total 9836took 0.14s

Learning Ising Models with Independent FailuresFeb 13 2019We give the first efficient algorithm for learning the structure of an Ising model that tolerates independent failures; that is, each entry of the observed sample is missing with some unknown probability p. Our algorithm matches the essentially optimal ... More

Sparse Polynomial Learning and Graph SketchingFeb 17 2014Nov 07 2014Let $f:\{-1,1\}^n$ be a polynomial with at most $s$ non-zero real coefficients. We give an algorithm for exactly reconstructing f given random examples from the uniform distribution on $\{-1,1\}^n$ that runs in time polynomial in $n$ and $2s$ and succeeds ... More

Learning Neural Networks with Two Nonlinear Layers in Polynomial TimeSep 18 2017Apr 20 2018We give a polynomial-time algorithm for learning neural networks with one layer of sigmoids feeding into any Lipschitz, monotone activation function (e.g., sigmoid or ReLU). We make no assumptions on the structure of the network, and the algorithm succeeds ... More

Moment-Matching PolynomialsJan 04 2013We give a new framework for proving the existence of low-degree, polynomial approximators for Boolean functions with respect to broad classes of non-product distributions. Our proofs use techniques related to the classical moment problem and deviate significantly ... More

Eigenvalue Decay Implies Polynomial-Time Learnability for Neural NetworksAug 11 2017We consider the problem of learning function classes computed by neural networks with various activations (e.g. ReLU or Sigmoid), a task believed to be computationally intractable in the worst-case. A major open problem is to understand the minimal assumptions ... More

Learning One Convolutional Layer with Overlapping PatchesFeb 07 2018We give the first provably efficient algorithm for learning a one hidden layer convolutional network with respect to a general class of (potentially overlapping) patches. Additionally, our algorithm requires only mild conditions on the underlying distribution. ... More

Bounding the Sensitivity of Polynomial Threshold FunctionsSep 28 2009Nov 09 2009We give the first non-trivial upper bounds on the average sensitivity and noise sensitivity of polynomial threshold functions. More specifically, for a Boolean function f on n variables equal to the sign of a real, multivariate polynomial of total degree ... More

An Invariance Principle for PolytopesDec 24 2009Sep 12 2012Let X be randomly chosen from {-1,1}^n, and let Y be randomly chosen from the standard spherical Gaussian on R^n. For any (possibly unbounded) polytope P formed by the intersection of k halfspaces, we prove that |Pr [X belongs to P] - Pr [Y belongs to ... More

Preserving Randomness for Adaptive AlgorithmsNov 02 2016We introduce the concept of a randomness steward, a tool for saving random bits when executing a randomized estimation algorithm $\mathsf{Est}$ on many adaptively chosen inputs. For each execution, the chosen input to $\mathsf{Est}$ remains hidden from ... More

Toward Attribute Efficient Learning AlgorithmsNov 27 2003We make progress on two important problems regarding attribute efficient learnability. First, we give an algorithm for learning decision lists of length $k$ over $n$ variables using $2^{\tilde{O}(k^{1/3})} \log n$ examples and time $n^{\tilde{O}(k^{1/3})}$. ... More

List-Decodable Linear RegressionMay 14 2019We give the first polynomial-time algorithm for robust regression in the list-decodable setting where an adversary can corrupt a greater than $1/2$ fraction of examples. For any $\alpha < 1$, our algorithm takes as input a sample $\{ (x_i,y_i)\}_{i \leq ... More

Polynomial-Time Approximation Schemes for Knapsack and Related Counting Problems using Branching ProgramsAug 18 2010We give a deterministic, polynomial-time algorithm for approximately counting the number of {0,1}-solutions to any instance of the knapsack problem. On an instance of length n with total weight W and accuracy parameter eps, our algorithm produces a (1 ... More

List-Decodable Linear RegressionMay 14 2019May 15 2019We give the first polynomial-time algorithm for robust regression in the list-decodable setting where an adversary can corrupt a greater than $1/2$ fraction of examples. For any $\alpha < 1$, our algorithm takes as input a sample $\{ (x_i,y_i)\}_{i \leq ... More

List-Decodable Linear RegressionMay 14 2019May 30 2019We give the first polynomial-time algorithm for robust regression in the list-decodable setting where an adversary can corrupt a greater than $1/2$ fraction of examples. For any $\alpha < 1$, our algorithm takes as input a sample $\{(x_i,y_i)\}_{i \leq ... More

Exact MAP Inference by Avoiding Fractional VerticesMar 08 2017Given a graphical model, one essential problem is MAP inference, that is, finding the most likely configuration of states according to the model. Although this problem is NP-hard, large instances can be solved in practice. A major open question is to ... More

Submodular Functions Are Noise StableJun 02 2011Jun 13 2011We show that all non-negative submodular functions have high {\em noise-stability}. As a consequence, we obtain a polynomial-time learning algorithm for this class with respect to any product distribution on $\{-1,1\}^n$ (for any constant accuracy parameter ... More

Reliably Learning the ReLU in Polynomial TimeNov 30 2016We give the first dimension-efficient algorithms for learning Rectified Linear Units (ReLUs), which are functions of the form $\mathbf{x} \mapsto \max(0, \mathbf{w} \cdot \mathbf{x})$ with $\mathbf{w} \in \mathbb{S}^{n-1}$. Our algorithm works in the ... More

Chip firing on Dynkin diagrams and McKay quiversJan 25 2016Feb 27 2016Two classes of avalanche-finite matrices and their critical groups (integer cokernels) are studied from the viewpoint of chip-firing/sandpile dynamics, namely, the Cartan matrices of finite root systems and the McKay-Cartan matrices for finite subgroups ... More

Threshold graphs, shifted complexes, and graphical complexesMar 04 2007We consider a variety of connections between threshold graphs, shifted complexes, and simplicial complexes naturally formed from a graph. These graphical complexes include the independent set, neighborhood, and dominance complexes. We present a number ... More

Chip-firing on general invertible matricesAug 18 2015We propose a generalization of the graphical chip-firing model allowing for the redistribution dynamics to be governed by any invertible integer matrix while maintaining the long term critical, superstable, and energy minimizing behavior of the classical ... More

A non-partitionable Cohen-Macaulay simplicial complexApr 16 2015Jun 07 2016A long-standing conjecture of Stanley states that every Cohen-Macaulay simplicial complex is partitionable. We disprove the conjecture by constructing an explicit counterexample. Due to a result of Herzog, Jahan and Yassemi, our construction also disproves ... More

Flow-firing processesFeb 06 2019We consider a discrete non-deterministic flow-firing process for rerouting flow on the edges of a planar complex. The process is an instance of higher-dimensional chip-firing. In the flow-firing process, flow on the edges of a complex is repeatedly diverted ... More

Chip-firing and energy minimization on M-matricesMar 07 2014Nov 21 2014We consider chip-firing dynamics defined by arbitrary M-matrices. M-matrices generalize graph Laplacians and were shown by Gabrielov to yield avalanche finite systems. Building on the work of Baker and Shokrieh, we extend the concept of energy minimizing ... More

The Bergman complex of a matroid and phylogenetic treesNov 21 2003May 04 2005We study the Bergman complex B(M) of a matroid M: a polyhedral complex which arises in algebraic geometry, but which we describe purely combinatorially. We prove that a natural subdivision of the Bergman complex of M is a geometric realization of the ... More

Shifted set families, degree sequences, and plethysmOct 26 2006Jan 10 2008We study, in three parts, degree sequences of k-families (or k-uniform hypergraphs) and shifted k-families. The first part collects for the first time in one place, various implications such as: Threshold implies Uniquely Realizable implies Degree-Maximal ... More

A Geometric Interpretation of the Characteristic Polynomial of Reflection ArrangementsJun 11 2009We consider projections of points onto fundamental chambers of finite real reflection groups. Our main result shows that for groups of type $A_n$, $B_n$, and $D_n$, the coefficients of the characteristic polynomial of the reflection arrangement are proportional ... More

Directed rooted forests in higher dimensionDec 24 2015Nov 18 2016For a graph G, the generating function of rooted forests, counted by the number of connected components, can be expressed in terms of the eigenvalues of the graph Laplacian. We generalize this result from graphs to cell complexes of arbitrary dimension. ... More

Scheduling ProblemsJan 13 2014Dec 02 2015We introduce the notion of a scheduling problem which is a boolean function $S$ over atomic formulas of the form $x_i \leq x_j$. Considering the $x_i$ as jobs to be performed, an integer assignment satisfying $S$ schedules the jobs subject to the constraints ... More

Directed Rooted Forests in Higher DimensionDec 24 2015Feb 23 2016For a graph G, the generating function of rooted forests, counted by the number of connected components, can be expressed in terms of the eigenvalues of the graph Laplacian. We generalize this result from graphs to cell complexes of arbitrary dimension. ... More

Projection volumes of hyperplane arrangementsJan 28 2010We prove that for any finite real hyperplane arrangement the average projection volumes of the maximal cones is given by the coefficients of the characteristic polynomial of the arrangement. This settles the conjecture of Drton and Klivans that this held ... More

Reliable operations on oscillatory functionsMay 14 1999Approximate $p$-point Leibniz derivation formulas as well as interpolatory Simpson quadrature sums adapted to oscillatory functions are discussed. Both theoretical considerations and numerical evidence concerning the dependence of the discretization errors ... More

Finiteness of the Hopping Induced Energy Corrections in CupratesMar 09 2009The paper continues the rigorous investigations of the mean field Green function solution of the effective two-dimensional two-band Hubbard model [N. M. Plakida et al., Phys. Rev. B, Vol.51, 16599 (1995)] of the superconducting phase transitions in cuprates, ... More

Rigorous derivation of the mean field Green functions of the two-band Hubbard model of superconductivityApr 05 2007The Green function (GF) equation of motion technique for solving the effective two-band Hubbard model of high-T_c superconductivity in cuprates [N.M. Plakida et al., Phys. Rev. B, v. 51, 16599 (1995); JETP, v. 97, 331 (2003)] rests on the Hubbard operator ... More

The boundary layer problem in Bayesian adaptive quadratureSep 25 2006The boundary layer of a finite domain [a, b] covers mesoscopic lateral neighbourhoods, inside [a, b], of the endpoints a and b. The correct diagnostic of the integrand behaviour at a and b, based on its sampling inside the boundary layer, is the first ... More

A Cheeger-Type Inequality on Simplicial ComplexesSep 23 2012Oct 26 2012In this paper, we consider a variation on Cheeger numbers related to the coboundary expanders recently defined by Dotterer and Kahle. A Cheeger-type inequality is proved, which is similar to a result on graphs due to Fan Chung. This inequality is then ... More

Mean field solutions to singlet hopping and superconducting pairing within a two-band Hubbard modelSep 25 2006The mean field Green function solution of the two-band singlet-hole Hubbard model for high-$T\sb{c}$ superconductivity in cuprates (Plakida, N.M. et al., Phys. Rev. B51, 16599 (1995), JETP 97, 331 (2003)) involves expressions of higher order correlation ... More

Signature of Fermi surface jumps in positron spectroscopy dataAug 05 1999A subtractionless method for solving Fermi surface sheets ({\tt FSS}), from measured $n$-axis-projected momentum distribution histograms by two-dimensional angular correlation of the positron-electron annihilation radiation ({\tt 2D-ACAR}) technique, ... More

The Positive Bergman Complex of an Oriented MatroidJun 07 2004We study the positive Bergman complex B+(M) of an oriented matroid M, which is a certain subcomplex of the Bergman complex B(M) of the underlying unoriented matroid. The positive Bergman complex is defined so that given a linear ideal I with associated ... More

Coxeter arrangements in three dimensionsJan 24 2015Let ${\mathcal A}$ be a finite real linear hyperplane arrangement in three dimensions. Suppose further that all the regions of ${\mathcal A}$ are isometric. We prove that ${\mathcal A}$ is necessarily a Coxeter arrangement. As it is well known that the ... More

On the topology of no $k$-equal spacesJul 31 2017We consider the topology of real no $k$-equal spaces via the theory of cellular spanning trees. Our main theorem proves that the rank of the $(k-2)$-dimensional homology of the no $k$-equal subspace of $\mathbb{R}$ is equal to the number of facets in ... More

Approximating Cayley diagrams versus Cayley graphsMar 25 2011Nov 15 2011We construct a sequence of finite graphs that weakly converge to a Cayley graph, but there is no labelling of the edges that would converge to the corresponding Cayley diagram. A similar construction is used to give graph sequences that converge to the ... More

Can all muscular load sharing patterns be regarded as optimal in some sense?Nov 16 2006Muscles crossing a joint usually outnumber its degrees of freedom, which renders the motor system underdetermined. Typically, optimization laws are postulated to cope with this redundancy. A natural question then arises whether all muscular load sharing ... More

Non-commutative rational Yang-Baxter mapsAug 13 2013Aug 14 2013Starting from multidimensional consistency of non-commutative lattice modified Gel'fand-Dikii systems we present the corresponding solutions of the functional (set-theoretic) Yang-Baxter equation, which are non-commutative versions of the maps arising ... More

On $τ$-function of the quadrilateral latticeDec 31 2008We investigate the $\tau$-function of the quadrilateral lattice using the nonlocal $\bar\partial$-dressing method, and we show that it can be identified with the Fredholm determinant of the integral equation which naturally appears within that approach. ... More

The normal dual congruences and the dual Bianchi latticeDec 15 2003The main goal of this paper is to find the discrete analogue of the Bianchi system in spaces of arbitrary dimesion together with its geometric interpretation. We show that the proper geometric framework of such generalization is the language of dual quadrilateral ... More

The affine Weyl group symmetry of Desargues maps and of the non-commutative Hirota-Miwa systemJun 17 2010We study recently introduced Desargues maps, which provide simple geometric interpretation of the non-commutative Hirota--Miwa system. We characterize them as maps of the A-type root lattice into a projective space such that images of vertices of any ... More

Quadratic reductions of quadrilateral latticesFeb 13 1998It is shown that quadratic constraints are compatible with the geometric integrability scheme of the multidimensional quadrilateral lattice equation. The corresponding Ribaucour reduction of the fundamental transformation of quadrilateral lattices is ... More

Vector boson scattering at high mass with ATLASOct 14 2008In the absence of a light Higgs boson, the mechanism of electroweak symmetry breaking will be best studied in processes of vector boson scattering at high mass. Various models predict resonances in this channel. Scalar and vector resonances have been ... More

Existence of traveling waves for the nonlocal Burgers equationMar 27 2006We study the equation $u_t +uu_x +u-K*u=0$ in the case of an arbitrary $K \geq 0$, which is a generalization of a model for radiating gas, in which $K(y)={1/2}e^{-|y|}$. Using a monotone iteration scheme argument we establish the existence of traveling ... More

Divide-And-Conquer Computation of Cylindrical Algebraic DecompositionFeb 04 2014We present a divide-and-conquer version of the Cylindrical Algebraic Decomposition (CAD) algorithm. The algorithm represents the input as a Boolean combination of subformulas, computes cylindrical algebraic decompositions of solution sets of the subformulas, ... More

Scientific Return of Coronagraphic Exoplanet Imaging and Spectroscopy Using WFIRSTDec 18 2014In this study, we explore and review the scientific potential for exoplanet characterization by a high-contrast optical coronagraph on WFIRST/AFTA. We suggest that the heterogeneity in albedo spectra and planet/star flux ratios as a function of orbital ... More

Highlights in the Study of Exoplanet AtmospheresSep 25 2014Exoplanets are now being discovered in profusion. However, to understand their character requires spectral models and data. These elements of remote sensing can yield temperatures, compositions, and even weather patterns, but only if significant improvements ... More

Spectra as Windows into Exoplanet AtmospheresDec 06 2013Understanding a planet's atmosphere is a necessary condition for understanding not only the planet itself, but also its formation, structure, evolution, and habitability, This puts a premium on obtaining spectra, and developing credible interpretative ... More

The Role of Dust Clouds in the Atmospheres of Brown DwarfsFeb 10 2009The new spectroscopic classes, L and T, are defined by the role of dust clouds in their atmospheres, the former by their presence and the latter by their removal and near absence. Moreover, the M to L and L to T transitions are intimately tied to the ... More

A Critique of Core--Collapse Supernova Theory Circa 1997Mar 02 1997There has been a new infusion of ideas in the study of the mechanism and early character of core--collapse supernovae. However, despite recent conceptual and computational progress, fundamental questions remain. Some are summarize herein.

Classification of the Killing Vectors in Nonexpanding HH-Spaces with LambdaNov 11 2011Conformal Killing equations and their integrability conditions for nonexpanding hyperheavenly spaces with Lambda are studied. Reduction of ten Killing equations to one master equation is presented. Classification of homothetic and isometric Killing vectors ... More

Comment on covariant Stora--Zumino chain termsMar 23 1999In a recent paper, Ekstrand proposed a simple expression from which covariant anomaly, covariant Schwinger term and higher covariant chain terms may be computed. We comment on the relation of his result to the earlier work of Tsutsui.

Massive Schwinger model within mass perturbation theoryApr 08 1997In this article we give a detailed discussion of the mass perturbation theory of the massive Schwinger model. After discussing some general features and briefly reviewing the exact solution of the massless case, we compute the vacuum energy density of ... More

Decay widths and scattering processes in massive QED$_2$Oct 06 1997Using mass perturbation theory, we infer the bound-state spectrum of massive QED$_2$ and compute some decay widths of unstable bound states. Further, we discuss scattering processes, where all the resonances and particle production thresholds are properly ... More

Vacuum Functional and Fermion Condensate in the Massive Schwinger ModelJul 11 1995We derive a systematic procedure of computing the vacuum functional and fermion condensate of the massive Schwinger model via a perturbative expansion in the fermion mass. We compute numerical results for the first nontrivial order.

Oscillatory behaviour in a lattice prey-predator systemOct 07 1999Using Monte Carlo simulations we study a lattice model of a prey-predator system. We show that in the three-dimensional model populations of preys and predators exhibit coherent periodic oscillations but such a behaviour is absent in lower-dimensional ... More

Dimensional reduction in a model with infinitely many absorbing statesOct 04 1999Using Monte Carlo method we study a two-dimensional model with infinitely many absorbing states. Our estimation of the critical exponent beta=0.273(5) suggests that the model belongs to the (1+1) rather than (2+1) directed-percolation universality class. ... More

All ASD complex and real 4-dimensional Einstein spaces with $Λ\ne 0$ admitting a nonnull Killing vectorDec 16 2013Feb 02 2015Anti-self-dual (ASD) 4-dimensional complex Einstein spaces with nonzero cosmological constant $\Lambda$ equipped with a nonnul Killing vector are considered. It is shown, that any conformally nonflat metric of such spaces can be always brought to a special ... More

A Hasse Principle for Periodic PointsSep 11 2012May 06 2013Let $F$ be a global field, let $\vp \in \Fx$ be a rational map of degree at least 2, and let $\a \in F$. We say that $\a $ is periodic if $\vpn (\a) = \a$ for some $n \geq 1$. A Hasse principle is the idea, or hope, that a phenomenon which happens everywhere ... More

Subset Space Public Announcement Logic RevisitedFeb 16 2013By a modification of the central definition given in [W\'ang and {\AA}gotnes, 2013], we provide semantics for public annoucements in subset spaces. We argue that these revised semantics improve on the original, and we provide a simple sound and complete ... More

Infinitesimal Thurston Rigidity and the Fatou-Shishikura InequalityFeb 26 1999We prove a refinement of the Fatou-Shishikura Inequality - that the total count of nonrepelling cycles of a rational map is less than or equal to the number of independent infinite forward critical orbits - from a suitable application of Thurston's Rigidity ... More

Multiple fundamental strings and waves to non-linear order in the background fieldsMay 23 2006Mar 30 2007The Chern-Simons actions of the multiple fundamental string and the multiple gravitational wave are established to full order in the background fields. Gauge invariance is checked. Special attention is drawn to the non-Abelian gauge transformations of ... More

On some examples of para-Hermite and para-Kähler Einstein spaces with $Λ\ne 0$Feb 09 2016Nov 14 2016Spaces equipped with two complementary (distinct) congruences of self-dual null strings and at least one congruence of anti-self-dual null strings are considered. It is shown that if such spaces are Einsteinian then the vacuum Einstein field equations ... More

Invariant sets for QMF functionsOct 08 2015Oct 13 2015A quadrature mirror filter (QMF) function can be considered as a $g$-function on a space of binary sequences. The QMF functions that give rise to multiresolution analyses are then distinguished by their invariant sets. By characterizing them, we answer ... More

The solution of a generalized secretary problem via analytic expressionsJul 26 2016Oct 18 2016Given integers $1\leq k<n$, the Gusein-Zade version of a generalized secretary problem is to choose one of the $k$ best of $n$ candidates for a secretary, which are interviewing in random order. The stopping rule in the selection is based only on the ... More

The classification of abelian groups generated by time-varying automata and by Mealy automata over the binary alphabetJul 26 2016For every natural number $n$, we classify abelian groups generated by an $n$-state time-varying automaton over the binary alphabet, as well as by an $n$-state Mealy automaton over the binary alphabet.

Local Realism in Quantum Many WorldsAug 06 2015Fundamental principle of classical physics -- local realism, means that freely chosen observations can be explained by a local (slower than light) real process. It is apparently violated in quantum mechanics as shown by Bell theorem. Despite extreme efforts ... More

Is mereology empirical? Composition for fermionsAug 31 2014How best to think about quantum systems under permutation invariance is a question that has received a great deal of attention in the literature. But very little attention has been paid to taking seriously the proposal that permutation invariance reflects ... More

Freeness in higher order frame bundlesSep 04 2015Aug 24 2016We provide counterexamples to P. Olver's freeness conjecture for $C^\infty$ actions. In fact, we show that a counterexample exists for any connected real Lie group with noncompact center, as well as for the additive group of the integers.

The energy dependence of $p_t$ angular correlations inferred from mean-$p_{t}$ fluctuation scale dependence in heavy ion collisions at the SPS and RHICMay 17 2006Dec 07 2006We present the first study of the energy dependence of $p_t$ angular correlations inferred from event-wise mean transverse momentum $<p_{t} >$ fluctuations in heavy ion collisions. We compare our large-acceptance measurements at CM energies $\sqrt{s_{NN}} ... More

The multiplicity dependence of inclusive $p_t$ spectra from p-p collisions at $\sqrt{s}$ = 200 GeVJun 23 2006Jun 26 2006We report measurements of transverse momentum $p_t$ spectra for ten event multiplicity classes of p-p collisions at $\sqrt{s} = 200$ GeV. By analyzing the multiplicity dependence we find that the spectrum shape can be decomposed into a part with amplitude ... More

Classification of the traceless Ricci tensor in 4-dimensional pseudo-Riemannian spaces of neutral signatureOct 29 2016The traceless Ricci tensor $C_{ab}$ in 4-dimensional pseudo-Riemannian spaces equipped with the metric of the neutral signature is analyzed. Its algebraic classification is given. This classification uses the properties of $C_{ab}$ treated as a matrix. ... More

Top-down and bottom-up excursions beyond the Standard Model: The example of left-right symmetries in supersymmetryApr 17 2014In this Ph.D thesis three main projects are presented. In the first one the phenomenology associated with the neutralinos and charginos sector of the left-right symmetric supersymmetric model is explored. After a detailed motivation of the study and construction ... More

Quadruple crossing number of knots and linksNov 12 2012Jan 28 2013A quadruple crossing is a crossing in a projection of a knot or link that has four strands of the knot passing straight through it. A quadruple crossing projection is a projection such that all of the crossings are quadruple crossings. In a previous paper, ... More

The Volatility in a Multi-share Financial Market ModelDec 16 2000Single index financial market models cannot account for the empirically observed complex interactions between shares in a market. We describe a multi-share financial market model and compare characteristics of the volatility, that is the standard deviation ... More

The Khovanov width of twisted links and closed 3-braidsJan 15 2009Jan 16 2009Khovanov homology is a bigraded Z-module that categorifies the Jones polynomial. The support of Khovanov homology lies on a finite number of slope two lines with respect to the bigrading. The Khovanov width is essentially the largest horizontal distance ... More

SUSY Searches at the TevatronAug 05 2008Numerous searches for evidence of supersymmetry at the Tevatron have been performed by the CDF and D0 collaborations. Recent results are presented here including squarks and gluinos in jets and missing transverse energy, stop in several different decay ... More

A Note on Domain Walls and the Parameter Space of N=1 Gauge TheoriesAug 21 2003Sep 22 2003We study the spectrum of BPS domain walls within the parameter space of N=1 U(N) gauge theories with adjoint matter and a cubic superpotential. Using a low energy description obtained by compactifying the theory on R^3 x S^1, we examine the wall spectrum ... More

Over Recurrence for Mixing TransformationsJan 16 2017We show that every invertible strong mixing transformation on a Lebesgue space has strictly over-recurrent sets. Also, we give an explicit procedure for constructing strong mixing transformations with no under-recurrent sets. This answers both parts of ... More

Transience and Recurrence of Markov Processes with Constrained Local TimeJun 15 2018Jun 29 2018We study Markov processes conditioned so that their local time must grow slower than a prescribed function. Building upon recent work on Brownian motion with constrained local time in [5] and [33], we study transience and recurrence for a broad class ... More

Uniformity in $C^*$-algebrasMay 15 2018We introduce a notion of a uniform structure on the set of all representations of a given separable, not necessarilly commutative $C^*$-algebra $\mathfrak{A}$ by introducing a suitable family of metrics on the set of representations of $\mathfrak{A}$ ... More

Stable Higgs bundles and Hermitian-Einstein metrics on non-Kähler manifoldsOct 17 2011Oct 27 2014Let $X$ be a compact Gauduchon manifold, and let $E$ and $V_0$ be holomorphic vector bundles over $X$. Suppose that $E$ is stable when considering all subsheaves preserved by a Higgs field $\theta\in H^0($End$(E)\otimes V_0)$. Then a modified version ... More

Existence of approximate Hermitian-Einstein structures on semi-stable bundlesDec 08 2010Aug 26 2013The purpose of this paper is to investigate canonical metrics on a semi-stable vector bundle E over a compact Kahler manifold X. It is shown that, if E is semi-stable, then Donaldson's functional is bounded from below. This implies that E admits an approximate ... More

Discrete free Abelian central stabilizers in a higher order frame bundleFeb 26 2016Jun 12 2017Let a real Lie group $G$ have a $C^\infty$ action on a real manifold $M$. Assume every nontrivial element of $G$ has nowhere dense fixpoint set in $M$. First, we show, in every frame bundle, except possibly the $0$th, that each stabilizer admits no nontrivial ... More

Freeness in higher order frame bundlesSep 04 2015Jun 12 2017We provide counterexamples to P. Olver's freeness conjecture for $C^\infty$ actions. In fact, we show that a counterexample exists for any connected real Lie group with noncompact center, as well as for the additive group of the integers.

The OPERA experiment Target TrackerJan 12 2007The main task of the Target Tracker detector of the long baseline neutrino oscillation OPERA experiment is to locate in which of the target elementary constituents, the lead/emulsion bricks, the neutrino interactions have occurred and also to give calorimetric ... More

A Paradigm Lost: New Theories for Aspherical PNeDec 09 1999Theoretical Models for the shaping of PNe are reviewed in light of new high resolution images. The new data indicate the purely hydrodynamic interacting stellar winds model can not recover the full variety of shapes and kinematics. New models, some speculative, ... More

Relations among divisors on the moduli space of curves with marked pointsMar 17 2000We prove relations among the classes of certain divisors on the moduli spaces of curves with marked points, generalizing the Brill-Noether Ray Theorem of Eisenbud and Harris.

Vacuum source-field correlations and advanced waves in quantum opticsOct 17 2017Jan 16 2018The solution to the wave equation as a Cauchy problem with prescribed fields at an initial time t=0 is purely retarded. Similarly, in the quantum theory of radiation the specification of Heisenberg picture photon annihilation and creation operators at ... More

A Dempster-Schafer approach to Bell's inequalitiesMar 30 2015Apr 23 2015We present an alternative approach to modeling Einstein-Podolsky-Rosen-Bohm (EPRB)-type experiments. The basis for our approach will be to replace the conventional Kolmogorov theory of probability, with the more general Dempster-Schafer theory of evidence. ... More

Structured Variational Inference for Coupled Gaussian ProcessesNov 03 2017Nov 29 2017Sparse variational approximations allow for principled and scalable inference in Gaussian Process (GP) models. In settings where several GPs are part of the generative model, theses GPs are a posteriori coupled. For many applications such as regression ... More

The Common HOL PlatformJul 31 2015The Common HOL project aims to facilitate porting source code and proofs between members of the HOL family of theorem provers. At the heart of the project is the Common HOL Platform, which defines a standard HOL theory and API that aims to be compatible ... More

Quantum stochastic convolution cocyclesAug 30 2006A concept of quantum stochastic convolution cocycle is introduced and studied in two different contexts -- purely algebraic and operator space theoretic. A quantum stochastic convolution cocycle is a quantum stochastic process on a coalgebra satisfying ... More

Local freeness in frame bundle prolongations of $C^\infty$ actionsAug 23 2016May 24 2017Let $G$~be a real Lie group and let $G^\circ$ be the identity component of~$G$. Let $G$~act on a $C^\infty$ real manifold~$M$. Assume the action is $C^\infty$. Assume that the fixpoint set of any nontrivial element of~$G^\circ$ has empty interior in~$M$. ... More

Computations of Floer Homology for certain Lagrangian Tori in closed 4-manifoldsNov 07 2006Jan 08 2008We compute the Lagrangian Floer cohomology groups of certain tori in closed simply connected symplectic 4-manifolds arising from Fintushel-Stern knot surgery. These manifolds are usually not symplectically aspherical. As a result of the computation we ... More