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

Shapes of free resolutions over a local ring

We classify the possible shapes of minimal free resolutions over a regular local ring. This illustrates the existence of free resolutions whose Betti numbers behave in surprisingly pathological ways. We also give an asymptotic characterization of the possible shapes of minimal free resolutions over hypersurface rings. Our key new technique uses asymptotic arguments to study formal Q-Betti sequences.Comment: 14 pages, 1 figure; v2: sections have been reorganized substantially and exposition has been streamline

Microwave Gaseous Discharges

Contains reports on six research projects.Atomic Energy Commission under Contract AT(30-1) 184

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

Class and rank of differential modules

A differential module is a module equipped with a square-zero endomorphism. This structure underpins complexes of modules over rings, as well as differential graded modules over graded rings. We establish lower bounds on the class--a substitute for the length of a free complex--and on the rank of a differential module in terms of invariants of its homology. These results specialize to basic theorems in commutative algebra and algebraic topology. One instance is a common generalization of the equicharacteristic case of the New Intersection Theorem of Hochster, Peskine, P. Roberts, and Szpiro, concerning complexes over noetherian commutative rings, and of a theorem of G. Carlsson on differential graded modules over graded polynomial rings.Comment: 27 pages. Minor changes; mainly stylistic. To appear in Inventiones Mathematica

Microwave Gaseous Discharges

Contains research objectives and reports on five research projects

Non-commutative desingularization of determinantal varieties, I

We show that determinantal varieties defined by maximal minors of a generic matrix have a non-commutative desingularization, in that we construct a maximal Cohen-Macaulay module over such a variety whose endomorphism ring is Cohen-Macaulay and has finite global dimension. In the case of the determinant of a square matrix, this gives a non-commutative crepant resolution.Comment: 52 pages, 3 figures, all comments welcom

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