far, so good. What [...]
Combinatorial Explosion
An amusing Japanese cartoon on combinatorial explosion: Tastefully done, I would say. The target audience consists not of this blog’s readers, but rather of their children. Hat tip: Michael Lugo Filed under: Art, Combinatorics, Computer Science, Fun Tagged: Combinatorial Explosion, Kindergarten Mathematics, Questions kids ask
A measure-theoretic definition of synergy?
Alice and Bob are fruit-pickers at an orange orchard. Alice can pick 6 baskets of oranges in one hour. In contrast, Bob can pick 7 baskets of oranges in the same period of time. However, if Alice and Bob work together, then they can pick a total of 15 baskets in one hour. As part [...]
Born under the second law of thermodynamics
[ source ] Neil Armstrong once portrayed himself as follows [1, 2]: I am, and ever will be, a white-socks, pocket-protector, nerdy engineer—born under the second law of thermodynamics, steeped in the steam tables, in love with free-body diagrams, transformed by Laplace, and propelled by compressible flow. As an engineer, I take a substantial amount [...]
From classical deduction to Bayesian probability
Terence Tao on classical deduction and Bayesian probability: In classical logic, one can represent one’s information about a system as a set of possible states that the system could be in, based on the information at hand. With each new measurement of the system, some possibilities could be eliminated, leading to an updated posterior set [...]