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Modeling the X-ray - UV Correlations in NGC 7469Jan 13 2000We model the correlated X-ray - UV observations of NGC 7469, for which well sampled data in both these bands have been obtained recently in a multiwavelength monitoring campaign. To this end we derive the transfer function in wavelength \ls and time lag ... More

Formation of Multifractal Population Patterns from Reproductive Growth and Local ResettlementFeb 04 2005Jul 25 2005We consider the general character of the spatial distribution of a population that grows through reproduction and subsequent local resettlement of new population members. We present several simple one and two-dimensional point placement models to illustrate ... More

Streaming supercomputing needs workflow-enabled programming-in-the-largeFeb 24 2017This is a position paper, submitted to the Future Online Analysis Platform Workshop (https://press3.mcs.anl.gov/futureplatform/), which argues that simple data analysis applications are common today, but future online supercomputing workloads will need ... More

Microsimulation Model Calibration using Incremental Mixture Approximate Bayesian ComputationApr 06 2018Aug 13 2018Microsimulation models (MSMs) are used to predict population-level effects of health care policies by simulating individual-level outcomes. Simulated outcomes are governed by unknown parameters that are chosen so that the model accurately predicts specific ... More

Characterization and valuation of uncertainty of calibrated parameters in stochastic decision modelsJun 11 2019We evaluated the implications of different approaches to characterize uncertainty of calibrated parameters of stochastic decision models (DMs) in the quantified value of such uncertainty in decision making. We used a microsimulation DM of colorectal cancer ... More

Neural Semantic Parsing over Multiple Knowledge-basesFeb 06 2017Apr 24 2017A fundamental challenge in developing semantic parsers is the paucity of strong supervision in the form of language utterances annotated with logical form. In this paper, we propose to exploit structural regularities in language in different domains, ... More

Decoupling Structure and Lexicon for Zero-Shot Semantic ParsingApr 21 2018Sep 22 2018Building a semantic parser quickly in a new domain is a fundamental challenge for conversational interfaces, as current semantic parsers require expensive supervision and lack the ability to generalize to new domains. In this paper, we introduce a zero-shot ... More

Don't paraphrase, detect! Rapid and Effective Data Collection for Semantic ParsingAug 26 2019Aug 29 2019A major hurdle on the road to conversational interfaces is the difficulty in collecting data that maps language utterances to logical forms. One prominent approach for data collection has been to automatically generate pseudo-language paired with logical ... More

Turbulent magnetic relaxation in pulsar wind nebulaeDec 07 2016We present a model for magnetic energy dissipation in a pulsar wind nebula. Better understanding of this process is required to assess the likelihood that certain astrophysical transients may be powered by the spin-down of a "millisecond magnetar." Examples ... More

Elementary invariants for centralizers of nilpotent matricesNov 01 2006We construct an explicit set of algebraically independent generators for the center of the universal enveloping algebra of the centralizer of a nilpotent matrix in the Lie algebra gl_N(C). In particular, this gives a new proof of the freeness of the center, ... More

Gamma-ray Bursts: Light on the distant UniverseDec 31 2008Observations of a long-lasting Gamma-ray burst, one that has the brightest optical counterpart yet discovered, challenge theoretical understanding of these bursts but may enhance their usefulness as cosmic probes.

Power Spectra for Galaxy Shape CorrelationsJul 27 2001Sep 06 2002It has recently been argued that the observed ellipticities of galaxies may be determined at least in part by the primordial tidal gravitational field in which the galaxy formed. Long-range correlations in the tidal field could thus lead to an ellipticity-ellipticity ... More

Symplectically replacing plumbings with Euler characteristic 2 4-manifoldsAug 17 2016A 2-replaceable linear plumbing is defined to be a linear plumbing whose lens space boundary, equipped with the canonical contact structure inherited from the standard contact structure on $S^3$, has a minimal strong symplectic filling of Euler characteristic ... More

Frogs on trees ?Sep 28 2016We study a system of simple random walks on $\mathcal{T}_{d,n} = \mathcal{V}_{d,n}, \mathcal{E}_{d,n})$, the $d$-ary tree of depth $n$, known as the frog model. Initially there are Pois($\lambda$) particles at each site, independently, with one additional ... More

Illustrating the Mezzo programming languageNov 27 2013When programmers want to prove strong program invariants, they are usually faced with a choice between using theorem provers and using traditional programming languages. The former requires them to provide program proofs, which, for many applications, ... More

Measures on Banach Manifolds, Random Surfaces, and Nonperturbative String Field Theory with Cut-offsJul 14 2008We construct a cut-off version of nonpertubative closed Bosonic string field theory in the light-cone gauge with imaginary string coupling constant. We show that the partition function is a continuous function of the string coupling constant, and conjecture ... More

A 3+1 Computational Scheme for Dynamic Spherically Symmetric Black Hole Spacetimes -- II: Time EvolutionJun 06 1999Dec 02 1999This is the second in a series of papers describing a 3+1 computational scheme for the numerical simulation of dynamic black hole spacetimes. We discuss the numerical time-evolution of a given black-hole-containing initial data slice in spherical symmetry. ... More

Exponential growth of homological torsion for towers of congruence subgroups of Bianchi groupsFeb 13 2013In this paper we prove that for suitable sequences of congruence subgroups of Bianchi groups, including the standard exhaustive sequences of a congruence subgroup, and even symmetric powers of the standard representation of Sl_2(C) the size of the torsion ... More

Recovering quantum graph spectrum from vertex dataNov 14 2014Mar 20 2015We study the question to what extent spectral information of a Schr\"odinger operator on a finite, compact metric graph subject to standard or $\delta$-type matching conditions can be recovered from a corresponding Titchmarsh-Weyl function on the boundary ... More

A universal sequence of integers generating balanced Steinhaus figures modulo an odd numberAug 18 2009Mar 30 2016In this paper, we partially solve an open problem, due to J.C. Molluzzo in 1976, on the existence of balanced Steinhaus triangles modulo a positive integer $n$, that are Steinhaus triangles containing all the elements of $\mathbb{Z}/n\mathbb{Z}$ with ... More

Constraining gamma-ray propagation on cosmic distancesOct 10 2013Studying the propagation of gamma rays on cosmological distances encompasses a variety of scientific fields, focusing on diffuse radiation fields such as the extragalactic background light, on the probe of the magnetism of the Universe on large scales, ... More

Polya's random walk theoremJan 16 2013Apr 18 2013This note presents a proof of P\'olya's random walk theorem using classical methods from special function theory and asymptotic analysis.

The effect of compression on the global optimization of atomic clustersJan 06 2000Recently, Locatelli and Schoen proposed a transformation of the potential energy that aids the global optimization of Lennard-Jones clusters with non-icosahedral global minima. These cases are particularly difficult to optimize because the potential energy ... More

On the magnetic flux problem in star formationJan 26 2012Strong magnetic fields play a crucial role in the removal of angular momentum from collapsing clouds and protostellar discs and are necessary for the formation of disc winds as well as jets from the inner disc and indeed, strong large-scale poloidal magnetic ... More

From pulsar scintillations to coronal heating: discontinuities in magnetohydrodynamicsApr 22 2015From pulsar scintillations we infer the presence of sheet-like structures in the ISM; it has been suggested that these are current sheets. Current sheets probably play an important role in heating the solar corona, and there is evidence for their presence ... More

Modulation effects within the mean-field theory of electrolyte solutionsSep 21 2009Oct 12 2010The consequences of source charge and surface modulation are studied within the framework of the Poisson-Boltzmann theory of electrolyte solutions. Through a consideration of various examples, it is found that inherent modulation can lead to both like-charge ... More

Uniqueness Trees: A Possible Polynomial Approach to the Graph Isomorphism ProblemJun 21 2016This paper presents the novel `uniqueness tree' algorithm, as one possible method for determining whether two finite, undirected graphs are isomorphic. We prove that the algorithm has polynomial time complexity in the worst case, and that it will always ... More

Approximating $C^0$-foliations by contact structuresSep 25 2015Sep 26 2016We show that any co-orientable foliation of dimension two on a closed orientable $3$-manifold with continuous tangent plane field can be $C^0$-approximated by both positive and negative contact structures unless all the leaves are simply connected. As ... More

Explaining the emergence of echo chambers on social media: the role of ideology and extremismSep 16 2016The emergence of politically driven divisions in online discussion networks has attracted a wealth of literature, but also one which has thus far been largely limited to single country studies. Hence whilst there is good evidence that these networks do ... More

Scaling relations between numerical simulations and physical systems they representNov 29 2011Jan 10 2012The dynamical equations describing the evolution of a physical system generally have a freedom in the choice of units, where different choices correspond to different physical systems that are described by the same equations. Since there are three basic ... More

$τ$ physics at LHCbSep 07 2015We report on the first searches for lepton flavour violating $\tau^-$ decays at a hadron collider. These include searches for the lepton flavour violating decay $\tau^-\to \mu^+\mu^-\mu^-$ and the lepton flavour and baryon number violating decays $\tau^-\to ... More

Pulsar Death at an Advanced AgeNov 26 1999I summarize the theory of acceleration of non-neutral particle beams by starvation electric fields along the polar magnetic field lines of rotation powered pulsars, including the effect of dragging of inertial frames which dominates the acceleration of ... More

Area scaling entropies for gravitating systemsMay 28 2001The entropy of a spherically symmetric distribution of matter in self-equilibrium is calculated. When gravitational effects are neglected, the entropy of the system is proportional to its volume. As effects due to gravitational self-interactions become ... More

Sensitivity to the cutoff value in the quadratic adaptive integrate-and-fire modelDec 05 2008The quadratic adaptive integrate-and-fire model (Izhikecih 2003, 2007) is recognized as very interesting for its computational efficiency and its ability to reproduce many behaviors observed in cortical neurons. For this reason it is currently widely ... More

On an invariant bilinear form on the space of automorphic forms via asymptoticsSep 01 2016We define a bilinear form B on the space of automorphic forms for a split reductive group G over a function field (the form B has been previously defined in the case G=SL(2)). The definition of B relies on certain asymptotics maps defined using the geometry ... More

Infinite and Giant Components in the Layers Percolation ModelNov 05 2016Nov 14 2016In this work we continue the investigation launched in [FHR16] of the structural properties of the structural properties of the Layers model, a dependent percolation model. Given an undirected graph $G=(V,E)$ and an integer $k$, let $T_k(G)$ denote the ... More

Rigidity of K-theory under deformation quantizationJul 16 1996Quantization, at least in some formulations, involves replacing some algebra of observables by a (more non-commutative) deformed algebra. In view of the fundamental role played by K-theory in non-commutative geometry and topology, it is of interest to ... More

On the mathematical modelling of measurementSep 20 2006The operations of linear algebra, calculus, and statistics are routinely applied to measurement scales but certain mathematical conditions must be satisfied in order for these operations to be applicable. We call attention to the conditions that lead ... More

The recension of the Kepler laws in EnglandJul 10 2010Aug 23 2010The purpose of this note consists of discrete rational reconstruction which took place during the years 1609-1630 and 1630-1666, ie, the year of the publication of their Astronomia Nova and the year of death of the great German astronomer Johannes Kepler, ... More

Tight Lower Bounds for Locally Differentially Private SelectionFeb 07 2018We prove a tight lower bound (up to constant factors) on the sample complexity of any non-interactive local differentially private protocol for optimizing a linear function over the simplex. This lower bound also implies a tight lower bound (again, up ... More

On The Existence Of Anisotropic Cosmological Models In Higher-Order Theories Of GravityJul 27 2010We investigate the behaviour on approach to the initial singularity in higher-order extensions of general relativity by finding exact cosmological solutions for a wide class of models in which the Lagrangian is allowed to depend nonlinearly upon the three ... More

Extensible Grounding of Speech for Robot InstructionJul 31 2018Spoken language is a convenient interface for commanding a mobile robot. Yet for this to work a number of base terms must be grounded in perceptual and motor skills. We detail the language processing used on our robot ELI and explain how this grounding ... More

An explicit analysis of the entropic penalty in linear programmingJun 05 2018Solving linear programs by using entropic penalization has recently attracted new interest in the optimization community, since this strategy forms the basis for the fastest-known algorithms for the optimal transport problem, with many applications in ... More

The Local Rotation Set is an IntervalAug 10 2015Let $Homeo\_0 (R 2 ; 0)$ be the set of all homeomorphisms of the plane isotopic to the identity and which fix 0. Recently in the article entitled "L'ensemble de rotation local autour d'un point fixe" Fr{\'e}d{\'e}ric Le Roux gave the definition of the ... More

Selective Atomic Heating in Plasmas: Implications for Quantum TheoryOct 29 2008A new model of quantum mechanics, Classical Quantum Mechanics, is based on the (nearly heretical) postulate that electrons are physical objects that obey classical physical laws. Indeed, ionization energies, excitation energies etc. are computed based ... More

Superdielectric Materials Composed of Sodium Chloride, Water and Porous AluminaApr 29 2014Superdielectric behavior was observed in pastes made of high surface area alumina filled to the level of incipient wetness with water containing dissolved sodium chloride (table salt). In some cases the dielectric constants were greater than 10^10.

GRBs from Magnetic Reconnection: Variability and Robustness of LightcurvesJun 04 2016The dissipation mechanism that powers gamma-ray bursts (GRBs) remains uncertain almost half a century after their discovery. The two main competing mechanisms are the extensively studied internal shocks and the less studied magnetic reconnection. Here ... More

Crippling Crypto-RansomwareSep 26 2018This research seeks to expose a major weakness in Crypto-ransomware by modeling it as four integral sub-systems consisting of: An Agent, a Command and Control Service (CNC), an anonymous payment channel (APC) and an obfuscated command channel (OCC). We ... More

Nuclear Matrix Elements for Double-Beta DecayOct 31 2015Recent progress in nuclear-structure theory has been dramatic. I describe recent and future applications of ab initio calculations and the generator coordinate method to double-beta decay. I also briefly discuss the old and vexing problem of the renormalization ... More

$\mathcal{U}(\mathfrak{h})$-free modules and coherent familiesJan 13 2015Feb 17 2016We investigate the category of U(h)-free g-modules. Using a functor from this category to the category of coherent families, we show that U(h)-free modules only can exist when g is of type A or C. We then proceed to classify isomorphism classes of U(h)-free ... More

Simple sl_{n+1}-module structures on U(h)Dec 19 2013We study the category M consisting of U(sl_{n+1})-modules whose restriction to U(h) is free of rank 1, in particular we classify isomorphism classes of objects in M and determine their submodule structure. This leads to new sl_{n+1}-modules. For n=1 we ... More

Colombeau Algebra: A pedagogical introductionAug 01 2013A simple pedagogical introduction to the Colombeau algebra of generalised functions is presented, leading the standard definition.

Representations of the oriented skein categoryDec 24 2017The oriented skein category $OS(z,t)$ is a ribbon category which underpins the definition of the HOMFLY-PT invariant of an oriented link, in the same way that the Temperley-Lieb category underpins the Jones polynomial. In this article, we develop its ... More

Perfect powers in elliptic divisibility sequencesJan 15 2011Jan 19 2011It is shown that there are finitely many perfect powers in an elliptic divisibility sequence whose first term is divisible by 2 or 3. For Mordell curves the same conclusion is shown to hold if the first term is greater than 1. Examples of Mordell curves ... More

Perfect powers generated by the twisted Fermat cubicFeb 14 2011Feb 22 2011On the twisted Fermat cubic, an elliptic divisibility sequence arises as the sequence of denominators of the multiples of a single rational point. It is shown that there are finitely many perfect powers in such a sequence whose first term is greater than ... More

Preferential attachment graphs with co-existing types of different fitnessesMar 23 2018Sep 06 2018We extend the work of Antunovi\'{c}, Mossel and R\'{a}cz on competing types in preferential attachment models to include cases where the types have different fitnesses, which may be either multiplicative or additive. We will show that, depending on the ... More

A Heavy Baryonic Galactic DiscApr 20 2012We investigate the possibility that the observed rotation of galaxies can be accounted for by invoking a massive baryonic disc with no need for non-baryonic dark matter or a massive halo. There are 5 primary reasons for suggesting this: 1. there are well ... More

Kazhdan-Lusztig polynomials and character formulae for the Lie superalgebra q(n)Jul 02 2002Sep 10 2002The problem of computing the characters of the finite dimensional irreducible representations of the Lie superalgebra $\mathfrak q(n)$ over $\C$ was solved in 1996 by I. Penkov and V. Serganova. In this article, we give a different approach relating the ... More

Tilting modules for Lie superalgebrasSep 18 2002This is a companion article to my papers on Kazhdan-Lusztig polynomials and character formulae for the Lie superalgebras gl(m|n) (much revised!) and q(n). The goal is to develop the general theory of tilting modules for Lie superalgebras, working in a ... More

Intersection times for critical branching random walkAug 22 2019We show that for a sequence of reversible Markov chains, the mixing-times are of smaller order than the maximal hitting times $t_{\mathrm{hit}}^{(n)}$ iff the product of the spectral-gap $\mathrm{gap}^{(n)}$ and $t_{\mathrm{hit}}^{(n)}$ diverges. This ... More

A spectral characterization for concentration of the cover timeSep 01 2018We prove that for a sequence of finite vertex-transitive graphs of increasing sizes, the cover times are asymptotically concentrated iff the product of the spectral-gap and the expected cover time diverges. In fact, we prove this for general reversible ... More

Simplifying and Refactoring Introductory CalculusNov 07 2018First year calculus is often taught in a way that is very burdensome to the student. Students have to memorize a diversity of processes for essentially performing the same task. However, many calculus processes can be simplified and streamlined so that ... More

Spin foamsMar 19 2013The spin foam framework provides a way to define the dynamics of canonical loop quantum gravity in a spacetime covariant way, by using a path integral over histories of quantum states which can be interpreted as `quantum space-times'. This chapter provides ... More

A proposed proper EPRL vertex amplitudeNov 11 2011Sep 13 2013As established in a prior work of the author, the linear simplicity constraints used in the construction of the so-called `new' spin-foam models mix three of the five sectors of Plebanski theory as well as two dynamical orientations, and this is the reason ... More

Braid Group Action and Quantum Affine AlgebrasApr 27 1994We lift the lattice of translations in the extended affine Weyl group to a braid group action on the quantum affine algebra. This action fixes the Heisenberg subalgebra pointwise. Loop like generators are found for the algebra which satisfy the relations ... More

Parity-induced Selmer Growth For Symplectic, Ordinary FamiliesMay 16 2008Let $p$ be an odd prime, and let $K/K_0$ be a quadratic extension of number fields. Denote by $K_\pm$ the maximal $\mathbb{Z}_p$-power extensions of $K$ that are Galois over $K_0$, with $K_+$ abelian over $K_0$ and $K_-$ dihedral over $K_0$. In this paper ... More

Dual canonical bases and Kazhdan-Lusztig polynomialsSep 29 2005Oct 10 2005We derive a formula for the entries of the (unitriangular) transition matrices between the standard monomial and dual canonical bases of the irreducible polynomial representations of U_q(gl_n) in terms of Kazhdan-Lusztig polynomials.

Ring structure, uniform expressions and intersection homologyMay 22 1998Although intersection homology lacks a ring structure, certain expressions (called uniform) in the intersection homology of an irreducible projective variety $X$ always give the same value, when computed via the decomposition theorem on any resolution ... More

Double Integrals for Euler's Constant and ln(4/Pi) and an Analog of Hadjicostas's FormulaNov 08 2002Jun 14 2004We give analogs for Euler's constant and ln(4/Pi) of the well-known double integrals for zeta(2) and zeta(3). We also give a series for ln(4/Pi) which reveals it to be an "alternating Euler constant."

The deformation theory of sheaves of commutative rings IIFeb 14 2011We compare the obstruction classes defined in arXiv:1101.4069 to those defined by Illusie. We also give sheaf theoretic proofs of some of the standard properties of the cotangent complex.

Canonical Least Favorable Submodels:A New TMLE Procedure for Multidimensional ParametersNov 03 2018Apr 11 2019This paper is a fundamental addition to the world of targeted maximum likelihood estimation (TMLE) (or likewise, targeted minimum loss estimation) for simultaneous estimation of multi-dimensional parameters of interest. TMLE, as part of the targeted learning ... More

An Easy Implementation of CV-TMLENov 12 2018Nov 13 2018In the world of targeted learning, cross-validated targeted maximum likelihood estimators, CV-TMLE [Zheng:2010aa], has a distinct advantage over TMLE [Laan:2006aa] in that one less condition is required of CV-TMLE in order to achieve asymptotic efficiency ... More

Classifying Linear Canonical RelationsAug 19 2015In this Master's thesis, we consider the problem of classifying, up to conjugation by linear symplectomorphisms, linear canonical relations (lagrangian correspondences) from a finite-dimensional symplectic vector space to itself. We give an elementary ... More

Loewner chains on the universal covering space of a Riemann surfaceDec 19 2008Let R be a hyperbolic Riemann surface with boundary $\partial R$ and suppose that $\gamma:[0,T]\to R\cup\partial R$ is a simple curve growing from the boundary of R. By lifting $R_{t}=R\setminus \gamma(0,t]$ to the universal covering space of R (which ... More

The K-homology class of the Euler characteristic operator is trivialJun 12 1998On any manifold M^n, the de Rham operator D=d+d^* (with respect to a complete Riemannian metric), with the grading of forms by parity of degree, gives rise by Kasparov theory to a class [D] in KO_0(M), which when M is closed maps to the Euler characteristic ... More

On connected degree sequencesNov 30 2015This note gives necessary and sufficient conditions for a sequence of non-negative integers to be the degree sequence of a connected simple graph. This result is implicit in a paper of Hakimi. A new alternative characterisation of these necessary and ... More

A Study of Nucleon Spin Struture from Quantum ChromodynamicsSep 27 2001Nov 29 2001I present an introduction to the field of Quantum Chromodynamics (QCD) with emphasis on nucleon spin structure and perturbative methods. After a somewhat comprehensive overview of perturbative QCD, including the systematics of renormalization, I introduce ... More

Duality and equivalence of module categories in noncommutative geometry II: Mukai duality for holomorphic noncommutative toriApr 12 2006This is the second in a series of papers intended to set up a framework to study categories of modules in the context of non-commutative geometries. In \cite{mem} we introduced the basic DG category $\Pc_{\A^\bullet}$, the perfect category of $\A^\bullet$, ... More

The Bounded Edge Coloring Problem and Offline Crossbar SchedulingDec 30 2015This paper introduces a variant of the classical edge coloring problem in graphs that can be applied to an offline scheduling problem for crossbar switches. We show that the problem is NP-complete, develop three lower bounds bounds on the optimal solution ... More

The Edge Group Coloring Problem with Applications to Multicast SwitchingDec 30 2015This paper introduces a natural generalization of the classical edge coloring problem in graphs that provides a useful abstraction for two well-known problems in multicast switching. We show that the problem is NP-hard and evaluate the performance of ... More

Maximium Priority MatchingsDec 28 2015Let $G=(V,E)$ be an undirected graph with $n$ vertices and $m$ edges, in which each vertex $u$ is assigned an integer priority in $[1,n]$, with 1 being the "highest" priority. Let $M$ be a matching of $G$. We define the priority score of $M$ to be an ... More

Uniformization By Classical Schottky GroupsJan 12 2006Mar 08 2006This paper has been withdrawn by the author due to an error in an inequality in the proof of Theorem 1.1.

The formation of stars in groupsNov 15 2001Observations of the dust and gas around embedded stellar clusters reveal some of the processes involved in their formation and evolution. Large scale mass infall with rates dM/dt=4e-4 solar masses/year is found to be disrupted on small scales by protostellar ... More

Algebraic K-theory and derived equivalences suggested by T-duality for torus orientifoldsApr 15 2016We show that certain isomorphisms of (twisted) KR-groups that underlie T-dualities of torus orientifold string theories have purely algebraic analogues in terms of algebraic K-theory of real varieties and equivalences of derived categories of (twisted) ... More

Topology, geometry, and equations of normal surface singularitiesSep 05 2005This expository talk is an expanded version of a lecture at G.-M. Greuel's 60th Birthday Conference in Kaiserslautern in October, 2004. We survey recent work of Neumann-Wahl and others on the relation between topology and geometry of normal surface singularities, ... More

Unique solvability of a coupling problem for entire functionsAug 28 2016We establish the unique solvability of a coupling problem for entire functions which arises in inverse spectral theory for singular second order ordinary differential equations/two-dimensional first order systems and is also of relevance for the integration ... More

Thom Objects Are CotorsorsOct 01 2018Let $C$ be a symmetric monoidal quasicategory, and $R$ an $E_n$-algebra of $C$ equipped with an action of an $n$-fold loop space $G$. We prove that the derived quotient of $R$ with respect to this action is a comodule over $R\otimes \Sigma^\infty_+BG$, ... More

The ADHM Construction and Anselmi's Topological AnomaliesFeb 18 2004We examine the anomalies arising in instanton calculus as detailed by Damiano Anslemi in 1994. Whereas Anselmi uses BRST theory, we use the ADHM construction to arrive at the same conclusions from a differential-geometric way. We observe that Anselmi's ... More

Groupoid C*-algebras and index theory on manifolds with singularitiesMay 10 2001The simplest case of a manifold with singularities is a manifold M with boundary, together with an identification of the boundary with a product M1 x P, where P is a fixed manifold. The associated singular space is obtained by collapsing P to a point. ... More

Supercharacter theories of dihedral groupsDec 20 2016The set of supercharacter theories of a fixed group $G$ forms a natural lattice. An open question in the study of supercharacter theories is to classify this lattice, and to date, this has only been done for the cyclic groups $\mathbb{Z}_n$. In this paper, ... More

A new approach to twisted K-theory of compact Lie groupsAug 18 2017Aug 09 2018This paper explores further the computation of the twisted K-theory and K-homology of compact simple Lie groups, previously studied by Hopkins, Moore, Maldacena-Moore-Seiberg, Braun, and Douglas, with a focus on groups of rank 2. We give a new method ... More

Normed symmetric monoidal categoriesAug 16 2017Nov 18 2017Let $G$ be a finite group. In this paper, we study $G$-categories equipped with an ordinary symmetric monoidal structure, together with a set of specified norm maps. We give an example and explain how the Hill-Hopkins-Ravenel norm functors arise from ... More

Reversibility of the non-backtracking random walkJul 06 2017Oct 02 2018Let $G$ be a connected graph of uniformly bounded degree. A $k$ non-backtracking random walk ($k$-NBRW) $(X_n)_{n =0}^{\infty}$ on $G$ evolves according to the following rule: Given $ (X_n)_{n =0}^{s}$, at time $s+1$ the walk picks at random some edge ... More

A survey of non-complex analogs of uniform algebrasOct 21 2010We survey commutative and non-commutative analogs of uniform algebras in the Archimedean settings and also offer some non-Archimedean examples. Constraints on the development of non-complex uniform algebras are also discussed.

The rational field is not universally definable in pseudo-exponentiationJul 03 2014May 12 2015We show that the field of rational numbers is not definable by a universal formula in Zilber's pseudo-exponential field.

Well-posedness of evolution equations with time-dependent nonlinear mobility: a modified minimizing movement schemeApr 26 2016We prove the existence of nonnegative weak solutions to a class of second and fourth order nonautonomous nonlinear evolution equations with an explicitly time-dependent mobility function posed on the whole space $\mathbb{R}^d$, for arbitrary $d\ge 1$. ... More

The gradient flow of a generalized Fisher information functional with respect to modified Wasserstein distancesMar 04 2016This article is concerned with the existence of nonnegative weak solutions to a particular fourth-order partial differential equation: it is a formal gradient flow with respect to a generalized Wasserstein transportation distance with nonlinear mobility. ... More

Exponential convergence to equilibrium in a Poisson-Nernst-Planck-type system with nonlinear diffusionMar 13 2015Sep 28 2015We investigate a Poisson-Nernst-Planck type system in three spatial dimensions where the strength of the electric drift depends on a possibly small parameter and the particles are assumed to diffuse quadratically. On grounds of the global existence result ... More

Geodesically convex energies and confinement of solutions for a multi-component system of nonlocal interaction equationsDec 10 2014Dec 17 2015We consider a system of $n$ nonlocal interaction evolution equations on $\mathbb{R}^d$ with a differentiable matrix-valued interaction potential $W$. Under suitable conditions on convexity, symmetry and growth of $W$, we prove $\lambda$-geodesic convexity ... More