Evolutionary consequences of behavioral diversity

Iterated games provide a framework to describe social interactions among groups of individuals. Recent work stimulated by the discovery of "zero-determinant" strategies has rapidly expanded our ability to analyze such interactions. This body of work has primarily focused on games in which players face a simple binary choice, to "cooperate" or "defect". Real individuals, however, often exhibit behavioral diversity, varying their input to a social interaction both qualitatively and quantitatively. Here we explore how access to a greater diversity of behavioral choices impacts the evolution of social dynamics in finite populations. We show that, in public goods games, some two-choice strategies can nonetheless resist invasion by all possible multi-choice invaders, even while engaging in relatively little punishment. We also show that access to greater behavioral choice results in more "rugged " fitness landscapes, with populations able to stabilize cooperation at multiple levels of investment, such that choice facilitates cooperation when returns on investments are low, but hinders cooperation when returns on investments are high. Finally, we analyze iterated rock-paper-scissors games, whose non-transitive payoff structure means unilateral control is difficult and zero-determinant strategies do not exist in general. Despite this, we find that a large portion of multi-choice strategies can invade and resist invasion by strategies that lack behavioral diversity -- so that even well-mixed populations will tend to evolve behavioral diversity.Comment: 26 pages, 4 figure

Cx43 and mechanotransduction in bone

Bone adaptation to changes in mechanical stimuli occurs by adjusting bone formation and resorption by osteoblasts and osteoclasts, to maintain optimal bone mass. Osteocytes coordinate the actions of these cells on the bone surface by sensing mechanical forces and producing cytokines that increase or prevent osteoblast and osteoclast differentiation and function. Channels formed by connexins (Cxs) and, in particular, connexin 43 (Cx43) in osteoblasts and osteocytes are central part of this mechanism to control bone mass. Cx43 hemichannels are opened by fluid flow and mediate the anti-apoptotic effect of mechanical stimulation in vitro, suggesting that Cx43 participates in mechanotransduction. However, mice lacking Cx43 in osteoblasts and/or osteocytes show an increased anabolic response to loading and decreased catabolic response to unloading. This evidence suggests that Cx43 channels expressed in osteoblastic cells are not required for the response to mechanical stimulation, but mediate the consequence of lack thereof. The molecular basis of these unexpected responses to mechanical stimulation is currently under investigation

On the Number of Iterations for Dantzig-Wolfe Optimization and Packing-Covering Approximation Algorithms

We give a lower bound on the iteration complexity of a natural class of Lagrangean-relaxation algorithms for approximately solving packing/covering linear programs. We show that, given an input with $m$ random 0/1-constraints on $n$ variables, with high probability, any such algorithm requires $\Omega(\rho \log(m)/\epsilon^2)$ iterations to compute a $(1+\epsilon)$-approximate solution, where $\rho$ is the width of the input. The bound is tight for a range of the parameters $(m,n,\rho,\epsilon)$. The algorithms in the class include Dantzig-Wolfe decomposition, Benders' decomposition, Lagrangean relaxation as developed by Held and Karp [1971] for lower-bounding TSP, and many others (e.g. by Plotkin, Shmoys, and Tardos [1988] and Grigoriadis and Khachiyan [1996]). To prove the bound, we use a discrepancy argument to show an analogous lower bound on the support size of $(1+\epsilon)$-approximate mixed strategies for random two-player zero-sum 0/1-matrix games

Magnet Laboratory Research

Contains reports on three research projects

Magnet Laboratory Research

Contains reports on three research projects

Proof Relevant Corecursive Resolution

Resolution lies at the foundation of both logic programming and type class context reduction in functional languages. Terminating derivations by resolution have well-defined inductive meaning, whereas some non-terminating derivations can be understood coinductively. Cycle detection is a popular method to capture a small subset of such derivations. We show that in fact cycle detection is a restricted form of coinductive proof, in which the atomic formula forming the cycle plays the role of coinductive hypothesis. This paper introduces a heuristic method for obtaining richer coinductive hypotheses in the form of Horn formulas. Our approach subsumes cycle detection and gives coinductive meaning to a larger class of derivations. For this purpose we extend resolution with Horn formula resolvents and corecursive evidence generation. We illustrate our method on non-terminating type class resolution problems.Comment: 23 pages, with appendices in FLOPS 201

A joint Chandra and Swift view of the 2015 X-Ray dust-scattering echo of V404 Cygni

We present a combined analysis of the Chandra and Swift observations of the 2015 X-ray echo of V404 Cygni. Using a stacking analysis, we identify eight separate rings in the echo. We reconstruct the soft X-ray light curve of the 2015 June outburst using the high-resolution Chandra images and cross-correlations of the radial intensity profiles, indicating that about 70% of the outburst fluence occurred during the bright flare at the end of the outburst on MJD 57199.8. By deconvolving the intensity profiles with the reconstructed outburst light curve, we show that the rings correspond to eight separate dust concentrations with precise distance determinations. We further show that the column density of the clouds varies significantly across the field of view, with the centroid of most of the clouds shifted toward the Galactic plane, relative to the position of V404 Cyg, invalidating the assumption of uniform cloud column typically made in attempts to constrain dust properties from light echoes. We present a new XSPEC spectral dust-scattering model that calculates the differential dust-scattering cross section for a range of commonly used dust distributions and compositions and use it to jointly fit the entire set of Swift echo data. We find that a standard Mathis-Rumpl-Nordsieck model provides an adequate fit to the ensemble of echo data. The fit is improved by allowing steeper dust distributions, and models with simple silicate and graphite grains are preferred over models with more complex composition. © 2016. The American Astronomical Society. All rights reserved

Mutant huntingtin enhances activation of dendritic Kv4 K+ channels in striatal spiny projection neurons

Huntington\u27s disease (HD) is initially characterized by an inability to suppress unwanted movements, a deficit attributable to impaired synaptic activation of striatal indirect pathway spiny projection neurons (iSPNs). To better understand the mechanisms underlying this deficit, striatal neurons in ex vivo brain slices from mouse genetic models of HD were studied using electrophysiological, optical and biochemical approaches. Distal dendrites of iSPNs from symptomatic HD mice were hypoexcitable, a change that was attributable to increased association of dendritic Kv4 potassium channels with auxiliary KChIP subunits. This association was negatively modulated by TrkB receptor signaling. Dendritic excitability of HD iSPNs was rescued by knocking-down expression of Kv4 channels, by disrupting KChIP binding, by restoring TrkB receptor signaling or by lowering mutant-Htt (mHtt) levels with a zinc finger protein. Collectively, these studies demonstrate that mHtt induces reversible alterations in the dendritic excitability of iSPNs that could contribute to the motor symptoms of HD

Kripke Semantics for Martin-L\"of's Extensional Type Theory

It is well-known that simple type theory is complete with respect to non-standard set-valued models. Completeness for standard models only holds with respect to certain extended classes of models, e.g., the class of cartesian closed categories. Similarly, dependent type theory is complete for locally cartesian closed categories. However, it is usually difficult to establish the coherence of interpretations of dependent type theory, i.e., to show that the interpretations of equal expressions are indeed equal. Several classes of models have been used to remedy this problem. We contribute to this investigation by giving a semantics that is standard, coherent, and sufficiently general for completeness while remaining relatively easy to compute with. Our models interpret types of Martin-L\"of's extensional dependent type theory as sets indexed over posets or, equivalently, as fibrations over posets. This semantics can be seen as a generalization to dependent type theory of the interpretation of intuitionistic first-order logic in Kripke models. This yields a simple coherent model theory, with respect to which simple and dependent type theory are sound and complete