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Look before you sweep: Visibility-aware motion planningJan 18 2019This paper addresses the problem of planning for a robot with a directional obstacle-detection sensor that must move through a cluttered environment. The planning objective is to remain safe by finding a path for the complete robot, including sensor, ... More

Focused Model-Learning and Planning for Non-Gaussian Continuous State-Action SystemsJul 26 2016Oct 02 2016We introduce a framework for model learning and planning in stochastic domains with continuous state and action spaces and non-Gaussian transition models. It is efficient because (1) local models are estimated only when the planner requires them; (2) ... More

Every Local Minimum is a Global Minimum of an Induced ModelApr 07 2019For non-convex optimization in machine learning, this paper proves that every local minimum achieves the global optimality of the perturbable gradient basis model at any differentiable point. As a result, non-convex machine learning is theoretically as ... More

Elimination of All Bad Local Minima in Deep LearningJan 02 2019In this paper, we theoretically prove that we can eliminate all suboptimal local minima by adding one neuron per output unit to any deep neural network, for multi-class classification, binary classification, and regression with an arbitrary loss function. ... More

Adaptive Importance Sampling for Estimation in Structured DomainsJan 16 2013Sampling is an important tool for estimating large, complex sums and integrals over high dimensional spaces. For instance, important sampling has been used as an alternative to exact methods for inference in belief networks. Ideally, we want to have a ... More

Accelerating EM: An Empirical StudyJan 23 2013Many applications require that we learn the parameters of a model from data. EM is a method used to learn the parameters of probabilistic models for which the data for some of the variables in the models is either missing or hidden. There are instances ... More

Learning sparse relational transition modelsOct 26 2018We present a representation for describing transition models in complex uncertain domains using relational rules. For any action, a rule selects a set of relevant objects and computes a distribution over properties of just those objects in the resulting ... More

Effect of Depth and Width on Local Minima in Deep LearningNov 20 2018Jun 17 2019In this paper, we analyze the effects of depth and width on the quality of local minima, without strong over-parameterization and simplification assumptions in the literature. Without any simplification assumption, for deep nonlinear neural networks with ... More

Generalization in Deep LearningOct 16 2017May 10 2019This paper provides non-vacuous and numerically-tight generalization guarantees for deep learning, as well as theoretical insights into why and how deep learning can generalize well, despite its large capacity, complexity, possible algorithmic instability, ... More

Regret bounds for meta Bayesian optimization with an unknown Gaussian process priorNov 23 2018Bayesian optimization usually assumes that a Bayesian prior is given. However, the strong theoretical guarantees in Bayesian optimization are often regrettably compromised in practice because of unknown parameters in the prior. In this paper, we adopt ... More

Effect of Depth and Width on Local Minima in Deep LearningNov 20 2018Mar 04 2019In this paper, we analyze the effects of depth and width on the quality of local minima, without strong over-parameterization and simplification assumptions in the literature. Without any simplification assumption, for deep nonlinear neural networks with ... More

Learning Finite-State Controllers for Partially Observable EnvironmentsJan 23 2013Reactive (memoryless) policies are sufficient in completely observable Markov decision processes (MDPs), but some kind of memory is usually necessary for optimal control of a partially observable MDP. Policies with finite memory can be represented as ... More

Learning to Rank for Synthesizing Planning HeuristicsAug 03 2016We investigate learning heuristics for domain-specific planning. Prior work framed learning a heuristic as an ordinary regression problem. However, in a greedy best-first search, the ordering of states induced by a heuristic is more indicative of the ... More

Learning to guide task and motion planning using score-space representationJul 26 2018In this paper, we propose a learning algorithm that speeds up the search in task and motion planning problems. Our algorithm proposes solutions to three different challenges that arise in learning to improve planning efficiency: what to predict, how to ... More

Towards Understanding Generalization via Analytical Learning TheoryFeb 21 2018Oct 01 2018This paper introduces a novel measure-theoretic theory for machine learning that does not require statistical assumptions. Based on this theory, a new regularization method in deep learning is derived and shown to outperform previous methods in CIFAR-10, ... More

STRIPS Planning in Infinite DomainsJan 01 2017May 28 2017Many robotic planning applications involve continuous actions with highly non-linear constraints, which cannot be modeled using modern planners that construct a propositional representation. We introduce STRIPStream: an extension of the STRIPS language ... More

FFRob: Leveraging Symbolic Planning for Efficient Task and Motion PlanningAug 03 2016Dec 01 2017Mobile manipulation problems involving many objects are challenging to solve due to the high dimensionality and multi-modality of their hybrid configuration spaces. Planners that perform a purely geometric search are prohibitively slow for solving these ... More

Learning What Information to Give in Partially Observed DomainsMay 21 2018Sep 27 2018In many robotic applications, an autonomous agent must act within and explore a partially observed environment that is unobserved by its human teammate. We consider such a setting in which the agent can, while acting, transmit declarative information ... More

Provably Safe Robot Navigation with Obstacle UncertaintyMay 31 2017As drones and autonomous cars become more widespread it is becoming increasingly important that robots can operate safely under realistic conditions. The noisy information fed into real systems means that robots must use estimates of the environment to ... More

Focused Model-Learning and Planning for Non-Gaussian Continuous State-Action SystemsJul 26 2016Oct 23 2016We introduce a framework for model learning and planning in stochastic domains with continuous state and action spaces and non-Gaussian transition models. It is efficient because (1) local models are estimated only when the planner requires them; (2) ... More

Backward-Forward Search for Manipulation PlanningApr 12 2016In this paper we address planning problems in high-dimensional hybrid configuration spaces, with a particular focus on manipulation planning problems involving many objects. We present the hybrid backward-forward (HBF) planning algorithm that uses a backward ... More

Learning Probabilistic Relational Dynamics for Multiple TasksJun 20 2012The ways in which an agent's actions affect the world can often be modeled compactly using a set of relational probabilistic planning rules. This paper addresses the problem of learning such rule sets for multiple related tasks. We take a hierarchical ... More

Deliberation Scheduling for Time-Critical Sequential Decision MakingMar 06 2013We describe a method for time-critical decision making involving sequential tasks and stochastic processes. The method employs several iterative refinement routines for solving different aspects of the decision making problem. This paper concentrates ... More

Bayesian Optimization with Exponential ConvergenceApr 05 2016This paper presents a Bayesian optimization method with exponential convergence without the need of auxiliary optimization and without the delta-cover sampling. Most Bayesian optimization methods require auxiliary optimization: an additional non-convex ... More

STRIPStream: Integrating Symbolic Planners and Blackbox SamplersFeb 23 2018Feb 27 2019Many planning applications involve complex relationships defined on high-dimensional, continuous variables. For example, robotic manipulation requires planning with kinematic, collision, visibility, and motion constraints involving robot configurations, ... More

Learning to Cooperate via Policy SearchMay 25 2001Cooperative games are those in which both agents share the same payoff structure. Value-based reinforcement-learning algorithms, such as variants of Q-learning, have been applied to learning cooperative games, but they only apply when the game state is ... More

Sampling-Based Methods for Factored Task and Motion PlanningJan 02 2018Feb 12 2019This paper presents a general-purpose formulation of a large class of discrete-time planning problems, with hybrid state and control-spaces, as factored transition systems. Factoring allows state transitions to be described as the intersection of several ... More

The Thing That We Tried Didn't Work Very Well : Deictic Representation in Reinforcement LearningDec 12 2012Most reinforcement learning methods operate on propositional representations of the world state. Such representations are often intractably large and generalize poorly. Using a deictic representation is believed to be a viable alternative: they promise ... More

Generalization in Machine Learning via Analytical Learning TheoryFeb 21 2018Mar 06 2019This paper introduces a novel measure-theoretic theory for machine learning that does not require statistical assumptions. Based on this theory, a new regularization method in deep learning is derived and shown to outperform previous methods in CIFAR-10, ... More

Focused Model-Learning and Planning for Non-Gaussian Continuous State-Action SystemsJul 26 2016Sep 22 2016We introduce a framework for model learning and planning in stochastic domains with continuous state and action spaces and non-Gaussian transition models. It is efficient because (1) local models are estimated only when the planner requires them; (2) ... More

FFRob: Leveraging Symbolic Planning for Efficient Task and Motion PlanningAug 03 2016Mobile manipulation problems involving many objects are challenging to solve due to the high dimensionality and multi-modality of their hybrid configuration spaces. Planners that perform a purely geometric search are prohibitively slow for solving these ... More

Guiding the search in continuous state-action spaces by learning an action sampling distribution from off-target samplesNov 04 2017In robotics, it is essential to be able to plan efficiently in high-dimensional continuous state-action spaces for long horizons. For such complex planning problems, unguided uniform sampling of actions until a path to a goal is found is hopelessly inefficient, ... More

Learning to Cooperate via Policy SearchAug 07 2014Cooperative games are those in which both agents share the same payoff structure. Value-based reinforcement-learning algorithms, such as variants of Q-learning, have been applied to learning cooperative games, but they only apply when the game state is ... More

On the Complexity of Solving Markov Decision ProblemsFeb 20 2013Markov decision problems (MDPs) provide the foundations for a number of problems of interest to AI researchers studying automated planning and reinforcement learning. In this paper, we summarize results regarding the complexity of solving MDPs and the ... More

Selecting Representative Examples for Program SynthesisNov 09 2017Jun 07 2018Program synthesis is a class of regression problems where one seeks a solution, in the form of a source-code program, mapping the inputs to their corresponding outputs exactly. Due to its precise and combinatorial nature, program synthesis is commonly ... More

Integrating Human-Provided Information Into Belief State Representation Using Dynamic FactorizationFeb 28 2018Jul 30 2018In partially observed environments, it can be useful for a human to provide the robot with declarative information that represents probabilistic relational constraints on properties of objects in the world, augmenting the robot's sensory observations. ... More

Learning Quickly to Plan Quickly Using Modular Meta-LearningSep 20 2018Feb 16 2019Multi-object manipulation problems in continuous state and action spaces can be solved by planners that search over sampled values for the continuous parameters of operators. The efficiency of these planners depends critically on the effectiveness of ... More

Hierarchical Solution of Markov Decision Processes using Macro-actionsJan 30 2013We investigate the use of temporally abstract actions, or macro-actions, in the solution of Markov decision processes. Unlike current models that combine both primitive actions and macro-actions and leave the state space unchanged, we propose a hierarchical ... More

Differentiable Algorithm Networks for Composable Robot LearningMay 28 2019This paper introduces the Differentiable Algorithm Network (DAN), a composable architecture for robot learning systems. A DAN is composed of neural network modules, each encoding a differentiable robot algorithm and an associated model; and it is trained ... More

Graph Element Networks: adaptive, structured computation and memoryApr 18 2019May 03 2019We explore the use of graph neural networks (GNNs) to model spatial processes in which there is no a priori graphical structure. Similar to finite element analysis, we assign nodes of a GNN to spatial locations and use a computational process defined ... More

Active model learning and diverse action sampling for task and motion planningMar 02 2018Aug 12 2018The objective of this work is to augment the basic abilities of a robot by learning to use new sensorimotor primitives to enable the solution of complex long-horizon problems. Solving long-horizon problems in complex domains requires flexible generative ... More

Solving POMDPs by Searching the Space of Finite PoliciesJan 23 2013Solving partially observable Markov decision processes (POMDPs) is highly intractable in general, at least in part because the optimal policy may be infinitely large. In this paper, we explore the problem of finding the optimal policy from a restricted ... More

Object-based World Modeling in Semi-Static Environments with Dependent Dirichlet-Process MixturesDec 02 2015To accomplish tasks in human-centric indoor environments, robots need to represent and understand the world in terms of objects and their attributes. We refer to this attribute-based representation as a world model, and consider how to acquire it via ... More

Graph Element Networks: adaptive, structured computation and memoryApr 18 2019May 13 2019We explore the use of graph neural networks (GNNs) to model spatial processes in which there is no a priori graphical structure. Similar to finite element analysis, we assign nodes of a GNN to spatial locations and use a computational process defined ... More

Few-Shot Bayesian Imitation Learning with Logic over ProgramsApr 12 2019We describe an expressive class of policies that can be efficiently learned from a few demonstrations. Policies are represented as logical combinations of programs drawn from a small domain-specific language (DSL). We define a prior over policies with ... More

Graph Element Networks: adaptive, structured computation and memoryApr 18 2019We explore the use of graph neural networks (GNNs) to model spatial processes in which there is a priori graphical structure. Similar to finite element analysis, we assign nodes of a GNN to spatial locations and use a computational process defined on ... More

Graph Element Networks: adaptive, structured computation and memoryApr 18 2019Jun 19 2019We explore the use of graph neural networks (GNNs) to model spatial processes in which there is no a priori graphical structure. Similar to finite element analysis, we assign nodes of a GNN to spatial locations and use a computational process defined ... More

Role of Iso-connectivity Topologies in Multi-agent InteractionsJun 11 2016In this paper, we present the benefits of exploring different topologies with equal connectivity measure, or iso-connectivity topologies, in relation to the multiagent system dynamics. The level of global information sharing ability among agents in a ... More

CAPIR: Collaborative Action Planning with Intention RecognitionJun 26 2012We apply decision theoretic techniques to construct non-player characters that are able to assist a human player in collaborative games. The method is based on solving Markov decision processes, which can be difficult when the game state is described ... More

Studies in Small Field InflationSep 09 2011May 29 2012We explore some issues in slow roll inflation in situations where field excursions are small compared to $M_p$. We argue that for small field inflation, minimizing fine tuning requires low energy supersymmetry and a tightly constrained structure. Hybrid ... More

A General Method for Obtaining a Lower Bound for the Ground State Entropy Density of the Ising Model With Short Range InteractionsApr 14 2001We present a general method for obtaining a lower bound for the ground state entropy density of the Ising Model with nearest neighbor interactions. Then, using this method, and with a random coupling constant configuration, we obtain a lower bound for ... More

Learning Policies with External MemoryMar 02 2001In order for an agent to perform well in partially observable domains, it is usually necessary for actions to depend on the history of observations. In this paper, we explore a {\it stigmergic} approach, in which the agent's actions include the ability ... More

Effective Caching for the Secure Content Distribution in Information-Centric NetworkingAug 01 2018The secure distribution of protected content requires consumer authentication and involves the conventional method of end-to-end encryption. However, in information-centric networking (ICN) the end-to-end encryption makes the content caching ineffective ... More

Hypermap-Homology Quantum Codes (Ph.D. thesis)Oct 20 2013We introduce a new type of sparse CSS quantum error correcting code based on the homology of hypermaps. Sparse quantum error correcting codes are of interest in the building of quantum computers due to their ease of implementation and the possibility ... More

A partial analogue of the Grothendieck-Springer resolution for symmetric spacesApr 19 2019Motivated by questions in the study of relative trace formulae, we construct a generalization of Grothendieck's simultaneous resolution over the regular locus of certain symmetric pairs. We use this space to prove a relative version of results of Donagi ... More

A Generalized Theta lifting, CAP representations, and Arthur parametersMar 07 2017Apr 19 2019We study a new lifting of automorphic representations using the theta representation $\Theta$ on the $4$-fold cover of the symplectic group, $\overline{\mathrm{Sp}}_{2r}(\mathbb{A})$. This lifting produces the first examples of CAP representations on ... More

L-modules and micro-supportDec 22 2001Jan 09 2005L-modules are a combinatorial analogue of constructible sheaves on the reductive Borel-Serre compactification of a locally symmetric space. We define the micro-support of an L-module; it is a set of irreducible modules for the Levi quotients of the parabolic ... More

Geometric rationality of equal-rank Satake compactificationsNov 07 2002Sep 18 2004Satake has constructed compactifications of symmetric spaces D=G/K which (under a condition called geometric rationality by Casselman) yield compactifications of the corresponding locally symmetric spaces. The different compactifications depend on the ... More

Understanding artificial intelligence ethics and safetyJun 11 2019A remarkable time of human promise has been ushered in by the convergence of the ever-expanding availability of big data, the soaring speed and stretch of cloud computing platforms, and the advancement of increasingly sophisticated machine learning algorithms. ... More

Zero forcing and maximum nullity for hypergraphsAug 29 2018The concept of zero forcing is extended from graphs to uniform hypergraphs in analogy with the way zero forcing was defined as an upper bound for the maximum nullity of the family of symmetric matrices whose nonzero pattern of entries is described by ... More

The autofeat Python Library for Automated Feature Engineering and SelectionJan 22 2019May 12 2019This paper describes the autofeat Python library, which provides a scikit-learn style linear regression model with automated feature engineering and selection capabilities. Complex non-linear machine learning models such as neural networks are in practice ... More

Monodromy of the generalized hypergeometric equation in the Frobenius basisJul 08 2014We consider monodromy groups of the generalized hypergeometric equation \begin{equation*} \big[z(\theta-\alpha_{1})\cdots (\theta-\alpha_{n})-(\theta+\beta_{1}-1)\cdots (\theta+\beta_{n}-1)\big]f(z) = 0\text{, where }\theta = z d/dz, \end{equation*} in ... More

A Generalized Theta lifting, CAP representations, and Arthur parametersMar 07 2017Jan 23 2018We study a new lifting of automorphic representations using the theta representation $\Theta$ on the $4$-fold cover of the symplectic group, $\overline{\mathrm{Sp}}_{2r}(\mathbb{A})$. This lifting produces the first examples of CAP representations on ... More

L-modules and the Conjecture of Rapoport and Goresky-MacPhersonDec 22 2001May 13 2005Consider the middle perversity intersection cohomology groups of various compactifications of a Hermitian locally symmetric space. Rapoport and independently Goresky and MacPherson have conjectured that these groups coincide for the reductive Borel-Serre ... More

L^2-cohomology of locally symmetric spaces, IDec 20 2004Jan 11 2006Let X be a locally symmetric space associated to a reductive algebraic group G defined over Q. L-modules are a combinatorial analogue of constructible sheaves on the reductive Borel-Serre compactification of X; they were introduced in [math.RT/0112251]. ... More

On the Cohomology of Locally Symmetric Spaces and of their CompactificationsJun 27 2003Jul 19 2003This expository article is an expanded version of talks given at the "Current Developments in Mathematics, 2002" conference. It gives an introduction to the (generalized) conjecture of Rapoport and Goresky-MacPherson which identifies the intersection ... More

On The Group Algebra Decomposition of a Jacobian VarietyMar 11 2016Given a compact Riemann surface X with an action of a finite group G, the group algebra Q[G] provides an isogenous decomposition of its Jacobian variety JX, known as the group algebra decomposition of JX. We obtain a method to concretely build a decomposition ... More

Learning to Acquire InformationApr 20 2017Jul 11 2017We consider the problem of diagnosis where a set of simple observations are used to infer a potentially complex hidden hypothesis. Finding the optimal subset of observations is intractable in general, thus we focus on the problem of active diagnosis, ... More

Residual Policy LearningDec 15 2018Jan 03 2019We present Residual Policy Learning (RPL): a simple method for improving nondifferentiable policies using model-free deep reinforcement learning. RPL thrives in complex robotic manipulation tasks where good but imperfect controllers are available. In ... More

Modular meta-learningJun 26 2018Many prediction problems, such as those that arise in the context of robotics, have a simplifying underlying structure that could accelerate learning. In this paper, we present a strategy for learning a set of neural network modules that can be combined ... More

Finding Frequent Entities in Continuous DataMay 08 2018In many applications that involve processing high-dimensional data, it is important to identify a small set of entities that account for a significant fraction of detections. Rather than formalize this as a clustering problem, in which all detections ... More

Modular meta-learningJun 26 2018May 02 2019Many prediction problems, such as those that arise in the context of robotics, have a simplifying underlying structure that, if known, could accelerate learning. In this paper, we present a strategy for learning a set of neural network modules that can ... More

Low-distortion slow light using two absorption resonancesJul 06 2006We consider group delay and broadening using two strongly absorbing and widely spaced resonances. We derive relations which show that very large pulse bandwidths coupled with large group delays and small broadening can be achieved. Unlike single resonance ... More

Adaptive identification of coherent statesAug 18 2015Jan 07 2016We present methods for efficient characterization of an optical coherent state $|\alpha\rangle$. We choose measurement settings adaptively and stochastically, based on data while it is collected. Our algorithm divides the estimation into two distinct ... More

A Joint Indoor WLAN Localization and Outlier Detection Scheme Using LASSO and Elastic-Net Optimization TechniquesOct 18 2016In this paper, we introduce two indoor Wireless Local Area Network (WLAN) positioning methods using augmented sparse recovery algorithms. These schemes render a sparse user's position vector, and in parallel, minimize the distance between the online measurement ... More

Reliable Semiclassical Computations in QCDApr 29 2010May 05 2010We revisit the question of whether or not one can perform reliable semiclassical QCD computations at zero temperature. We study correlation functions with no perturbative contributions, and organize the problem by means of the operator product expansion, ... More

A Reduced Complexity Cross-correlation Interference Mitigation Technique on a Real-time Software-defined Radio GPS L1 ReceiverJun 30 2019The U.S. global position system (GPS) is one of the existing global navigation satellite systems (GNSS) that provides position and time information for users in civil, commercial and military backgrounds. Because of its reliance on many applications nowadays, ... More

Transparent Boundary Conditions for the Time-Dependent Schrödinger Equation with a Vector PotentialDec 11 2018We consider the problem of constructing transparent boundary conditions for the time-dependent Schr\"odinger equation with a compactly supported binding potential and, if desired, a spatially uniform, time-dependent electromagnetic vector potential. Such ... More

Norm-preserving discretization of integral equations for elliptic PDEs with internal layers I: the one-dimensional caseMay 29 2013We investigate the behavior of integral formulations of variable coefficient elliptic partial differential equations (PDEs) in the presence of steep internal layers. In one dimension, the equations that arise can be solved analytically and the condition ... More

Propagation time for probabilistic zero forcingDec 24 2018Zero forcing is a coloring game played on a graph that was introduced more than ten years ago in several different applications. The goal is to color all the vertices blue by repeated use of a (deterministic) color change rule. Probabilistic zero forcing ... More

Cyclical Learning Rates for Training Neural NetworksJun 03 2015Apr 04 2017It is known that the learning rate is the most important hyper-parameter to tune for training deep neural networks. This paper describes a new method for setting the learning rate, named cyclical learning rates, which practically eliminates the need to ... More

A new mixed potential representation for the equations of unsteady, incompressible flowSep 22 2018Sep 27 2018We present a new integral representation for the unsteady, incompressible Stokes or Navier-Stokes equations, based on a linear combination of heat and harmonic potentials. For velocity boundary conditions, this leads to a coupled system of integral equations: ... More

Cyclical Learning Rates for Training Neural NetworksJun 03 2015Oct 26 2016It is known that the learning rate is the most important hyper-parameter to tune for training deep neural networks. This paper describes a new method for setting the learning rate, named cyclical learning rates, which practically eliminates the need to ... More

Auxiliary Variables in TLA+Mar 15 2017May 29 2017Auxiliary variables are often needed for verifying that an implementation is correct with respect to a higher-level specification. They augment the formal description of the implementation without changing its semantics--that is, the set of behaviors ... More

Fast elliptic solvers in cylindrical coordinates and the Coulomb collision operatorFeb 10 2011In this paper, we describe a new class of fast solvers for separable elliptic partial differential equations in cylindrical coordinates $(r,\theta,z)$ with free-space radiation conditions. By combining integral equation methods in the radial variable ... More

Best Practices for Applying Deep Learning to Novel ApplicationsApr 05 2017This report is targeted to groups who are subject matter experts in their application but deep learning novices. It contains practical advice for those interested in testing the use of deep neural networks on applications that are novel for deep learning. ... More

How to find real-world applications for compressive sensingMay 06 2013Jun 26 2013The potential of compressive sensing (CS) has spurred great interest in the research community and is a fast growing area of research. However, research translating CS theory into practical hardware and demonstrating clear and significant benefits with ... More

An adaptive fast Gauss transform in two dimensionsDec 01 2017A variety of problems in computational physics and engineering require the convolution of the heat kernel (a Gaussian) with either discrete sources, densities supported on boundaries, or continuous volume distributions. We present a unified fast Gauss ... More

The coalescent and its descendantsJun 08 2010The coalescent revolutionised theoretical population genetics, simplifying, or making possible for the first time, many analyses, proofs, and derivations, and offering crucial insights about the way in which the structure of data in samples from populations ... More

Universality for conditional measures of the Bessel point processApr 08 2019The Bessel point process is a rigid point process on the positive real line and its conditional measure on a bounded interval $[0,R]$ is almost surely an orthogonal polynomial ensemble. In this article, we show that if $R$ tends to infinity, one almost ... More

Parity Sheaves and Smith TheoryAug 28 2017Sep 08 2017We develop a connection between parity complexes and Smith theory for varieties equipped with an action of a cyclic group of prime order $p$. We define a sheaf-theoretic Tate cohomology theory and study the corresponding notion of Tate-parity complex. ... More

Hands-On Universe: A Global Program for Education and Public Outreach in AstronomySep 21 2001Hands-On Universe (HOU) is an educational program that enables students to investigate the Universe while applying tools and concepts from science, math, and technology. Using the Internet, HOU participants around the world request observations from an ... More

Modular meta-learning in abstract graph networks for combinatorial generalizationDec 19 2018Modular meta-learning is a new framework that generalizes to unseen datasets by combining a small set of neural modules in different ways. In this work we propose abstract graph networks: using graphs as abstractions of a system's subparts without a fixed ... More

Planning for Decentralized Control of Multiple Robots Under UncertaintyFeb 12 2014We describe a probabilistic framework for synthesizing control policies for general multi-robot systems, given environment and sensor models and a cost function. Decentralized, partially observable Markov decision processes (Dec-POMDPs) are a general ... More

A fast solver for the narrow capture and narrow escape problems in the sphereJun 10 2019We present an efficient method to solve the narrow capture and narrow escape problems for the sphere. The narrow capture problem models the equilibrium behavior of a Brownian particle in the exterior of a sphere whose surface is reflective, except for ... More

Inverse Obstacle scattering in two dimensions with multiple frequency data and multiple angles of incidenceAug 22 2014We consider the problem of reconstructing the shape of an impenetrable sound-soft obstacle from scattering measurements. The input data is assumed to be the far-field pattern generated when a plane wave impinges on an unknown obstacle from one or more ... More

A disciplined approach to neural network hyper-parameters: Part 1 -- learning rate, batch size, momentum, and weight decayMar 26 2018Apr 24 2018Although deep learning has produced dazzling successes for applications of image, speech, and video processing in the past few years, most trainings are with suboptimal hyper-parameters, requiring unnecessarily long training times. Setting the hyper-parameters ... More

Variants on the minimum rank problem: A survey IIFeb 25 2011Oct 08 2014The minimum rank problem for a (simple) graph $G$ is to determine the smallest possible rank over all real symmetric matrices whose $ij$th entry (for $i\neq j$) is nonzero whenever $\{i,j\}$ is an edge in $G$ and is zero otherwise. This paper surveys ... More

Hybrid asymptotic/numerical methods for the evaluation of layer heat potentials in two dimensionsMar 20 2018We present a hybrid asymptotic/numerical method for the accurate computation of single and double layer heat potentials in two dimensions. It has been shown in previous work that simple quadrature schemes suffer from a phenomenon called "geometrically-induced ... More

Combining Physical Simulators and Object-Based Networks for ControlApr 13 2019Physics engines play an important role in robot planning and control; however, many real-world control problems involve complex contact dynamics that cannot be characterized analytically. Most physics engines therefore employ . approximations that lead ... More