Constant Rank Bimatrix Games are PPAD-hard

The rank of a bimatrix game (A,B) is defined as rank(A+B). Computing a Nash equilibrium (NE) of a rank-$0$, i.e., zero-sum game is equivalent to linear programming (von Neumann'28, Dantzig'51). In 2005, Kannan and Theobald gave an FPTAS for constant rank games, and asked if there exists a polynomial time algorithm to compute an exact NE. Adsul et al. (2011) answered this question affirmatively for rank-$1$ games, leaving rank-2 and beyond unresolved. In this paper we show that NE computation in games with rank $\ge 3$, is PPAD-hard, settling a decade long open problem. Interestingly, this is the first instance that a problem with an FPTAS turns out to be PPAD-hard. Our reduction bypasses graphical games and game gadgets, and provides a simpler proof of PPAD-hardness for NE computation in bimatrix games. In addition, we get: * An equivalence between 2D-Linear-FIXP and PPAD, improving a result by Etessami and Yannakakis (2007) on equivalence between Linear-FIXP and PPAD. * NE computation in a bimatrix game with convex set of Nash equilibria is as hard as solving a simple stochastic game. * Computing a symmetric NE of a symmetric bimatrix game with rank $\ge 6$ is PPAD-hard. * Computing a (1/poly(n))-approximate fixed-point of a (Linear-FIXP) piecewise-linear function is PPAD-hard. The status of rank-$2$ games remains unresolved

Time Domain Simulations of Arm Locking in LISA

Arm locking is a technique that has been proposed for reducing laser frequency fluctuations in the Laser Interferometer Space Antenna (LISA), a gravitational-wave observatory sensitive in the milliHertz frequency band. Arm locking takes advantage of the geometric stability of the triangular constellation of three spacecraft that comprise LISA to provide a frequency reference with a stability in the LISA measurement band that exceeds that available from a standard reference such as an optical cavity or molecular absorption line. We have implemented a time-domain simulation of arm locking including the expected limiting noise sources (shot noise, clock noise, spacecraft jitter noise, and residual laser frequency noise). The effect of imperfect a priori knowledge of the LISA heterodyne frequencies and the associated 'pulling' of an arm locked laser is included. We find that our implementation meets requirements both on the noise and dynamic range of the laser frequency.Comment: Revised to address reviewer comments. Accepted by Phys. Rev.

Settling Some Open Problems on 2-Player Symmetric Nash Equilibria

Over the years, researchers have studied the complexity of several decision versions of Nash equilibrium in (symmetric) two-player games (bimatrix games). To the best of our knowledge, the last remaining open problem of this sort is the following; it was stated by Papadimitriou in 2007: find a non-symmetric Nash equilibrium (NE) in a symmetric game. We show that this problem is NP-complete and the problem of counting the number of non-symmetric NE in a symmetric game is #P-complete. In 2005, Kannan and Theobald defined the "rank of a bimatrix game" represented by matrices (A, B) to be rank(A+B) and asked whether a NE can be computed in rank 1 games in polynomial time. Observe that the rank 0 case is precisely the zero sum case, for which a polynomial time algorithm follows from von Neumann's reduction of such games to linear programming. In 2011, Adsul et. al. obtained an algorithm for rank 1 games; however, it does not solve the case of symmetric rank 1 games. We resolve this problem

Band alignment at metal/ferroelectric interfaces: insights and artifacts from first principles

Based on recent advances in first-principles theory, we develop a general model of the band offset at metal/ferroelectric interfaces. We show that, depending on the polarization of the film, a pathological regime might occur where the metallic carriers populate the energy bands of the insulator, making it metallic. As the most common approximations of density functional theory are affected by a systematic underestimation of the fundamental band gap of insulators, this scenario is likely to be an artifact of the simulation. We provide a number of rigorous criteria, together with extensive practical examples, to systematically identify this problematic situation in the calculated electronic and structural properties of ferroelectric systems. We discuss our findings in the context of earlier literature studies, where the issues described in this work have often been overlooked. We also discuss formal analogies to the physics of polarity compensation at LaAlO3/SrTiO3 interfaces, and suggest promising avenues for future research.Comment: 29 pages, 23 figure

Carrier-mediated magnetoelectricity in complex oxide heterostructures

While tremendous success has been achieved to date in creating both single phase and composite magnetoelectric materials, the quintessential electric-field control of magnetism remains elusive. In this work, we demonstrate a linear magnetoelectric effect which arises from a novel carrier-mediated mechanism, and is a universal feature of the interface between a dielectric and a spin-polarized metal. Using first-principles density functional calculations, we illustrate this effect at the SrRuO$_3$/SrTiO$_3$ interface and describe its origin. To formally quantify the magnetic response of such an interface to an applied electric field, we introduce and define the concept of spin capacitance. In addition to its magnetoelectric and spin capacitive behavior, the interface displays a spatial coexistence of magnetism and dielectric polarization suggesting a route to a new type of interfacial multiferroic

Improving Taxonomic Delimitation of Fungal Species in the Age of Genomics and Phenomics

Species concepts have long provided a source of debate among biologists. These lively debates have been important for reaching consensus on how to communicate across scientific disciplines and for advancing innovative strategies to study evolution, population biology, ecology, natural history, and disease epidemiology. Species concepts are also important for evaluating variability and diversity among communities, understanding biogeographical distributions, and identifying causal agents of disease across animal and plant hosts. While there have been many attempts to address the concept of species in the fungi, there are several concepts that have made taxonomic delimitation especially challenging. In this review we discuss these major challenges and describe methodological approaches that show promise for resolving ambiguity in fungal taxonomy by improving discrimination of genetic and functional traits. We highlight the relevance of eco-evolutionary theory used in conjunction with integrative taxonomy approaches to improve the understanding of interactions between environment, ecology, and evolution that give rise to distinct species boundaries. Beyond recent advances in genomic and phenomic methods, bioinformatics tools and modeling approaches enable researchers to test hypothesis and expand our knowledge of fungal biodiversity. Looking to the future, the pairing of integrative taxonomy approaches with multi-locus genomic sequencing and phenomic techniques, such as transcriptomics and proteomics, holds great potential to resolve many unknowns in fungal taxonomic classification

Improving Taxonomic Delimitation of Fungal Species in the Age of Genomics and Phenomics

Species concepts have long provided a source of debate among biologists. These lively debates have been important for reaching consensus on how to communicate across scientific disciplines and for advancing innovative strategies to study evolution, population biology, ecology, natural history, and disease epidemiology. Species concepts are also important for evaluating variability and diversity among communities, understanding biogeographical distributions, and identifying causal agents of disease across animal and plant hosts. While there have been many attempts to address the concept of species in the fungi, there are several concepts that have made taxonomic delimitation especially challenging. In this review we discuss these major challenges and describe methodological approaches that show promise for resolving ambiguity in fungal taxonomy by improving discrimination of genetic and functional traits. We highlight the relevance of eco-evolutionary theory used in conjunction with integrative taxonomy approaches to improve the understanding of interactions between environment, ecology, and evolution that give rise to distinct species boundaries. Beyond recent advances in genomic and phenomic methods, bioinformatics tools and modeling approaches enable researchers to test hypothesis and expand our knowledge of fungal biodiversity. Looking to the future, the pairing of integrative taxonomy approaches with multi-locus genomic sequencing and phenomic techniques, such as transcriptomics and proteomics, holds great potential to resolve many unknowns in fungal taxonomic classification

New primary renal diagnosis codes for the ERA-EDTA

The European Renal Association-European Dialysis and Transplant Association (ERA-EDTA) Registry has produced a new set of primary renal diagnosis (PRD) codes that are intended for use by affiliated registries. It is designed specifically for use in renal centres and registries but is aligned with international coding standards supported by the WHO (International Classification of Diseases) and the International Health Terminology Standards Development Organization (SNOMED Clinical Terms). It is available as supplementary material to this paper and free on the internet for non-commercial, clinical, quality improvement and research use, and by agreement with the ERA-EDTA Registry for use by commercial organizations. Conversion between the old and the new PRD codes is possible. The new codes are very flexible and will be actively managed to keep them up-to-date and to ensure that renal medicine can remain at the forefront of the electronic revolution in medicine, epidemiology research and the use of decision support systems to improve the care of patients

Dimerization of the voltage-sensing phosphatase controls its voltage-sensing and catalytic activity.

Multimerization is a key characteristic of most voltage-sensing proteins. The main exception was thought to be the Ciona intestinalis voltage-sensing phosphatase (Ci-VSP). In this study, we show that multimerization is also critical for Ci-VSP function. Using coimmunoprecipitation and single-molecule pull-down, we find that Ci-VSP stoichiometry is flexible. It exists as both monomers and dimers, with dimers favored at higher concentrations. We show strong dimerization via the voltage-sensing domain (VSD) and weak dimerization via the phosphatase domain. Using voltage-clamp fluorometry, we also find that VSDs cooperate to lower the voltage dependence of activation, thus favoring the activation of Ci-VSP. Finally, using activity assays, we find that dimerization alters Ci-VSP substrate specificity such that only dimeric Ci-VSP is able to dephosphorylate the 3-phosphate from PI(3,4,5)P3 or PI(3,4)P2 Our results indicate that dimerization plays a significant role in Ci-VSP function