Gauge-gravity duality -- Super Yang Mills Quantum Mechanics

We describe the conjectured holographic duality between Yang-Mills quantum mechanics and type IIa string theory. This duality allows us to use lattice Monte Carlo simulations to probe the physics of the gravitational theory - for example, at low energies it provides a computation of black hole entropy in terms of a sum over microstates of the dual gauge theory. Numerical results are presented of the 4 supercharge theory at finite temperatureComment: 7 pages, 6 figures, Talk at lattice 200

Agent based cooperative theory formation in pure mathematics

The HR program, Colton et al. (1999), performs theory formation in domains of pure mathematics. Given only minimal information about a domain, it invents concepts, make conjectures, proves theorems and finds counterexamples to false conjectures. We present here a multi-agent version of HR which may provide a model for how individual mathematicians perform separate investigations but communicate their results to the mathematical community, learning from others as they do. We detail the exhaustive categorisation problem to which we have applied a multi-agent approach.

Gauge theory duals of black hole - black string transitions of gravitational theories on a circle

We study the black hole - black string phase transitions of gravitational theories compactified on a circle using the holographic duality conjecture. The gauge theory duals of these theories are maximally supersymmetric and strongly coupled 1 + 1 dimensional SU(N) Yang-Mills theories compactified on a circle, in the large $N$ limit. We perform the strongly coupled finite temperature gauge theory calculations on a lattice, using the recently developed exact lattice supersymmetry methods based on topological twisting and orbifolding. The spatial Polyakov line serves as relevant order parameter of the confinement - deconfinement phase transitions in the gauge theory duals.Comment: v2: 8 pages, 2 figures. References added. Talk given at the 6th International Symposium on Quantum Theory and Symmetries (QTS6), Lexington, Kentucky, 20-25 Jul 200

Fair assignment of indivisible objects under ordinal preferences

We consider the discrete assignment problem in which agents express ordinal preferences over objects and these objects are allocated to the agents in a fair manner. We use the stochastic dominance relation between fractional or randomized allocations to systematically define varying notions of proportionality and envy-freeness for discrete assignments. The computational complexity of checking whether a fair assignment exists is studied for these fairness notions. We also characterize the conditions under which a fair assignment is guaranteed to exist. For a number of fairness concepts, polynomial-time algorithms are presented to check whether a fair assignment exists. Our algorithmic results also extend to the case of unequal entitlements of agents. Our NP-hardness result, which holds for several variants of envy-freeness, answers an open question posed by Bouveret, Endriss, and Lang (ECAI 2010). We also propose fairness concepts that always suggest a non-empty set of assignments with meaningful fairness properties. Among these concepts, optimal proportionality and optimal weak proportionality appear to be desirable fairness concepts.Comment: extended version of a paper presented at AAMAS 201

An investigation into the effects of complex topography on particle dry deposition

There is a requirement to predict the spatial variation of particle dry deposition following a nuclear accident. The interaction of landscape features, atmospheric flow and particle dry deposition has been investigated with this in mind. Wind tunnel studies have been used with computational fluid dynamics to predict the deposition rate relative to a flat landscape. Good quantitative agreement was seen for this relative deposition rate. Landscape shapes showed significant effects on deposition rate, increasing it by more than two in some cases, over limited areas. The effect of turbulence intensity, in the absence of landscape features, was also studied and a weak relationship to dry deposition was observed. Computational fluid dynamics methods used in wind tunnel comparisons were extended to a wide range of landscape cases. Deposition rates varied spatially around the landscape features. In general, for hills and ridges, deposition was seen to increase on the windward face, decrease on the leeward face and near wake, and increase in the further wake, before returning to the flat case value. The computational results were applied to a real landscape with the use of a customised geographical information system. Good general agreement was seen when compared with a test case

Black hole thermodynamics from simulations of lattice Yang-Mills theory

We report on lattice simulations of 16 supercharge SU(N) Yang-Mills quantum mechanics in the 't Hooft limit. Maldacena duality conjectures that in this limit the theory is dual to IIA string theory, and in particular that the behavior of the thermal theory at low temperature is equivalent to that of certain black holes in IIA supergravity. Our simulations probe the low temperature regime for N <= 5 and the intermediate and high temperature regimes for N <= 12. We observe 't Hooft scaling and at low temperatures our results are consistent with the dual black hole prediction. The intermediate temperature range is dual to the Horowitz-Polchinski correspondence region, and our results are consistent with smooth behavior there. We include the Pfaffian phase arising from the fermions in our calculations where appropriate.Comment: 4 pages, 4 figure

Mechanism of Notch Pathway Activation and Its Role in the Regulation of Olfactory Plasticity in Drosophila melanogaster

The neural plasticity of sensory systems is being increasingly recognized as playing a role in learning and memory. We have previously shown that Notch, part of an evolutionarily conserved intercellular signaling pathway, is required in adult Drosophila melanogaster olfactory receptor neurons (ORNs) for the structural and functional plasticity of olfactory glomeruli that is induced by chronic odor exposure. In this paper we address how long-term exposure to odor activates Notch and how Notch in conjunction with chronic odor mediates olfactory plasticity. We show that upon chronic odor exposure a non-canonical Notch pathway mediates an increase in the volume of glomeruli by a mechanism that is autonomous to ORNs. In addition to activating a pathway that is autonomous to ORNs, chronic odor exposure also activates the Notch ligand Delta in second order projection neurons (PNs), but this does not appear to require acetylcholine receptor activation in PNs. Delta on PNs then feeds back to activate canonical Notch signaling in ORNs, which restricts the extent of the odor induced increase in glomerular volume. Surprisingly, even though the pathway that mediates the increase in glomerular volume is autonomous to ORNs, nonproductive transsynaptic Delta/Notch interactions that do not activate the canonical pathway can block the increase in volume. In conjunction with chronic odor, the canonical Notch pathway also enhances cholinergic activation of PNs. We present evidence suggesting that this is due to increased acetylcholine release from ORNs. In regulating physiological plasticity, Notch functions solely by the canonical pathway, suggesting that there is no direct connection between morphological and physiological plasticity

Mechanism of Notch Pathway Activation and Its Role in the Regulation of Olfactory Plasticity in Drosophila melanogaster

The neural plasticity of sensory systems is being increasingly recognized as playing a role in learning and memory. We have previously shown that Notch, part of an evolutionarily conserved intercellular signaling pathway, is required in adult Drosophila melanogaster olfactory receptor neurons (ORNs) for the structural and functional plasticity of olfactory glomeruli that is induced by chronic odor exposure. In this paper we address how long-term exposure to odor activates Notch and how Notch in conjunction with chronic odor mediates olfactory plasticity. We show that upon chronic odor exposure a non-canonical Notch pathway mediates an increase in the volume of glomeruli by a mechanism that is autonomous to ORNs. In addition to activating a pathway that is autonomous to ORNs, chronic odor exposure also activates the Notch ligand Delta in second order projection neurons (PNs), but this does not appear to require acetylcholine receptor activation in PNs. Delta on PNs then feeds back to activate canonical Notch signaling in ORNs, which restricts the extent of the odor induced increase in glomerular volume. Surprisingly, even though the pathway that mediates the increase in glomerular volume is autonomous to ORNs, nonproductive transsynaptic Delta/Notch interactions that do not activate the canonical pathway can block the increase in volume. In conjunction with chronic odor, the canonical Notch pathway also enhances cholinergic activation of PNs. We present evidence suggesting that this is due to increased acetylcholine release from ORNs. In regulating physiological plasticity, Notch functions solely by the canonical pathway, suggesting that there is no direct connection between morphological and physiological plasticity

Computational Aspects of Multi-Winner Approval Voting

We study computational aspects of three prominent voting rules that use approval ballots to elect multiple winners. These rules are satisfaction approval voting, proportional approval voting, and reweighted approval voting. We first show that computing the winner for proportional approval voting is NP-hard, closing a long standing open problem. As none of the rules are strategyproof, even for dichotomous preferences, we study various strategic aspects of the rules. In particular, we examine the computational complexity of computing a best response for both a single agent and a group of agents. In many settings, we show that it is NP-hard for an agent or agents to compute how best to vote given a fixed set of approval ballots from the other agents