Reallocating Multiple Facilities on the Line

We study the multistage $K$-facility reallocation problem on the real line, where we maintain $K$ facility locations over $T$ stages, based on the stage-dependent locations of $n$ agents. Each agent is connected to the nearest facility at each stage, and the facilities may move from one stage to another, to accommodate different agent locations. The objective is to minimize the connection cost of the agents plus the total moving cost of the facilities, over all stages. $K$-facility reallocation was introduced by de Keijzer and Wojtczak, where they mostly focused on the special case of a single facility. Using an LP-based approach, we present a polynomial time algorithm that computes the optimal solution for any number of facilities. We also consider online $K$-facility reallocation, where the algorithm becomes aware of agent locations in a stage-by-stage fashion. By exploiting an interesting connection to the classical $K$-server problem, we present a constant-competitive algorithm for $K = 2$ facilities

Olfactory Learning Deficits in Mutants for leonardo, a Drosophila Gene Encoding a 14-3-3 Protein

AbstractStudies of Drosophila and other insects have indicated an essential role for the mushroom bodies in learning and memory. The leonardo gene encodes a Drosophila protein highly homologous to the vertebrate 14-3-3ζ isoform, a protein well studied for biochemical roles but without a well established biological function. The gene is expressed abundantly and preferentially in mushroom body neurons. Mutant alleles that reduce LEONARDO protein levels in the mushroom bodies significantly decrease the capacity for olfactory learning, but do not affect sensory modalities or brain neuroanatomy that are requisite for conditioning. These results establish a biological role for 14-3-3 proteins in mushroom body–mediated learning and memory processes, and suggest that proteins known to interact with them, such as RAF-1 or other protein kinases, may also have this biological function

Logarithmic Conformal Field Theory Solutions of Two Dimensional Magnetohydrodynamics

We consider the application of logarithmic conformal field theory in finding solutions to the turbulent phases of 2-dimensional models of magnetohydrodynamics. These arise upon dimensional reduction of standard (infinite conductivity) 3-dimensional magnetohydrodynamics, after taking various simplifying limits. We show that solutions of the corresponding Hopf equations and higher order integrals of motion can be found within the solutions of ordinary turbulence proposed by Flohr, based on the tensor product of the logarithmic extension ${\tilde c}_{6,1}$ of the non-unitary minimal model $c_{6,1}$. This possibility arises because of the existence of a continuous hidden symmetry present in the latter models, and the fact that there appear several distinct dimension -1 and -2 primary fields.Comment: 15 pages, Latex; references adde

A third functional isoform enriched in mushroom body neurons is encoded by the Drosophila 14-3-3ζ gene

Abstract14-3-3 Proteins are highly conserved across eukaryotes, typically encoded by multiple genes in most species. Drosophila has only two such genes, 14-3-3ζ (leo), encoding two isoforms LEOI and LEOII, and 14-3-3ε. We report a bona fide third functional isoform encoded by leo divergent from the other two in structurally and functionally significant areas, thus increasing 14-3-3 diversity in Drosophila. Furthermore, we used a novel approach of spatially restricted leo abrogation by RNA-interference and revealed differential LEO distribution in adult heads, with LEOIII enrichment in neurons essential for learning and memory in Drosophila

Evolutionary Game Theory Squared: Evolving Agents in Endogenously Evolving Zero-Sum Games

The predominant paradigm in evolutionary game theory and more generally online learning in games is based on a clear distinction between a population of dynamic agents that interact given a fixed, static game. In this paper, we move away from the artificial divide between dynamic agents and static games, to introduce and analyze a large class of competitive settings where both the agents and the games they play evolve strategically over time. We focus on arguably the most archetypal game-theoretic setting -- zero-sum games (as well as network generalizations) -- and the most studied evolutionary learning dynamic -- replicator, the continuous-time analogue of multiplicative weights. Populations of agents compete against each other in a zero-sum competition that itself evolves adversarially to the current population mixture. Remarkably, despite the chaotic coevolution of agents and games, we prove that the system exhibits a number of regularities. First, the system has conservation laws of an information-theoretic flavor that couple the behavior of all agents and games. Secondly, the system is Poincar\'{e} recurrent, with effectively all possible initializations of agents and games lying on recurrent orbits that come arbitrarily close to their initial conditions infinitely often. Thirdly, the time-average agent behavior and utility converge to the Nash equilibrium values of the time-average game. Finally, we provide a polynomial time algorithm to efficiently predict this time-average behavior for any such coevolving network game.Comment: To appear in AAAI 202

Semi Bandit Dynamics in Congestion Games: Convergence to Nash Equilibrium and No-Regret Guarantees

In this work, we introduce a new variant of online gradient descent, which provably converges to Nash Equilibria and simultaneously attains sublinear regret for the class of congestion games in the semi-bandit feedback setting. Our proposed method admits convergence rates depending only polynomially on the number of players and the number of facilities, but not on the size of the action set, which can be exponentially large in terms of the number of facilities. Moreover, the running time of our method has polynomial-time dependence on the implicit description of the game. As a result, our work answers an open question from (Du et. al, 2022).Comment: ICML 202