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On uniqueness of P-twistsNov 17 2017Jun 13 2019We prove that for any $\mathbb{P}^n$-functor $F$, split or non-split, all the convolutions (double cones) of the three-term complex $FHR \rightarrow FR \rightarrow$ Id defining its $\mathbb{P}$-twist are isomorphic.

Multiplicative structure on the Hochschild cohomology of crossed product algebrasNov 15 2005Dec 08 2005Consider a smooth affine algebraic variety $X$ over an algebraically closed field, and let a finite group $G$ act on it. We assume that the characteristic of the field is greater than the dimension of $X$ and the order of $G$. An explicit formula for ... More

Spherical functorsNov 28 2007Sep 25 2013This paper has been withdrawn and replaced by arXiv:1309.5035. In this paper we describe some examples of so called spherical functors between triangulated categories, which generalize the notion of a spherical object. We also give sufficient conditions ... More

Affine tangles and irreducible exotic sheavesFeb 07 2008Feb 05 2016We construct a weak representation of the category of framed affine tangles on a disjoint union of triangulated categories ${\mathcal D}_{2n}$. The categories we use are that of coherent sheaves on Springer fibers over a nilpotent element of $sl_{2n}$ ... More

On uniqueness of P-twistsNov 17 2017Jun 23 2018We prove that for any $\mathbb{P}^n$-functor $F$, split or non-split, all the convolutions (double cones) of the three-term complex $FHR \rightarrow FR \rightarrow$ Id defining its $\mathbb{P}$-twist are isomorphic.

Exotic t-structures for two-block Springer fibersFeb 02 2016We study the exotic t-structure on the derived category of coherent sheaves on two-block Springer fibre (i.e. for a nilpotent matrix of type (m+n,n) in type A). The exotic t-structure has been defined by Bezrukavnikov and Mirkovic for Springer theoretic ... More

On adjunctions for Fourier-Mukai transformsApr 18 2010Aug 16 2012We show that the adjunction counits of a Fourier-Mukai transform $\Phi$ from $D(X_1)$ to $D(X_2)$ arise from maps of the kernels of the corresponding Fourier-Mukai transforms. In a very general setting of proper separable schemes of finite type over a ... More

$\mathbb{P}^n$-functorsMay 14 2019Aug 04 2019We propose a new theory of (non-split) P^n-functors. These are F: A -> B for which the adjunction monad RF is a repeated extension of Id_A by powers of an autoequivalence H and three conditions are satisfied: the monad condition, the adjoints condition, ... More

$\mathbb{P}^n$-functorsMay 14 2019We propose a new theory of (non-split) P^n-functors. These are F: A -> B for which the adjunction monad RF is a repeated extension of Id_A by powers of an autoequivalence H and three conditions are satisfied: the monad condition, the adjoints condition, ... More

Bar category of modules and homotopy adjunction for tensor functorsDec 30 2016Jul 31 2018Given a DG-category A we introduce the bar category of modules Modbar(A). It is a DG-enhancement of the derived category D(A) of A which is isomorphic to the category of DG A-modules with A-infinity morphisms between them. However, it is defined intrinsically ... More

Spherical DG-functorsSep 19 2013Oct 19 2015For two DG-categories A and B we define the notion of a spherical Morita quasi-functor A -> B. We construct its associated autoequivalences: the twist T of D(B) and the co-twist F of D(A). We give powerful sufficiency criteria for a quasi-functor to be ... More

Orthogonally spherical objects and spherical fibrationsNov 02 2010Oct 19 2015We introduce a relative version of the spherical objects of Seidel and Thomas. Define an object E in the derived category D(Z x X) to be spherical over Z if the corresponding functor from D(Z) to D(X) gives rise to autoequivalences of D(Z) and D(X) in ... More

Stability conditions for Slodowy slices and real variations of stabilityAug 07 2011Dec 18 2014We provide examples of an explicit submanifold in Bridgeland stabilities space of a local Calabi-Yau, and propose a new variant of definition of stabilities on a triangulated category, which we call a "real variation of stability conditions". We discuss ... More

Topological Parameters for Time-Space TradeoffFeb 13 2013In this paper we propose a family of algorithms combining tree-clustering with conditioning that trade space for time. Such algorithms are useful for reasoning in probabilistic and deterministic networks as well as for accomplishing optimization tasks. ... More

Efficient Hashing with Lookups in two Memory AccessesJul 09 2004The study of hashing is closely related to the analysis of balls and bins. It is well-known that instead of using a single hash function if we randomly hash a ball into two bins and place it in the smaller of the two, then this dramatically lowers the ... More

Minimum Enclosing Polytope in High DimensionsJul 08 2004We study the problem of covering a given set of $n$ points in a high, $d$-dimensional space by the minimum enclosing polytope of a given arbitrary shape. We present algorithms that work for a large family of shapes, provided either only translations and ... More

Bucket Elimination: A Unifying Framework for Several Probabilistic InferenceFeb 13 2013Probabilistic inference algorithms for finding the most probable explanation, the maximum aposteriori hypothesis, and the maximum expected utility and for updating belief are reformulated as an elimination--type algorithm called bucket elimination. This ... More

A non-expert view on Turing machines, Proof Verifiers, and Mental reasoningOct 30 2010Mar 01 2012The paper explores known results related to the problem of identifying if a given program terminates on all inputs -- this is a simple generalization of the halting problem. We will see how this problem is related and the notion of proof verifiers. We ... More

Can Knowledge be preserved in the long run?Nov 09 2010Feb 06 2011Can (scientific) knowledge be reliably preserved over the long term? We have today very efficient and reliable methods to encode, store and retrieve data in a storage medium that is fault tolerant against many types of failures. But does this guarantee ... More

A Scheme for Approximating Probabilistic InferenceFeb 06 2013This paper describes a class of probabilistic approximation algorithms based on bucket elimination which offer adjustable levels of accuracy and efficiency. We analyze the approximation for several tasks: finding the most probable explanation, belief ... More

Criticality in the Quantum Kicked Rotor with a Smooth PotentialAug 13 2008We investigate the possibility of an Anderson type transition in the quantum kicked rotor with a smooth potential due to dynamical localization of the wavefunctions. Our results show the typical characteristics of a critical behavior i.e multifractal ... More

Best-First AND/OR Search for Most Probable ExplanationsJun 20 2012The paper evaluates the power of best-first search over AND/OR search spaces for solving the Most Probable Explanation (MPE) task in Bayesian networks. The main virtue of the AND/OR representation of the search space is its sensitivity to the structure ... More

Electrodynamics in Skyrmions MergingJan 28 2014Apr 05 2014In a recent study the coalescence of magnetic skyrmions was observed in a metallic chiral magnet Fe0.5Co0.5Si when the skyrmion phase is destroyed, and numerical simulations demonstrated the existence of a monopole at the merging point of two skyrmion ... More

Supercurrent-induced Skyrmion dynamics and Tunable Weyl points in Chiral Magnet with SuperconductivityJul 08 2016Aug 25 2016Recent studies show superconductivity provides new perspectives on spintronics. We study a heterostructure composed of an s-wave superconductor and a cubic chiral-magnet that can stabilize a topological spin texture, a skyrmion. We propose a supercurrent-induced ... More

Optimal amortized regret in every intervalApr 29 2013Consider the classical problem of predicting the next bit in a sequence of bits. A standard performance measure is {\em regret} (loss in payoff) with respect to a set of experts. For example if we measure performance with respect to two constant experts ... More

Oscillation collapse in coupled quantum van der Pol oscillatorsSep 15 2017Nov 18 2017The classical self-oscillations can collapse merely due to their mutual couplings. We investigate this oscillation collapse in quantum van der Pol oscillators. For a pair of quantum oscillators, the steady-state mean phonon number is shown to be lower ... More

Approximate Inference Algorithms for Hybrid Bayesian Networks with Discrete ConstraintsJul 04 2012In this paper, we consider Hybrid Mixed Networks (HMN) which are Hybrid Bayesian Networks that allow discrete deterministic information to be modeled explicitly in the form of constraints. We present two approximate inference algorithms for HMNs that ... More

Supercurrent-induced Skyrmion dynamics and Tunable Weyl points in Chiral Magnet with SuperconductivityJul 08 2016Nov 30 2016Recent studies show superconductivity provides new perspectives on spintronics. We study a heterostructure composed of an s-wave superconductor and a cubic chiral-magnet that can stabilize a topological spin texture, a skyrmion. We propose a supercurrent-induced ... More

Computing strong regular characteristic pairs with Groebner basesJul 31 2019The W-characteristic set of a polynomial ideal is the minimal triangular set contained in the reduced lexicographical Groebner basis of the ideal. A pair (C,G) of polynomial sets is a strong regular characteristic pair if G is a reduced lexicographical ... More

A Differential Equations Approach to Optimizing Regret Trade-offsMay 07 2013We consider the classical question of predicting binary sequences and study the {\em optimal} algorithms for obtaining the best possible regret and payoff functions for this problem. The question turns out to be also equivalent to the problem of optimal ... More

Hexadecapole fluctuation mechanism for s-wave heavy fermion superconductor CeCu2Si2: Interplay between intra- and inter-orbital Cooper pairsFeb 28 2019In heavy-fermion superconductors, it is widely believed that the superconducting gap function has sign-reversal due to the strong electron correlation. However, recently discovered fully-gapped s-wave superconductivity in CeCu2Si2 has clarified that strong ... More

Bounding Search Space Size via (Hyper)tree DecompositionsJun 13 2012This paper develops a measure for bounding the performance of AND/OR search algorithms for solving a variety of queries over graphical models. We show how drawing a connection to the recent notion of hypertree decompositions allows to exploit determinism ... More

Fast-rate and optimistic-rate error bounds for L1-regularized regressionAug 01 2011We consider the prediction error of linear regression with L1 regularization when the number of covariates p is large relative to the sample size n. When the model is k-sparse and well-specified, and restricted isometry or similar conditions hold, the ... More

Learning Two layer Networks with Multinomial Activation and High ThresholdsMar 21 2019Giving provable guarantees for learning neural networks is a core challenge of machine learning theory. Most prior work gives parameter recovery guarantees for one hidden layer networks. In this work we study a two layer network where the top node instead ... More

A Simple Insight into Iterative Belief Propagation's SuccessOct 19 2012In Non - ergodic belief networks the posterior belief OF many queries given evidence may become zero.The paper shows that WHEN belief propagation IS applied iteratively OVER arbitrary networks(the so called, iterative OR loopy belief propagation(IBP)) ... More

An Empirical Study of w-Cutset Sampling for Bayesian NetworksOct 19 2012The paper studies empirically the time-space trade-off between sampling and inference in a sl cutset sampling algorithm. The algorithm samples over a subset of nodes in a Bayesian network and applies exact inference over the rest. Consequently, while ... More

The Relationship Between AND/OR Search and Variable EliminationJul 04 2012In this paper we compare search and inference in graphical models through the new framework of AND/OR search. Specifically, we compare Variable Elimination (VE) and memoryintensive AND/OR Search (AO) and place algorithms such as graph-based backjumping ... More

Identifying Independencies in Causal Graphs with FeedbackFeb 13 2013We show that the d -separation criterion constitutes a valid test for conditional independence relationships that are induced by feedback systems involving discrete variables.

Mini-Bucket Heuristics for Improved SearchJan 23 2013The paper is a second in a series of two papers evaluating the power of a new scheme that generates search heuristics mechanically. The heuristics are extracted from an approximation scheme called mini-bucket elimination that was recently introduced. ... More

The Mind Grows CircuitsMar 01 2012Mar 17 2012There is a vast supply of prior art that study models for mental processes. Some studies in psychology and philosophy approach it from an inner perspective in terms of experiences and percepts. Others such as neurobiology or connectionist-machines approach ... More

Extended Bayesian Information Criteria for Gaussian Graphical ModelsNov 30 2010Gaussian graphical models with sparsity in the inverse covariance matrix are of significant interest in many modern applications. For the problem of recovering the graphical structure, information criteria provide useful optimization objectives for algorithms ... More

Bayesian model choice and information criteria in sparse generalized linear modelsDec 23 2011We consider Bayesian model selection in generalized linear models that are high-dimensional, with the number of covariates p being large relative to the sample size n, but sparse in that the number of active covariates is small compared to p. Treating ... More

Exact block-wise optimization in group lasso and sparse group lasso for linear regressionOct 16 2010Nov 11 2010The group lasso is a penalized regression method, used in regression problems where the covariates are partitioned into groups to promote sparsity at the group level. Existing methods for finding the group lasso estimator either use gradient projection ... More

Escher degree of non-periodic L-tilings by 2 prototilesFeb 21 2012For a given tiling of the euclidean plane ${\bf E}^2$, we call the degree of freedom of perturbed edges of prototiles {\it escher degree}. In this paper we consider non-periodic L-tilings by 2 prototiles and obtain the escher degree of them.

ROCKET: Robust Confidence Intervals via Kendall's Tau for Transelliptical Graphical ModelsFeb 26 2015Mar 23 2015Undirected graphical models are used extensively in the biological and social sciences to encode a pattern of conditional independences between variables, where the absence of an edge between two nodes $a$ and $b$ indicates that the corresponding two ... More

An Evaluation of Structural Parameters for Probabilistic Reasoning: Results on Benchmark CircuitsFeb 13 2013Many algorithms for processing probabilistic networks are dependent on the topological properties of the problem's structure. Such algorithms (e.g., clustering, conditioning) are effective only if the problem has a sparse graph captured by parameters ... More

Contraction and uniform convergence of isotonic regressionJun 06 2017Oct 31 2018We consider the problem of isotonic regression, where the underlying signal $x$ is assumed to satisfy a monotonicity constraint, that is, $x$ lies in the cone $\{ x\in\mathbb{R}^n : x_1 \leq \dots \leq x_n\}$. We study the isotonic projection operator ... More

Multiple testing with the structure adaptive Benjamini-Hochberg algorithmJun 25 2016Sep 13 2017In multiple testing problems, where a large number of hypotheses are tested simultaneously, false discovery rate (FDR) control can be achieved with the well-known Benjamini-Hochberg procedure, which adapts to the amount of signal present in the data. ... More

Multiple testing with the structure adaptive Benjamini-Hochberg algorithmJun 25 2016In multiple testing problems, where a large number of hypotheses are tested simultaneously, false discovery rate (FDR) control can be achieved with the well-known Benjamini-Hochberg procedure, which adapts to the amount of signal present in the data. ... More

ROCKET: Robust Confidence Intervals via Kendall's Tau for Transelliptical Graphical ModelsFeb 26 2015Sep 01 2017Undirected graphical models are used extensively in the biological and social sciences to encode a pattern of conditional independences between variables, where the absence of an edge between two nodes $a$ and $b$ indicates that the corresponding two ... More

The p-filter: multi-layer FDR control for grouped hypothesesDec 10 2015Oct 29 2016In many practical applications of multiple hypothesis testing using the False Discovery Rate (FDR), the given hypotheses can be naturally partitioned into groups, and one may not only want to control the number of false discoveries (wrongly rejected null ... More

High-dimensional Ising model selection with Bayesian information criteriaMar 13 2014Mar 05 2015We consider the use of Bayesian information criteria for selection of the graph underlying an Ising model. In an Ising model, the full conditional distributions of each variable form logistic regression models, and variable selection techniques for regression ... More

Accumulation tests for FDR control in ordered hypothesis testingMay 27 2015Jun 25 2016Multiple testing problems arising in modern scientific applications can involve simultaneously testing thousands or even millions of hypotheses, with relatively few true signals. In this paper, we consider the multiple testing problem where prior information ... More

Multiphoton Quantum Optics and Quantum State EngineeringJan 09 2007We present a review of theoretical and experimental aspects of multiphoton quantum optics. Multiphoton processes occur and are important for many aspects of matter-radiation interactions that include the efficient ionization of atoms and molecules, and, ... More

Realistic continuous-variable quantum teleportation with non-Gaussian resourcesOct 14 2009Dec 10 2009We present a comprehensive investigation of nonideal continuous-variable quantum teleportation implemented with entangled non-Gaussian resources. We discuss in a unified framework the main decoherence mechanisms, including imperfect Bell measurements ... More

Hierarchies of Geometric EntanglementDec 25 2007May 28 2008We introduce a class of generalized geometric measures of entanglement. For pure quantum states of $N$ elementary subsystems, they are defined as the distances from the sets of $K$-separable states ($K=2,...,N$). The entire set of generalized geometric ... More

Flavor entanglement in neutrino oscillations in the wave packet descriptionOct 22 2015Dec 17 2015The wave packet approach to neutrino oscillations provides an enlightening description of quantum decoherence induced, during propagation, by localization effects. Within this approach, we show that a deeper insight into the dynamical aspects of particle ... More

Proceedings of the Twenty-Second Conference on Uncertainty in Artificial Intelligence (2006)Aug 25 2012Aug 28 2014This is the Proceedings of the Twenty-Second Conference on Uncertainty in Artificial Intelligence, which was held in Cambridge, MA, July 13 - 16 2006.

Hybrid Processing of Beliefs and ConstraintsJan 10 2013This paper explores algorithms for processing probabilistic and deterministic information when the former is represented as a belief network and the latter as a set of boolean clauses. The motivating tasks are 1. evaluating beliefs networks having a large ... More

Alternating minimization and alternating descent over nonconvex setsSep 13 2017Feb 25 2019We analyze the performance of alternating minimization for loss functions optimized over two variables, where each variable may be restricted to lie in some potentially nonconvex constraint set. This type of setting arises naturally in high-dimensional ... More

Gradient descent with nonconvex constraints: local concavity determines convergenceMar 22 2017Oct 19 2017Many problems in high-dimensional statistics and optimization involve minimization over nonconvex constraints-for instance, a rank constraint for a matrix estimation problem-but little is known about the theoretical properties of such optimization problems ... More

On the Construction of Knockoffs in Case-Control StudiesDec 29 2018Consider a case-control study in which we have a random sample, constructed in such a way that the proportion of cases in our sample is different from that in the general population---for instance, the sample is constructed to achieve a fixed ratio of ... More

On entanglement in neutrino mixing and oscillationsMar 29 2010We report on recent results about entanglement in the context of particle mixing and oscillations. We study in detail single-particle entanglement arising in two-flavor neutrino mixing. The analysis is performed first in the context of Quantum Mechanics, ... More

Entanglement in neutrino oscillationsJul 30 2007Apr 17 2009Flavor oscillations in elementary particle physics are related to multi-mode entanglement of single-particle states. We show that mode entanglement can be expressed in terms of flavor transition probabilities, and therefore that single-particle entangled ... More

A field-theoretical approach to entanglement in neutrino mixing and oscillationsJan 30 2014Jun 04 2014The phenomena of particle mixing and flavor oscillations in elementary particle physics can be addressed by the point of view of quantum information theory, and described in terms of multi-mode entanglement of single-particle states. In this paper we ... More

Universal $κ$-Poincaré covariant differential calculus over $κ$-Minkowski spaceDec 10 2013Apr 02 2014Unified graded differential algebra, generated by $\kappa$-Minkowski noncommutative (NC) coordinates, Lorentz generators and anticommuting one-forms, is constructed. It is compatible with $\kappa$-Poincar\'e-Hopf algebra. For time- and space-like deformations, ... More

Differential algebras on kappa-Minkowski space and action of the Lorentz algebraMar 13 2012We propose two families of differential algebras of classical dimension on kappa-Minkowski space. The algebras are constructed using realizations of the generators as formal power series in a Weyl super-algebra. We also propose a novel realization of ... More

EigenPrism: Inference for High-Dimensional Signal-to-Noise RatiosMay 08 2015Jun 28 2016Consider the following three important problems in statistical inference, namely, constructing confidence intervals for (1) the error of a high-dimensional ($p>n$) regression estimator, (2) the linear regression noise level, and (3) the genetic signal-to-noise ... More

Lower bounds on Locality Sensitive HashingOct 29 2005Nov 26 2005Given a metric space $(X,d_X)$, $c\ge 1$, $r>0$, and $p,q\in [0,1]$, a distribution over mappings $\h:X\to \mathbb N$ is called a $(r,cr,p,q)$-sensitive hash family if any two points in $X$ at distance at most $r$ are mapped by $\h$ to the same value ... More

A knockoff filter for high-dimensional selective inferenceFeb 10 2016May 03 2018This paper develops a framework for testing for associations in a possibly high-dimensional linear model where the number of features/variables may far exceed the number of observational units. In this framework, the observations are split into two groups, ... More

Structure of multiphoton quantum optics. II. Bipartite systems, physical processes, and heterodyne squeezed statesAug 18 2003Extending the scheme developed for a single mode of the electromagnetic field in the preceding paper ``Structure of multiphoton quantum optics. I. Canonical formalism and homodyne squeezed states'', we introduce two-mode nonlinear canonical transformations ... More

Structure of multiphoton quantum optics. I. Canonical formalism and homodyne squeezed statesAug 14 2003Aug 19 2003We introduce a formalism of nonlinear canonical transformations for general systems of multiphoton quantum optics. For single-mode systems the transformations depend on a tunable free parameter, the homodyne local oscillator angle; for n-mode systems ... More

Teleportation of squeezing: Optimization using non-Gaussian resourcesSep 30 2010Nov 24 2010We study the continuous-variable quantum teleportation of states, statistical moments of observables, and scale parameters such as squeezing. We investigate the problem both in ideal and imperfect Vaidman-Braunstein-Kimble protocol setups. We show how ... More

Discovering Multiple Truths with a Hybrid ModelMay 14 2017Many data management applications require integrating information from multiple sources. The sources may not be accurate and provide erroneous values. We thus have to identify the true values from conflicting observations made by the sources. The problem ... More

Twists, realizations and Hopf algebroid structure of kappa-deformed phase spaceMay 14 2013Jan 03 2014The quantum phase space described by Heisenberg algebra possesses undeformed Hopf algebroid structure. The $\kappa$-deformed phase space with noncommutative coordinates is realized in terms of undeformed quantum phase space. There are infinitely many ... More

Controlling the false discovery rate via knockoffsApr 22 2014Oct 14 2015In many fields of science, we observe a response variable together with a large number of potential explanatory variables, and would like to be able to discover which variables are truly associated with the response. At the same time, we need to know ... More

Sparse Prediction with the $k$-Support NormApr 23 2012Jun 12 2012We derive a novel norm that corresponds to the tightest convex relaxation of sparsity combined with an $\ell_2$ penalty. We show that this new {\em $k$-support norm} provides a tighter relaxation than the elastic net and is thus a good replacement for ... More

Topological Winding and Unwinding in Metastable Bose-Einstein CondensatesApr 24 2007Feb 12 2008Topological winding and unwinding in a quasi-one-dimensional metastable Bose-Einstein condensate are shown to be manipulated by changing the strength of interaction or the frequency of rotation. Exact diagonalization analysis reveals that quasidegenerate ... More

Quantum phase transition in one-dimensional Bose-Einstein condensates with attractive interactionsOct 10 2002Motivated by the recent development of the Feshbach technique, we studied the ground and low-lying excited states of attractive Bose-Einstein condensates on a one-dimensional ring as a function of the strength of interactions. The Gross-Pitaevskii mean-field ... More

Metastable Quantum Phase Transitions in a One-Dimensional Bose GasMay 05 2010Jul 28 2010This is a chapter for a book. The first paragraph of this chapter is as follows: "Ultracold quantum gases offer a wonderful playground for quantum many body physics, as experimental systems are widely controllable, both statically and dynamically. One ... More

Global identifiability of linear structural equation modelsMar 04 2010May 13 2011Structural equation models are multivariate statistical models that are defined by specifying noisy functional relationships among random variables. We consider the classical case of linear relationships and additive Gaussian noise terms. We give a necessary ... More

Critical fluctuations in a soliton formation of attractive Bose-Einstein condensatesNov 29 2005Mar 22 2006We employ mean-field, Bogoliubov, and many-body theories to study critical fluctuations in position and momentum of a Bose-Einstein condensate whose translation symmetry is spontaneously broken due to attractive interactions. In a homogeneous system, ... More

Symmetry Breaking and Enhanced Condensate Fraction in a Matter-Wave Bright SolitonJun 30 2004Mar 11 2005An exact diagonalization study reveals that a matter-wave bright soliton and the Goldstone mode are simultaneously created in a quasi-one-dimensional attractive Bose-Einstein condensate by superpositions of quasi-degenerate low-lying many-body states. ... More

MOCCA: mirrored convex/concave optimization for nonconvex composite functionsOct 29 2015Jun 29 2016Many optimization problems arising in high-dimensional statistics decompose naturally into a sum of several terms, where the individual terms are relatively simple but the composite objective function can only be optimized with iterative algorithms. In ... More

K-Poincare-Hopf algebra and Hopf algebroid structure of phase space from twistMar 05 2013Sep 09 2013We unify k-Poincare algebra and k-Minkowski spacetime by embeding them into quantum phase space. The quantum phase space has Hopf algebroid structure to which we apply the twist in order to get k- deformed Hopf algebroid structure and k-deformed phase ... More

Adiabatic and nonadiabatic spin torques induced by spin-triplet supercurrentJun 07 2017Sep 16 2017We study spin transfer torques induced by a spin-triplet supercurrent in a magnet with the superconducting proximity effect. By a perturbative approach, we show that spin-triplet correlations realize new types of torques, which are analogous to the adiabatic ... More

Fast Distributed Approximation for Max-CutJul 26 2017Finding a maximum cut is a fundamental task in many computational settings. Surprisingly, it has been insufficiently studied in the classic distributed settings, where vertices communicate by synchronously sending messages to their neighbors according ... More

AND/OR Multi-Valued Decision Diagrams (AOMDDs) for Graphical ModelsJan 15 2014Inspired by the recently introduced framework of AND/OR search spaces for graphical models, we propose to augment Multi-Valued Decision Diagrams (MDD) with AND nodes, in order to capture function decomposition structure and to extend these compiled data ... More

Decomposition of polynomial sets into characteristic pairsFeb 28 2017A characteristic pair is a pair (G,C) of polynomial sets in which G is a reduced lexicographic Groebner basis, C is the minimal triangular set contained in G, and C is normal. In this paper, we show that any finite polynomial set P can be decomposed algorithmically ... More

An equivalence between stationary points for rank constraints versus low-rank factorizationsDec 02 2018Two common approaches in low-rank optimization problems are either working directly with a rank constraint on the matrix variable, or optimizing over a low-rank factorization so that the rank constraint is implicitly ensured. In this paper, we study the ... More

Recursive Sketches for Modular Deep LearningMay 29 2019Aug 06 2019We present a mechanism to compute a sketch (succinct summary) of how a complex modular deep network processes its inputs. The sketch summarizes essential information about the inputs and outputs of the network and can be used to quickly identify key components ... More

A Power and Prediction Analysis for Knockoffs with Lasso StatisticsDec 18 2017Knockoffs is a new framework for controlling the false discovery rate (FDR) in multiple hypothesis testing problems involving complex statistical models. While there has been great emphasis on Type-I error control, Type-II errors have been far less studied. ... More

Convergence Results for Neural Networks via ElectrodynamicsFeb 01 2017Dec 04 2018We study whether a depth two neural network can learn another depth two network using gradient descent. Assuming a linear output node, we show that the question of whether gradient descent converges to the target function is equivalent to the following ... More

A knockoff filter for high-dimensional selective inferenceFeb 10 2016This paper develops a framework for testing for associations in a possibly high-dimensional linear model where the number of features/variables may far exceed the number of observational units. In this framework, the observations are split into two groups, ... More

Privacy and Statistical Risk: Formalisms and Minimax BoundsDec 15 2014We explore and compare a variety of definitions for privacy and disclosure limitation in statistical estimation and data analysis, including (approximate) differential privacy, testing-based definitions of privacy, and posterior guarantees on disclosure ... More

Half-trek criterion for generic identifiability of linear structural equation modelsJul 27 2011Oct 03 2012A linear structural equation model relates random variables of interest and corresponding Gaussian noise terms via a linear equation system. Each such model can be represented by a mixed graph in which directed edges encode the linear equations and bidirected ... More

Differential forms and k-Minkowski spacetime from extended twistNov 28 2012Jul 05 2013We analyze bicovariant differential calculus on $\kappa$-Minkowski spacetime. It is shown that corresponding Lorentz generators and noncommutative coordinates compatible with bicovariant calculus cannot be realized in terms of commutative coordinates ... More

Empirical Evaluation of Approximation Algorithms for Probabilistic DecodingJan 30 2013It was recently shown that the problem of decoding messages transmitted through a noisy channel can be formulated as a belief updating task over a probabilistic network [McEliece]. Moreover, it was observed that iterative application of the (linear time) ... More

Recursive Sketches for Modular Deep LearningMay 29 2019We present a mechanism to compute a sketch (succinct summary) of how a complex modular deep network processes its inputs. The sketch summarizes essential information about the inputs and outputs of the network and can be used to quickly identify key components ... More

Weight Distributions for Successive Cancellation Decoding of Polar CodesAug 19 2019In this paper, we derive the exact weight distributions for the successive cancellation decoding of polar codes. The results allow to get an estimate of the decoding error probability and to show a link between the first nonzero components of the weight ... More