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Speech recognition for medical conversationsNov 20 2017Jun 20 2018In this work we explored building automatic speech recognition models for transcribing doctor patient conversation. We collected a large scale dataset of clinical conversations ($14,000$ hr), designed the task to represent the real word scenario, and ... More

Blazars in Context in the Fermi EraMar 20 2013Blazars are the most plentiful gamma-ray source at GeV energies, and despite detailed study, there is much that is not known about these sources. In this review I explore some recent results on blazars, including the controversy of the "blazar sequence", ... More

Sheaves, Cosheaves and ApplicationsMar 13 2013Dec 17 2014This thesis develops the theory of sheaves and cosheaves with an eye towards applications in science and engineering. To provide a theory that is computable, we focus on a combinatorial version of sheaves and cosheaves called cellular sheaves and cosheaves, ... More

Norm inequalities in generalized Morrey spacesMay 29 2012May 14 2014We prove that Calder\'on-Zygmund operators, Marcinkiewicz operators, maximal operators associated to Bochner-Riesz operators, operators with rough kernel as well as commutators associated to these operators which are known to be bounded on weighted Morrey ... More

Topological Data Analysis and CosheavesNov 03 2014Mar 04 2015This paper contains an expository account of persistent homology and its usefulness for topological data analysis. An alternative foundation for level-set persistence is presented using sheaves and cosheaves.

The Mezard-Parisi equation for matchings in pseudo-dimension d>1Sep 09 2014We establish existence and uniqueness of the solution to the cavity equation for the random assignment problem in pseudo-dimension $d>1$, as conjectured by Aldous and Bandyopadhyay (Annals of Applied Probability, 2005) and W\"astlund (Annals of Mathematics, ... More

The interpolation method for random graphs with prescribed degreesApr 26 2014We consider large random graphs with prescribed degrees, such as those generated by the configuration model. In the regime where the empirical degree distribution approaches a limit $\mu$ with finite mean, we establish the systematic convergence of a ... More

PDE Approaches to Graph AnalysisApr 30 2015This paper surveys and discusses recent work adapting partial differential equation (PDE) models to discrete structures.

The Thompson-Lyons transfer lemma for fusion systemsMar 24 2013Apr 25 2014In this note, a generalization of the Thompson transfer lemma and its various extensions, most recently due to Lyons, is proven in the context of saturated fusion systems. A strengthening of Alperin's fusion theorem is also given in this setting, following ... More

Unramified geometric class field theory and Cartier dualityOct 08 2017We prove a generalized Albanese property for the Picard stack of a smooth projective curve, which in particular implies Deligne's unramified geometric class field theory. This Albanese property also specializes to the Cartier self-duality of the Picard ... More

Nearby cycles of Whittaker sheaves on Drinfeld's compactificationFeb 14 2017In this article we study the perverse sheaf on Drinfeld's compactification obtained by applying the geometric Jacquet functor (alias nearby cycles) to a nondegenerate Whittaker sheaf. Namely, we describe its restrictions along the defect stratification ... More

The big projective module as a nearby cycles sheafNov 30 2014Aug 22 2016We give a new geometric construction of the big projective module in the principal block of the BGG category $\mathscr{O}$, or rather the corresponding $\mathscr{D}$-module on the flag variety. Namely, given a one-parameter family of nondegenerate additive ... More

The sensitivity of past and near-future lunar radio experiments to ultra-high-energy cosmic rays and neutrinosJan 12 2016Various experiments have been conducted to search for the radio emission from ultra-high-energy particles interacting in the lunar regolith. Although they have not yielded any detections, they have been successful in establishing upper limits on the flux ... More

A new weight system on chord diagrams via hyperkähler geometryFeb 25 2000A weight system on graph homology was constructed by Rozansky and Witten using a compact hyperk\"ahler manifold. A variation of this construction utilizing holomorphic vector bundles over the manifold gives a weight system on chord diagrams. We investigate ... More

Foliations on hypersurfaces in holomorphic symplectic manifoldsDec 20 2008Let Y be a hypersurface in a 2n-dimensional holomorphic symplectic manifold X. The restriction $\sigma|_Y$ of the holomorphic symplectic form induces a rank one foliation on Y. We investigate situations where this foliation has compact leaves; in such ... More

Ulam Sphere Size Analysis for Permutation and Multipermutation Codes Correcting Translocation ErrorsDec 11 2017Jan 08 2019Permutation and multipermutation codes in the Ulam metric have been suggested for use in non-volatile memory storage systems such as flash memory devices. In this paper we introduce a new method to calculate permutation sphere sizes in the Ulam metric ... More

Brace Bar-Cobar DualitySep 11 2013Sep 12 2013Using Kadeishvili's formulas with appropriate signs, we show that the classical cobar construction from coalgebras to algebras \Omega: CoAlg -> Alg can be enhanced to a functor from Hopf algebras to E_2 algebras (for a certain choice of E_2 operad) \Omega ... More

A family of structure isomorphisms for the Cohomological Hall Algebra of an acyclic quiverAug 01 2019For any acyclic quiver, we establish a family of structure isomorphisms for its cohomological Hall algebra (CoHA). The domain of each isomorphism is a tensor product of subalgebras in which each factor is isomorphic to the CoHA of the quiver with a single ... More

Irreducibility of some quantum representations of mapping class groupsSep 22 1999The SU(2) TQFT representation of the mapping class group of a closed surface of genus g, at a root of unity of prime order, is shown to be irreducible. Some examples of reducible representations are also given.

Generating mapping class groups with elements of fixed finite orderOct 12 2017We show that for any $k$ at least $6$ and $g$ sufficiently large, the mapping class group of a surface of genus $g$ can be generated by three elements of order $k$. We also show that this can be done with four elements of order $5$. We additionally prove ... More

Lagrangian fibrations by Prym varietiesMay 08 2019We survey Lagrangian fibrations of holomorphic symplectic varieties, both compact and non-compact, whose fibres are Jacobians and Prym varieties.

Semi-Streaming Algorithms for Annotated Graph StreamsJul 13 2014Aug 10 2015Considerable effort has been devoted to the development of streaming algorithms for analyzing massive graphs. Unfortunately, many results have been negative, establishing that a wide variety of problems require $\Omega(n^2)$ space to solve. One of the ... More

Combinatorially Generated Piecewise Activation FunctionsMay 17 2016In the neuroevolution literature, research has primarily focused on evolving the number of nodes, connections, and weights in artificial neural networks. Few attempts have been made to evolve activation functions. Research in evolving activation functions ... More

Every totally real algebraic integer is a tree eigenvalueFeb 18 2013Sep 04 2014Graph eigenvalues are examples of totally real algebraic integers, i.e. roots of real-rooted monic polynomials with integer coefficients. Conversely, the fact that every totally real algebraic integer occurs as an eigenvalue of some finite graph is a ... More

Compton Dominance and the Blazar SequenceDec 04 2012Does the "blazar sequence" exist, or is it a result of a selection effect, due to the difficulty in measuring the redshifts of blazars with both high synchrotron peak frequencies (\gtrsim 10^{15} Hz) and luminosities (\gtrsim 10^{46} erg s^{-1})? We explore ... More

Geodesic deviation at higher orders via covariant bitensorsJul 25 2014We review a simple but instructive application of the formalism of covariant bitensors, to use a deviation vector field along a fiducial geodesic to describe a neighboring worldline, in an exact and manifestly covariant manner, via the exponential map. ... More

Modeling Fermi Large Area Telescope and Multiwavelength Data from BlazarsFeb 18 2016Blazars are active galactic nuclei with relativistic jets pointed at the Earth, making them extremely bright at essentially all wavelengths, from radio to gamma rays. I review the modeling of this broadband spectral energy distributions of these objects, ... More

The cavity method for counting spanning subgraphs subject to local constraintsMar 16 2011Using the theory of negative association for measures and the notion of random weak limits of sparse graphs, we establish the validity of the cavity method for counting spanning subgraphs subject to local constraints in asymptotically tree-like graphs. ... More

Surjections of unit groups and semi-inversesOct 16 2017Given a surjective ring homomorphism, we study when the induced group homomorphism on unit groups is surjective. To this end, we introduce notions of generalized inverses and units, as well as a class of rings such that the set of closed points in the ... More

Local ill-posedness of the 1D Zakharov systemFeb 08 2006Aug 24 2006Ginibre-Tsutsumi-Velo (1997) proved local well-posedness for the Zakharov system for any dimension $d$, in the inhomogeneous Sobolev spaces $(u,n)\in H^k(\mathbb{R}^d)\times H^s(\mathbb{R}^d)$ for a range of exponents $k$, $s$ depending on $d$. Here we ... More

Intrinsic square functions on functions spaces including weighted Morrey spacesMay 01 2012Apr 16 2013We prove that the intrinsic square functions including Lusin area integral and Littlewood-Paley $g^{\ast}_{\lambda}$-function as defined by Wilson, are bounded in a class of function spaces include weighted Morrey spaces. The corresponding commutators ... More

The initial-boundary value problem for the Korteweg-de Vries equationJul 08 2005Feb 23 2006We prove local well-posedness of the initial-boundary value problem for the Korteweg-de Vries equation on the right half-line, left half-line, and line segment, in the low regularity setting. This is accomplished by introducing an analytic family of boundary ... More

Almost sure global well posedness for the BBM equation with infinite $L^{2}$ initial dataJan 12 2019We consider the probabilistic Cauchy problem for the Benjamin-Bona-Mahony equation (BBM) on the one-dimensional torus $\mathbb{T}$ with initial data below $L^{2}(\mathbb{T})$. With respect to random initial data of strictly negative Sobolev regularity, ... More

Functors on Posets Left Kan Extend to Cosheaves: an ErratumJul 22 2019In this note we give a self-contained proof of a fundamental statement in the study of cosheaves over a poset. Specifically, if a functor has domain a poset and co-domain a co-complete category, then the left Kan extension of that functor along the embedding ... More

Moduli spaces of sheaves on K3 surfacesMar 02 2016In this survey article we describe moduli spaces of simple, stable, and semistable sheaves on K3 surfaces, following the work of Mukai, O'Grady, Huybrechts, Yoshioka, and others. We also describe some recent developments, including applications to the ... More

Source-LDA: Enhancing probabilistic topic models using prior knowledge sourcesJun 02 2016A popular approach to topic modeling involves extracting co-occurring n-grams of a corpus into semantic themes. The set of n-grams in a theme represents an underlying topic, but most topic modeling approaches are not able to label these sets of words ... More

Summary: Acoustic Detection of EHE NeutrinosNov 15 2006Neutrino astronomy was initiated primarily to search for TeV to PeV neutrinos from Active Galactic Nuclei, and the optical Cherenkov technique is well suited for this energy range. Interest has grown recently in detecting EeV neutrinos, particularly the ... More

Products of functions in $\BMO$ and $\H^{1}$ spaces on spaces of homogeneous typeFeb 18 2009We give an extension to certain \textit{RD-space} $\X$, i.e space of homogeneous type in the sense of Coifman and Weiss, which has the reverse doubling property, of the definition and various properties of the product of functions in $\BMO(\X)$ and $\H^{1}(\X)$, ... More

On the Density of Happy NumbersOct 17 2011Mar 01 2015The happy function $H: \mathbb{N} \rightarrow \mathbb{N}$ sends a positive integer to the sum of the squares of its digits. A number $x$ is said to be happy if the sequence $\{H^n(x)\}^\infty_{n=1}$ eventually reaches one. A basic open question regarding ... More

Thermoacoustic Tomography in Elastic MediaMay 04 2011Oct 11 2011We investigate the problem of recovering the initial displacement f for a solution u of a linear, isotropic, non-homogeneous elastic wave equation, given measurements of u on [0,T] x \partial \Omega, where \Omega\subset\R^3 is some bounded domain containing ... More

Comparisons of polychromatic and monochromatic Ramsey theoryMar 06 2012May 17 2012We compare the strength of polychromatic and monochromatic Ramsey theory in several set-theoretic domains. We show that the rainbow Ramsey theorem does not follow from ZF, nor does the rainbow Ramsey theorem imply Ramsey's theorem over ZF. Extending the ... More

Structured Learning via Logistic RegressionJul 03 2014A successful approach to structured learning is to write the learning objective as a joint function of linear parameters and inference messages, and iterate between updates to each. This paper observes that if the inference problem is "smoothed" through ... More

Inflationary Quantum Cosmology: General Framework and Exact Bianchi I SolutionJul 29 2004Sep 11 2004Using the methods of loop quantum gravity, we derive a framework for describing an inflationary, homogeneous universe in a purely quantum theory. The classical model is formulated in terms of the Ashtekar-Sen connection variables for a general subclass ... More

Theories of Dark Energy with Screening MechanismsNov 26 2010Despite the overwhelming evidence for the existence of dark energy and dark matter, their underlying fundamental physics remains unknown. This review article explores the tantalizing possibility that the dark sector includes new light degrees of freedom ... More

Chameleon Field TheoriesJun 18 2013Chameleons are light scalar fields with remarkable properties. Through the interplay of self-interactions and coupling to matter, chameleon particles have a mass that depends on the ambient matter density. The manifestation of the fifth force mediated ... More

H-infinity is not E-infinityOct 19 2009Apr 19 2014We provide an example of a spectrum over S^0 with an H_\infty structure which does not rigidify to an E_3 structure. It follows that in the category of spectra over S^0 not every H_\infty ring spectrum comes from an underlying E_\infty ring spectrum. ... More

Grothendieck classes of quiver cycles as iterated residuesOct 14 2013In the case of Dynkin quivers we establish a formula for the Grothendieck class of a quiver cycle as the iterated residue of a certain rational function, for which we provide an explicit combinatorial construction. Moreover, we utilize a new definition ... More

Asymptotics and 6j-symbolsJan 18 2002Oct 15 2002Recent interest in the Kashaev-Murakami-Murakami hyperbolic volume conjecture has made it seem important to be able to understand the asymptotic behaviour of certain special functions arising from representation theory -- for example, of the quantum 6j-symbols ... More

Kirby calculus in manifolds with boundaryDec 15 1998Suppose there are two framed links in a compact, connected 3-manifold (possibly with boundary, or non-orientable) such that the associated 3-manifolds obtained by surgery are homeomorphic (relative to their common boundary, if there is one.) How are the ... More

Deformations of holomorphic Lagrangian fibrationsSep 09 2005Let $X\to\P^n$ be a $2n$-dimensional projective holomorphic symplectic manifold admitting a Lagrangian fibration over $\P^n$. Matsushita proved that the fibration can be deformed in a codimension one family in the moduli space $\mathrm{Def}(X)$ of deformations ... More

Twisted Fourier-Mukai transforms for holomorphic symplectic fourfoldsSep 09 2005We apply the methods of C{\u{a}}ld{\u{a}}raru to construct a twisted Fourier-Mukai transform between a pair of holomorphic symplectic four-folds. More precisely, we obtain an equivalence between the derived category of coherent sheaves on a certain four-fold ... More

The Laplace transform of the lognormal distributionMar 15 2018In this paper, we explore the analytic continuation of the Laplace transform of the lognormal distribution. Two integral expressions of the analytic continuation are provided, one of which takes the form of a Mellin-Barnes integral. As a corollary, we ... More

On Lagrangian fibrations by Jacobians IISep 19 2011Let Y->P^n be a flat family of reduced Gorenstein curves, such that the compactified relative Jacobian X=\bar{J}^d(Y/P^n) is a Lagrangian fibration. We prove that X is a Beauville-Mukai integrable system if n=3, 4, or 5, and the curves are irreducible ... More

Abelian fibred holomorphic symplectic manifoldsApr 20 2004We study holomorphic symplectic manifolds which are fibred by abelian varieties. This structure is a higher dimensional analogue of an elliptic fibration on a K3 surface. We investigate when a holomorphic symplectic manifold is fibred in this way, and ... More

On the Cohomology of the Lie Algebra Arising from the Lower Central Series of a p-GroupMar 26 2003We study the cohomology H*(A) = Ext_A(k,k) of a locally finite, connected, cocommutative Hopf algebra A over k = F_p. Specifically, we are interested in those algebras A for which H*(A) is generated as an algebra by H^1(A) and H^2(A). We shall call such ... More

Learning Convex Inference of MarginalsJun 13 2012Graphical models trained using maximum likelihood are a common tool for probabilistic inference of marginal distributions. However, this approach suffers difficulties when either the inference process or the model is approximate. In this paper, the inference ... More

Maximum Likelihood Learning With Arbitrary Treewidth via Fast-Mixing Parameter SetsSep 30 2015Oct 30 2015Inference is typically intractable in high-treewidth undirected graphical models, making maximum likelihood learning a challenge. One way to overcome this is to restrict parameters to a tractable set, most typically the set of tree-structured parameters. ... More

Unbounded and dominating reals in Hechler extensionsJan 13 2012We give results exploring the relationship between dominating and unbounded reals in Hechler extensions, as well as the relationships among the extensions themselves. We show that in the standard Hechler extension there is an unbounded real which is dominated ... More

Up-down asymmetric tokamaksNov 21 2016Nov 22 2016Bulk toroidal rotation has proven capable of stabilising both dangerous MHD modes and turbulence. In this thesis, we explore a method to drive rotation in large tokamaks: up-down asymmetry in the magnetic equilibrium. We seek to maximise this rotation ... More

Spectral atoms of unimodular random treesSep 29 2016We use the Mass Transport Principle to analyze the local recursion governing the resolvent $(A-z)^{-1}$ of the adjacency operator of unimodular random trees. In the limit where the complex parameter $z$ approaches a given location $\lambda$ on the real ... More

Up-down asymmetric tokamaksNov 21 2016Nov 23 2016Bulk toroidal rotation has proven capable of stabilising both dangerous MHD modes and turbulence. In this thesis, we explore a method to drive rotation in large tokamaks: up-down asymmetry in the magnetic equilibrium. We seek to maximise this rotation ... More

Les Houches Lectures on Physics Beyond the Standard Model of CosmologyDec 06 2013In these Lectures, I review various extensions of the Lambda-Cold Dark Matter model, characterized by additional light degrees of freedom in the dark sector. In order to reproduce the successful phenomenology of GR in the solar system, these fields must ... More

Probabilistic Couplings for Probabilistic ReasoningOct 27 2017Nov 01 2017This thesis explores proofs by coupling from the perspective of formal verification. Long employed in probability theory and theoretical computer science, these proofs construct couplings between the output distributions of two probabilistic processes. ... More

A characterization of the 2-fusion system of L_4(q)Mar 24 2013Oct 25 2014We study a saturated fusion system F on a finite 2-group S having a Baumann component based on a dihedral 2-group. Assuming F is 2-perfect with no nontrivial normal 2-subgroups, and the centralizer of the component is a cyclic 2-group, it is shown that ... More

The T-algebra spectral sequence: Comparisons and applicationsAug 27 2013Apr 22 2014In previous work with Niles Johnson the author constructed a spectral sequence for computing homotopy groups of spaces of maps between structured objects such as G-spaces and E_n-ring spectra. In this paper we study special cases of this spectral sequence ... More

Isotrivial elliptic K3 surfaces and Lagrangian fibrationsJun 04 2014A fibration is said to be isotrivial if all of its smooth fibres are isomorphic to a single fixed variety. We classify the elliptic K3 surfaces that are isotrivial, and use them to construct Lagrangian fibrations that are isotrivial. We then modify the ... More

Lagrangian fibrations on Hilbert schemes of points on K3 surfacesSep 09 2005Oct 07 2005Let $\mathrm{Hilb}^gS$ be the Hilbert scheme of $g$ points on a K3 surface $S$. Suppose that $\mathrm{Pic}S\cong\Z C$ where $C$ is a smooth curve with $C^2=2(g-1)n^2$. We prove that $\mathrm{Hilb}^gS$ is a Lagrangian fibration.

Learning Graphical Model Parameters with Approximate Marginal InferenceJan 15 2013Likelihood based-learning of graphical models faces challenges of computational-complexity and robustness to model mis-specification. This paper studies methods that fit parameters directly to maximize a measure of the accuracy of predicted marginals, ... More

Acoustic detection of astrophysical neutrinos in South Pole iceDec 30 2011When high-energy particles interact in dense media to produce a particle shower, most of the shower energy is deposited in the medium as heat. This causes the medium to expand locally and emit a shock wave with a medium-dependent peak frequency on the ... More

Dualities between Cellular Sheaves and CosheavesJul 23 2016This paper affirms a conjecture of MacPherson: that the derived category of cellular sheaves is equivalent to the derived category of cellular cosheaves. We give a self-contained treatment of cellular sheaves and cosheaves and note that certain classical ... More

A Bayesian analysis pipeline for continuous GW sources in the PTA bandMay 03 2013The direct detection of Gravitational Waves (GWs) by Pulsar Timing Arrays (PTAs) is very likely within the next decade. While the stochastic GW background is a promising candidate for detection it is also possible that single resolvable sources may be ... More

Deep Learning for Limit Order BooksJan 08 2016Jul 05 2016This paper develops a new neural network architecture for modeling spatial distributions (i.e., distributions on R^d) which is computationally efficient and specifically designed to take advantage of the spatial structure of limit order books. The new ... More

Measurement of gamma and 2 beta + gammaDec 20 2004Jan 26 2005We report on the initial measurements of the angle gamma and the sum of angles 2 beta + gamma of the Unitarity Triangle. When compared with indirect information on the value of gamma from other measurements of CKM parameters, the measurement of these ... More

A Dark Matter SuperfluidJul 10 2015In this talk we present a novel framework that unifies the stunning success of MOND on galactic scales with the triumph of the LambdaCDM model on cosmological scales. This is achieved through the rich and well-studied physics of superfluidity. The dark ... More

Another Path for the Emergence of Modified Galactic Dynamics from Dark Matter SuperfluidityFeb 18 2016Apr 20 2016In recent work we proposed a novel theory of dark matter (DM) superfluidity that matches the successes of the LambdaCDM model on cosmological scales while simultaneously reproducing MOdified Newtonian Dynamics (MOND) phenomenology on galactic scales. ... More

Fading Gravity and Self-InflationDec 06 2006Dec 02 2007We study the cosmology of a toy modified theory of gravity in which gravity shuts off at short distances, as in the fat graviton scenario of Sundrum. In the weak-field limit, the theory is perturbatively local, ghost-free and unitary, although likely ... More

A resolution of singularities for Drinfeld's compactification by stable mapsJun 05 2016Drinfeld's relative compactification plays a basic role in the theory of automorphic sheaves, and its singularities encode representation-theoretic information in the form of intersection cohomology. We introduce a resolution of singularities consisting ... More

Pseudo-Anosov homeomorphisms and the lower central series of a surface groupFeb 21 2007Let Gamma_k be the lower central series of a surface group Gamma of a compact surface S with one boundary component. A simple question to ponder is whether a mapping class of S can be determined to be pseudo-Anosov given only the data of its action on ... More

Classical 6j-symbols and the tetrahedronDec 15 1998Mar 22 1999A classical 6j-symbol is a real number which can be associated to a labelling of the six edges of a tetrahedron by irreducible representations of SU(2). This abstract association is traditionally used simply to express the symmetry of the 6j-symbol, which ... More

Fourier-Mukai transforms, mirror symmetry, and generalized K3 surfacesSep 14 2012We study generalized complex structures on K3 surfaces, in the sense of Hitchin. For each real parameter t between one and infinity we exhibit two families of generalized K3 surfaces, (M,cal{I}_{zeta}) and (M,cal{J}_{zeta}), parametrized by zeta in CP^1, ... More

On Lagrangian fibrations by Jacobians IMar 07 2008Sep 16 2011Let Y->P^n be a flat family of integral Gorenstein curves, such that the compactified relative Jacobian X=\bar{J}^d(Y/P^n) is a Lagrangian fibration. We prove that the degree of the discriminant locus Delta in P^n is at least 4n+2, and we prove that X ... More

Free Energy of Multiple Systems of Spherical Spin Glasses with Constrained OverlapsJun 26 2018The free energy of multiple systems of spherical spin glasses with constrained overlaps was first studied in arXiv:math/0604082. The authors proved an upper bound of the constrained free energy using Guerra's interpolation. In this paper, we prove this ... More

Efficient estimation of the error distribution function in heteroskedastic nonparametric regression with missing dataOct 27 2016A residual-based empirical distribution function is proposed to estimate the distribution function of the errors of a heteroskedastic nonparametric regression with responses missing at random based on completely observed data, and this estimator is shown ... More

Improved study of the $β$-function of $SU(3)$ gauge theory with $N_f = 10 $ massless domain-wall fermionsNov 05 2018Jan 20 2019I perform an improved study of the $\beta$-function of $ SU(3) $ lattice gauge theory with $N_f=10$ massless optimal domain-wall fermions in the fundamental representation, which serves as a check to what extent the scenario in the previous work [arXiv:1603.08854; ... More

Tight Algorithms for Vertex Cover with Hard Capacities on Multigraphs and HypergraphsJun 25 2016Jan 22 2017In this paper we give a f-approximation algorithm for the minimum unweighted Vertex Cover problem with Hard Capacity constraints (VCHC) on f-hypergraphs. This problem generalizes standard vertex cover for which the best known approximation ratio is also ... More

Leptogenesis and CPT ViolationDec 05 2010Jul 13 2011We construct a model in which neutrinos and anti-neutrinos acquire the same mass but slightly different energy dispersion relations.Despite CPT violation, spin-statistics is preserved. We find that leptogenesis can be easily explained within this model, ... More

Coulomb excitations in rhombohedral graphiteDec 28 2018Feb 23 2019Low-energy electronic properties of ABC-stacked graphite are studied by the tight-binding model. There are linear and parabolic bands with and without degeneracy. They show strongly anisotropic dispersions. ABC-stacked grahite is a semimetal due to slight ... More

Nontrivial surface topological physics from strong and weak topological insulators and superconductorsOct 05 2014We investigate states on the surface of strong and weak topological insulators and superconductors that have been gapped by a symmetry breaking term. The surface of a strong 3D topological insulator gapped by a magnetic material is well known to possess ... More

Interleaved Polar (I-Polar) CodesAug 02 2019By inserting interleavers between intermediate stages of the polar encoder, a new class of polar codes, termed interleaved polar (i-polar) codes, is proposed. By the uniform interleaver assumption, we derive the weight enumerating function (WEF) and input-output ... More

Nonequilibrium Effects and Self Heating in Single Electron Coulomb Blockade DevicesOct 12 1995Oct 16 1995We present a comprehensive investigation of nonequilibrium effects and self heating in single electron transfer devices based primarily on the Coulomb blockade effect. During an electron trapping process, a hot electron may be deposited in a quantum dot ... More

Path Integral for Off-Shell SupersymmetryJun 01 2015Off-shell supersymmetry, which restricts sparticles to appear only off-shell, solves the gauge hierarchy problem and unifies the gauge couplings in the usual way. Without introducing any new interactions or exacerbating the naturalness, this idea has ... More

On Neutrino Flavor StatesSep 16 2012Nov 26 2012We review the issues associated with the construction of neutrino flavor states. We then provide a consistent proof that the flavor states are approximately well-defined only if neutrinos are ultra-relativistic or the mass differences are negligible compared ... More

Tensor Variable Elimination for Plated Factor GraphsFeb 08 2019May 17 2019A wide class of machine learning algorithms can be reduced to variable elimination on factor graphs. While factor graphs provide a unifying notation for these algorithms, they do not provide a compact way to express repeated structure when compared to ... More

Latent Alignment and Variational AttentionJul 10 2018Nov 07 2018Neural attention has become central to many state-of-the-art models in natural language processing and related domains. Attention networks are an easy-to-train and effective method for softly simulating alignment; however, the approach does not marginalize ... More

Off-Shell SupersymmetryDec 08 2014Nov 23 2015Supersymmetry does not dictate the way we should quantize the fields in the supermultiplets, and so we have the freedom to quantize the Standard Model (SM) particles and their superpartners differently. We propose a generalized quantization scheme under ... More

Scaling behaviour of non-equilibrium planar $N$-atic spin systems under weak fluctuationsJun 07 2019Starting from symmetry considerations, we derive the generic hydrodynamic equation of non-equilibrium $XY$ spin systems with $N$-atic symmetry under weak fluctuations. Through a systematic treatment we demonstrate that, in two dimensions, these systems ... More

Tensor Variable Elimination for Plated Factor GraphsFeb 08 2019A wide class of machine learning algorithms can be reduced to variable elimination on factor graphs. While factor graphs provide a unifying notation for these algorithms, they do not provide a compact way to express repeated structure when compared to ... More

Single-Electron Transport in Nanostructured Dirac MaterialsJan 05 2016The relativistic dynamics of electronic excitations in two-dimensional Dirac materials such as graphene and the surface states of topological insulators gives rise to superb electronic properties relevant to a wide range of applications and fundamental ... More

Helical Majorana edge mode in a superconducting antiferromagnetic quantum spin Hall insulatorAug 18 2017Aug 10 2018A two-dimensional time-reversal symmetric topological superconductor is a fully gapped system possessing a helical Majorana mode on the edges. This helical Majorana edge mode (HMEM), which is a Kramer's pair of two chiral Majorana edge modes in the opposite ... More