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Spectral Embedding Norm: Looking Deep into the Spectrum of the Graph LaplacianOct 25 2018The extraction of clusters from a dataset which includes multiple clusters and another significant portion of "background" samples is a task of practical importance. The traditional spectral clustering algorithm, relying on the leading $K$ eigenvectors ... More

Learning spatially-correlated temporal dictionaries for calcium imagingFeb 08 2019Calcium imaging has become a fundamental neural imaging technique, aiming to recover the individual activity of hundreds of neurons in a cortical region. Current methods (mostly matrix factorization) are aimed at detecting neurons in the field-of-view ... More

The Geometry of Nodal Sets and Outlier DetectionJun 05 2017Let $(M,g)$ be a compact manifold and let $-\Delta \phi_k = \lambda_k \phi_k$ be the sequence of Laplacian eigenfunctions. We present a curious new phenomenon which, so far, we only managed to understand in a few highly specialized cases: the family of ... More

A Study of "Churn" in Tweets and Real-Time Search Queries (Extended Version)May 30 2012The real-time nature of Twitter means that term distributions in tweets and in search queries change rapidly: the most frequent terms in one hour may look very different from those in the next. Informally, we call this phenomenon "churn". Our interest ... More

Co-manifold learning with missing dataOct 16 2018Representation learning is typically applied to only one mode of a data matrix, either its rows or columns. Yet in many applications, there is an underlying geometry to both the rows and the columns. We propose utilizing this coupled structure to perform ... More

Visualizing the PHATE of Neural NetworksAug 07 2019Understanding why and how certain neural networks outperform others is key to guiding future development of network architectures and optimization methods. To this end, we introduce a novel visualization algorithm that reveals the internal geometry of ... More

Randomized Near Neighbor Graphs, Giant Components, and Applications in Data ScienceNov 13 2017If we pick $n$ random points uniformly in $[0,1]^d$ and connect each point to its $k-$nearest neighbors, then it is well known that there exists a giant connected component with high probability. We prove that in $[0,1]^d$ it suffices to connect every ... More

Diffusion NetsJun 25 2015Non-linear manifold learning enables high-dimensional data analysis, but requires out-of-sample-extension methods to process new data points. In this paper, we propose a manifold learning algorithm based on deep learning to create an encoder, which maps ... More

Data-Driven Tree Transforms and MetricsAug 18 2017We consider the analysis of high dimensional data given in the form of a matrix with columns consisting of observations and rows consisting of features. Often the data is such that the observations do not reside on a regular grid, and the given order ... More

Hierarchical Coupled Geometry Analysis for Neuronal Structure and Activity Pattern DiscoveryNov 06 2015In the wake of recent advances in experimental methods in neuroscience, the ability to record in-vivo neuronal activity from awake animals has become feasible. The availability of such rich and detailed physiological measurements calls for the development ... More

A geometric approach to Hall algebras I: Higher AssociativityNov 28 2016We construct a geometric system from which the Hall algebra can be recovered. This system inherently satisfies higher associativity conditions and thus leads to a categorification of the Hall algebra. We then suggest how to use this approach to construct ... More

Higher Segal spaces and Lax $\mathbb{A}_\infty$-algebrasMay 08 2019The notion of a higher Segal space was introduced by Dyckerhoff and Kapranov as a general framework for studying higher associativity inherent in a wide range of mathematical objects. In the present work we formalize the connection between this notion ... More

Higher Segal spaces and Lax $\mathbb{A}_\infty$-algebrasMay 08 2019Jul 16 2019The notion of a higher Segal space was introduced by Dyckerhoff and Kapranov as a general framework for studying higher associativity inherent in a wide range of mathematical objects. In the present work we formalize the connection between this notion ... More

Symmetric self-adjoint Hopf categories and a categorical Heisenberg doubleJun 16 2014Feb 29 2016Motivated by the work of of A. Zelevinsky on positive self-adjoint Hopf algebras, we define what we call a symmetric self-adjoint Hopf structure for a certain kind of semisimple abelian categories. It is known that every positive self-adjoint Hopf algebra ... More

Symmetric self-adjoint Hopf categories and a categorical Heisenberg doubleJun 16 2014Nov 26 2016Motivated by the work of of A. Zelevinsky on positive self-adjoint Hopf algebras, we define what we call a symmetric self-adjoint Hopf structure for a certain kind of semisimple abelian categories. It is known that every positive self-adjoint Hopf algebra ... More

A Uniform Version of the Petrov-Khovanskii TheoremAug 09 2011An Abelian integral is the integral over the level curves of a Hamiltonian $H$ of an algebraic form $\omega$. The infinitesimal Hilbert sixteenth problem calls for the study of the number of zeros of Abelian integrals in terms of the degrees $H$ and $\omega$. ... More

MESON2016 -- Concluding RemarksSep 15 2016Several topics presented and discussed at MESON2016 are highlighted, including pentaquarks, dibaryons and meson-nuclear bound states.

A Theoretically Grounded Application of Dropout in Recurrent Neural NetworksDec 16 2015May 25 2016Recurrent neural networks (RNNs) stand at the forefront of many recent developments in deep learning. Yet a major difficulty with these models is their tendency to overfit, with dropout shown to fail when applied to recurrent layers. Recent results at ... More

Old and New in Strangeness Nuclear PhysicsNov 01 2018Feb 15 2019Several persistent problems in strangeness nuclear physics are discussed in this opening talk at HYP2018, Portsmouth-Norfolk VA, June 2018: (i) the $^3_{\Lambda}$H and $^3_{\Lambda}$n (if existing) lifetimes; (ii) charge symmetry breaking in $\Lambda$ ... More

Limits on $\boldmath n {\bar n}$ oscillations from nuclear stabilityJul 13 1999Nov 04 1999The relationship between the lower limit on the nuclear stability lifetime as derived from the non disappearance of `stable` nuclei ($T_{d}~\gtrsim~5.4~\times~10^{31}$ yr), and the lower limit thus implied on the oscillation time $(\tau_{n \bar n})$ of ... More

Comment on "Lattice determination of $Σ$-$Λ$ mixing"Jun 03 2015Jul 19 2015A recent lattice QCD (LQCD) calculation of $\Sigma$-$\Lambda$ mixing by the QCDSF-UKQCD Collaboration [Phys. Rev. D 91, 074512 (2015)] finds a mixing angle about half of that found from the Dalitz-von Hippel (DvH) flavor SU(3) mass formula which relates ... More

Does the derivative of the energy density functional provide a proper quantitative formulation of electronegativity?Sep 27 2012It is pointed out that the derivative of the energy density functional does not provide a valid local electronegativity measure, in spite of its appealing property of becoming constant for ground-state equilibrium systems.

Stability of equilibrium under constraints: Role of second-order constrained derivativesAug 13 2007Jul 22 2010In the stability analysis of an equilibrium, given by a stationary point of a functional F[n] (free energy functional, e.g.), the second derivative of F[n] plays the essential role. If the system in equilibrium is subject to the conservation constraint ... More

Quantitative estimates in approximation by Bernstein-Durrmeyer-Choquet operators with respect to monotone and submodular set functionsNov 23 2015For the qualitative results of pointwise and uniform approximation obtained in \cite{Gal-Opris}, we present general quantitative estimates in terms of the modulus of continuity and in terms of a $K$-functional, for the generalized multivariate Bernstein-Durrmeyer ... More

Maximally additively reducible subsets of the integersAug 14 2019Let $A, B \subseteq \mathbb{N}$ be two finite sets of natural numbers. We say that $B$ is an additive divisor for $A$ if there exists some $C \subseteq \mathbb{N}$ with $A = B+C$. We prove that among those subsets of $\{0, 1, \ldots, k\}$ which have $0$ ... More

Multiplicity Estimates: a Morse-theoretic approachJun 07 2014Aug 13 2015The problem of estimating the multiplicity of the zero of a polynomial when restricted to the trajectory of a non-singular polynomial vector field, at one or several points, has been considered by authors in several different fields. The two best (incomparable) ... More

Neutrino signals in electron-capture storage-ring experimentsJul 07 2014Jun 15 2016Neutrino signals in electron-capture decays of hydrogen-like parent ions P in storage-ring experiments at GSI are reconsidered, with special emphasis placed on the storage-ring quasi-circular motion of the daughter ions D in two-body decays P --> D + ... More

Why the traditional concept of local hardness does not workJul 21 2011Apr 25 2012Finding a proper local measure of chemical hardness has been a long-standing aim of density functional theory. The traditional approach to defining a local hardness index, by the derivative of the chemical potential with respect to the electron density ... More

Meson Assisted Strange DibaryonsNov 29 2010Aug 10 2011The state of the art in dibaryons with strangeness is reviewed, including the K^{-}pp dibaryon which signals the onset of antikaon-nuclear binding. A new type of strange dibaryons is highlighted, where the primary binding mechanism is provided by strong ... More

Overview of Strangeness Nuclear PhysicsApr 26 2009Apr 30 2009Selected topics in Strangeness Nuclear Physics are reviewed: Lambda-hypernuclear spectroscopy and structure, Sigma-hyperon nuclear interaction, multistrangeness, and anti-kaons in nuclei.

Neutrino effects in two-body electron-capture measurements at GSISep 07 2008May 30 2010Oscillatory behavior of electron capture rates in the two-body decay of hydrogen-like ions into recoil ions plus undetected neutrinos, with a period of approximately 7 s, was reported in storage ring single-ion experiments at the GSI Laboratory, Darmstadt. ... More

Structure and Width of the d*(2380) DibaryonMar 23 2018In this contribution, dedicated to the memory of Walter Greiner, we discuss the structure and width of the recently established d*(2380) dibaryon, confronting the consequences of our Pion Assisted Dibaryons hadronic model with those of quark motivated ... More

Lambda-Lambda hypernuclei and stranger systemsDec 17 2003Recent experiments on production of Lambda-Lambda hypernuclei have renewed interest in extracting the Lambda-Lambda interaction from the few events identified since the inception of this field forty years ago. Few-body calculations relating to this issue ... More

To bind or not to bind: Lambda-Lambda hypernuclei and Xi hyperonsNov 22 2002Four-body Faddeev-Yakubovsky calculations for Lambda-Lambda-p-n do not produce a bound state for Lambda-Lambda hydrogen 4, although suitably defined three-body Faddeev calculations for Lambda-Lambda-d produce a 1+ bound state for Lambda-Lambda interactions ... More

Physics of Antiproton Nuclear Interactions near ThresholdJun 27 2001Antiproton-nucleus optical potentials fitted to $\bar p$-atom level shifts and widths are used to calculate the recently reported very low energy ($p_{L}<100$ MeV/c) $\bar p$ cross sections for annihilation on light nuclei. The apparent suppression of ... More

Pfaffian Intersections and Multiplicity CyclesJan 14 2015Aug 13 2015We consider the problem of estimating the intersection multiplicity between an algebraic variety and a Pfaffian foliation, at every point of the variety. We show that this multiplicity can be majorized at every point $p$ by the local algebraic multiplicity ... More

Density of algebraic points on Noetherian varietiesApr 03 2017Let $\Omega\subset{\mathbb R}^n$ be a relatively compact domain. A finite collection of real-valued functions on $\Omega$ is called a \emph{Noetherian chain} if the partial derivatives of each function are expressible as polynomials in the functions. ... More

Zero counting and invariant sets of differential equationsOct 01 2015Consider a polynomial vector field $\xi$ in $\mathbb{C}^n$ with algebraic coefficients, and $K$ a compact piece of a trajectory. Let $N(K,d)$ denote the maximal number of isolated intersections between $K$ and an algebraic hypersurface of degree $d$. ... More

Finiteness properties of formal Lie group actionsMay 21 2014Aug 13 2015Following ideas of Arnold and Seigal-Yakovenko, we prove that the space of matrix coefficients of a formal Lie group action belongs to a Noetherian ring. Using this result we extend the uniform intersection multiplicity estimates of these authors from ... More

Some effective estimates for André-Oort in $Y(1)^n$Sep 14 2018Let $X\subset Y(1)^n$ be a subvariety defined over a number field $\mathbb F$ and let $(P_1,\ldots,P_n)\in X$ be a special point not contained in a positive-dimensional special subvariety of $X$. We show that the if a coordinate $P_i$ corresponds to an ... More

Pion-assisted $NΔ$ and $ΔΔ$ dibaryons, and beyondNov 30 2014Feb 26 2015Experimental evidence for $I(J^P)=0(3^+)$ $\Delta\Delta$ dibaryon ${\cal D}_{03}(2370)$ has been presented recently by the WASA-at-COSY Collaboration. Here I review new hadronic-basis Faddeev calculations of $L=0$ nonstrange pion-assisted $N\Delta$ and ... More

Recent studies of kaonic atoms and nuclear clustersJan 10 2013Sep 08 2013Recent studies of kaonic atoms, few-body kaonic quasibound states and kaonic nuclei are reviewed, with emphasis on implementing the subthreshold energy dependence of the Kbar-N interaction in chiral interaction models that are consistent with the SIDDHARTA ... More

The ground-state energy and external potential as functionals of the electron density and their derivativesAug 18 2011Aug 22 2011It is shown that the ground-state energy as a functional solely of the electron density is determined by the asymptotic value of the derivative of the degree-one homogeneous extension of the universal density functional F[n] at the given electron number. ... More

Proof of non-extremal nature of excited-state energies in nonrelativistic quantum mechanics with the use of constrained derivativesApr 20 2011Apr 26 2011With the use of a second derivative test based on constrained second derivatives, a proof is given that excited states in nonrelativistic quantum mechanics are saddle points of the energy expectation value, and is shown, further, how to determine their ... More

Antikaon-nucleus dynamics: from quasibound states to kaon condensationDec 11 2009Aug 20 2010Coupled-channel Kbar-N dynamics near threshold and its repercussions in few-body Kbar-nuclear systems are briefly reviewed, highlighting studies of a K^-pp quasibound state. In heavier nuclei, the extension of mean-field calculations to multi-Kbar nuclear ... More

Comment on recent Strangeness -2 predictionsJan 07 2013Apr 26 2013It is pointed out that the Chiral Constituent Quark Model (CCQM) interactions that bind the H dibaryon and Lambda-Lambda-3H overbind Lambda-Lambda-6He by more than 4 MeV, thus outdating the CCQM in the strangeness S=-2 sector.

pi^- decay rates of p-shell hypernuclei revisitedApr 07 2009Aug 12 2009Explicit expressions for the parity-violating s-wave and the parity-conserving p-wave contributions to pi- weak-decay rates of Lambda hypernuclei in the 1p shell are given in the weak-coupling limit, to update previous shell-model calculations and to ... More

The hypernuclear physics heritage of Dick Dalitz (1925-2006)Jan 01 2007Mar 28 2007The major contributions of Richard H. Dalitz to hypernuclear physics, since his first paper in 1955 to his last one in 2005 covering a span of 50 years during which he founded and led the theoretical study of hypernuclei, are reviewed from a personal ... More

$\bar K$-Nuclear Deeply Bound States?Apr 25 2006Following the prediction by Akaishi and Yamazaki of relatively narrow $\bar K$-nuclear states, deeply bound by over 100 MeV where the main decay channel $\bar K N \to \pi \Sigma$ is closed, several experimental signals in stopped $K^-$ reactions on light ... More

Introducing Time Dependence into the Static Maxwell EquationsJun 27 2001Using to a minimum extent special relativity input, and relying on the Lorentz-force expression for the force acting on a charged particle in motion under the influence of electric (E) and magnetic (B) fields, the Maxwell curl equations are shown to follow ... More

Differentiation of functionals with variables coupled by constraints: Analysis through a fluid-dynamical modelJan 11 2007Mar 08 2007Analysing an application in liquid film dynamics, a guide for obtaining the corresponding constrained functional derivatives for constraints coupling the functional variables is given. The use of constrained derivatives makes the proper account for constraints ... More

Optimizations of Management Algorithms for Multi-Level Memory HierarchyJul 22 2017In the near future the SCM is predicted to modify the form of new programs, the access form to storage, and the way that storage devices themselves are built. Therefore, a combination between the SCM and a designated Memory Allocation Manager (MAM) that ... More

Hopf categories and the categorification of the Heisenberg algebra via graphical calculusDec 20 2016We explore the connection between the notion of Hopf category and the categorification of the infinite dimensional Heisenberg algebra via graphical calculus proposed by M.Khovanov. We show that the existence of a Hopf structure on a semisimple symmetric ... More

Bezout-type Theorems for Differential FieldsJan 13 2015Mar 02 2015We prove analogs of the Bezout and the Bernstein-Kushnirenko-Khovanskii theorems for systems of algebraic differential conditions over differentially closed fields. Namely, given a system of algebraic conditions on the first $l$ derivatives of an $n$-tuple ... More

Multiplicity estimates, analytic cycles and Newton polytopesJul 04 2014Nov 19 2014We consider the problem of estimating the multiplicity of a polynomial when restricted to the smooth analytic trajectory of a (possibly singular) polynomial vector field at a given point or points, under an assumption known as the D-property. Nesterenko ... More

The mathematics of functional differentiation under conservation constraintMar 09 2006Dec 12 2006The mathematics of K-conserving functional differentiation, with K being the integral of some invertible function of the functional variable, is clarified. The most general form for constrained functional derivatives is derived from the requirement that ... More

Hall categories and KLR categorificationOct 16 2018This paper is the first step in the project of categorifying the bialgebra structure on the half of quantum group $U_{q}(\mathfrak{g})$ by using geometry and Hall algebras. We equip the category of D-modules on the moduli stack of objects of the category ... More

The Rayleigh-Lamb wave propagation in dielectric elastomer layers subjected to large deformationsJun 26 2011The propagation of waves in soft dielectric elastomer layers is investigated. To this end incremental motions superimposed on homogeneous finite deformations induced by bias electric fields and pre-stretch are determined. First we examine the case of ... More

Semigroups of Operators on Spaces of Fuzzy-Number-Valued Functions with Applications to Fuzzy Differential EquationsJun 17 2013In this paper we introduce and study semigroups of operators on spaces of fuzzy-number-valued functions, and various applications to fuzzy differential equations are presented. Starting from the space of fuzzy numbers, many new spaces sharing the same ... More

The pion-nucleon $σ$ term from pionic atomsJan 10 2019Apr 11 2019Earlier work suggested that the in-medium $\pi N$ threshold isovector amplitude $b_1(\rho)$ gets renormalized in pionic atoms by about 30% away from its $\rho=0$ free-space value, relating such renormalization to the leading low-density decrease of the ... More

Towards Robust Evaluations of Continual LearningMay 24 2018Nov 06 2018The experiments used in current continual learning research do not faithfully assess fundamental challenges of learning continually. We examine standard evaluations and show why these evaluations make some types of continual learning approaches look better ... More

Symplectic configurationsApr 06 2005Sep 03 2006We define a class of symplectic fibrations called symplectic configurations. They are natural generalization of Hamiltonian fibrations. Their geometric and topological properties are investigated. We are mainly concentrated on integral symplectic manifolds. ... More

The s-wave repulsion and deeply bound pionic atoms: fact and fancyNov 27 2002Fits to a large data set of pionic atoms show that the `missing' s-wave repulsion is accounted for when a density dependence suggested recently by Weise is included in the isovector term of the s-wave pion optical potential. The importance of using large ... More

Gradual training of deep denoising auto encodersDec 19 2014Stacked denoising auto encoders (DAEs) are well known to learn useful deep representations, which can be used to improve supervised training by initializing a deep network. We investigate a training scheme of a deep DAE, where DAE layers are gradually ... More

High-order maximum principles for the stability analysis of positive bilinear control systemsJul 13 2014We consider a continuous-time positive bilinear control system (PBCS), i.e. a bilinear control system with Metzler matrices. The positive orthant is an invariant set of such a system, and the corresponding transition matrix C(t) is entrywise nonnegative ... More

Self-organized criticality in single neuron excitabilityOct 28 2012Aug 07 2013We present experimental and theoretical arguments, at the single neuron level, suggesting that neuronal response fluctuations reflect a process that positions the neuron near a transition point that separates excitable and unexcitable phases. This view ... More

Learning the Dimensionality of Hidden VariablesJan 10 2013A serious problem in learning probabilistic models is the presence of hidden variables. These variables are not observed, yet interact with several of the observed variables. Detecting hidden variables poses two problems: determining the relations to ... More

Kaonic atoms and in-medium $K^-N$ amplitudesJan 18 2012May 09 2012Recent work on the connection between in-medium subthreshold $K^-N$ amplitudes and kaonic atom potentials is updated by using a next to leading order chirally motivated coupled channel separable interaction model that reproduces $\bar KN$ observables ... More

In-medium nuclear interactions of low-energy hadronsMay 27 2007Aug 16 2007Experimental and theoretical developments of the last decade in the study of exotic atoms and some related low-energy reactions are reviewed, in order to provide information on the in-medium hadron-nucleon t matrix over a wide range of densities up to ... More

a-T-menability of groups acting on treesNov 13 2003We present some partial results concerning a-T-menability of groups acting on trees. Various known results are given uniform proofs.

On a class of degenerate parabolic equations with dynamic boundary conditionsSep 02 2011Feb 17 2012We consider a quasi-linear parabolic equation with nonlinear dynamic boundary conditions occurring as a natural generalization of the semilinear reaction-diffusion equation with dynamic boundary conditions. The corresponding class of initial and boundary ... More

Remarks on the Choquet Integral Calculus on $[a, t]$, with $a\in \mathbb{R}$Feb 06 2019In this note, we extend the considerations for the Choquet integral calculus on the interval $[0, t]$ introduced in \cite{Su}, \cite{Su3}, to the case of an interval $[a, t]$, with arbitrary $a\in \mathbb{R}$.

Analytical and numerical analyses of the micromechanics of soft fibrous connective tissuesJan 02 2012State of the art research and treatment of biological tissues require accurate and efficient methods for describing their mechanical properties. Indeed, micromechanics motivated approaches provide a systematic method for elevating relevant data from the ... More

Decomposing Björner's MatrixNov 30 2010We give an alternative proof of a (former) conjecture of Bj\"orner stating that the matrix expressing face numbers in terms of g numbers is totally non-negative. We briefly discuss the case of simple flag polytopes.

Networks of Influence Diagrams: A Formalism for Representing Agents' Beliefs and Decision-Making ProcessesJan 15 2014This paper presents Networks of Influence Diagrams (NID), a compact, natural and highly expressive language for reasoning about agents beliefs and decision-making processes. NIDs are graphical structures in which agents mental models are represented as ... More

The Pila-Wilkie theorem for subanalytic families: a complex analytic approachMay 15 2016We present a complex analytic proof of the Pila-Wilkie theorem for subanalytic sets. In particular, we replace the use of $C^r$-smooth parametrizations by a variant of Weierstrass division.

Polynomial Bounds for Oscillation of Solutions of Fuchsian SystemsAug 21 2008Oct 05 2009We study the problem of placing effective upper bounds for the number of zeros of solutions of Fuchsian systems on the Riemann sphere. The principal result is an explicit (non-uniform) upper bound, polynomially growing on the frontier of the class of ... More

Differentially Private Continual LearningFeb 18 2019Catastrophic forgetting can be a significant problem for institutions that must delete historic data for privacy reasons. For example, hospitals might not be able to retain patient data permanently. But neural networks trained on recent data alone will ... More

Relativistic three-body calculations of a Y=1, I=3/2, JP=2+ pi-Lambda-N -- pi-Sigma-N dibaryonSep 18 2012Jan 08 2013The pi-Lambda-N - pi-Sigma-N coupled-channel system with quantum numbers (Y,I,JP) = (1,3/2,2+) is studied in a relativistic three-body model, using two-body separable interactions in the dominant p-wave pion-baryon and 3S1 YN channels. Three-body equations ... More

Three-body model calculations of Nucleon-Delta and Delta-Delta dibaryon resonancesFeb 13 2014Mar 13 2014Three-body hadronic models with separable pairwise interactions are formulated and solved to calculate resonance masses and widths of L=0 N-Delta and Delta-Delta dibaryons using relativistic kinematics. For N-Delta, I(JP)=1(2+) and 2(1+) resonances slightly ... More

Coupled channels calculation of a pion-Lambda-nucleon quasibound stateMar 26 2010May 20 2010We extend the study of a JP=2+, I=3/2 pion-Lambda-nucleon quasibound state [Phys. Rev. D 78, 014013 (2008)] by solving nonrelativistic Faddeev equations, using 3S1-3D1, Lambda N - Sigma N coupled channels Chiral Quark Model local interactions, and pion-nucleon ... More

Smooth waves and shocks of finite amplitude in soft materialsJan 02 2019Recently developed soft materials exhibit nonlinear wave propagation with potential applications for energy trapping, shock mitigation and wave focusing. We address finitely deformed materials subjected to combined transverse and axial impacts, and study ... More

Asymptotic dimension and uniform embeddingsJul 16 2006We show that the type function of a space with finite asymptotic dimension estimates its Hilbert (or any $l^p$) compression. The method allows to obtain the lower bound of the compression of the lamplighter group $Z\wr Z$, which has infinite asymptotic ... More

Adaptive Confidence Smoothing for Generalized Zero-Shot LearningDec 24 2018May 13 2019Generalized zero-shot learning (GZSL) is the problem of learning a classifier where some classes have samples and others are learned from side information, like semantic attributes or text description, in a zero-shot learning fashion (ZSL). Training a ... More

Sharp estimates for the global attractor of scalar reaction-diffusion equations with a Wentzell boundary conditionMar 16 2011Jul 10 2011In this paper, we derive optimal upper and lower bounds on the dimension of the attractor AW for scalar reaction-diffusion equations with a Wentzell (dynamic) boundary condition. We are also interested in obtaining explicit bounds about the constants ... More

Observational and Physical Classification of SupernovaeNov 27 2016This chapter describes the current classification scheme of supernovae (SNe). This scheme has evolved over many decades and now includes numerous SN Types and sub-types. Many of these are universally recognized, while there are controversies regarding ... More

A Theoretically Grounded Application of Dropout in Recurrent Neural NetworksDec 16 2015Oct 05 2016Recurrent neural networks (RNNs) stand at the forefront of many recent developments in deep learning. Yet a major difficulty with these models is their tendency to overfit, with dropout shown to fail when applied to recurrent layers. Recent results at ... More

Uniform upper bounds for the cyclicity of the zero solution of the Abel differential equationApr 09 2015Given two polynomials $P,q$ we consider the following question: "how large can the index of the first non-zero moment $\tilde{m}_k=\int_a^b P^k q$ be, assuming the sequence is not identically zero?". The answer $K$ to this question is known as the moment ... More

Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep LearningJun 06 2015Oct 04 2016Deep learning tools have gained tremendous attention in applied machine learning. However such tools for regression and classification do not capture model uncertainty. In comparison, Bayesian models offer a mathematically grounded framework to reason ... More

Improving the Gaussian Process Sparse Spectrum Approximation by Representing Uncertainty in Frequency InputsMar 09 2015Mar 20 2015Standard sparse pseudo-input approximations to the Gaussian process (GP) cannot handle complex functions well. Sparse spectrum alternatives attempt to answer this but are known to over-fit. We suggest the use of variational inference for the sparse spectrum ... More

Synthesis of Parametric Programs using Genetic Programming and Model CheckingFeb 27 2014Formal methods apply algorithms based on mathematical principles to enhance the reliability of systems. It would only be natural to try to progress from verification, model checking or testing a system against its formal specification into constructing ... More

Energy surface, chemical potentials, Kohn-Sham energies in spin-polarized density functional theoryOct 26 2009Jul 19 2010On the basis of the zero-temperature grand canonical ensemble generalization of the energy E[N,N_s,v,B] for fractional particle N and spin N_s numbers, the energy surface over the (N,N_s) plane is displayed and analyzed in the case of homogeneous external ... More

Entrainment of the intrinsic dynamics of single isolated neurons by natural-like inputJan 31 2013Neuronal dynamics is intrinsically unstable, producing activity fluctuations that are essentially scale-free. Here we show that while these scale-free fluctuations are independent of temporal input statistics, they can be entrained by input variation. ... More

Kaonic atoms and in-medium K-N amplitudes II: interplay between theory and phenomenologyNov 27 2012Jan 23 2013A microscopic kaonic-atom optical potential $V^{(1)}_{K^-}$ is constructed, using the Ikeda-Hyodo-Weise NLO chiral $K^-N$ subthreshold scattering amplitudes constrained by the kaonic hydrogen SIDDHARTA measurement, and incorporating Pauli correlations ... More

Traces of Theta^+ pentaquark in K^+ nucleus dynamicsNov 12 2004Jan 21 2005Long-standing anomalies in K^+ nucleus integral cross sections could be resolved by extending the impulse-approximation t*rho optical-potential framework to incorporate K^+ absorption on pairs of nucleons. Substantially improved fits to the data at p(lab)=500-700 ... More

Intersection multiplicities of Noetherian functionsAug 08 2011We provide a partial answer to the following problem: \emph{give an effective upper bound on the multiplicity of non-isolated common zero of a tuple of Noetherian functions}. More precisely, consider a foliation defined by two commuting polynomial vector ... More

An Effective Equation of State for Dense Matter with StrangenessApr 09 1997Jul 08 1997An effective equation of state (EoS) which generalizes the Lattimer-Swesty equation for nuclear matter is presented for matter at supernuclear densities including strange baryons. It contains an adjustable baryon potential energy density, based on models ... More

A diquark model for the d*(2380) dibaryon resonance?May 12 2019Diquark models have been applied with varying degree of success to tetraquark and pentaquark states involving both light and heavy quark degrees of freedom. We discuss the applicability of such models to light quark dibaryons, viewed as three-diquark ... More

Fractional Conductance in Strongly Interacting 1D SystemsFeb 21 2019We study one dimensional clean systems with few channels and strong electron-electron interactions. We find that in several circumstances, even when time reversal symmetry holds, they may lead to two terminal fractional quantized conductance and fractional ... More

Room for an S = +1 pentaquark in K^+ - nucleus phenomenologyNov 14 2005Feb 02 2006Evidence for excitation of exotic S=+1 pentaquark degrees of freedom is presented by studying optical-potential fits to K^+ - nucleus total, reaction and elastic-differential cross section data at p(lab) = 500 - 700 MeV/c. Estimates of the underlying ... More