These are my recent Pinboard.in links:
[1203.1644] The B36/S125 “2×2″ Life-Like Cellular Automaton
“The B36/S125 (or “2x2”) cellular automaton is one that takes place on a 2D square lattice much like Conway’s Game of Life. Although it exhibits high-level behaviour that is similar to Life, such as chaotic but eventually stable evolution and the existence of a natural diagonal glider, the individual objects that the rule contains generally look very different from their Life counterparts. In this article, a history of notable discoveries in the 2×2 rule is provided, and the fundamental patterns of the automaton are described. Some theoretical results are derived along the way, including a proof that the speed limits for diagonal and orthogonal spaceships in this rule are c/3 and c/2, respectively. A Margolus block cellular automaton that 2×2 emulates is investigated, and in particular a family of oscillators made up entirely of 2 x 2 blocks are analyzed and used to show that there exist oscillators with period 2m(2k — 1) for any integers m,k geq 1.”
cellular-automata artificial-life discrete-mathematics emergence mathematical-recreations nudge-targets- “We present a new algorithm to solve polynomial equations, and publish its code, which is 1.6−3 times faster than the ZROOTS subroutine that is commercially available from Numerical Recipes, depending on application. The largest improvement, when compared to naive solvers, comes from a fail-safe procedure that permits us to skip the majority of the calculations in the great majority of cases, without risking catastrophic failure in the few cases that these are actually required. Second, we identify a discriminant that enables a rational choice between Laguerre’s Method and Newton’s Method (or a new intermediate method) on a case-by-case basis. We briefly review the history of root solving and demonstrate that “Newton’s Method” was discovered neither by Newton (1671) nor by Raphson (1690), but only by Simpson (1740). Some of the arguments leading to this conclusion were first given by the British historian of science Nick Kollerstrom in 1992, but these do not appear to have penetrated the astronomical community. Finally, we argue that Numerical Recipes should voluntarily surrender its copyright protection for non-profit applications, despite the fact that, in this particular case, such protection was the major stimulant for developing our improved algorithm.”
algorithms numerical-methods optics nudge-targets [1203.1065] Subspace clustering of high-dimensional data: a predictive approach
“In several application domains, high-dimensional observations are collected and then analysed in search for naturally occurring data clusters which might provide further insights about the nature of the problem. In this paper we describe a new approach for partitioning such high-dimensional data. Our assumption is that, within each cluster, the data can be approximated well by a linear subspace estimated by means of a principal component analysis (PCA). The proposed algorithm, Predictive Subspace Clustering (PSC) partitions the data into clusters while simultaneously estimating cluster-wise PCA parameters. The algorithm minimises an objective function that depends upon a new measure of influence for PCA models. A penalised version of the algorithm is also described for carrying our simultaneous subspace clustering and variable selection. The convergence of PSC is discussed in detail, and extensive simulation results and comparisons to competing methods are presented. The comparative performance of PSC has been assessed on six real gene expression data sets for which PSC often provides state-of-art results.”
ain’t-performance-space statistics clustering cure-for-dimensionality algorithms[1203.1067] Cortical free association dynamics: distinct phases of a latching network
“… The occurrence and duration of latching dynamics is found through simulations to depend critically on the strength of local attractor states, expressed in the Potts model by a parameter w. Here we describe with simulations and then analytically the boundaries between distinct phases of no latching, of transient and sustained latching, deriving a phase diagram in the plane w-T, where T parametrizes thermal noise effects. Implications for real cortical dynamics are briefly reviewed in the conclusions.”
neural-networks biologically-inspired dynamical-systems emergent-design nudge-targets- “One of the more surprising things I’ve noticed while working on Y Combinator is how frightening the most ambitious startup ideas are. In this essay I’m going to demonstrate this phenomenon by describing some. Any one of them could make you a billionaire. That might sound like an attractive prospect, and yet when I describe these ideas you may notice you find yourself shrinking away from them.”
every-idea-is-born startups innovation [1201.6054] Attainability in Repeated Games with Vector Payoffs
“We introduce the concept of attainable sets of payoffs in two-player repeated games with vector payoffs. A set of payoff vectors is called {em attainable} if player 1 can ensure that there is a finite horizon $T$ such that after time $T$ the distance between the set and the cumulative payoff is arbitrarily small, regardless of what strategy player 2 is using. This paper focuses on the case where the attainable set consists of one payoff vector. In this case the vector is called an attainable vector. We study properties of the set of attainable vectors, and characterize when a specific vector is attainable and when every vector is attainable.”
game-theory agent-based multiobjective-optimization nudge-targets[1203.1080] Data Structure Lower Bounds on Random Access to Grammar-Compressed Strings
“In this paper we investigate the problem of building a static data structure that represents a string s using space close to its compressed size, and allows fast access to individual characters of s. …”
grammars algorithms nudge-targets