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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.

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

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

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.

Scaling and Balancing for High-Performance Computation of Optimal ControlsOct 25 2018It is well-known that proper scaling can increase the efficiency of computational problems. In this paper we define and show that a balancing technique can substantially improve the computational efficiency of optimal control algorithms. We also show ... More

Serial Correlations in Single-Subject fMRI with Sub-Second TRMay 30 2017Oct 27 2017When performing statistical analysis of single-subject fMRI data, serial correlations need to be taken into account to allow for valid inference. Otherwise, the variability in the parameter estimates might be under-estimated resulting in increased false-positive ... More

Potential of 4d-VAR for exigent forecasting of severe weatherFeb 14 2011Severe storms, tropical cyclones, and associated tornadoes, floods, lightning, and microbursts threaten life and property. Reliable, precise, and accurate alerts of these phenomena can trigger defensive actions and preparations. However, these crucial ... 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

A Radial Measurement of the Galaxy Tidal Alignment Magnitude with BOSS DataFeb 21 2018The anisotropy of galaxy clustering in redshift space has long been used to probe the rate of growth of cosmological perturbations. However, if galaxies are aligned by large-scale tidal fields, then a sample with an orientation-dependent selection effect ... More

Tuning the antiferromagnetic helical pitch length and nanoscale domain size in Fe$_3$PO$_4$O$_3$ by magnetic dilutionSep 29 2017The insulating magnetic material Fe3PO4O3 features a non-centrosymmetric lattice composed of Fe^{3+} triangular units. Frustration, due to competing near neighbor ($J_1$) and next nearest neighbor ($J_2$) antiferromagnetic interactions, was recently suggested ... More

Dynamics of nanoscale bubbles growing in a tapered conduitDec 09 2017We predict the dynamics and shapes of nanobubbles growing in a supersaturated solution confined within a tapered, Hele-Shaw device with a small opening angle $\Phi \ll 1$. Our study is inspired by experimental observations of the growth and translation ... 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

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.

The core of adjoint functorsDec 01 2011Jan 03 2012There is a lot of redundancy in the usual definition of adjoint functors. We define and prove the core of what is required. First we do this in the hom-enriched context. Then we do it in the cocompletion of a bicategory with respect to Kleisli objects, ... More

Monoidal categories in, and linking, geometry and algebraJan 14 2012Oct 04 2012This is a report on aspects of the theory and use of monoidal categories. The first section introduces the main concepts through the example of the category of vector spaces. String notation is explained and shown to lead naturally to a link between knot ... More

Skew-closed categoriesMay 30 2012Sep 01 2012Spurred by the new examples found by Kornel Szlach\'anyi of a form of lax monoidal category, the author felt the time ripe to publish a reworking of Eilenberg-Kelly's original paper on closed categories appropriate to the laxer context. The new examples ... More

The rigidity of periodic body-bar frameworks on the three-dimensional fixed torusMar 29 2012We present necessary and sufficient conditions for the generic rigidity of body-bar frameworks on the three-dimensional fixed torus. These frameworks correspond to infinite periodic body-bar frameworks in $\mathbb{R}^3$ with a fixed periodic lattice.

Inductive constructions for frameworks on a two-dimensional fixed torusMar 29 2012Nov 06 2014An infinite periodic framework in the plane can be represented as a framework on a torus, using a $\mathbb Z^2$-labelled gain graph. We find necessary and sufficient conditions for the generic minimal rigidity of frameworks on the two-dimensional fixed ... 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

Reaction diffusion equations with super-linear absorption: universal bounds, uniqueness for the Cauchy problem, boundedness of stationary solutionsAug 24 2004Consider classical solutions to the parabolic reaction diffusion equation $$ &u_t =Lu+f(x,u), (x,t)\in R^n\times(0,\infty); &u(x,0) =g(x)\ge0, x\in R^n; &u\ge0, $$ where $$ L=\sum_{i,j=1}^na_{i,j}(x)\frac{\partial^2}{\partial x_i \partial x_j}+\sum_{i=1}^nb_i(x)\frac\partial{\partial ... More

Polynomials as spansMar 10 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 Joachim ... More

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

On the Existence of a Closed, Embedded, Rotational $λ$-HypersurfaceSep 15 2017In this paper we show the existence of a closed, embedded $\lambda$-hypersurfaces $\Sigma \subset \mathbb{R}^{2n}$. The hypersurface is diffeomorhic to $\mathbb{S}^{n-1} \times \mathbb{S}^{n-1} \times \mathbb{S}^1$ and exhibits $SO(n) \times SO(n)$ symmetry. ... 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

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

In-vivo magnetic resonance imaging of hyperpolarized silicon particlesMay 15 2013Silicon-based micro and nanoparticles have gained popularity in a wide range of biomedical applications due to their biocompatibility and biodegradability in-vivo, as well as a flexible surface chemistry, which allows drug loading, functionalization and ... More

Broad NeVIII 774 Emission From QuasarsNov 07 1997NeVIII 774 is an important tracer of the high-ionization gas in QSOs. We examine the NeVIII emission-line properties using new HST-FOS spectra of four sources, mean spectra derived from two QSO samples in the HST archives, and new photoionization calculations. ... More

Toward the first quantum simulation with quantum speedupNov 29 2017With quantum computers of significant size now on the horizon, we should understand how to best exploit their initially limited abilities. To this end, we aim to identify a practical problem that is beyond the reach of current classical computers, but ... More

Binary Pulsar Distances and Velocities from Gaia Data Release 2Jun 15 2018Aug 28 2018The second data release from the Gaia mission (Gaia DR2) includes, among its billion entries, as- trometric parameters for binary companions to a number of known pulsars, including white dwarf companions to millisecond pulsars and the non-degenerate components ... More

Determining the spin of two stellar-mass black holes from disk reflection signaturesFeb 10 2009We present measurements of the dimensionless spin parameters and inner-disk inclination of two stellar mass black holes. The spin parameter of SWIFT J1753.5-0127 and GRO J1655-40 are estimated by modelling the strong reflection signatures present in their ... 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

Calorimetric and magnetic study for Ni$_{50}$Mn$_{36}$In$_{14}$ and relative cooling power in paramagnetic inverse magnetocaloric systemsJun 28 2015The non-stoichiometric Heusler alloy Ni$_{50}$Mn$_{36}$In$_{14}$ undergoes a martensitic phase transformation in the vicinity of 345 K, with the high temperature austenite phase exhibiting paramagnetic rather than ferromagnetic behavior, as shown in similar ... More

Direct Measure of Giant Magnetocaloric Entropy Contributions in Ni-Mn-InJun 19 2015Jan 02 2016Off-stoichiometric alloys based on Ni 2 MnIn have drawn attention due to the coupled first order magnetic and structural transformations, and the large magnetocaloric entropy associated with the transformations. Here we describe calorimetric and magnetic ... More

Comparability and Cocomparability BigraphsFeb 01 2019We propose bipartite analogues of comparability and cocomparability graphs. Surprizingly, the two classes coincide. We call these bipartite graphs cocomparability bigraphs. We characterize cocomparability bigraphs in terms of vertex orderings, forbidden ... More

A systematic look at the Very High and Low/Hard state of GX 339-4: Constraining the black hole spin with a new reflection modelApr 01 2008Apr 22 2008We present a systematic study of GX 339-4 in both its very high and low hard states from simultaneous observations made with XMM-Newton and RXTE in 2002 and 2004. The X-ray spectra of both these extreme states exhibit strong reflection signatures, with ... More

Allocation strategies for high fidelity models in the multifidelity regimeDec 30 2018We propose a novel approach to allocating resources for expensive simulations of high fidelity models when used in a multifidelity framework. Allocation decisions that distribute computational resources across several simulation models become extremely ... More

Automated optimization of large quantum circuits with continuous parametersOct 19 2017Jun 01 2018We develop and implement automated methods for optimizing quantum circuits of the size and type expected in quantum computations that outperform classical computers. We show how to handle continuous gate parameters and report a collection of fast algorithms ... 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

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

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

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

Which Hydrogen Balmer Lines Are Most Reliable for Determining White Dwarf Atmospheric Parameters?Oct 15 2014Our preliminary results from laboratory experiments studying white dwarf (WD) photospheres show a systematic difference between experimental plasma conditions inferred from measured H$\beta$ absorption line profiles versus those from H$\gamma$. One hypothesis ... More

RF Processing of X-band Accelerator Structures at the NLCTAAug 20 2000During the initial phase of operation, the linacs of the Next Linear Collider (NLC) will contain roughly 5000 X-Band accelerator structures that will accelerate beams of electrons and positrons to 250 GeV. These structures will nominally operate at an ... More

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

Electrically controlled long-distance spin transport through an antiferromagnetic insulatorMay 07 2018Spintronics uses spins, the intrinsic angular momentum of electrons, as an alternative for the electron charge. Its long-term goal is in the development of beyond-Moore low dissipation technology devices. Recent progress demonstrated the long-distance ... More

Isomorphism of graph classes related to the circular-ones propertyMar 21 2012We give a linear-time algorithm that checks for isomorphism between two 0-1 matrices that obey the circular-ones property. This algorithm leads to linear-time isomorphism algorithms for related graph classes, including Helly circular-arc graphs, \Gamma-circular-arc ... More

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

Intrinsic galaxy alignments from the 2SLAQ and SDSS surveys: luminosity and redshift scalings and implications for weak lensing surveysJan 24 2007Oct 28 2007Correlations between intrinsic shear and the density field on large scales, a potentially important contaminant for cosmic shear surveys, have been robustly detected at low redshifts with bright galaxies in SDSS data. Here we present a more detailed characterization ... 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

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

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

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

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

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

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

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

Cyclic Hodge Integrals and Loop Schur FunctionsJan 10 2014We conjecture an evaluation of three-partition cyclic Hodge integrals in terms of loop Schur functions. Our formula implies the orbifold Gromov-Witten/Donaldson-Thomas correspondence for toric Calabi-Yau threefolds with transverse type A singularities. ... More

The speed of a general random walk reinforced by its recent historySep 07 2017We 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

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

On Thompson's group T and algebraic K-theoryJan 02 2014Dec 11 2017Using a theorem of L\"uck-Reich-Rognes-Varisco, we show that the Whitehead group of Thompson's group T is infinitely generated, even when tensored with the rationals. To this end we describe the structure of the centralizers and normalizers of the finite ... More

Asymptotics for Exit Problem and Principal Eigenvalue for a Class of Non-Local Elliptic Operators Related to Diffusion Processes with Random Jumps and Vanishing DiffusionMay 18 2011Let $D\subset R^d$ be a bounded domain and denote by $\mathcal P(D)$ the space of probability measures on $D$. Let \begin{equation*} L=\frac12\nabla\cdot a\nabla +b\nabla \end{equation*} be a second order elliptic operator. Let $\mu\in\mathcal P(D)$ and ... 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

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

Closed categories, star-autonomy, and monoidal comonadsDec 04 2007This paper determines what structure is needed for internal homs in a monoidal category C to be liftable to the category C^G of Eilenberg-Moore coalgebras for a monoidal comonad G on C. We apply this to lift star-autonomy with the view to recasting the ... More

Combinatorial categorical equivalences of Dold-Kan typeFeb 28 2014Mar 29 2019We prove a class of equivalences of additive functor categories that are relevant to enumerative combinatorics, representation theory, and homotopy theory. Let $\mathscr{X}$ denote an additive category with finite direct sums and split idempotents. The ... 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

Limit sets for modules over groups on CAT(0) spaces -- from the Euclidean to the hyperbolicJun 14 2013Oct 30 2016The 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

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

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

Quantum categories, star autonomy, and quantum groupoidsJan 20 2003Apr 04 2003A useful general concept of bialgebroid seems to be resolving itself in recent publications; we give a treatment in terms of modules and enriched categories. We define the term "quantum category". The definition of antipode for a bialgebroid is less resolved ... 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

Overcoming the language barrier in mobile user interface design: A case study on a mobile health appMay 16 2016This research report proposes a structured solution to address the need for awareness of cultural and language in user design. It will include evaluated research on established methods that already exist. Discussed ideas about how to address this situation ... More

Associativity and Thompson's GroupMay 23 2005Given a set S equipped with a binary operation (we call this a "bracket algebra") one may ask to what extent the binary operation satisfies some of the consequences of the associative law even when it is not actually associative? We define a subgroup ... More

A Graph-Based Inference Method for Conditional IndependenceMar 20 2013The graphoid axioms for conditional independence, originally described by Dawid [1979], are fundamental to probabilistic reasoning [Pearl, 19881. Such axioms provide a mechanism for manipulating conditional independence assertions without resorting to ... More

Sigma Invariants of Direct Products of GroupsJul 31 2008Aug 05 2009The Product Conjecture for the homological Bieri-Neumann-Strebel-Renz invariants is proved over a field. Under certain hypotheses the Product Conjecture is shown to also hold over Z, even though D. Schuetz has recently shown that the Conjecture is false ... More

Higher horospherical limit sets for G-modules over CAT(0) spacesDec 15 2017Oct 15 2018The Sigma-invariants of Bieri-Neumann-Strebel and Bieri-Renz involve an action of a discrete group G on a geometrically suitable space M. In the early versions, M was always a finite-dimensional Euclidean space on which G acted by translations. A substantial ... 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

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

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

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

Diffusive Search with spatially dependent ResettingMay 01 2018Dec 03 2018Consider a stochastic search model with resetting for an unknown stationary target $a\in\mathbb{R}$ with known distribution $\mu$. The searcher begins at the origin and performs Brownian motion with diffusion constant $D$. The searcher is also armed with ... More

Why quantum computing is hard - and quantum cryptography is not provably secureJan 30 2013Despite high hopes for quantum computation in the 1990s, progress in the past decade has been slow; we still cannot perform computation with more than about three qubits and are no closer to solving problems of real interest than a decade ago. Separately, ... More

Zeros of Lattice Sums: 3. Reduction of the Generalised Riemann Hypothesis to Specific GeometriesOct 22 2016Apr 08 2017The location of zeros of the basic double sum over the square lattice is studied. This sum can be represented in terms of the product of the Riemann zeta function and the Dirichlet beta function, so that the assertion that all its non-trivial zeros lie ... More

A Hochschild homology Euler characteristic for circle actionsOct 27 1998We define a "circle Euler characteristic" of a circle action on a compact manifold or finite complex X. It lies in the first Hochschild homology group of ZG where G is the fundamental group of X. It is analogous in many ways to the ordinary Euler characteristic. ... More

On the Use of Computer Programs as MoneyAug 02 2016Money is a technology for promoting economic prosperity. Over history money has become increasingly abstract, it used to be hardware, gold coins and the like, now it is mostly software, data structures located in banks. Here I propose the logical conclusion ... More

Connectivity properties of group actions on non-positively curved spaces II: The geometric invariantsNov 03 1998This is the second of two papers but has been written so as to have minimal dependence on the first paper (which is also on this archive). Let G be a group and let M be a CAT(0) proper metric space (e.g. a simply connected complete Riemannian manifold ... 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

Evidence Absorption and Propagation through Evidence ReversalsMar 27 2013The arc reversal/node reduction approach to probabilistic inference is extended to include the case of instantiated evidence by an operation called "evidence reversal." This not only provides a technique for computing posterior joint distributions on ... More

A note on Positivity of the CM line bundleMay 11 2006Aug 09 2006We show that positivity of the CM line associated to a family of polarised varieties is intimately related to the stability of its members. We prove that the CM line is nef on any curve which meets the stable locus, and that it is pseudoeffective (i.e. ... 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

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

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

Covering morphisms of crossed complexes and of cubical omega-groupoids with connection are closed under tensor productSep 28 2010Feb 27 2011The aim is the theorems of the title and the corollary that the tensor product of two free crossed resolutions of groups or groupoids is also a free crossed resolution of the product group or groupoid. The route to this corollary is through the equivalence ... More

Weak Hopf monoids in braided monoidal categoriesJan 26 2008We develop the theory of weak bimonoids in braided monoidal categories and show them to be quantum categories in a certain sense. Weak Hopf monoids are shown to be quantum groupoids. Each separable Frobenius monoid R leads to a weak Hopf monoid R \otimes ... More

Scaling limits for some random trees constructed inhomogeneouslyNov 04 2016We define some new sequences of recursively constructed random combinatorial trees, and show that, after properly rescaling graph distance and equipping the trees with the uniform measure on vertices, each sequence converges almost surely to a real tree ... More