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Posts

April 26, 2015

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6:28 PM | Three models of chemical computing
+Lucius Meredith  pointed to stochastic pi-calculus ans SPiM  in a discussion about chemlambda. I take this as reference http://research.microsoft.com/en-us/projects/spim/ssb.pdf (say pages 8-13 to have a anchor for the discussion). Analysis: SPiM side – The nodes of the graphs are molecules, the arrows are channels. – As described there the procedure is to take a (huge … Continue reading Three models of chemical computing →
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2:54 PM | Improve chemical computing complexity by a 1000 times factor, easily
That is, if autonomous computing molecules are possible, as described in the model shown in the Molecular computers. To be exactly sure about about the factor, I need to know the answer for the following question: What is the most complex chemical computation done without external intervention, from the moment when the (solution, DNA molecule, … Continue reading Improve chemical computing complexity by a 1000 times factor, easily →
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1:07 PM | Condolences
My thoughts are with the family and friends of my neighbor, friend and an incredibly thoughtful soul Dan who fell pursuing Mr. Everest, a victim of the quake. 
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4:36 AM | Compact objects
If is a noncommutative ring, then Morita theory tells us that cannot in general be recovered from its category of modules; that is, there can be a ring , not isomorphic to , such that . This means, for example, that “free” is not a categorical property of modules, since it depends on a choice […]

April 25, 2015

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12:06 AM | Streaming H
Items  I_i s (+ve integers,  I_i \in [1,U]) arrive one after another, and for any n, after having seen n items, you have to return an approximation to H_n which is the H-index of the first n items. I_1,...,I_n  (The H-index of a set of number is largest k such that there are at least k items each >= k). A student in Rutgers posed this problem.This problem has a simple worstcase solution: sing log_{1+\eps} U space, get  (1+\eps) one-sided error approximation by maintaining […]
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12:00 AM | Peirce’s 1880 “Algebra Of Logic” Chapter 3 • Comment 7.4
Dyadic relations enjoy yet another form of graph-theoretic representation as labeled bipartite graphs or labeled bigraphs.  I’ll just call them bigraphs here, letting the labels be understood in this logical context. The figure below shows the bigraphs of the 16 … Continue reading →

April 24, 2015

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8:39 PM | EC & Sigmetrics accepted papers are out
I’m a little late in posting about this, but at this point the schedule for Sigmetrics is up, as is the list of accepted papers at EC.  So, it’s a good point to take a look at each to compare. First of all, congrats to all the folks in RSRG with paper(s)…we managed to get […]
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8:28 PM | When is Cheryl’s Birthday?
Birthdays are a fun tradition that you get to celebrate with your friends and family once a year…that is, if you tell them when your birthday is.  In a logic puzzle that has been making the rounds on the Internet, … Continue reading →
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7:00 PM | CFP: Fifth Workshop on Social Computing and User-Generated Content
SCUGC 2015: The 5th Workshop on Social Computing and User-Generated Content https://sites.google.com/site/scugc2015/ June 16, 2015, Portland, Oregon. in conjunction with ACM Conference on Economics and Computation (ACM-EC 2015). SUBMISSIONS DUE: April 25, 2015 midnight EDT. The  workshop will bring together researchers and practitioners from a variety of relevant fields, including economics, computer science, and social […]
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3:56 PM | “Statistical Concepts in Their Relation to Reality” by E.S. Pearson
To complete the last post, here’s Pearson’s portion of the “triad”  “Statistical Concepts in Their Relation to Reality” by E.S. PEARSON (1955) SUMMARY: This paper contains a reply to some criticisms made by Sir Ronald Fisher in his recent article on “Scientific Methods and Scientific Induction”. Controversies in the field of mathematical statistics seem largely […]
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3:50 PM | A second opinion on “Slay peer review” article
“It is no good just finding particular instances where peer review has failed because I can point you to specific instances where peer review has been very successful,” she said. She feared that abandoning peer review would make scientific literature no more reliable than the blogosphere, consisting of an unnavigable mass of articles, most of … Continue reading A second opinion on “Slay peer review” article →
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1:43 PM | Chenevier on the Eigencurve
Today I wanted to mention a theorem of Chenever about components of the Eigencurve. Let denote weight space (which is basically a union of discs), and let be the Coleman-Mazur eigencurve together with its natural map to It will do … Continue reading →
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1:00 PM | Bouncing a quantum particle back and forth
If you have not seen my previous two posts, you should read them first. Shooting a classical particle …and scattering a quantum particle In the two previous posts, I shot particles (okay, simulated the shooting on a computer) at a single potential barrier and looked at what happens. What happens when we have more than […]
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12:26 PM | … and scattering a quantum particle
In the previous post we shot a classical particle at a potential barrier. In this post we shoot a quantum particle. Whereas the behaviour of the classical particle is governed by Newton’s laws (where the external force providing the acceleration is given as minus the gradient of the potential), we allow our quantum particle to […]
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11:20 AM | Fifty Years of Moore's Law
Gordon Moore formulated his famous law in a paper dated fifty years and five days ago. We all have seen how Moore's law has changed real-world computing, but how does it relate to computational complexity? In complexity we typically focus on running times but we really care about how large a problem we can solve in current technology. In one of my early posts I showed how this view can change how we judge running time improvements from faster algorithms. Improved technology also […]
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9:19 AM | Shooting a classical particle…
Here’s a small animation of what happens when you try to shoot a classical particle when there’s a potential barrier. For small initial kinetic energies, the particle bounces back. For large initial kinetic energies, the particle goes over the hump, first decelerating and then accelerating in the process. (It may be best to watch this […]

April 23, 2015

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7:26 PM | 311 – HW 8
HW 8 is due Tuesday, April 28, at the beginning of lecture. Work in hyperbolic geometry. Given a triangle , recall that its Saccheri quadrilateral based at is defined as follows: Let be the midpoint of and be the midpoint of . Let be the feet of the perpendiculars from and to  respectively. Continuing with […]
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7:11 PM | Categories in Control
To understand ecosystems, ultimately will be to understand networks. – B. C. Patten and M. Witkamp A while back I decided one way to apply my math skills to help save the planet was to start pushing toward green mathematics: a kind of mathematics that can interact with biology and ecology just as fruitfully as […]
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5:57 PM | Jamesian epistemology formalised: an explication of 'The Will to Believe'
Famously, William James held that there are two commandments that govern our epistemic life.There are two ways of looking at our duty in the matter of opinion, --- ways entirely different, and yet ways about whose difference the theory of knowledge seems hitherto to have shown very little concern. We must know the truth; and we must avoid error, --- these are our first and great commandments as would be knowers; but they are not two ways of stating an identical commandment [...] Believe truth! […]
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5:46 PM | A comparison of two models of computation: chemlambda and Turing machines
The purpose is to understand clearly what is this story about. The most simple stuff, OK? in order to feel it in familiar situations. Proceed. Chemlambda is a collection of rules about rewritings done on pieces of files in a certain format. Without an algorithm which tells which rewrite to use, where and when,  chemlambda … Continue reading A comparison of two models of computation: chemlambda and Turing machines →
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5:30 PM | Peirce’s 1880 “Algebra Of Logic” Chapter 3 • Comment 7.3
Dyadic relations have graph-theoretic representations as directed graphs with loops, also known as pseudo-digraphs in some schools of graph theory.  I’ll just call them digraphs here, letting their loopiness be taken for granted in this logical context. The figure below … Continue reading →
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3:27 PM | Il colombre
E' il pesce che i marinai sopra tutti temono, in ogni mare del mondo. E' uno squalo tremendo e misterioso, più astuto dell'uomo. Per motivi che forse nessuno saprà mai, sceglie la sua vittima, e quando l'ha scelta la insegue per anni e anni, per una intera vita, finché è riuscito a divorarla. E lo strano è questo: che nessuno riesce a scorgerlo se non la vittima e le persone del suo stesso sangue.Io non l'avevo mai visto. Ma dalle descrizioni che ho sentito fare tante volte, l'ho subito […]

April 22, 2015

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11:16 PM | Thinking big at Yahoo
I’m speaking in the “Yahoo Labs Big Thinkers” series on Friday 26 June. I hope I can live up to the title! My talk is on “Exploring the boundaries of predictability: what can we forecast, and when should we give up?”  Essentially I will start with some of the ideas in this post, and then discuss some of […]
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10:04 PM | Thoughts on ToME’s Adventure Mode
I’ve done several posts explaining why I think roguelikes are a great genre of game to play. It is probable that the most important feature of a roguelike for me is permadeath. For example, see this post for reasons why. … Continue reading →
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4:07 PM | MathReviews
I will be taking a leave from BSU this coming academic year, and moving to Ann Arbor, to work as an Associate Editor at MathReviews.
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2:42 PM | Il genio di Leander Starr
Cos'è il Genio? Una possibile definizione è: colui che riesce a scoprire un modo semplice per risolvere problemi complessi(1). In questo senso non tutti i Premi Nobel scientifici possono essere considerati dei geni, ma la definizione calza a pennello praticamente con tutti loro, esclusi quelli letterari e politici. D'altra parte questa definizione è più difficile da applicare al mondo dell'arte, dove, a mio giudizio, l'attributo di genio è decisamente abusato. E' però possibile che alcuni […]
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1:47 PM | The New Oracle Result! The new circuit result! which do you care about?
You have likely heard of the new result by Ben Roco, and Li-Yang on random oracles (see here for preprint) from either Lance or Scott or some other source: Lance's headline was PH infinite under random oracle Scott's headline was Two papers but when he stated the result he also stated it as a random oracle result. The paper itself has the title An average case depth hierarchy theorem for Boolean circuits and the abstract is: We prove an average-case depth hierarchy theorem for Boolean […]
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1:40 PM | Groups and Group Actions: Lecture 8.5
In which we wonder what a non-integer lecture is anyway. OK, of course there isn’t a lecture 8.5.  But I promised that I’d post with questions for you to consider before lecture 9, so here is that post. Preparation for Lecture 9 Lagrange’s theorem says that the order of a subgroup divides the order of […]
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7:23 AM | Travelling Thilaksha
One of my PhD students, Thilaksha Tharanganie, has been very successful in getting travel funding to attend conferences. She was the subject of a write-up in today’s Monash News. We encourage students to attend conferences, and provide funding for them to attend one international conference and one local conference during their PhD candidature. Thilaksha was […]
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4:12 AM | NEYMAN: “Note on an Article by Sir Ronald Fisher” (3 uses for power, Fisher’s fiducial argument)
Note on an Article by Sir Ronald Fisher By Jerzy Neyman (1956) Summary (1) FISHER’S allegation that, contrary to some passages in the introduction and on the cover of the book by Wald, this book does not really deal with experimental design is unfounded. In actual fact, the book is permeated with problems of experimentation.  […]
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