Results for "Edwin Fong"

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On the marginal likelihood and cross-validationMay 21 2019In Bayesian statistics, the marginal likelihood, also known as the evidence, is used to evaluate model fit as it quantifies the joint probability of the data under the prior. In contrast, non-Bayesian models are typically compared using cross-validation ... More
Scalable Nonparametric Sampling from Multimodal Posteriors with the Posterior BootstrapFeb 08 2019Increasingly complex datasets pose a number of challenges for Bayesian inference. Conventional posterior sampling based on Markov chain Monte Carlo can be too computationally intensive, is serial in nature and mixes poorly between posterior modes. Further, ... More
Decorated CorelationsMar 29 2017Let $\mathcal C$ be a category with finite colimits, and let $(\mathcal E,\mathcal M)$ be a factorisation system on $\mathcal C$ with $\mathcal M$ stable under pushouts. Writing $\mathcal C;\mathcal M^{\mathrm{op}}$ for the symmetric monoidal category ... More
Methods for Accelerating Conway's Doomsday Algorithm (part 1)Jun 20 2010Jan 27 2011We propose a modification of a key component in the Doomsday Algorithm for calculating the day of the week of any calendar date. In particular, we propose to replace the calculation of the required term: \lfloor \frac{x}{12} \rfloor + x \bmod 12 + \lfloor ... More
The Algebra of Open and Interconnected SystemsSep 17 2016Herein we develop category-theoretic tools for understanding network-style diagrammatic languages. The archetypal network-style diagrammatic language is that of electric circuits; other examples include signal flow graphs, Markov processes, automata, ... More
Elliptification of Rectangular ImagerySep 22 2017We present and discuss different algorithms for converting rectangular imagery into elliptical regions. We will focus primarily on methods that use mathematical mappings with explicit and invertible equations. We will also present different post-processing ... More
Causal Theories: A Categorical Perspective on Bayesian NetworksJan 26 2013In this dissertation we develop a new formal graphical framework for causal reasoning. Starting with a review of monoidal categories and their associated graphical languages, we then revisit probability theory from a categorical perspective and introduce ... More
Elliptification of Rectangular ImagerySep 22 2017Aug 17 2018We present and discuss different algorithms for converting rectangular imagery into elliptical regions. We will focus primarily on methods that use mathematical mappings with explicit and invertible equations. The key idea is to start with invertible ... More
Decorated CospansFeb 03 2015Aug 11 2015Let $\mathcal C$ be a category with finite colimits, writing its coproduct $+$, and let $(\mathcal D, \otimes)$ be a braided monoidal category. We describe a method of producing a symmetric monoidal category from a lax braided monoidal functor $F: (\mathcal ... More
Generalized Yang-Mills actions from Dirac operator determinantsApr 08 2001We consider the quantum effective action of Dirac fermions on four dimensional flat Euclidean space coupled to external vector- and axial Yang-Mills fields, i.e., the logarithm of the (regularized) determinant of a Dirac operator on flat R^4 twisted by ... More
MicroRNA Systems BiologyDec 20 2007Recently, microRNAs (miRNAs) have emerged as central posttranscriptional regulators of gene expression. miRNAs regulate many key biological processes, including cell growth, death, development and differentiation. This discovery is challenging the central ... More
Correction to "A Note on Gallager's Capacity Theorem for Waveform Channels"Jul 19 2012Nov 04 2013We correct an alleged contradiction to Gallager's capacity theorem for waveform channels as presented in a poster at the 2012 IEEE International Symposium on Information Theory.
Cocycles for Boson and Fermion Bogoliubov TransformationsMay 05 1993Unitarily implementable Bogoliubov transformations for charged, relativistic bos\-ons and fermions are discussed, and explicit formulas for the 2-cocycles appearing in the group product of their implementers are derived. In the fermion case this provides ... More
Explicit solution of the (quantum) elliptic Calogero-Sutherland modelJan 14 2004Dec 09 2008We derive explicit formulas for the eigenfunctions and eigenvalues of the elliptic Calogero-Sutherland model as infinite series, to all orders and for arbitrary particle numbers and coupling parameters. The eigenfunctions obtained provide an elliptic ... More
Quantum Gauge Theories and Noncommutative GeometryAug 01 1996I review results from recent investigations of anomalies in fermion--Yang Mills systems in which basic notions from noncommutative geometry (NCG) where found to naturally appear. The general theme is that derivations of anomalies from quantum field theory ... More
Waterfilling Theorems in the Time-Frequency Plane for the Heat Channel and a Related SourceApr 02 2014Apr 28 2014The capacity of the heat channel, a linear time-varying (LTV) filter with additive white Gaussian noise (AWGN), is characterized by waterfilling in the time-frequency plane. Similarly, the rate distortion function for a related nonstationary source is ... More
Astrometric asteroid masses: a simultaneous determinationFeb 18 2014Using over 89 million astrometric observations of 349,737 numbered minor planets, an attempt was made to determine the masses of 230 of them by simultaneously solving for corrections to all orbital elements and the masses. For 132 minor planets an acceptable ... More
Coulomb and spin-orbit interaction matrix elements in d^2d' configurationSep 10 1998Oct 10 1998The $d^2d'$ configuration is analysed in group-theoretical terms. Starting from the table given by Condon and Odabasi (1980) for the configuration $d^2d'$, we determine a set of convenient group-theoretical basis states, and rewrite the Coulomb matrix ... More
On anomalies and noncommutative geometryJul 17 1995I discuss examples where basic structures from Connes' noncommutative geometry naturally arise in quantum field theory. The discussion is based on recent work, partly collaboration with J. Mickelsson.
Non--commutative Integration CalculusJan 20 1995We discuss a non--commutative integration calculus arising in the mathematical description of anomalies in fermion--Yang--Mills systems. We consider the differential complex of forms $u_0\ccr{\eps}{u_1}\cdots\ccr{\eps}{u_n}$ with $\eps$ a grading operator ... More
Fermion Current Algebras and Schwinger Terms in 3+1 DimensionsApr 24 1993Apr 24 1993We discuss the restricted linear group in infinite dimensions modeled by the Schatten class of rank $2p=4$ which contains $(3+1)$-dimensional analog of the loop groups and is closely related to Yang-Mills theory with fermions in $(3+1)$-dimensions. We ... More
Initial conditions to cosmological N-body simulations, or how to run an ensemble of simulationsMar 04 2005Jun 11 2005The conventional method of generating initial conditions for cosmological N-body simulations introduces a significant error in the real-space statistical properties of the particles. More specifically, the finite box size leads to a significant underestimate ... More
Anyons and the elliptic Calogero-Sutherland modelJul 27 2000Feb 07 2001We obtain a second quantization of the elliptic Calogero-Sutherland (eCS) model by constructing a quantum field theory model of anyons on a circle and at a finite temperature. This yields a remarkable identity involving anyon correlation functions and ... More
General Composite Non-Abelian Strings and Flag Manifold Sigma ModelsAug 22 2019We fully investigate the symmetry breaking patterns occurring upon creation of composite non-Abelian strings: vortex strings in non-Abelian theories where different sets of colours have different amounts of flux. After spontaneous symmetry breaking, there ... More
Exactly solvable models for 2D correlated fermionsJun 04 2002Jun 06 2003I discuss many-body models for interacting fermions in two space dimensions which can be solved exactly using group theory. The simplest example is a model of a quantum Hall system: 2D fermions in a constant magnetic field and a particular non-local 4-point ... More
Understanding genomic alterations in cancer genomes using an integrative network approachSep 10 2014In recent years, cancer genome sequencing and other high-throughput studies of cancer genomes have generated many notable discoveries. In this review, Novel genomic alteration mechanisms, such as chromothripsis (chromosomal crisis) and kataegis (mutation ... More
Remarkable identities related to the (quantum) elliptic Calogero-Sutherland modelJun 24 2004Nov 04 2005We present further remarkable functional identities related to the elliptic Calogero-Sutherland (eCS) system. We derive them from a second quantization of the eCS model within a quantum field theory model of anyons on a circle and at finite temperature. ... More
Dynamics of Phase Separation of Crystal SurfacesMar 09 1993We investigate the dynamical evolution of a thermodynamically unstable crystal surface into a hill-and-valley structure. We demonstrate that, for quasi one-dimensional ordering, the equation of motion maps exactly to the modified Cahn-Hilliard equation ... More
On 4-Dimensional J-Invariant Shrinking Ricci SolitonsJan 19 2014As of today, there are very few known complete shrinking Ricci solitons in dimension 4, and all examples discovered so far are K\"ahler and/or Einstein. In this note, we prove that any four dimensional J-invariant gradient shrinking Ricci solitons satisfy ... More
Cut-Set Bounds for Multimessage Multicast Networks with Independent Channels and Zero-Delay EdgesJun 01 2015Apr 26 2016We consider a communication network consisting of nodes and directed edges that connect the nodes. The network may contain cycles. The communications are slotted where the duration of each time slot is equal to the maximum propagation delay experienced ... More
Impact of contact resistance in Lorenz number measurementsNov 10 2017Jan 07 2018We analyze the effect of contact resistance on the Lorenz number measurement based on direct electronic thermal conductivity experiments. The contact resistance can significantly limit the experimental measured value when the Lorenz number is enhanced, ... More
On the collapsing rate of the Kähler-Ricci flow with finite-time singularityDec 27 2011This short note studies the collapsing behavior of the K\"ahler-Ricci flow on a compact K\"ahler manifold X admitting a holomorphic submersion X -> B where B is a K\"ahler manifold of lower dimension than X. We give cohomological and curvature conditions ... More
Stability and Kinetics of Step Motion on Crystal SurfacesDec 01 1993The kinetics of monoatomic steps in diffusion-controlled crystal growth and evaporation processes are investigated analytically using a Green's function approach. Integro-differential equations of motion for the steps are derived; and a systematic linear ... More
Classes of Delay-Independent Multimessage Multicast Networks with Zero-Delay NodesOct 20 2014Sep 11 2015In a network, a node is said to incur a delay if its encoding of each transmitted symbol involves only its received symbols obtained before the time slot in which the transmitted symbol is sent (hence the transmitted symbol sent in a time slot cannot ... More
Baryogenesis from Symmetry PrincipleAug 14 2015Dec 07 2015In this work, a formalism based on symmetry which allows one to express asymmetries of all the particles in terms of conserved charges is developed. The manifestation of symmetry allows one to easily determine the viability of a baryogenesis scenario ... More
Results in Workflow Resiliency: Complexity, New Formulation, and ASP EncodingSep 26 2018First proposed by Wang and Li in 2007, workflow resiliency is a policy analysis for ensuring that, even when an adversarial environment removes a subset of workers from service, a workflow can still be instantiated to satisfy all the security constraints. ... More
Net2Vec: Quantifying and Explaining how Concepts are Encoded by Filters in Deep Neural NetworksJan 10 2018Mar 29 2018In an effort to understand the meaning of the intermediate representations captured by deep networks, recent papers have tried to associate specific semantic concepts to individual neural network filter responses, where interesting correlations are often ... More
An application of liaison theory to the Eisenbud-Green-Harris conjectureNov 05 2013In this paper, we apply liaison theory to the Eisenbud-Green-Harris conjecture and prove that the conjecture holds for a certain subclass of homogeneous ideals in the linkage class of a complete intersection ideal. In the case of three variables, we prove ... More
A recipe for black box functorsDec 10 2018The task of constructing compositional semantics for network-style diagrammatic languages, such as electrical circuits or chemical reaction networks, has been dubbed the black boxing problem, as it gives semantics that describes the properties of each ... More
Boltzmann's Entropy and Kähler-Ricci SolitonsMay 25 2016We study a Boltzmann's type entropy functional (which appeared in existing literature) defined on K\"ahler metrics of a fixed K\"ahler class. The critical points of this functional are gradient K\"ahler-Ricci solitons, and the functional was known to ... More
Hilbert functions of colored quotient rings and a generalization of the Clements-Lindström theoremMar 13 2014Dec 02 2014Given a polynomial ring $S = \Bbbk[x_1, \dots, x_n]$ over a field $\Bbbk$, and a monomial ideal $M$ of $S$, we say the quotient ring $R = S/M$ is Macaulay-Lex if for every graded ideal of $R$, there exists a lexicographic ideal of $R$ with the same Hilbert ... More
Universal Constructions for (Co)Relations: categories, monoidal categories, and propsOct 11 2017Aug 31 2018Calculi of string diagrams are increasingly used to present the syntax and algebraic structure of various families of circuits, including signal flow graphs, electrical circuits and quantum processes. In many such approaches, the semantic interpretation ... More
Kähler-Ricci Flow on Projective Bundles over Kähler-Einstein ManifoldsApr 20 2011Oct 19 2011We study the K\"ahler-Ricci flow on a class of projective bundles $\mathbb{P}(\mathcal{O}_\Sigma \oplus L)$ over compact K\"ahler-Einstein manifold $\Sigma^n$. Assuming the initial K\"ahler metric $\omega_0$ admits a U(1)-invariant momentum profile, we ... More
Azbel-Hofstadter model on triangular lattice revisitedApr 12 2001In the present paper, the mean of Lyapunov exponents for the Azbel-Hofstadter model on the triangular lattice is calculated. It is recently proposed that [Phys. Rev. Lett. {\bf 85}, 4920 (2000)], for the case of the square lattice, this quantity can be ... More
Sharp interface limit of a non-mass-conserving Cahn--Hilliard system with source terms and non-solenoidal Darcy flowFeb 21 2019We study the sharp interface limit of a non-mass-conserving Cahn--Hilliard--Darcy system with the weak compactness method developed in Chen (J. Differential Geometry, 1996). The source term present in the Cahn--Hilliard component is a product of the order ... More
Corelations are the prop for extraspecial commutative Frobenius monoidsJan 11 2016Jan 30 2016Just as binary relations between sets may be understood as jointly monic spans, so too may equivalence relations on the disjoint union of sets be understood as jointly epic cospans. With the ensuing notion of composition inherited from the pushout of ... More
Bachet's Problem: as few weights to weigh them allOct 26 2010A problem that enjoys an enduring popularity asks: "what is the least number of pound weights that can be used on a scale pan to weigh any integral number of pounds from 1 to 40 inclusive, if the weights can be placed in either of the scale pans ?" W.W. ... More
Finding and solving Calogero-Moser type systems using Yang-Mills gauge theoriesSep 16 1999Sep 21 1999Yang-Mills gauge theory models on a cylinder coupled to external matter charges provide powerful means to find and solve certain non-linear integrable systems. We show that, depending on the choice of gauge group and matter charges, such a Yang-Mills ... More
An Explicit Formula for the Local zeta Function of a Laurent PolynomialFeb 21 2014Apr 08 2016In a recent paper Z\'u\~niga-Galindo and the author begun the study of the local zeta functions for Laurent polynomials. In this work we continue this study by giving a very explicit formula for the local zeta function associated to a Laurent polynomial ... More
A Leray spectral sequence for noncommutative differential fibrationsAug 25 2011This paper describes the Leray spectral sequence associated to a differential fibration. The differential fibration is described by base and total differential graded algebras. The cohomology used is noncommutative differential sheaf cohomology. For this ... More
On the range of lattice models in high dimensions - extended versionJun 22 2018In this paper we investigate the scaling limit of the range (the set of visited vertices) for a class of critical lattice models, starting from a single initial particle at the origin. We give conditions on the random sets and an associated "ancestral ... More
A Semantics for Approximate Program TransformationsApr 19 2013An approximate program transformation is a transformation that can change the semantics of a program within a specified empirical error bound. Such transformations have wide applications: they can decrease computation time, power consumption, and memory ... More
On the Angular Width of Diffractive Beam in Anisotropic MediaDec 15 20112-D diffraction patterns arising in the far-field region were investigated theoretically for the case, when the plane wave with non collinear group and phase velocities is incident on the wide slit in opaque screen with arbitrary orientation. This investigation ... More
Photoelectric cross-sections of gas and dust in protoplanetary disksJul 18 2011We provide simple polynomial fits to the X-ray photoelectric cross-sections (0.03 < E < 10keV) for mixtures of gas and dust found in protoplanetary disks. Using the solar elemental abundances of Asplund et al. (2009) we treat the gas and dust components ... More
Construction by bosonization of a fermion-phonon modelMar 06 2015Dec 03 2015We discuss an extension of the (massless) Thirring model describing interacting fermions in one dimension which are coupled to phonons and where all interactions are local. This fermion-phonon model can be solved exactly by bosonization. We present a ... More
Weak convergence of measure-valued processes and $r$-point functionsOct 16 2007We prove a sufficient set of conditions for a sequence of finite measures on the space of cadlag measure-valued paths to converge to the canonical measure of super-Brownian motion in the sense of convergence of finite-dimensional distributions. The conditions ... More
Level-Rank Duality in Chern-Simons Theory from a Non-Supersymmetric Brane ConfigurationAug 20 2014We derive level-rank duality in pure Chern-Simons gauge theories from a non-supersymmetric Seiberg duality by using a non-supersymmetric brane configuration in type IIB string theory. The brane configuration consists of fivebranes, N D3 antibranes and ... More
Chiral Schwinger models without gauge anomaliesApr 25 2000We find a large class of quantum gauge models with massless fermions where the coupling to the gauge fields is not chirally symmetric and which nevertheless do not suffer from gauge anomalies. To be specific we study two dimensional Abelian models in ... More
Susceptibilities, the Specific Heat and a Cumulant in Two-Flavour QCDJun 13 1994We study the quark mass dependence of various response functions, which contribute to chiral susceptibilities and the specific heat in the staggered fermion formulation of two-flavour QCD. This yields information about the critical exponents $\alpha$, ... More
Massive quark scattering at strong coupling from AdS/CFTNov 02 2009May 26 2010We extend the analysis of Alday and Maldacena for obtaining gluon scattering amplitudes at strong coupling to include external massive quark states. Our quarks are actually the N=2 hypermultiplets which arise when D7-brane probes are included in the AdS_5 ... More
The Chemical Evolution of Protoplanetary DisksAug 25 2009The origins of planets, and perhaps life itself, is intrinsically linked to the chemistry of planet formation. In this chapter we will attempt to explore the chemistry of planet-forming disks from the perspective of knowledge gained from decades of solar ... More
Exact solutions of two complementary 1D quantum many-body systems on the half-lineApr 07 2004May 13 2004We consider two particular 1D quantum many-body systems with local interactions related to the root system $C_N$. Both models describe identical particles moving on the half-line with non-trivial boundary conditions at the origin, and they are in many ... More
The dimension of the boundary of super-Brownian motionNov 09 2017We show that the Hausdorff dimension of the boundary of $d$-dimensional super-Brownian motion is $0$, if $d=1$, $4-2\sqrt2$, if $d=2$, and $(9-\sqrt{17})/2$, if $d=3$.
Spectral triples from bimodule connections and Chern connectionsAug 19 2015Sep 03 2015We give a geometrical construction of Connes spectral triples or noncommutative Dirac operators $D$ starting with a bimodule connection on the proposed spinor bundle. The theory is applied to the example of $M_2(\Bbb C)$, and also applies to the standard ... More
Making the small oblique parameters largeSep 14 1993We compute the oblique parameters, including the three new parameters $ V $, $ W $ and $ X $ introduced recently by the Montreal group, for the case of one scalar multiplet of arbitrary weak isospin $ J $ and weak hypercharge $ Y $. We show that, when ... More
Hot Leptogenesis from Thermal Dark MatterJul 10 2017Mar 30 2018In this work, we investigate a scenario in which heavy Majorana Right-Handed Neutrinos (RHNs) are in thermal equilibrium with a dark sector with temperature higher than the Standard Model (SM) thermal bath. Specifically, we consider the scenario in which ... More
Additive monotones for resource theories of parallel-combinable processes with discardingMay 06 2015Nov 05 2015A partitioned process theory, as defined by Coecke, Fritz, and Spekkens, is a symmetric monoidal category together with an all-object-including symmetric monoidal subcategory. We think of the morphisms of this category as processes, and the morphisms ... More
A Noether Theorem for Markov ProcessesMar 09 2012Noether's theorem links the symmetries of a quantum system with its conserved quantities, and is a cornerstone of quantum mechanics. Here we prove a version of Noether's theorem for Markov processes. In quantum mechanics, an observable commutes with the ... More
The Galactic and Sub-Galactic Environments of Short-Duration Gamma-Ray Bursts: Implications for the ProgenitorsDec 21 2009The study of short-duration gamma-ray bursts (GRBs) has undergone a revolution in recent years thanks to the discovery of the first afterglows and host galaxies in May 2005. In this review we summarize our current knowledge of the galactic and sub-galactic ... More
Quark masses, mixings, and CP violation from spontaneous breaking of flavor $SU(3)^{3}$Jul 16 2013Feb 25 2014A ${\cal G}_{\cal F}=SU(3)_{Q}\times SU(3)_{u}\times SU(3)_{d}$ invariant scalar potential breaking spontaneously the quark flavor symmetry can explain the standard model flavor puzzle. The approximate alignment in flavor space of the vacuum expectation ... More
Ultra-sensitive and Wide Bandwidth Thermal Measurements of Graphene at Low TemperaturesFeb 26 2012May 30 2012Graphene is a material with remarkable electronic properties and exceptional thermal transport properties near room temperature, which have been well examined and understood. However at very low temperatures the thermodynamic and thermal transport properties ... More
A Compositional Framework for Passive Linear NetworksApr 22 2015Nov 16 2018Passive linear networks are used in a wide variety of engineering applications, but the best studied are electrical circuits made of resistors, inductors and capacitors. We describe a category where a morphism is a circuit of this sort with marked input ... More
Supplying bells and whistles in symmetric monoidal categoriesAug 07 2019It is common to encounter symmetric monoidal categories $\mathcal{C}$ for which every object is equipped with an algebraic structure, in a way that is compatible with the monoidal product and unit in $\mathcal{C}$. We define this formally and say that ... More
Holographic Corrections to Meson Scattering AmplitudesNov 01 2016Nov 03 2016We compute meson scattering amplitudes using the holographic duality between confining gauge theories and string theory, in order to consider holographic corrections to the Veneziano amplitude and associated higher-point functions. The generic nature ... More
A product formula for the eigenfunctions of a quartic oscillatorDec 12 2013Sep 12 2016We consider the Schr\"odinger operator on the real line with an even quartic potential. Our main result is a product formula of the type $\psi_k(x)\psi_k(y) = \int_{\mathbb{R}} \psi_k(z)\mathcal{K}(x,y,z)dz$ for its eigenfunctions $\psi_k$. The kernel ... More
Taste symmetry breaking at finite temperatureJul 27 2012The breaking of the taste symmetry is studied in the temperature range between 140 MeV to 550 MeV. In order to investigate this violation we have calculated the screening masses of the various taste states fitting the exponential decay of the spatial ... More
Neural Stain Normalization and Unsupervised Classification of Cell Nuclei in Histopathological Breast Cancer ImagesNov 09 2018In this paper, we develop a complete pipeline for stain normalization, segmentation, and classification of nuclei in hematoxylin and eosin (H&E) stained breast cancer histopathology images. In the first step, we use a CNN-based stain transfer technique ... More
Incremental Sequence LearningNov 09 2016Dec 01 2016Deep learning research over the past years has shown that by increasing the scope or difficulty of the learning problem over time, increasingly complex learning problems can be addressed. We study incremental learning in the context of sequence learning, ... More
Elementary Derivation of the Chiral AnomalyDec 15 1994Jan 24 1995An elementary derivation of the chiral gauge anomaly in all even dimensions is given in terms of noncommutative traces of pseudo-differential operators.
Chemical Models of Collapsing EnvelopesOct 07 1999We discuss recent models of chemical evolution in the developing and collapsing protostellar envelopes associated with low-mass star formation. In particular, the effects of depletion of gas-phase molecules onto grain surfaces is considered. We show that ... More
Analysis of a Cahn--Hilliard system with non-zero Dirichlet conditions modeling tumor growth with chemotaxisApr 01 2016We consider a diffuse interface model for tumor growth consisting of a Cahn--Hilliard equation with source terms coupled to a reaction-diffusion equation, which models a tumor growing in the presence of a nutrient species and surrounded by healthy tissue. ... More
Computing Ground States of Spin-1 Bose-Einstein Condensates by the Normalized Gradient FlowNov 05 2007In this paper, we propose an efficient and accurate numerical method for computing the ground state of spin-1 Bose-Einstein condensates (BEC) by using the normalized gradient flow or imaginary time method. The key idea is to find a third projection or ... More
Seven Sketches in Compositionality: An Invitation to Applied Category TheoryMar 14 2018Oct 12 2018This book is an invitation to discover advanced topics in category theory through concrete, real-world examples. It aims to give a tour: a gentle, quick introduction to guide later exploration. The tour takes place over seven sketches, each pairing an ... More
Warping Peirce Quincuncial PanoramasNov 14 2010Sep 26 2015The Peirce quincuncial projection is a mapping of the surface of a sphere to the interior of a square. It is a conformal map except for four points on the equator. These points of non-conformality cause significant artifacts in photographic applications. ... More
Quantum phase transitions of two-species bosons in square latticeSep 15 2010We investigate various quantum phase transitions of attractive two-species bosons in a square lattice. Using the algorithm based on the tensor product states, the phase boundaries of the pair superfluid states with nonzero pair condensate density \emph{and} ... More
Hydrodynamics of electrons in grapheneOct 23 2017Jan 05 2018Generic interacting many-body quantum systems are believed to behave as classical fluids on long time and length scales. Due to rapid progress in growing exceptionally pure crystals, we are now able to experimentally observe this collective motion of ... More
Global weak solutions and asymptotic limits of a Cahn--Hilliard--Darcy system modelling tumour growthAug 31 2016Oct 23 2016We study the existence of weak solutions to a Cahn--Hilliard--Darcy system coupled with a convection-reaction-diffusion equation through the fluxes, through the source terms and in Darcy's law. The system of equations arises from a mixture model for tumour ... More
A Compositional Framework for Passive Linear NetworksApr 22 2015Sep 28 2016Passive linear networks are used in a wide variety of engineering applications, but the best studied are electrical circuits made of resistors, inductors and capacitors. We describe a category where a morphism is a circuit of this sort with marked input ... More
Graphical Regular LogicDec 14 2018Jun 20 2019Regular logic can be regarded as the internal language of regular categories, but the logic itself is generally not given a categorical treatment. In this paper, we understand the syntax and proof rules of regular logic in terms of the free regular category ... More
Analysis of a Cahn--Hilliard system with non-zero Dirichlet conditions modeling tumor growth with chemotaxisApr 01 2016May 03 2017We consider a diffuse interface model for tumor growth consisting of a Cahn--Hilliard equation with source terms coupled to a reaction-diffusion equation, which models a tumor growing in the presence of a nutrient species and surrounded by healthy tissue. ... More
Incremental Sequence LearningNov 09 2016Deep learning research over the past years has shown that by increasing the scope or difficulty of the learning problem over time, increasingly complex learning problems can be addressed. We study incremental learning in the context of sequence learning, ... More
Bayesian Ensembles of Crowds and Deep Learners for Sequence TaggingNov 02 2018Current methods for sequence tagging, a core task in NLP, are data hungry. Crowdsourcing is a relatively cheap way to obtain labeled data, but the annotators are unreliable, so redundant labeling and aggregation techniques are required. We evaluate multiple ... More
Signatures of Nucleon Disappearance in Large Underground DetectorsJun 13 2002Mar 29 2003For neutrons bound inside nuclei, baryon instability can manifest itself as a decay into undetectable particles (e.g., $\it n \to \nu \nu \bar{\nu} $), i.e., as a disappearance of a neutron from its nuclear state. If electric charge is conserved, a similar ... More
Extrinsic curvature effects in brane-world scenariosMar 16 2011Mar 31 2011We consider models of bosons on curved 3+1 dimensional space-time embedded in a higher dimensional flat ambient space. We propose to derive (rather than postulate) equations of motions by assuming that a standard Klein-Gordon field on ambient space is ... More
Bethe-Salpeter Equation -- The OriginsNov 07 2008This article was originally written for scholarpedia.org. It describes the origins and related background of Bethe-Salpeter equation.
Nuclear Astrophysics Before 1957Nov 20 2007I discuss especially my summer with Willy Fowler at Kellogg Radiation in 1951, where I did my "triple-alpha" work. I also go back even earlier to Arthur Eddington and Hans Bethe. I also mention the 1953 summer school in Ann Arbor.
Meson Screening Masses at high Temperature in quenched QCD with improved Wilson QuarksMar 29 2001We report on a lattice investigation of improved quenched Wilson fermions above and below the confinement-deconfinement phase transition. Results on meson screening masses as well as spatial wave functions are presented. Moreover, the meson dispersion ... More
(3+1)-Dimensional Schwinger Terms and Non-commutative GeometryJul 29 1994We discuss 2-cocycles of the Lie algebra $\Map(M^3;\g)$ of smooth, compactly supported maps on 3-dimensional manifolds $M^3$ with values in a compact, semi-simple Lie algebra $\g$. We show by explicit calculation that the Mickelsson-Faddeev-Shatashvili ... More
A Topologically Stable Solution in Quantum ElectrodynamicsNov 30 1993This paper constructs exact classical solutions of the equations of QED. These are constructed in 4+2 dimensional space, which fibers over the usual 3+1 dimensional space-time. The solution is stationary and localised about a topological singularity in ... More
Taste symmetry violation at finite temperatureJan 06 2013Symmetries play a distinctive role at the high temperature phase transition in QCD. Therefore the spectrum of screening masses has been investigated with emphasis on taste breaking. Although taste violation is an UV effect the relevant operators could ... More