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Extraction of Generalized Parton Distribution Observables from Deeply Virtual Electron Proton Scattering ExperimentsMar 13 2019We provide the general expression of the cross section for exclusive deeply virtual photon electroproduction from a spin 1/2 target using current parameterizations of the off-forward correlation function in a nucleon for different beam and target polarization ... More

G-valued crystalline representations with minuscule p-adic Hodge typeMar 03 2014Aug 01 2015We study G-valued semi-stable Galois deformation rings where G is a reductive group. We develop a theory of Kisin modules with G-structure and use this to identify the connected components of crystalline deformation rings of minuscule p-adic Hodge type ... More

Five or six step scenario for evolution?Nov 13 2007The prediction that (due to the limited amount of hydrogen available as fuel in the Sun) the future duration of our favourable terrestrial environment will be short (compared with the present age of the Earth) has been interpreted as evidence for a hard ... More

Mechanics and Equilibrium Geometry of Black Holes, Membranes, and StringsNov 29 2004This course is designed to give a mathematically coherent introduction to the classical thory of black holes and also of strings and membranes (which are like the horizon of a black hole in being examples of physical systems based on a dynamically evolving ... More

Generalised mass variation formula for a stationary axisymmetric star or black hole with surrounding accretion discJun 07 2002The general relativistic mass-energy variation formula for axisymmetric equilibrium states of a selfgravitating system is developed in the particular case for which the relevant matter consists of a perfectly conducting multiconstituent fluid (or superfluid) ... More

Energy dominance and the Hawking Ellis vacuum conservation theoremMay 02 2002At a time when uninhibited speculation about negative tension -- and by implication negative mass density -- world branes has become commonplace, it seems worthwhile to call attention to the risk involved in sacrificing traditional energy positivity postulates ... More

Essentials of Classical Brane DynamicsDec 10 2000Jan 29 2001This article provides a self contained overview of the geometry and dynamics of relativistic brane models, of the category that includes point particle, string, and membrane representations for phenomena that can be considered as being confined to a worldsheet ... More

Formally renormalisable gravitationally self interacting string modelsOct 22 1998It has recently been shown how the effect of the divergent part of the gravitational self interaction for a classical string model in 4 dimensions can be allowed for by a renormalisation of its stress energy tensor and in the elastic case a corresponding ... More

The regular conducting fluid model for relativistic thermodynamicsSep 07 2012The "regular" model presented here can be considered to be the most natural solution to the problem of constructing the simplest possible relativistic analogue of the category of classical Fourier--Euler thermally conducting fluid models as characterised ... More

Cancellation of linearised axion-dilaton self interaction divergence in stringsJan 21 2000The force densities exerted on a localised material system by linearised interaction with fields of axionic and dilatonic type are shown to be describable very generally by relatively simple expressions that are well behaved for fields of purely external ... More

Dynamics of Cosmic Strings and other Brane modelsNov 08 1996The supporting worldsheet of a string, membrane, or other higher dimensional brane, is analysed in terms of its first, second, and third fundamental tensors, and its inner and outer curvature tensors. The dynamical equations governing the models appropriate ... More

Weak containment and Rokhlin entropyFeb 22 2016We define a new notion of weak containment for joinings, and we show that this notion implies an inequality between relative Rokhlin entropies. This leads to new upper bounds to Rokhlin entropy. We also use this notion to study how Pinsker algebras behave ... More

Rankin-Cohen brackets and Serre derivatives as Poincaré seriesJan 05 2018May 28 2018We give expressions for the Serre derivatives of Eisenstein and Poincar\'e series as well as their Rankin-Cohen brackets with arbitrary modular forms in terms of the Poincar\'e averaging construction, and derive several identities for the Ramanujan tau ... More

Vector-valued Hirzebruch-Zagier series and class number sumsNov 28 2017Mar 11 2018For any number $m \equiv 0,1 \, (4)$ we correct the generating function of Hurwitz class number sums $\sum_r H(4n - mr^2)$ to a modular form (or quasimodular form if $m$ is a square) of weight two for the Weil representation attached to a binary quadratic ... More

Poincaré square series for the Weil representationApr 22 2017Jun 11 2017We calculate the Jacobi Eisenstein series of weight $k \ge 3$ for a certain representation of the Jacobi group, and evaluate these at $z = 0$ to give coefficient formulas for a family of modular forms $Q_{k,m,\beta}$ of weight $k \ge 5/2$ for the (dual) ... More

Vector-valued Eisenstein series of small weightJun 12 2017Oct 19 2017We study the (mock) Eisenstein series $E_k$ of weight $k \in \{1,3/2,2\}$ for the Weil representation on an even lattice, defined as the result of Bruinier and Kuss's coefficient formula for the Eisenstein series naively evaluated at $k$. We describe ... More

Positive entropy actions of countable groups factor onto Bernoulli shiftsApr 14 2018We prove that if a free ergodic action of a countably infinite group has positive Rokhlin entropy (or, less generally, positive sofic entropy) then it factors onto all Bernoulli shifts of lesser or equal entropy. This extends to all countably infinite ... More

Capturing Forms in Dense Subsets of Finite FieldsNov 25 2012Nov 29 2012An open problem of arithmetic Ramsey theory asks if given a finite $r$-colouring $c:\mathbb{N}\to\{1,...,r\}$ of the natural numbers, there exist $x,y\in \mathbb{N}$ such that $c(xy)=c(x+y)$ apart from the trivial solution $x=y=2$. More generally, one ... More

Cohen-Lenstra Moments for Some Nonabelian GroupsJun 25 2016Aug 10 2016Cohen and Lenstra detailed a heuristic for the distribution of odd p-class groups for imaginary quadratic fields. One such formulation of this distribution is that the expected number of surjections from the class group of an imaginary quadratic field ... More

Classical dynamics of strings and branes, with application to vortonsDec 09 2011These notes offer an introductory overview of the essentials of classical brane dynamics in a space-time background of arbitrary dimension, using a systematic geometric treatment emphasising the role of the second fundamental tensor and its trace, the ... More

Objective and subjective time in anthropic reasoningAug 17 2007Oct 23 2007The original formulation of the (weak) anthropic principle was prompted by a question about objective time at a macroscopic level, namely the age of the universe when ``anthropic'' observers such as ourselves would be most likely to emerge. Theoretical ... More

Micro-Anthropic Principle for Quantum theoryMar 11 2005Probabilistic models (developped by workers such as Boltzmann, on foundations due to pioneers such as Bayes) were commonly regarded merely as approximations to a deterministic reality before the roles were reversed by the quantum revolution (under the ... More

Frozen rigging model of the energy dominated universeDec 28 2004Feb 23 2005Composite rigging systems, involving membranes that meet on strings that meet on monopoles, arise naturally by the Kibble mechanism as topological defects in field theories involving spontaneous symmetry breaking. Such systems will tend to freeze out ... More

Cold, warm, and composite (cool) cosmic string modelsOct 18 2002The dynamical behaviour of a cosmic string is strongly affected by any reduction of the effective string tension $T$ below the constant value $T=m^2$ say that characterizes the simple, longitudinally Lorentz invariant, Goto Nambu string model in terms ... More

Amalgamated Codazzi Raychaudhuri identity for foliationMay 13 1997It is shown how a pure background tensor formalism provides a concise but explicit and highly flexible machinery for the generalised curvature analysis of individual embedded surfaces and foliations such as arise in the theory of topological defects in ... More

Non-Abelian current oscillations in harmonic string loops: existence of throbbing vortonsFeb 17 2012It is shown that a string carrying a field of harmonic type can have circular vorton states of a new "throbbing" kind, for which the worldsheet geometry is stationary but the internal structure undergoes periodic oscillation.

Stability of winding cosmic wall lattices with X type junctionsMay 02 2006Nov 30 2009This work confirms the stability of a class of domain wall lattice models that can produce accelerated cosmological expansion, with pressure to density ratio $w=-1/3$ at early times, and with $w=-2/3$ at late times when the lattice scale becomes large ... More

Anthropic interpretation of quantum theoryMar 01 2004The problem of interpreting quantum theory on a large (e.g. cosmological) scale has been commonly conceived as a search for objective reality in a framework that is fundamentally probabilistic. The Everett programme attempts to evade the issue by the ... More

Relativistic superfluid models for rotating neutron starsJan 16 2001This article starts by providing an introductory overview of the theoretical mechanics of rotating neutron stars as developped to account for the frequency variations, and particularly the discontinuous glitches, observed in pulsars. The theory suggests, ... More

Recent developments in Vorton TheoryDec 08 1997This article provides a concise overview of recent theoretical results concerning the theory of vortons, which are defined to be (centrifugally supported) equilibrium configurations of (current carrying) cosmic string loops. Following a presentation of ... More

Electromagnetic self interaction in stringsApr 30 1997To facilitate the treatment of electromagnetic effects in applications such as dynamically perturbed vortons, this work employs a covariantly formulated string-source Green measure to obtain a coherent relativistic scheme for describing the self interaction ... More

Poincaré square series of small weightJul 20 2017We extend the author's earlier computation and give coefficient formulas for the (quasimodular) Poincar\'e square series of weight 3/2 and weight 2 for the dual Weil representation for an even lattice.

Character sums over Bohr setsSep 28 2014Apr 28 2015We prove character sum estimates for additive Bohr subsets modulo a prime. These estimates are analogous to classical character sum bounds of Polya-Vinogradov and Burgess. These estimates are applied to obtain results on recurrence mod $p$ by special ... More

Weak containment and Rokhlin entropyFeb 22 2016May 30 2017We define a new notion of weak containment for joinings, and we show that this notion implies an inequality between relative Rokhlin entropies. This leads to new upper bounds to Rokhlin entropy. We also use this notion to study how Pinsker algebras behave ... More

Krieger's finite generator theorem for actions of countable groups IMay 14 2014May 30 2017For an ergodic probability-measure-preserving action $G \curvearrowright (X, \mu)$ of a countable group $G$, we define the Rokhlin entropy $h_G^{\mathrm{Rok}}(X, \mu)$ to be the infimum of the Shannon entropies of countable generating partitions. It is ... More

Ergodic actions of countable groups and finite generating partitionsJun 26 2012We prove that if an ergodic action of a countable group on a probability space admits a generating partition having finite Shannon entropy then it admits a finite generating partition.

A quasisymmetric function generalization of the chromatic symmetric functionApr 15 2010Jan 03 2011The chromatic symmetric function $X_G$ of a graph $G$ was introduced by Stanley. In this paper we introduce a quasisymmetric generalization $X^k_G$ called the $k$-chromatic quasisymmetric function of $G$ and show that it is positive in the fundamental ... More

Fermi-LAT constraints on diffuse Dark Matter annihilation from the Galactic HaloDec 03 2010Our Galaxy resides in the center of a vast "Halo" of Dark Matter (DM). This concentration produces, in many viable particle physics models, an indirect Weakly Interacting Massive Particle (WIMP) annihilation signal that peaks in the Fermi-LAT's energy ... More

Krieger's finite generator theorem for ergodic actions of countable groups IIJan 14 2015Jan 22 2015We continue the study of Rokhlin entropy, an isomorphism invariant for ergodic probability-measure-preserving actions of general countable groups introduced in the previous paper. We prove that every free ergodic action with finite Rokhlin entropy admits ... More

Classical Anthropic Everett model: indeterminacy in a preordained multiverseMar 05 2012Although ultimately motivated by quantum theoretical considerations, Everett's many-world idea remains valid, as an approximation, in the classical limit. However to be applicable it must in any case be applied in conjunction with an appropriate anthropic ... More

Superconducting Superfluids in Neutron StarsOct 05 2000For treatment of the layers below the crust of a neutron star it is useful to employ a relativistic model involving three independently moving constituents, representing superfluid neutrons, superfluid protons, and degenerate negatively charged leptons. ... More

Old and New Processes of Vorton FormationSep 26 1999After a brief explanation of the concept of a vorton, quantitative estimates of the vorton population that would be produced in various cosmic string scenarios are reviewed. Attention is drawn to previously unconsidered mechanisms that might give rise ... More

Fields In Nonaffine Bundles II. Gauge coupled generalization of harmonic mappings and their Bunting identitiesNov 02 2009The general purpose bitensorially gauge-covariant differentiation procedure set up in the preceding article is specialised to the particular case of bundles with nonlinear fibres that are endowed with a torsion free Riemannian or pseudo-Riemannian structure. ... More

The significance of numerical coincidences in natureOct 18 2007This is the first part of a survey whose ultimate purpose is to clarify the significance of the famous coincidence between the Hubble age of the universe and a certain combination of microphysical parameters. In this part the way is prepared by a discussion ... More

Poly-essential and general Hyperelastic World (brane) modelsApr 22 2006This article provides a unified treatment of an extensive category of non-linear classical field models whereby the universe is represented (perhaps as a brane in a higher dimensional background) in terms of a structure of a mathematically convenient ... More

Quasi gravity in branesJun 04 2001In contrast with pseudo-gravitational effects that are mathematically analogous but physically quite distinct from gravity, this presentation deals with a kind of quasi-gravitational effect that can act in an asymmetrically moving brane worldsheet in ... More

Transonic Elastic Model for Wiggly Goto-Nambu StringNov 30 1994The hitherto controversial proposition that a ``wiggly" Goto-Nambu cosmic string can be effectively represented by an elastic string model of exactly transonic type (with energy density $U$ inversely proportional to its tension $T$) is shown to have a ... More

Metaplectic Eisenstein DistributionsJan 04 2018In this paper, we define distributional analogues of the metaplectic Eisenstein series for $\text{SL}_2(\mathbb{R})$, which we refer to as metaplectic Eisenstein distributions. We prove that these distributions have meromorphic continuation and give an ... More

The rings of Hilbert modular forms for $\mathbb{Q}(\sqrt{29})$ and $\mathbb{Q}(\sqrt{37})$Sep 23 2018Sep 27 2018We use Borcherds products and their restrictions to Hirzebruch-Zagier curves to determine generators and relations for the graded rings of Hilbert modular forms for the fields $\mathbb{Q}(\sqrt{29})$ and $\mathbb{Q}(\sqrt{37})$. These seem to be the first ... More

Remarks on the theta decomposition of vector-valued Jacobi formsJun 08 2018Feb 11 2019We study the theta decomposition of Jacobi forms of nonintegral lattice index for a representation that arises in the theory of Weil representations associated to even lattices, and suggest possible applications.

Every action of a non-amenable group is the factor of a small actionNov 04 2013Jul 03 2014It is well known that if $G$ is a countable amenable group and $G \curvearrowright (Y, \nu)$ factors onto $G \curvearrowright (X, \mu)$, then the entropy of the first action must be greater than or equal to the entropy of the second action. In particular, ... More

The Additive Structure of Cartesian Products Spanning Few Distinct DistancesJul 12 2016Guth and Katz proved that any point set $\mathcal P$ in the plane determines $\Omega(|\mathcal P|/\log|\mathcal P|)$ distinct distances. We show that when near to this lower bound, a point set $\mathcal P$ of the form $A\times A$ must satisfy $|A-A|\ll ... More

Multideviations: The hidden structure of Bell's theoremsDec 14 2015Specification of the strongest possible Bell inequalities for arbitrarily complicated physical scenarios -- any number of observers choosing between any number of observables with any number of possible outcomes -- is currently an open problem. Here I ... More

Local models for Weil-restricted groupsDec 22 2014Jan 31 2015We extend the group theoretic construction of local models of Pappas and Zhu to the case of groups obtained by Weil restriction along a possibly wildly ramified extension. This completes the construction of local models for all reductive groups when $p ... More

Dilatonic formulation for conducting cosmic string modelsFeb 19 2000It is shown how the the introduction of a suitably defined dilatonic auxiliary field, $\Phi$ say, makes it possible for the non-linear Lagrangian for a generic elastic string model, of the kind appropriate for representing superconducting cosmic strings, ... More

Fields in nonaffine bundles. IV. Harmonious non-Abelian currents in string defectsJan 06 2010This article continues the study of the category of harmonious field models that was recently introduced as a kinetically non-linear generalisation of the well known harmonic category of multiscalar fields over a supporting brane wordsheet in a target ... More

Fields in Nonaffine Bundles. I. The general bitensorially covariant differentiation procedureOct 24 2009The standard covariant differentiation procedure for fields in vector bundles is generalised so as to be applicable to fields in general nonaffine bundles in which the fibres may have an arbitrary nonlinear structure. In addition to the usual requirement ... More

Mechanics of cosmic ringsMar 02 2007In a flat background, simple non-conducting string loops have no strictly stationary equilibrium states, but for cosmic string loops of superconducting kind such ``vorton'' states will exist, with rotating circular configurations appropriately describable ... More

Symplectic Structure in Brane MechanicsFeb 12 2003This article treats the generalisation to brane dynamics of the covariant canonical variational procedure leading to the construction of a conserved bilinear symplectic current in the manner originally developped by Witten, Zuckerman and others in the ... More

Regularisation of classical self interaction in stringsFeb 04 1998A general method of regularisation of classical self interaction in strings is extended from the electromagnetic case (for which it was originally developed) to the gravitation case, for which the result can also be represented as a renormalisation.

Has the black hole equilibrium problem been solved?Dec 08 1997When the term ``black hole'' was originally coined in 1968, it was immediately conjectured that the only pure vacuum equilibrium states were those of the Kerr family. Efforts to confirm this made rapid progress during the ``classical phase'' from 1968 ... More

Overpartition $M2$-rank differences, class number relations, and vector-valued mock Eisenstein seriesAug 08 2017Sep 25 2018We prove that the generating function of overpartition $M2$-rank differences is, up to coefficient signs, a component of the vector-valued mock Eisenstein series attached to a certain quadratic form. We use this to compute analogs of the class number ... More

A p-adic completion of Zagier's Eisenstein seriesNov 20 2017Nov 21 2017This note points out that for any odd prime $p$, Zagier's weight $3/2$ mock Eisenstein series can be completed to a $p$-adic modular form in a way that bears some resemblance to its completion to a harmonic Maass form.

A subgroup formula for f-invariant entropyFeb 23 2012Jun 25 2012We study a measure entropy for finitely generated free group actions called f-invariant entropy. The f-invariant entropy was developed by Lewis Bowen and is essentially a special case of his measure entropy theory for actions of sofic groups. In this ... More

Finite entropy actions of free groups, rigidity of stabilizers, and a Howe-Moore type phenomenonMay 23 2012Jan 13 2015We study a notion of entropy for probability measure preserving actions of finitely generated free groups, called f-invariant entropy, introduced by Lewis Bowen. In the degenerate case, the f-invariant entropy is negative infinity. In this paper we investigate ... More

The Koopman representation and positive Rokhlin entropyApr 14 2018In a prior paper, the author generalized the classical factor theorem of Sinai to actions of arbitrary countably infinite groups. In the present paper, we use this theorem and the techniques of its proof in order to study connections between positive ... More

Krieger's finite generator theorem for actions of countable groups IIJan 14 2015May 30 2017We continue the study of Rokhlin entropy, an isomorphism invariant for probability-measure-preserving actions of countable groups introduced in the previous paper. We prove that every free ergodic action with finite Rokhlin entropy admits generating partitions ... More

Burnside's Problem, spanning trees, and tilingsApr 07 2011Nov 05 2011In this paper we study geometric versions of Burnside's Problem and the von Neumann Conjecture. This is done by considering the notion of a translation-like action. Translation-like actions were introduced by Kevin Whyte as a geometric analogue of subgroup ... More

Strategies for Addressing Spreadsheet Compliance ChallengesNov 29 2007Most organizations today use spreadsheets in some form or another to support critical business processes. However the financial resources, and developmental rigor dedicated to them are often minor in comparison to other enterprise technology. The increasing ... More

Renormalisation of gravitational self interaction for wiggly stringsJun 24 1998Apr 09 1999It is shown that for any elastic string model with energy density $U$ and tension $T$, the divergent contribution from gravitational self interaction can be allowed for by an action renormalisation proportional to $(U-T)^2$. This formula is applied to ... More

Brane dynamics for treatment of cosmic strings and vortonsMay 22 1997This course provides a self contained introduction to the general theory of relativistic brane models, of the category that includes point particle, string, and membrane representations for phenomena that can be considered as being confined to a worldsheet ... More

Hominid evolution: genetics versus memeticsNov 15 2010Jul 29 2011The last few million years on planet Earth have witnessed two remarkable phases of hominid development, starting with a phase of biological evolution characterised by rather rapid increase of the size of the brain. This has been followed by a phase of ... More

Fields in nonaffine bundles. III. Effective symmetries and conserved currents in strings and higher branesDec 02 2009The principles of a previously developed formalism for the covariant treatment of multi-scalar fields for which (as in a nonlinear sigma model) the relevant target space is not of affine type -- but curved -- are recapitulated. Their application is extended ... More

Half century of black-hole theory: from physicists' purgatory to mathematicians' paradiseApr 15 2006Although implicit in the discovery of the Schwarzschild solution 40 years earlier, the issues raised by the theory of what are now known as black holes were so unsettling to physicists of Einstein's generation that the subject remained in a state of semiclandestine ... More

Vortex Dynamics in SuperfluidsJul 09 1999Superfluid condensates are known to occur in contexts ranging from laboratory liquid helium to neutron stars, and are also likely to occur in cosmological phenomena such as axion fields. In the zero temperature limit, such condensates are describable ... More

Anthropic principle in cosmologyJun 27 2006A brief explanation of the meaning of the anthropic principle - as a prescription for the attribution of a priori probability weighting - is illustrated by various cosmological and local applications, in which the relevant conclusions are contrasted with ... More

Krieger's finite generator theorem for ergodic actions of countable groups IMay 14 2014Jan 15 2015For an ergodic probability-measure-preserving action $G \curvearrowright (X, \mu)$ of a countable group $G$, we define the Rokhlin entropy $h_G^{\mathrm{Rok}}(X, \mu)$ to be the infimum of the Shannon entropies of countable generating partitions. It is ... More

Computing antisymmetric modular forms and theta liftsOct 30 2018Dec 20 2018We describe an algorithm to compute bases of antisymmetric vector-valued cusp forms with rational Fourier coefficients for the Weil representation associated to a finite quadratic module. The forms we construct always span all cusp forms in weight at ... More

Bernoulli shifts with bases of equal entropy are isomorphicMay 21 2018We prove that if $G$ is a countably infinite group and $(L, \lambda)$ and $(K, \kappa)$ are probability spaces having equal Shannon entropy, then the Bernoulli shifts $G \curvearrowright (L^G, \lambda^G)$ and $G \curvearrowright (K^G, \kappa^G)$ are isomorphic. ... More

Metrics of Special Curvature with SymmetryOct 24 2006Various curvature conditions are studied on metrics admitting a symmetry group. We begin by examining a method of diagonalizing cohomogeneity-one Einstein manifolds and determine when this method can and cannot be used. Examples, including the well-known ... More

Self-Excitation: An Enabler for Online Thermal Estimation and Model Predictive Control of BuildingsDec 27 2015This paper investigates a method to improve buildings' thermal predictive control performance via online identification and excitation (active learning process) that minimally disrupts normal operations. In previous studies we have demonstrated scalable ... More

Some Aspects of Measurement Error in Linear Regression of Astronomical DataMay 18 2007I describe a Bayesian method to account for measurement errors in linear regression of astronomical data. The method allows for heteroscedastic and possibly correlated measurement errors, and intrinsic scatter in the regression relationship. The method ... More

Measurement Error Models in AstronomyDec 08 2011I discuss the effects of measurement error on regression and density estimation. I review the statistical methods that have been developed to correct for measurement error that are most popular in astronomical data analysis, discussing their advantages ... More

The Broadband Spectrum of Galaxy ClustersDec 02 2007We examine whether nonthermal protons energized during a cluster merger are simultaneously responsible for the Coma cluster's diffuse radio flux (via secondary decay) and the departure of its intra-cluster medium (ICM) from a thermal profile via Coulomb ... More

Cost, $\ell^2$-Betti numbers and the sofic entropy of some algebraic actionsSep 08 2015Sep 29 2015In 1987, Ornstein and Weiss discovered that the Bernoulli $2$-shift over the rank two free group factors onto the seemingly larger Bernoulli $4$-shift. With the recent creation of an entropy theory for actions of sofic groups (in particular free groups), ... More

Hand Posture's Effect on Touch Screen Text Input Behaviors: A Touch Area Based StudyApr 08 2015Mobile devices with touch keyboards have become ubiquitous, but text entry on these devices remains slow and errorprone. Understanding touch patterns during text entry could be useful in designing robust error-correction algorithms for soft keyboards. ... More

Kalb-Ramond coupled vortex fibration model for relativistic superfluid dynamicsNov 12 1996The macroscopic dynamics of a rotating superfluid deviates from that of a simple perfect fluid due to the effect of vorticity quantisation, which gives rise to a substructure of cosmic string type line defects that results in a local anisotropy whereby ... More

Supersonic String Model for Witten VorticesNov 29 1994A new cosmic string model specified by two independent mass parameters is introduced for the purpose of providing a realistic representation of the macroscopic dynamical behaviour of Witten type (superconducting) vortex defects of the vacuum. Unlike the ... More

A Homological Approach to FactorizationFeb 19 2013Dec 14 2016Mott noted a one-to-one correspondence between saturated multiplicatively closed subsets of a domain D and directed convex subgroups of the group of divisibility D. With this, we construct a functor between inclusions into saturated localizations of D ... More

Kisin modules with descent data and parahoric local modelsOct 26 2015Jan 11 2018We construct a moduli space $Y^{\mu, \tau}$ of Kisin modules with tame descent datum $\tau$ and with fixed $p$-adic Hodge type $\leq \mu$, for some finite extension $K/\mathbb{Q}_p$. We show that this space is smoothly equivalent to the local model for ... More

LSTM-Based Zero-Velocity Detection for Robust Inertial NavigationJul 13 2018We present a method to improve the accuracy of a zero-velocity-aided inertial navigation system (INS) by replacing the standard zero-velocity detector with a long short-term memory (LSTM) neural network. While existing threshold-based zero-velocity detectors ... More

A comprehensive theory of cascading via-paths and the reciprocal pointer chain methodMar 30 2016In this paper, we consolidate and expand upon the current theory and potential applications of the set of $k$ best \emph{cascading via-paths} (CVPs) and the \emph{reciprocal pointer chain} (RPC) method for identifying them. CVPs are a collection of up ... More

Krieger's finite generator theorem for actions of countable groups IIIMay 26 2017We continue the study of Rokhlin entropy, an isomorphism invariant for probability-measure-preserving actions of countable groups introduced in Part I. In this paper we prove a non-ergodic finite generator theorem and use it to establish sub-additivity ... More

Twisted component sums of vector-valued modular formsMar 18 2019We construct isomorphisms between spaces of vector-valued modular forms for the dual Weil representation and certain spaces of scalar-valued modular forms in the case that the underlying finite quadratic module $A$ has order $p$ or $2p$, where $p$ is ... More

Unified Music Theories for General Equal-Temperament SystemsNov 10 2016Why are white and black piano keys in an octave arranged as they are today? This article examines the relations between abstract algebra and key signature, scales, degrees, and keyboard configurations in general equal-temperament systems. Without confining ... More

Predictions for bottomonia suppression in 5.023 TeV Pb-Pb collisionsMay 11 2016Aug 30 2016We compute the suppression of the bottomonia states Upsilon(1S), Upsilon(2S), Upsilon(3S), chi_b(1P), chi_b(2P), and chi_b(3P) states in Large Hadron Collider (LHC) sqrt(s_NN)) = 5.023 TeV Pb-Pb collisions. For the background evolution we use 3+1d anisotropic ... More

A sub-exponential transition of the chromatic generalized Ramsey numbersJul 16 2015A simple graph-product type construction shows that for all natural numbers $r \ge q$, there exists an edge-coloring of the complete graph on $2^r$ vertices using $r$ colors where the graph consisting of the union of arbitrary $q$ color classes has chromatic ... More

Online Model Estimation for Predictive Thermal Control of BuildingsDec 27 2015This study proposes a general, scalable method to learn control-oriented thermal models of buildings that could enable wide-scale deployment of cost-effective predictive controls. An Unscented Kalman Filter augmented for parameter and disturbance estimation ... More

How Xenopus laevis replicates DNA reliably even though its origins of replication are located and initiated stochasticallyNov 04 2006DNA replication in Xenopus laevis is extremely reliable, failing to complete before cell division no more than once in 10,000 times; yet replication origins sites are located and initiated stochastically. Using a model based on 1d theories of nucleation ... More

Covariant Kinetic Theory with an Application to the Coma ClusterMay 02 2005In this paper, we introduce a novel solution to the covariant Landau equation for a pure electron plasma. The method conserves energy and particle number, and reduces smoothly to the Rosenbluth potentials of non-relativistic theory. In addition, we find ... More