Teach Me What You Want to Play: Learning Variants of Connect Four through Human-Robot Interaction

This paper investigates the use of game theoretic representations to represent and learn how to play interactive games such as Connect Four. We combine aspects of learning by demonstration, active learning, and game theory allowing a robot to leverage its developing representation of the game to conduct question/answer sessions with a person, thus filling in gaps in its knowledge. The paper demonstrates a method for teaching a robot the win conditions of the game Connect Four and its variants using a single demonstration and a few trial examples with a question and answer session led by the robot. Our results show that the robot can learn arbitrary win conditions for the game with little prior knowledge of the win conditions and then play the game with a human utilizing the learned win conditions. Our experiments also show that some questions are more important for learning the game's win conditions. We believe that this method could be broadly applied to a variety of interactive learning scenarios.Comment: The final authenticated publication is available online at https://doi.org/10.1007/978-3-030-62056-1_4

Resolution of null fiber and conormal bundles on the Lagrangian Grassmannian

We study the null fiber of a moment map related to dual pairs. We construct an equivariant resolution of singularities of the null fiber, and get conormal bundles of closed $K_C$-orbits in the Lagrangian Grassmannian as the categorical quotient. The conormal bundles thus obtained turn out to be a resolution of singularities of the closure of nilpotent $K_C$-orbits, which is a "quotient" of the resolution of the null fiber.Comment: 17 pages; completely revised and add reference

Global phosphoproteomic profiling reveals perturbed signaling in a mouse model of dilated cardiomyopathy

Phospholamban (PLN) plays a central role in Ca2+ homeostasis in cardiac myocytes through regulation of the sarco(endo)plasmic reticulum Ca2+-ATPase 2A (SERCA2A) Ca2+ pump. An inherited mutation converting arginine residue 9 in PLN to cysteine (R9C) results in dilated cardiomyopathy (DCM) in humans and transgenic mice, but the downstream signaling defects leading to decompensation and heart failure are poorly understood. Here we used precision mass spectrometry to study the global phosphorylation dynamics of 1,887 cardiac phosphoproteins in early affected heart tissue in a transgenic R9C mouse model of DCM compared with wild-type littermates. Dysregulated phosphorylation sites were quantified after affinity capture and identification of 3,908 phosphopeptides from fractionated whole-heart homogenates. Global statistical enrichment analysis of the differential phosphoprotein patterns revealed selective perturbation of signaling pathways regulating cardiovascular activity in early stages of DCM. Strikingly, dysregulated signaling through the Notch-1 receptor, recently linked to cardiomyogenesis and embryonic cardiac stem cell development and differentiation but never directly implicated in DCM before, was a prominently perturbed pathway. We verified alterations in Notch-1 downstream components in early symptomatic R9C transgenic mouse cardiomyocytes compared with wild type by immunoblot analysis and confocal immunofluorescence microscopy. These data reveal unexpected connections between stress-regulated cell signaling networks, specific protein kinases, and downstream effectors essential for proper cardiac function

Schur Q-functions and degeneracy locus formulas for morphisms with symmetries

We give closed-form formulas for the fundamental classes of degeneracy loci associated with vector bundle maps given locally by (not necessary square) matrices which are symmetric (resp. skew-symmetric) w.r.t. the main diagonal. Our description uses essentially Schur Q-polynomials of a bundle, and is based on a certain push-forward formula for these polynomials in a Grassmann bundle.Comment: 22 pages, AMSTEX, misprints corrected, exposition improved. to appear in the Proceedings of Intersection Theory Conference in Bologna, "Progress in Mathematics", Birkhause

Containment and equivalence of weighted automata: Probabilistic and max-plus cases

This paper surveys some results regarding decision problems for probabilistic and max-plus automata, such as containment and equivalence. Probabilistic and max-plus automata are part of the general family of weighted automata, whose semantics are maps from words to real values. Given two weighted automata, the equivalence problem asks whether their semantics are the same, and the containment problem whether one is point-wise smaller than the other one. These problems have been studied intensively and this paper will review some techniques used to show (un)decidability and state a list of open questions that still remain

Joint analysis of stressors and ecosystem services to enhance restoration effectiveness

With increasing pressure placed on natural systems by growing human populations, both scientists and resource managers need a better understanding of the relationships between cumulative stress from human activities and valued ecosystem services. Societies often seek to mitigate threats to these services through large-scale, costly restoration projects, such as the over one billion dollar Great Lakes Restoration Initiative currently underway. To help inform these efforts, we merged high-resolution spatial analyses of environmental stressors with mapping of ecosystem services for all five Great Lakes. Cumulative ecosystem stress is highest in near-shore habitats, but also extends offshore in Lakes Erie, Ontario, and Michigan. Variation in cumulative stress is driven largely by spatial concordance among multiple stressors, indicating the importance of considering all stressors when planning restoration activities. In addition, highly stressed areas reflect numerous different combinations of stressors rather than a single suite of problems, suggesting that a detailed understanding of the stressors needing alleviation could improve restoration planning. We also find that many important areas for fisheries and recreation are subject to high stress, indicating that ecosystem degradation could be threatening key services. Current restoration efforts have targeted high-stress sites almost exclusively, but generally without knowledge of the full range of stressors affecting these locations or differences among sites in service provisioning. Our results demonstrate that joint spatial analysis of stressors and ecosystem services can provide a critical foundation for maximizing social and ecological benefits from restoration investments. www.pnas.org/lookup/suppl/doi:10.1073/pnas.1213841110/-/DCSupplementa

Moduli of Abelian varieties, Vinberg theta-groups, and free resolutions

We present a systematic approach to studying the geometric aspects of Vinberg theta-representations. The main idea is to use the Borel-Weil construction for representations of reductive groups as sections of homogeneous bundles on homogeneous spaces, and then to study degeneracy loci of these vector bundles. Our main technical tool is to use free resolutions as an "enhanced" version of degeneracy loci formulas. We illustrate our approach on several examples and show how they are connected to moduli spaces of Abelian varieties. To make the article accessible to both algebraists and geometers, we also include background material on free resolutions and representation theory.Comment: 41 pages, uses tabmac.sty, Dedicated to David Eisenbud on the occasion of his 65th birthday; v2: fixed some typos and added reference

Triangle-Free Penny Graphs: Degeneracy, Choosability, and Edge Count

We show that triangle-free penny graphs have degeneracy at most two, list coloring number (choosability) at most three, diameter $D=\Omega(\sqrt n)$, and at most $\min\bigl(2n-\Omega(\sqrt n),2n-D-2\bigr)$ edges.Comment: 10 pages, 2 figures. To appear at the 25th International Symposium on Graph Drawing and Network Visualization (GD 2017