Fixed-Length Strong Coordination

We consider the problem of synthesizing joint distributions of signals and actions over noisy channels in the finite-length regime. For a fixed blocklength $n$ and an upper bound on the distance $\varepsilon$, a coding scheme is proposed such that the induced joint distribution is $\varepsilon$-close in $L^1$ distance to a target i.i.d. distribution. The set of achievable target distributions and rate for asymptotic strong coordination can be recovered from the main result of this paper by having $n$ that tends to infinity.Comment: 5 pages, 2 figure

Efficient Local Search in Coordination Games on Graphs

We study strategic games on weighted directed graphs, where the payoff of a player is defined as the sum of the weights on the edges from players who chose the same strategy augmented by a fixed non-negative bonus for picking a given strategy. These games capture the idea of coordination in the absence of globally common strategies. Prior work shows that the problem of determining the existence of a pure Nash equilibrium for these games is NP-complete already for graphs with all weights equal to one and no bonuses. However, for several classes of graphs (e.g. DAGs and cliques) pure Nash equilibria or even strong equilibria always exist and can be found by simply following a particular improvement or coalition-improvement path, respectively. In this paper we identify several natural classes of graphs for which a finite improvement or coalition-improvement path of polynomial length always exists, and, as a consequence, a Nash equilibrium or strong equilibrium in them can be found in polynomial time. We also argue that these results are optimal in the sense that in natural generalisations of these classes of graphs, a pure Nash equilibrium may not even exist.Comment: Extended version of a paper accepted to IJCAI1

First-principles thermodynamic modeling of lanthanum chromate perovskites

Tendencies toward local atomic ordering in (A,A′)(B,B′)O_(3−δ) mixed composition perovskites are modeled to explore their influence on thermodynamic, transport, and electronic properties. In particular, dopants and defects within lanthanum chromate perovskites are studied under various simulated redox environments. (La_(1−x),Sr_x)(Cr_(1−y),Fe_y)O_(3−δ) (LSCF) and (La_(1−x),Sr_x)(Cr_(1−y),Ru_y)O_(3−δ) (LSCR) are modeled using a cluster expansion statistical thermodynamics method built upon a density functional theory database of structural energies. The cluster expansions are utilized in lattice Monte Carlo simulations to compute the ordering of Sr and Fe(Ru) dopant and oxygen vacancies (Vac). Reduction processes are modeled via the introduction of oxygen vacancies, effectively forcing excess electronic charge onto remaining atoms. LSCR shows increasingly extended Ru-Vac associates and short-range Ru-Ru and Ru-Vac interactions upon reduction; LSCF shows long-range Fe-Fe and Fe-Vac interaction ordering, inhibiting mobility. First principles density functional calculations suggest that Ru-Vac associates significantly decrease the activation energy of Ru-Cr swaps in reduced LSCR. These results are discussed in view of experimentally observed extrusion of metallic Ru from LSCR nanoparticles under reducing conditions at elevated temperature

Zero Error Coordination

In this paper, we consider a zero error coordination problem wherein the nodes of a network exchange messages to be able to perfectly coordinate their actions with the individual observations of each other. While previous works on coordination commonly assume an asymptotically vanishing error, we assume exact, zero error coordination. Furthermore, unlike previous works that employ the empirical or strong notions of coordination, we define and use a notion of set coordination. This notion of coordination bears similarities with the empirical notion of coordination. We observe that set coordination, in its special case of two nodes with a one-way communication link is equivalent with the "Hide and Seek" source coding problem of McEliece and Posner. The Hide and Seek problem has known intimate connections with graph entropy, rate distortion theory, Renyi mutual information and even error exponents. Other special cases of the set coordination problem relate to Witsenhausen's zero error rate and the distributed computation problem. These connections motivate a better understanding of set coordination, its connections with empirical coordination, and its study in more general setups. This paper takes a first step in this direction by proving new results for two node networks

Smoothed Efficient Algorithms and Reductions for Network Coordination Games

Worst-case hardness results for most equilibrium computation problems have raised the need for beyond-worst-case analysis. To this end, we study the smoothed complexity of finding pure Nash equilibria in Network Coordination Games, a PLS-complete problem in the worst case. This is a potential game where the sequential-better-response algorithm is known to converge to a pure NE, albeit in exponential time. First, we prove polynomial (resp. quasi-polynomial) smoothed complexity when the underlying game graph is a complete (resp. arbitrary) graph, and every player has constantly many strategies. We note that the complete graph case is reminiscent of perturbing all parameters, a common assumption in most known smoothed analysis results. Second, we define a notion of smoothness-preserving reduction among search problems, and obtain reductions from $2$-strategy network coordination games to local-max-cut, and from $k$-strategy games (with arbitrary $k$) to local-max-cut up to two flips. The former together with the recent result of [BCC18] gives an alternate $O(n^8)$-time smoothed algorithm for the $2$-strategy case. This notion of reduction allows for the extension of smoothed efficient algorithms from one problem to another. For the first set of results, we develop techniques to bound the probability that an (adversarial) better-response sequence makes slow improvements on the potential. Our approach combines and generalizes the local-max-cut approaches of [ER14,ABPW17] to handle the multi-strategy case: it requires a careful definition of the matrix which captures the increase in potential, a tighter union bound on adversarial sequences, and balancing it with good enough rank bounds. We believe that the approach and notions developed herein could be of interest in addressing the smoothed complexity of other potential and/or congestion games

Strong Coordination with Polar Codes

In this paper, we design explicit codes for strong coordination in two-node networks. Specifically, we consider a two-node network in which the action imposed by nature is binary and uniform, and the action to coordinate is obtained via a symmetric discrete memoryless channel. By observing that polar codes are useful for channel resolvability over binary symmetric channels, we prove that nested polar codes achieve a subset of the strong coordination capacity region, and therefore provide a constructive and low complexity solution for strong coordination.Comment: 7 pages doublespaced, presented at the 50th Annual Allerton Conference on Communication, Control and Computing 201

Effects of particle-size ratio on jamming of binary mixtures

We perform a systematic numerical study of the effects of the particle-size ratio $R \ge 1$ on the properties of jammed binary mixtures. We find that changing $R$ does not qualitatively affect the critical scaling of the pressure and coordination number with the compression near the jamming transition, but the critical volume fraction at the jamming transition varies with $R$. Moreover, the static structure factor (density correlation) $S(k)$ strongly depends on $R$ and shows distinct long wave-length behaviors between large and small particles. Thus the previously reported behavior of $S(k)\sim k$ in the long wave-length limit is only a special case in the $R\to 1$ limit, and cannot be simply generalized to jammed systems with $R>1$.Comment: 5 pages and 4 figures, submitted to Soft Matter, special issue on Granular and Jammed Material