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Instantons and the Ground State of the Massive Schwinger ModelFeb 16 1993We study the massive Schwinger model, quantum electrodynamics of massive, Dirac fermions, in 1+1 dimensions; with space compactified to a circle. In the limit that transitions to fermion--anti-fermion pairs can be neglected, we study the full ground state. ... More

Proposed measurements of the interlayer magnetoresistance of underdoped cuprate superconductors can distinguish closed pockets from open arcs in the Fermi surfaceSep 06 2010Sep 08 2010An outstanding question concerning the underdoped cuprate concerns the true nature of their Fermi surface which appears as a set of disconnected arcs. Theoretical models have proposed two distinct possibilities: (1) each arc is the observable part of ... More

Interlayer magnetoresistance in an anisotropic pseudogap stateJun 04 2009The interlayer magnetoresistance of a quasi-two-dimensional layered metal with a d-wave pseudogap is calculated semiclassically. An expression for the interlayer resistivity as a function of the strength and direction of the magnetic field, the magnitude ... More

Standing spin-wave mode structure and linewidth in partially disordered perpendicularly magnetized sub-micron Permalloy disc arraysJul 19 2010Jul 16 2014Standing spin wave mode frequencies and linewidths in partially disordered perpendicular magnetized arrays of sub-micron Permalloy discs are measured using broadband ferromagnetic resonance and compared to analytical results from a single, isolated disc. ... More

Metal-insulator transition and charge ordering in the extended Hubbard model at one-quarter fillingFeb 13 2002We study with exact diagonalization the zero temperature properties of the quarter-filled extended Hubbard model on a square lattice. We find that increasing the ratio of the intersite Coulomb repulsion, $V$, to the band width drives the system from a ... More

A cell filtration of the restriction of a cell moduleApr 08 2015We give a new proof that the restriction of a cell module of the Hecke algebra of the symmetric group on $n$ letters, to the Hecke algebra of the symmetric group on $n-1$ letters, has a filtration by cell modules.

Palm distributions of wave characteristics in encountering seasJun 17 2008Distributions of wave characteristics of ocean waves, such as wave slope, waveheight or wavelength, are an important tool in a variety of oceanographic applications such as safety of ocean structures or in the study of ship stability, as will be the focus ... More

Self-Tuning at Large (Distances): 4D Description of Runaway Dilaton CaptureSep 14 2015We complete here a three-part study (see also arXiv:1506.08095 and 1508.00856) of how codimension-two objects back-react gravitationally with their environment, with particular interest in situations where the transverse `bulk' is stabilized by the interplay ... More

A Problem With delta-functions: Stress-Energy Constraints on Bulk-Brane Matching (with comments on arXiv:1508.01124)Sep 14 2015We critically assess a recent assertion (arXiv:1508.01124) concerning using delta-functions to analyze how higher-codimension branes back-react on their environment. We also briefly summarize the state of the art: describing how stress-energy balance ... More

Contact-Aided Invariant Extended Kalman Filtering for Robot State EstimationApr 19 2019Legged robots require knowledge of pose and velocity in order to maintain stability and execute walking paths. Current solutions either rely on vision data, which is susceptible to environmental and lighting conditions, or fusion of kinematic and contact ... More

Transfer reaction code with nonlocal interactionsJun 23 2016We present a suite of codes (NLAT for nonlocal adiabatic transfer) to calculate the transfer cross section for single-nucleon transfer reactions, $(d,N)$ or $(N,d)$, including nonlocal nucleon-target interactions, within the adiabatic distorted wave approximation. ... More

Charge symmetry violation in the determination of strangeness form factorsFeb 05 2019The strange quark contributions to the electromagnetic form factors of the proton are ideal quantities to study the role of hidden flavor in the properties of the proton. This has motivated intense experimental measurements of these form factors. A major ... More

Fast R-CNNApr 30 2015Sep 27 2015This paper proposes a Fast Region-based Convolutional Network method (Fast R-CNN) for object detection. Fast R-CNN builds on previous work to efficiently classify object proposals using deep convolutional networks. Compared to previous work, Fast R-CNN ... More

Kan extensions and cartesian monoidal categoriesSep 23 2014The existence of adjoints to algebraic functors between categories of models of Lawvere theories follows from finite-product-preservingness surviving left Kan extension. A result along these lines was proved in Appendix 2 of Brian Day's 1970 PhD thesis. ... More

Pointwise extensions and sketches in bicategoriesSep 23 2014We make a few remarks concerning pointwise extensions in a bicategory which include the case of bicategories of enriched categories. We show that extensions, pointwise or not, can be replaced by extensions along very special fully faithful maps. This ... More

Unstable products of smooth curvesJun 22 2005Aug 24 2005We give examples of smooth surfaces with negative first Chern class which are slope unstable with respect to certain polarisations, and so have Kahler classes that do not admit any constant scalar curvature Kahler metrics. We also compare this to the ... More

The monoidal centre as a limitApr 04 2003The centre of a monoidal category is a braided monoidal category. Monoidal categories are monoidal objects (or pseudomonoids) in the monoidal bicategory of categories. This paper provides a universal construction in a braided monoidal bicategory that ... More

Categorical and combinatorial aspects of descent theoryMar 14 2003Mar 20 2003There is a construction which lies at the heart of descent theory. The combinatorial aspects of this paper concern the description of the construction in all dimensions. The description is achieved precisely for strict n-categories and outlined for weak ... More

Vector product and composition algebras in braided monoidal additive categoriesDec 10 2018This is an account of some work of Markus Rost and his students Dominik Boos and Susanne Maurer. We adapt it to the braided monoidal setting.

Number of arithmetic progressions in dense random subsets of $\mathbb{Z}/n\mathbb{Z}$Jul 26 2019We examine the behavior of the number of $k$ term arithmetic progressions in a random subset of $\mathbb{Z}/n\mathbb{Z}$. If $k=3$ and the subset is chosen uniformly at random, then we show that the resulting distribution, while obeying a central limit ... More

Semistability and CAT(0) GeometryMar 20 2017We explain why semistability of a one-ended proper CAT(0) space can be determined by the geodesic rays. This is applied to boundaries of CAT(0) groups.

The Information Flow Problem on Clock NetworksMay 17 2016The information flow problem on a network asks whether $r$ senders, $v_1,v_2, \ldots ,v_r$ can each send messages to $r$ corresponding receivers $v_{n+1}, \ldots ,v_{n+r}$ via intermediate nodes $v_{r+1}, \ldots ,v_n$. For a given finite $R \subset \mathbb{Z}^+$, ... More

Transience/Recurrence and the speed of a one-dimensional random walk in a "have your cookie and eat it" environmentFeb 06 2009Jun 07 2009Consider a simple random walk on the integers with the following transition mechanism. At each site $x$, the probability of jumping to the right is $\omega(x)\in[\frac12,1)$, until the first time the process jumps to the left from site $x$, from which ... More

Weighted Tensor Products of Joyal Species, Graphs, and CharadesMar 10 2015Jan 17 2016Motivated by the weighted Hurwitz product on sequences in an algebra, we produce a family of monoidal structures on the category of Joyal species. We suggest a family of tensor products for charades. We begin by seeing weighted derivational algebras and ... More

Wreaths, mixed wreaths and twisted coactionsOct 24 2016Distributive laws between two monads in a 2-category $\CK$, as defined by Jon Beck in the case $\CK=\mathrm{Cat}$, were pointed out by the author to be monads in a 2-category $\mathrm{Mnd}\CK$ of monads. Steve Lack and the author defined wreaths to be ... More

Polynomials as spansMar 10 2019May 07 2019The paper defines polynomials in a bicategory $\mathscr{M}$. Polynomials in bicategories $\mathrm{Spn}\mathscr{C} \ $ of spans in a finitely complete category $\mathscr{C} \ $ agree with polynomials in $\mathscr{C} \ $ as defined by Nicola Gambino and ... More

Entanglement-based 3D magnetic gradiometry with an ultracold atomic scattering haloJun 21 2019Ultracold collisions of Bose-Einstein condensates can be used to generate a large number of counterpropagating pairs of entangled atoms, which collectively form a thin spherical shell in momentum space, called a scattering halo. Here we generate a scattering ... More

LSTM knowledge transfer for HRV-based sleep stagingSep 12 2018Automated sleep stage classification using heart-rate variability is an active field of research. In this work limitations of the current state-of-the-art are addressed through the use of deep learning techniques and their efficacy is demonstrated. First, ... More

Precision spectroscopy of high rotational states in H_2 investigated by Doppler-free two-photon laser spectroscopy in the EF^1Σ_g^+ - X^1Σ_g^+ systemJan 03 2013Recently a high precision spectroscopic investigation of the EF^1\Sigma_g^+ - X^1\Sigma_g^+ system of molecular hydrogen was reported yielding information on QED and relativistic effects in a sequence of rotational quantum states in the X^1\Sigma^+_g$ ... More

φ^4 Solitary Waves in a Parabolic Potential: Existence, Stability, and Collisional DynamicsMay 01 2018We explore a {\phi}^4 model with an added external parabolic potential term. This term dramatically alters the spectral properties of the system. We identify single and multiple kink solutions and examine their stability features; importantly, all of ... More

Oxygen-vacancy tuning of magnetism in SrTi$_{0.75}$Fe$_{0.125}$Co$_{0.125}$O$_{3-δ}$ perovskiteJul 12 2019We use density functional theory to calculate the structure, band-gap and magnetic properties of oxygen-deficient SrTi$_{1-x-y}$Fe$_x$Co$_y$O$_{3-\delta}$ with x = y = 0.125 and ${\delta}$ = (0,0.125,0.25). The valence and the high or low spin-states ... More

The demise of the filesystem and multi level service architectureJul 26 2019Jul 31 2019Many astronomy data centres still work on filesystems. Industry has moved on; current practice in computing infrastructure is to achieve Big Data scalability using object stores rather than POSIX file systems. This presents us with opportunities for portability ... More

Efficient operators for studying higher partial wavesNov 04 2017An extended multi-hadron operator is developed to extract the spectra of irreducible representations in the finite volume. The irreducible representations of the cubic group are projected using a coordinate-space operator. The correlation function of ... More

Contact-Aided Invariant Extended Kalman Filtering for Legged Robot State EstimationMay 26 2018This paper derives a contact-aided inertial navigation observer for a 3D bipedal robot using the theory of invariant observer design. Aided inertial navigation is fundamentally a nonlinear observer design problem; thus, current solutions are based on ... More

Paramagnetic limiting of the upper critical field of the layered organic superconductor $κ-(BEDT-TTF)_2Cu(SCN)_2$Apr 13 1999We report detailed measurements of the interlayer magnetoresistance of the layered organic superconductor $\kappa -(BEDT-TTF)_2Cu(SCN)_2$ for temperatures down to 0.5 K and fields up to 30 tesla. The upper critical field is determined from the resistive ... More

Fast domain wall propagation in uniaxial nanowires with transverse fieldsJun 21 2012Aug 18 2013Under a magnetic field along its axis, domain wall motion in a uniaxial nanowire is much slower than in the fully anisotropic case, typically by several orders of magnitude (the square of the dimensionless Gilbert damping parameter). However, with the ... More

An Optimal Control Theory for Accelerated OptimizationFeb 24 2019Accelerated optimization algorithms can be generated using a double-integrator model for the search dynamics imbedded in an optimal control problem.

Design of the Millennium Villages Project Sampling Plan: a simulation study for a multi-module surveyJul 09 2015The Millennium Villages Project (MVP) is a ten-year integrated rural development project implemented in ten sub-Saharan African sites. At its conclusion we will conduct an evaluation of its causal effect on a variety of development outcomes, measured ... More

Low RF power plasma ignition and detection for in-situ cleaning of 1.3 GHz 9-cell cavitiesFeb 08 2019Superconducting Radio Frequency (SRF) cavities performance preservation is crucial, from vertical test to accelerator operation. Field Emission (FE) is still one of the performance limiting factors to overcome and plasma cleaning has been proven successful ... More

Legged Robot State-Estimation Through Combined Forward Kinematic and Preintegrated Contact FactorsDec 15 2017Feb 25 2018State-of-the-art robotic perception systems have achieved sufficiently good performance using Inertial Measurement Units (IMUs), cameras, and nonlinear optimization techniques, that they are now being deployed as technologies. However, many of these methods ... More

Short range order in the quantum XXZ honeycomb lattice material BaCo$_2$(PO$_4$)$_2$Dec 17 2017Apr 14 2018We present observations of highly frustrated quasi two-dimensional (2D) magnetic correlations in the honeycomb lattice layers of the S$_{eff}$ = 1/2 compound $\gamma$-BaCo$_2$(PO$_4$)$_2$ ($\gamma$-BCPO). Specific heat shows a broad peak comprised of ... More

MSSM Effects in Top-antitop Production at the LHCJul 27 2007We report on a calculation of the effects of supersymmetry on the cross-section for top-antitop production at LHC. A numerical study is carried out for the ten benchmarks of the Snowmass accord. It is found that the higher order effects involving supersymmetric ... More

Bruggeman Approach for Isotropic Chiral Mixtures RevisitedJun 03 2019Two interpretations of the Bruggeman approach for the homogenization of isotropic chiral mixtures are shown to lead to different results. Whereas the standard interpretation is shown to yield the average-polarizability-density approach, a recent interpretation ... More

Active Disassembly and Reassembly of Actin Networks Induces Distinct Biphasic MechanicsOct 10 2017Actin is a key component of the cytoskeleton, which plays central roles in cell motility, division, growth, and tensile strength. To enable this wide range of transient mechanical processes and properties, networks of actin filaments continuously disassemble ... More

Linear-Time Algorithms for Finding Tucker Submatrices and Lekkerkerker-Boland SubgraphsDec 31 2013Lekkerkerker and Boland characterized the minimal forbidden induced subgraphs for the class of interval graphs. We give a linear-time algorithm to find one in any graph that is not an interval graph. Tucker characterized the minimal forbidden submatrices ... More

Laboratory Measurements of White Dwarf Photospheric Spectral Lines: H$β$May 14 2015We spectroscopically measure multiple hydrogen Balmer line profiles from laboratory plasmas to investigate the theoretical line profiles used in white dwarf atmosphere models. X-ray radiation produced at the Z Pulsed Power Facility at Sandia National ... More

Geometric phase and dimensionality reduction in locomoting living systemsJun 26 2019The apparent ease with which animals move requires the coordination of their many degrees of freedom to manage and properly utilize environmental interactions. Identifying effective strategies for locomotion has proven challenging, often requiring detailed ... More

Linear-Time Recognition of Probe Interval GraphsJul 21 2013The interval graph for a set of intervals on a line consists of one vertex for each interval, and an edge for each intersecting pair of intervals. A probe interval graph is a variant that is motivated by an application to genomics, where the intervals ... More

An approach to intersection theory on singular varieties using motivic complexesNov 21 2013May 20 2016We introduce techniques of Suslin, Voevodsky, and others into the study of singular varieties. Our approach is modeled after Goresky-MacPherson intersection homology. We provide a formulation of perversity cycle spaces leading to perversity homology theory ... More

Limit sets for modules over groups on CAT(0) spaces -- from the Euclidean to the hyperbolicJun 14 2013Apr 17 2014The observation that the 0-dimensional Geometric Invariant $\Sigma ^{0}(G;A)$ of Bieri-Neumann-Strebel-Renz can be interpreted as a horospherical limit set opens a direct trail from Poincar\'{e}'s limit set $\Lambda (\Gamma)$ of a discrete group $\Gamma ... More

Wilson's ratio and the spin splitting of magnetic oscillations in quasi-two-dimensional metalsMay 05 1999Sep 07 1999A simple consistency check is proposed for the Fermi liquid description of the low-temperature properties of quasi-two-dimensional metals. In a quasi-two-dimensional Fermi liquid the Zeeman splitting of magnetic oscillations can be used to determine g^*, ... More

Ginzburg-Landau theory of phase transitions in quasi-one-dimensional systemsJan 18 1995A wide range of quasi-one-dimensional materials, consisting of weakly coupled chains, undergo three-dimensional phase transitions that can be described by a complex order parameter. A Ginzburg-Landau theory is derived for such a transition. It is shown ... More

The Infinite Limit of Random Permutations Avoiding Patterns of Length ThreeJun 20 2018Jul 04 2018For $\tau\in S_3$, let $\mu_n^{\tau}$ denote the uniformly random probability measure on the set of $\tau$-avoiding permutations in $S_n$. Let $\mathbb{N}^*=\mathbb{N}\cup\{\infty\}$ with an appropriate metric and denote by $S(\mathbb{N},\mathbb{N}^*)$ ... More

Matrix coefficients of unitary representations and associated compactificationsDec 20 2011Jul 11 2012We study, for a locally compact group $G$, the compactifications $(\pi,G^\pi)$ associated with unitary representations $\pi$, which we call {\it $\pi$-Eberlein compactifications}. We also study the Gelfand spectra $\Phi_{\mathcal{A}}(\pi)}$ of the uniformly ... More

Exceptional knot homologyMay 07 2015The goal of this article is twofold. First, we find a natural home for the double affine Hecke algebras (DAHA) in the physics of BPS states. Second, we introduce new invariants of torus knots and links called "hyperpolynomials" that address the "problem ... More

Coalgebras governing both weighted Hurwitz products and their pointwise transformsOct 18 2015We give further insights into the weighted Hurwitz product and the weighted tensor product of Joyal species. Our first group of results relate the Hurwitz product to the pointwise product, including the interaction with Rota--Baxter operators. Our second ... More

Asymptotics of Partial Density Functions for DivisorsDec 04 2013Aug 23 2016We study the asymptotic behaviour of the partial density function associated to sections of a positive hermitian line bundle that vanish to a particular order along a fixed divisor $Y$. Assuming the data in question is invariant under an $S^1$-action ... More

Torsors, herds and flocksDec 23 2009Sep 23 2010This paper presents non-commutative and structural notions of torsor. The two are related by the machinery of Tannaka-Krein duality.

Anisotropic scattering in angular-dependent magnetoresistance oscillations of quasi-2D and quasi-1D metals: beyond the relaxation-time approximationApr 17 2008The electrical resistivity for a current moving perpendicular to layers (chains) in quasi-2D (quasi-1D) metals under an applied magnetic field of varying orientation is studied using Boltzmann transport theory. We consider the simplest non-trivial quasi-2D ... More

Direct observation of Feshbach enhanced $\it{s}$-wave scattering of fermionsSep 30 2015Oct 08 2015We directly measured the normalized $\it{s}$-wave scattering cross-section of ultracold $^{40}\rm{K}$ atoms across a magnetic-field Feshbach resonance by colliding pairs of degenerate Fermi gases (DFGs) and imaging the scattered atoms. We extracted the ... More

A changing wind collisionDec 15 2017We report on the first detection of a global change in the X-ray emitting properties of a wind-wind collision, thanks to XMM-Newton observations of the massive SMC system HD5980. While its lightcurve had remained unchanged between 2000 and 2005, the X-ray ... More

Verifying the Steane code with QuantomaticJun 19 2013Dec 30 2014In this paper we give a partially mechanized proof of the correctness of Steane's 7-qubit error correcting code, using the tool Quantomatic. To the best of our knowledge, this represents the largest and most complicated verification task yet carried out ... More

Transience/Recurrence and Growth Rates for Diffusion Processes in Time-Dependent DomainsMay 18 2015Jan 12 2016Let $\mathcal{K}\subset R^d$, $d\ge2$, be a smooth, bounded domain satisfying $0\in\mathcal{K}$, and let $f(t),\ t\ge0$, be a smooth, continuous, nondecreasing function satisfying $f(0)>1$. Define $D_t=f(t)\mathcal{K}\subset R^d$. Consider a diffusion ... More

Transience, recurrence and speed of diffusions with a non-Markovian two-phase "use it or lose it" driftOct 08 2012We investigate the transience/recurrence of a non-Markovian, one-dimensional diffusion process which consists of a Brownian motion with a non-anticipating drift that has two phases---a transient to $+\infty$ mode which is activated when the diffusion ... More

Kemeny's constant for one-dimensional diffusionsMar 28 2019Let $X(\cdot)$ be a non-degenerate, positive recurrent one-dimensional diffusion process on $\mathbb{R}$ with invariant probability density $\mu(x)$, and let $\tau_y=\inf\{t\ge0: X(t)=y\}$ denote the first hitting time of $y$. Let $\mathcal{X}$ be a random ... More

Explicit and Almost Explicit Spectral Calculations for Diffusion OperatorsAug 22 2008The diffusion operator $$ H_D=-\frac12\frac d{dx}a\frac d{dx}-b\frac d{dx}=-\frac12\exp(-2B)\frac d{dx}a\exp(2B)\frac d{dx}, $$ where $B(x)=\int_0^x\frac ba(y)dy$, defined either on $R^+=(0,\infty)$ with the Dirichlet boundary condition at $x=0$, or on ... More

The Genus-One Global Mirror Theorem for the Quintic ThreefoldMar 20 2017We prove the genus-one restriction of the all-genus Landau-Ginzburg/Calabi-Yau conjecture of Chiodo and Ruan, stated in terms of the geometric quantization of an explicit symplectomorphism determined by genus-zero invariants. This provides the first evidence ... More

Kuratowski's Theorem for Two Closure OperatorsSep 06 2011A celebrated 1922 theorem of Kuratowski states that there are at most 14 distinct sets arising from applying the operations of complementation and closure, any number of times, in any order, to a subset of a topological space. In this paper we consider ... More

The Speed of a Random Walk Excited By Its Recent HistoryMay 30 2013Feb 09 2014Let $N$ and $M$ be positive integers satisfying $1\le M\le N$, and let $0<p_0<p_1<1$. Define a process $\{X_n\}_{n=0}^\infty$ on $\mathbb{Z}$ as follows. At each step, the process jumps either one step to the right or one step to the left, according to ... More

Curve crossing for random walks reflected at their maximumAug 13 2007Let $R_n=\max_{0\leq j\leq n}S_j-S_n$ be a random walk $S_n$ reflected in its maximum. Except in the trivial case when $P(X\ge0)=1$, $R_n$ will pass over a horizontal boundary of any height in a finite time, with probability 1. We extend this by giving ... More

Hopf rings for grading and differentialsJun 25 2018In the category of abelian groups, Pareigis constructed a Hopf ring whose comodules are differential graded abelian groups. We show that this Hopf ring can be obtained by combining grading and differential Hopf rings using semidirect product in fairly ... More

A stability result using the matrix norm to bound the permanentJun 23 2016We prove a stability version of a general result that bounds the permanent of a matrix in terms of its operator norm. More specifically, suppose $A$ is an $n \times n$ matrix over $\mathbb{C}$ (resp. $\mathbb{R}$), and let $\mathcal{P}$ denote the set ... More

Algebraic and Logical Methods in Quantum ComputationOct 08 2015Feb 15 2017This thesis contains contributions to the theory of quantum computation. We first define a new method to efficiently approximate special unitary operators. Specifically, given a special unitary U and a precision {\epsilon} > 0, we show how to efficiently ... More

Optimal ancilla-free Clifford+V approximation of z-rotationsSep 15 2014Mar 06 2015We describe a new efficient algorithm to approximate z-rotations by ancilla-free Clifford+V circuits, up to a given precision epsilon. Our algorithm is optimal in the presence of an oracle for integer factoring: it outputs the shortest Clifford+V circuit ... More

Holography for asymptotically locally Lifshitz spacetimesJul 22 2011May 12 2014We give a definition of asymptotically locally Lifshitz spacetimes, with boundary data appropriate for a non-relativistic theory on the boundary. Solutions satisfying these boundary conditions are constructed in an asymptotic expansion. We identify the ... More

Pair production of black holes in a $U(1) \otimes U(1)$ theoryJan 26 1994Mar 21 1994Charged dilaton black hole solutions have recently been found for an action with two $U(1)$ gauge fields and a dilaton field. I investigate new exact solutions of this theory analogous to the C-metric and Ernst solutions of classical general relativity. ... More

Neutral stability height correction for ocean windsJul 07 2011Adjusting ocean wind observations to a standard height, usually 10 m, requires the use of a boundary layer model, and knowledge of the thermodynamical variables. Height adjustment is complicated by the fact that a necessary parameter, the roughness height, ... More

PSD-throttling on TreesJun 14 2019PSD-forcing is a coloring process on a graph that colors vertices blue by starting with an initial set $B$ of blue vertices and applying a color change rule (CCR-$\Zp$). The PSD-throttling number is the minimum of the sum of the cardinality of $B$ and ... More

The Hyperplane is the Only Stable, Smooth Solution to the Isoperimetric Problem in Gaussian SpaceJul 26 2013Dec 08 2014We study stable smooth solutions to the isoperimetric type problem for a Gaussian weight on Euclidean Space. That is, we study hypersurfaces $\Sigma^n \subset \mathbb R^{n+1}$ that are second order stable critical points of compact variations that minimize ... More

One-Dimensional Diffusions That Eventually Stop Down-CrossingDec 10 2009Consider a diffusion process corresponding to the operator $L=\frac12a\frac{d^2}{dx^2}+b\frac d{dx}$ and which is transient to $+\infty$. For $c>0$, we give an explicit criterion in terms of the coefficients $a$ and $b$ which determines whether or not ... More

Optimizing the Drift in a Diffusive Search for a Random Stationary TargetMar 28 2018May 01 2018Let $a\in\mathbb{R}$ denote an unknown stationary target with a known distribution $\mu\in\mathcal{P(\mathbb{R}})$, the space of probability measures on $\mathbb{R}$. A diffusive searcher $X(\cdot)$ sets out from the origin to locate the target. The time ... More

End-To-End Prediction of Emotion From Heartbeat Data Collected by a Consumer Fitness TrackerJul 16 2019Automatic detection of emotion has the potential to revolutionize mental health and wellbeing. Recent work has been successful in predicting affect from unimodal electrocardiogram (ECG) data. However, to be immediately relevant for real-world applications, ... More

Detecting Tampering in a Random HypercubeJan 17 2012Sep 04 2012Consider the random hypercube $H_2^n(p_n)$ obtained from the hypercube $H_2^n$ by deleting any given edge with probabilty $1-p_n$, independently of all the other edges. A diameter path in $H_2^n$ is a longest geodesic path in $H_2^n$. Consider the following ... More

Permutations avoiding a certain pattern of length three under Mallows distributionsAug 04 2019Aug 15 2019We consider permutations avoiding a certain pattern of length three under the family of Mallows distributions. In particular, we obtain rather precise bounds on the asymptotic probability as $n\to\infty$ that a permutation $\sigma\in S_n$ under the Mallows ... More

Real setsApr 28 2017Jan 16 2018After reviewing a universal characterization of the extended positive real numbers published by Denis Higgs in 1978, we define a category which provides an answer to the questions: \begin{itemize} \item what is a set with half an element? \item what is ... More

Adams operations on the virtual K-theory of P(1,n)Feb 14 2013We analyze the structure of the virtual (orbifold) K-theory ring of the complex orbifold P(1,n) and its virtual Adams (or power) operations, by using the non-Abelian localization theorem of Edidin-Graham. In particular, we identify the group of virtual ... More

Turbulent fluctuations and the excitation of Z Cam outburstsApr 19 2017Z Cam variables are a subclass of dwarf nova that lie near a global bifurcation between outbursting ("limit cycle") and non-outbursting ("standstill") states. It is believed that variations in the secondary star's mass-injection rate instigate transitions ... More

Approximating stationary distributions of fast mixing Glauber dynamics, with applications to exponential random graphsDec 15 2017Oct 11 2018We provide a general bound on the Wasserstein distance between two arbitrary distributions of sequences of Bernoulli random variables. The bound is in terms of a mixing quantity for the Glauber dynamics of one of the sequences, and a simple expectation ... More

The speed of a general random walk reinforced by its recent historySep 07 2017Mar 28 2019We consider several variants of a class of random walks whose increment distributions depend on the average value of the process over its most recent $N$ steps. We investigate the speed of the process, and in particular, the limiting speed as the "history ... More

Genus six curves, K3 surfaces, and stable pairsDec 26 2018A general smooth curve of genus six lies on a quintic del Pezzo surface. In \cite{AK11}, Artebani and Kond\=o construct a birational period map for genus six curves by taking ramified double covers of del Pezzo surfaces. The map is not defined for special ... More

Extremes for the inradius in the Poisson line tessellationJan 31 2015A Poisson line tessellation is observed within a window. With each cell of the tessellation, we associate the inradius, which is the radius of the largest ball contained in the cell. Using Poisson approximation, we compute the limit distributions of the ... More

Majorana Neutrino Masses Can Save One Family TechnicolourJul 05 1993We make non perturbative estimates of the electroweak radiative correction parameter $S$ in dynamical symmetry breaking models with Majorana neutrino masses. The Majorana masses are treated as perturbations to a Non Local Chiral Model of the strong interactions. ... More

Hodge-Riemann bilinear relations for Schur classes of ample vector bundlesMay 31 2019Jul 02 2019Let $X$ be a $d$ dimensional projective manifold, $E$ be an ample vector bundle on $X$ and $0\le \lambda_N\le \lambda_{N-1} \le \cdots \le \lambda_1 \le \operatorname{rank}(E)$ be a partition of $d-2$. We prove that the Schur class $s_{\lambda}(E)\in ... More

On the strange domain of attraction to generalized Dickman distributions for sums of independent random variablesNov 22 2016Jan 04 2017Let $\{B_k\}_{k=1}^\infty, \{X_k\}_{k=1}^\infty$ all be independent random variables. Assume that $\{B_k\}_{k=1}^\infty$ are $\{0,1\}$-valued Bernoulli random variables satisfying $B_k\stackrel{\text{dist}}{=}\text{Ber}(p_k)$, with $\sum_{k=1}^\infty ... More

Extension creation under comonadic base changeSep 07 2018The forgetful functor $\mathscr{U}:\mathscr{V}^\mathscr{G}\rightarrow \mathscr{V}$ from the monoidal category of Eilenberg-Moore coalgebras for a cocontinuous Hopf comonad $\mathscr{G}$ induces a change of base functor $\widetilde{\mathscr{U}}:\mathscr{V}^\mathscr{G}\text{-}\mathrm{Mod}\rightarrow ... More

Tannaka duality and convolution for duoidal categoriesNov 24 2011Given a horizontal monoid M in a duoidal category F, we examine the relationship between bimonoid structures on M and monoidal structures on the category of right M-modules which lift the vertical monoidal structure of F. We obtain our result using a ... More

Product blocking measures and a particle system proof of the Jacobi triple productJun 02 2016Dec 08 2016We review product form blocking measures in the general framework of nearest neighbor asymmetric one dimensional misanthrope processes. This class includes exclusion, zero range, bricklayers, and many other models. We characterize the cases when such ... More

A sum involving the greatest-integer functionJun 28 2019We determine properties of the set of values of $ [nx] - ([x]/1 + [2x]/2 + \cdots + [nx]/x) $ as $n$ and $x$ vary.

Small Time Convergence of Subordinators with Regularly or Slowly Varying Canonical MeasureJun 26 2018We consider subordinators $X_\alpha=(X_\alpha(t))_{t\ge 0}$ in the domain of attraction at 0 of a stable subordinator $(S_\alpha(t))_{t\ge 0}$ (where $\alpha\in(0,1)$); thus, with the property that $\overline{\Pi}_\alpha$, the tail function of the canonical ... More

Forecasting Short-term Dynamics of Fair-Weather Cumuli using Dynamic Mode DecompositionJul 30 2019Application of Dynamic Mode Decomposition to clear-sky index forecasting of shadowing effects of convective fair-weather cumulus clouds is presented. Cloud dynamics are captured by sequences of visible-light photographic video frames. This method can ... More