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Generalized Bayesian Updating and the Loss-Likelihood BootstrapSep 22 2017In this paper, we revisit the weighted likelihood bootstrap and show that it is well-motivated for Bayesian inference under misspecified models. We extend the underlying idea to a wider family of inferential problems. This allows us to calibrate an analogue ... More

Scalable Nonparametric Sampling from Multimodal Posteriors with the Posterior BootstrapFeb 08 2019Increasingly complex datasets pose a number of challenges for Bayesian inference. Conventional posterior sampling based on Markov chain Monte Carlo can be too computationally intensive, is serial in nature and mixes poorly between posterior modes. Further, ... More

The intrinsic torsion of SU(3) and G_2 structuresFeb 26 2002We analyse the relationship between the components of the intrinsic torsion of an SU(3) structure on a 6-manifold and a G_2 structure on a 7-manifold. Various examples illustrate the type of SU(3) structure that can arise as a reduction of a metric with ... More

On Estimating Many Means, Selection Bias, and the BootstrapNov 15 2013With recent advances in high throughput technology, researchers often find themselves running a large number of hypothesis tests (thousands+) and esti- mating a large number of effect-sizes. Generally there is particular interest in those effects estimated ... More

Perspectives for Top Quark Physics at the (I)LCNov 27 2014Linear e+e- colliders provide a rich set of opportunities for top quark physics, crucial for the understanding of electroweak symmetry breaking and for the search for physics beyond the Standard Model. A ttbar threshold scan in e+e- annihilation enables ... More

Higgs Physics at future Linear Colliders - A Case for precise VertexingJan 24 2014Jan 27 2014The discovery of a Higgs boson by the experiments at the LHC marks a major breakthrough in particle physics, with far-reaching consequences for our understanding of the fundamental principles of our Universe. To fully explore this unique particle, experiments ... More

On the Capacity of Noisy ComputationsMay 16 2011This paper presents an analysis of the concept of capacity for noisy computations, i.e. algorithms implemented by unreliable computing devices (e.g. noisy Turing Machines). The capacity of a noisy computation is defined and justified by companion coding ... More

"Densities" and maximal monotonicity IJul 04 2014Oct 31 2015We discuss "Banach SN spaces", which include Hilbert spaces, negative Hilbert spaces, and the product of any real Banach space with its dual. We introduce "L-positive" sets, which generalize monotone multifunctions from a Banach space into its dual. We ... More

Analogs of the M-Function in the Theory of Orthogonal Polynomials on the Unit CircleNov 04 2003We show that the multitude of applications of the Weyl-Titchmarsh m-function leads to a multitude of different functions in the theory of orthogonal polynomials on the unit circle that serve as analogs of the m-function.

On universal and periodic $β$-expansions, and the Hausdorff dimension of the set of all expansionsDec 06 2012May 28 2013In this paper we study the topology of a set naturally arising from the study of $\beta$-expansions. After proving several elementary results for this set we study the case when our base is Pisot. In this case we give necessary and sufficient conditions ... More

Tensor products of maximal abelian subalgebras of C*-algebrasNov 01 2007Nov 27 2007It is shown that if $C_1$ and $C_2$ are maximal abelian self-adjoint subalgebras (masas) of C*-algebras $A_1$ and $A_2$, respectively, then the completion $C_1\otimes C_2$ of the algebraic tensor product $C_1\odot C_2$ of $C_1$ and $C_2$ in any C*-tensor ... More

The Legendre-Fenchel transform from a category theoretic perspectiveJan 15 2015The Legendre-Fenchel transform is a classical piece of mathematics with many applications. In this paper we show how it arises in the context of category theory using categories enriched over the extended real numbers $\overline{ \mathbb{R}}:=[-\infty,+\infty]$. ... More

Collective Phenomena and Non-Finite State Computation in a Human Social SystemNov 30 2012Sep 19 2013We investigate the computational structure of a paradigmatic example of distributed social interaction: that of the open-source Wikipedia community. We examine the statistical properties of its cooperative behavior, and perform model selection to determine ... More

Primitive Part-of-Speech Tagging using Word Length and Sentential StructureAug 23 1998It has been argued that, when learning a first language, babies use a series of small clues to aid recognition and comprehension, and that one of these clues is word length. In this paper we present a statistical part of speech tagger which trains itself ... More

Group Minds and the Case of WikipediaJul 08 2014Oct 13 2014Group-level cognitive states are widely observed in human social systems, but their discussion is often ruled out a priori in quantitative approaches. In this paper, we show how reference to the irreducible mental states and psychological dynamics of ... More

State Transfer instead of Teleportation in Measurement-based Quantum ComputationFeb 26 2004Quantum measurement is universal for quantum computation. The model of quantum computation introduced by Nielsen and further developed by Leung relies on a generalized form of teleportation. In order to simulate any n-qubit unitary transformation with ... More

Towards Minimal Resources of Measurement-based Quantum ComputationApr 02 2007We improve the upper bound on the minimal resources required for measurement-based quantum computation. Minimizing the resources required for this model is a key issue for experimental realization of a quantum computer based on projective measurements. ... More

SSDB spaces and maximal monotonicityDec 31 2009Jun 17 2010In this paper, we develop some of the theory of SSD spaces and SSDB spaces, and deduce some results on maximally monotone multifunctions on a reflexive Banach space.

Nonreflexive Banach SSD spacesOct 25 2008Nov 03 2008In this paper, we unify the theory of SSD spaces, part of the theory of strongly representable multifunctions, and the theory of the equivalence of various classes of maximally monotone multifunctions.

The Bosonic String Measure at Two and Three Loops and Symplectic Transformations of the Volume FormOct 28 1994Oct 29 1994Symplectic modular invariance of the bosonic string partition function has been verified at genus 2 and 3 using the period matrix coordinatization of moduli space. A calculation of the transformation of the holomorphic part of the differential volume ... More

Effectively Closed Infinite-Genus Surfaces and the String CouplingDec 09 2003Dec 10 2003The class of effectively closed infinite-genus surfaces, defining the completion of the domain of string perturbation theory, can be included in the category $O_G$, which is characterized by the vanishing capacity of the ideal boundary. The cardinality ... More

Connections and Generalized Gauge TransformationsFeb 01 1996Mar 11 1996Elimination of the fibre coordinate dependence from the connection form transformation rule for a bundle with a coset manifold standard fibre reduces the structure group. The nonlinear SU(4) action on an $S^7$ bundle is applied to the dimensional reduction ... More

Infinite-genus surfaces and the universal GrassmannianMay 26 1995Mar 29 1996Correlation functions can be calculated on Riemann surfaces using the operator formalism. The state in the Hilbert space of the free field theory on the punctured disc, corresponding to the Riemann surface, is constructed at infinite genus, verifying ... More

Time, Quantum Mechanics, and ProbabilityNov 07 2001A "geometric" intepretation of probability is proposed, modelled on the treatment of tense in 4-dimensional spacetime. It is applied to Everett's approach to quantum mechanics, as formulated in terms of consistent histories. Standard objections to Everett's ... More

Heavy quark jet quenching with collisional plus radiative energy loss and path length fluctuationsJan 22 2007With the QGP opacity computed perturbatively and with the global entropy constraints imposed by the observed $dN_{ch}/dy\approx1000$, radiative energy loss alone cannot account for the observed suppression of single non-photonic electrons. We show that ... More

Optimal static output feedback design through direct searchApr 28 2011Dec 21 2011The aim of this paper and associated presentation is to put forward derivative-free optimization methods for control design. The important element, still ignored at the end of 2011 in systems and control (i.e. this element has apparently never been used ... More

A Geometric Bohr toposFeb 06 2015In this short note, we construct a variant of the Bohr topos of a C*-algebra which takes into account the topology of the algebra in a finer way and such that this construction is stable under pullback along geometric morphisms. This generalizes a construction ... More

Conflict and Computation on Wikipedia: a Finite-State Machine Analysis of Editor InteractionsDec 14 2015Jul 20 2016What is the boundary between a vigorous argument and a breakdown of relations? What drives a group of individuals across it? Taking Wikipedia as a test case, we use a hidden Markov model to approximate the computational structure and social grammar of ... More

Leptonic Decays of CharmSep 23 2015We present results of various searches for leptonic decays of charm mesons performed with the Belle detector. Also discussed are $D^0 \to \gamma\gamma$ decays.

Geometric Bernstein Asymptotics and the Drinfeld-Lafforgue-Vinberg degeneration for arbitrary reductive groupsJul 03 2016We define and study the Drinfeld-Lafforgue-Vinberg compactification of the moduli stack of G-bundles Bun_G for an arbitrary reductive group G; its definition is given in terms of the Vinberg semigroup of G, and is due to Drinfeld (unpublished). Throughout ... More

Chance in the Everett interpretationSep 15 2016The notion of objective probability or chance, as a physical trait of the world, has proved elusive; the identification of chances with actual frequencies does not succeed. An adequate theory of chance should explain not only the connection of chance ... More

Algebraic models of homotopy types and the homotopy hypothesisSep 15 2016We introduce and study a notion of cylinder coherator similar to the notion of Grothendieck coherator which define more flexible notion of weak infinity groupoids. We show that each such cylinder coherator produces a combinatorial semi-model category ... More

Finite Range Decomposition for Gaussian Measures with Improved RegularityMar 22 2016We consider a family of gradient Gaussian vector fields on the torus $(\mathbb{Z}/L^N\mathbb{Z})^d$. Adams, Koteck\'{y} and M\"{u}ller established in [AKM13, arXiv:1202.1158] the existence of a uniform finite range decomposition of the corresponding covariance ... More

On The Capacity Of Noisy ComputationsMar 22 2016This paper presents an analysis of the concept of capacity for noisy com- putations, i.e. functions implemented by unreliable or random devices. An information theoretic model of noisy computation of a perfect function f (measurable function between sequence ... More

Local bounds for $L^p$ norms of Maass forms in the level aspectFeb 03 2015We apply techniques from harmonic analysis to study the $L^p$ norms of Maass forms of varying level on a quaternion division algebra. Our first result gives a candidate for the local bound for the sup norm in terms of the level, which is new when the ... More

Sup norms of Maass forms on semisimple groupsMay 27 2014We prove a power saving over the local bound for the sup norm of a Hecke-Maass form on a class of groups that includes split classical groups and complex groups.

Bounds for multiplicities of automorphic forms of cohomological type on GL_2Feb 18 2010Aug 13 2010We prove various results on the cohomology of arithmetic lattices arising from quaternion algebras over a number field with at least one complex place, including a strong restriction on the allowable weights of cuspidal cohomological automorphic forms ... More

Peres-Horodecki separability criterion for continuous variable systemsSep 14 1999The Peres-Horodecki criterion of positivity under partial transpose is studied in the context of separability of bipartite continuous variable states. The partial transpose operation admits, in the continuous case, a geometric interpretation as mirror ... More

A Short Guide to Anyons and Modular FunctorsOct 17 2016To the working physicist, anyon theory is meant to describe certain quasi-particle excitations occurring in two dimensional topologically ordered systems. A typical calculation using this theory will involve operations such as $\otimes$ to combine anyons, ... More

The twisted Drinfeld double of a finite group via gerbes and finite groupoidsMar 14 2005The twisted Drinfeld double (or quasi-quantum double) of a finite group with a 3-cocycle is identified with a certain twisted groupoid algebra. The groupoid is the loop (or inertia) groupoid of the original group and the twisting is shown geometrically ... More

Comparison of Spreadsheets with other Development Tools (limitations, solutions, workarounds and alternatives)Jan 24 2008The spreadsheet paradigm has some unique risks and challenges that are not present in more traditional development technologies. Many of the recent advances in other branches of software development have bypassed spreadsheets and spreadsheet developers. ... More

A Guide to NIP theoriesAug 20 2012Jul 21 2014This text is an introduction to the study of NIP (or dependent) theories. It is meant to serve two purposes. The first is to present various aspects of NIP theories and give the reader the background material needed to understand almost any paper on the ... More

How accurate is Limber's equation?Sep 06 2006Aug 24 2007The so-called Limber equation is widely used in the literature to relate the projected angular clustering of galaxies to the spatial clustering of galaxies in an approximate way. This paper gives estimates of where the regime of applicability of Limber's ... More

Kondo screening cloud in a double-quantum dot systemFeb 16 2005We analyze the transport properties of two artificial magnetic impurities coupled togethervia a tunable RKKY interaction mediated by conduction electrons of a finite size one dimensional wire. We show that the sign of the RKKY interaction can be controlled ... More

Asymptotic behaviour of iterates of Volterra operators on L^p(0,1)Sep 27 2004We derive asymptotic information on the iterates of a Volterra convolution operator acting on L^p(0,1), subject to a mild smoothness condition on the kernel. In particular, an asymptotically equal sequence of rank 1 operators is obtained, leading to a ... More

The Gradient Flow of the Möbius energy: $\varepsilon$-regularity and consequencesJan 26 2016In this article we study the gradient flow of the M\"obius energy introduced by O'Hara in 1991. We will show a fundamental $\varepsilon$-regularity result that allows us to bound the infinity norm of all derivatives for some time if the energy is small ... More

On the Hausdorff dimension of regular points of inviscid Burgers equation with stable initial dataFeb 09 2007Feb 21 2007Consider an inviscid Burgers equation whose initial data is a Levy a-stable process Z with a > 1. We show that when Z has positive jumps, the Hausdorff dimension of the set of Lagrangian regular points associated with the equation is strictly smaller ... More

The lower tail problem for homogeneous functionals of stable processes with no negative jumpsJan 23 2007Sep 17 2007Let Z be a strictly a-stable real Levy process (a>1) and X be a fluctuating b-homogeneous additive functional of Z. We investigate the asymptotics of the first passage-time of X above 1, and give a general upper bound. When Z has no negative jumps, we ... More

Partial elimination ideals and secant conesJan 20 2010Nov 18 2010For any $k \in \Nat$, we show that the cone of $(k+1)$-secant lines of a closed subscheme $Z \subset \mathbb{P}^n_K$ over an algebraically closed field $K$ running through a closed point $p \in \mathbb{P}^n_K$ is defined by the $k$-th partial elimination ... More

Local results for flows whose speed or height satisfies a bound of the form $\frac c t$Jun 27 2007In this paper we prove local results for solutions to the Ricci flow (heat flow) whose speed (height) is bounded by $\frac c t$ for some time interval $ t \in (0,T)$. These results are contained in chapter 7 of the author's habilitation thesis, University ... More

Ricci flow of almost non-negatively curved three manifoldsDec 04 2006In this paper we study the evolution of almost non-negatively curved (possibly singular) three dimensional metric spaces by Ricci flow. The non-negatively curved metric spaces which we consider arise as limits of smooth Riemannian manifolds (M_i,g_i), ... More

Algebraic families of constant scalar curvature Kähler metricsMar 17 2015We give a new proof of the fact that the condition of a Fano manifold admitting a K\"ahler-Einstein metric is Zariski-open (provided that the automorphism group is discrete). This proof does not use the characterisation involving stability. The arguments ... More

Quantum Logic as Classical LogicJun 13 2014Apr 27 2015We propose a semantic representation of the standard quantum logic QL within a classical, normal modal logic, and this via a lattice-embedding of orthomodular lattices into Boolean algebras with one modal operator. Thus our classical logic is a completion ... More

Logic of Non-Monotonic Interactive Proofs (Formal Theory of Temporary Knowledge Transfer)Aug 09 2012Jan 31 2013We propose a monotonic logic of internalised non-monotonic or instant interactive proofs (LiiP) and reconstruct an existing monotonic logic of internalised monotonic or persistent interactive proofs (LiP) as a minimal conservative extension of LiiP. Instant ... More

Robust MRAC augmentation of flight control laws for center of gravity adaptationApr 07 2016When an aircraft is flying and burning fuel the center of gravity (c.g.) of the aircraft shifts slowly. The c.g. can also be shifted abruptly when e.g. a fighter aircraft releases a weapon. The shift in c.g. is difficult to measure or estimate so the ... More

Conscious observers clarify many worldsAug 03 2009In this brief note I argue that putting conscious observers at the center of the considerations clarifies and strengthens the many-worlds interpretation. The basic assumption, which seems extremely plausible based on our current understanding of the brain ... More

Complete C*-categories and a topos theoretic Green-Julg theoremDec 10 2015We investigate what would be a correct definition of categorical completeness for C*-categories and propose several variants of such a definition that make the category of Hilbert modules over a C*-algebra a free (co)completion. We extend results about ... More

Toposes, quantales and C* algebras in the atomic caseNov 14 2013We start by reviewing the relation between toposes and Grothendieck quantales. We improve results of previous work on this relation by giving both a characterisation of the map from the tensor product of two internal sup-lattices to another sup-lattice ... More

Complex anti-self-dual instantons and Cayley submanifoldsFeb 10 2003Aug 13 2003We describe a glueing construction for a certain self-dual reduction of the Yang-Mills equations in dimension 8.

A variant of continuous logic and applications to fixed point theoryOct 18 2016In aiming to apply to a broader class of examples the Avigad-Iovino "ultraproducts and metastability" approach to obtaining uniformity for convergence of sequences, we construct a variant of continuous logic that in particular is able to handle discontinuous ... More

CMV matrices: Five years afterMar 03 2006CMV matrices are the unitary analog of Jacobi matrices; we review their general theory.

Computing the GIT-fanMay 18 2012Aug 31 2012We present an algorithm to compute the GIT-fan of algebraic torus actions on affine varieties.

Spontaneous Breaking of Rotational Symmetry with Arbitrary Defects and a Rigidity EstimateAug 22 2014Jan 27 2015The goal of this paper is twofold. First we prove a rigidity estimate, which generalises the theorem on geometric rigidity of Friesecke, James and M\"uller to 1-forms with non-vanishing exterior derivative. Second we use this estimate to prove a kind ... More

Rack homology and conjectural Leibniz homologyFeb 07 2014This article presents results being consistent with conjectures of J.-L. Loday about the existence and properties of a Leibniz homology for groups. Introducing L-sets we prove that (pointed) rack homology has properties this conjectural Leibniz homology ... More

An Erlang Implementation of Multiparty Session ActorsAug 11 2016By requiring co-ordination to take place using explicit message passing instead of relying on shared memory, actor-based programming languages have been shown to be effective tools for building reliable and fault-tolerant distributed systems. Although ... More

A spectral sequence in odd Khovanov homology (Eine Spektralsequenz in ungerader Khovanov-Homologie)Nov 09 2011Ozsvath, Rasmussen and Szabo constructed odd Khovanov homology. It is a link invariant which has the same reduction modulo 2 as (even) Khovanov homology. Szabo introduced a spectral sequence with mod 2 coefficients from mod 2 Khovanov homology to another ... More

Singularity of Full Scaling Limits of Planar Nearcritical PercolationJan 22 2013Jul 16 2014We consider full scaling limits of planar nearcritical percolation in the Quad-Crossing-Topology introduced by Schramm and Smirnov. We show that two nearcritical scaling limits with different parameters are singular with respect to each other. The results ... More

Singularity of Nearcritical Percolation Exploration PathsOct 19 2011Apr 09 2014We show that the laws of scaling limits of nearcritical percolation exploration paths with different parameters are singular with respect to each other. This generalises a result of Nolin and Werner, using a similar technique. As a corollary, the singularity ... More

A solvable version of the Baer--Suzuki TheoremFeb 10 2009Suppose that G is a finite group and x in G has prime order p > 3. Then x is contained in the solvable radical of G if (and only if) <x,x^g> is solvable for all g in G. If G is an almost simple group and x in G has prime order p > 3 then this implies ... More

Generalized SART Methods for Tomographic ImagingMar 13 2018Jan 10 2019Nowadays, the field computed tomography (CT) encompasses a large variety of settings, ranging from nanoscale to meter-sized objects imaged by different kinds of radiation in various acquisition modes. This experimental diversity challenges the flexibility ... More

A family of partitions of the set of walks on a directed graphSep 11 2014Nov 17 2014We present a family of partitions of $W_\mathcal{G}$, the set of walks on a directed graph $\mathcal{G}$. Each partition in this family is identified by an integer sequence $K$, which specifies a collection of cycles on $\mathcal{G}$ with a certain well-defined ... More

Infinite primitive directed graphsFeb 01 2006A group $G$ of permutations of a set $\Omega$ is {\em primitive} if it acts transitively on $\Omega$, and the only $G$-invariant equivalence relations on $\Omega$ are the trivial and universal relations. A graph $\Gamma$ is {\em primitive} if its automorphism ... More

Type decomposition in NIP theoriesApr 13 2016May 01 2016We prove that any type in an NIP theory can be decomposed into a stable part (a generically stable partial type) and a distal-like quotient.

Analysis of Galerkin and SDFEM on piecewise equidistant meshes for turning point problems exhibiting an interior layerApr 05 2016We consider singularly perturbed boundary value problems with a simple interior turning point whose solutions exhibit an interior layer. These problems are discretised using higher order finite elements on layer-adapted piecewise equidistant meshes proposed ... More

Analysis of Galerkin and streamline-diffusion FEMs on piecewise equidistant meshes for turning point problems exhibiting an interior layerApr 05 2016Sep 28 2017We consider singularly perturbed boundary value problems with a simple interior turning point whose solutions exhibit an interior layer. These problems are discretised using higher order finite elements on layer-adapted piecewise equidistant meshes proposed ... More

FEM-analysis on graded meshes for turning point problems exhibiting an interior layerMar 15 2016We consider singularly perturbed boundary value problems with a simple interior turning point whose solutions exhibit an interior layer. These problems are discretised using higher order finite elements on layer-adapted graded meshes proposed by Liseikin. ... More

The domination number of plane triangulationsJun 18 2018We introduce a class of plane graphs called weak near-triangulations, and prove that this class is closed under certain graph operations. Then we use the properties of weak near-triangulations to prove that every plane triangulation on $n>6$ vertices ... More

Quasi-ordered RingsJun 14 2017Jul 27 2017A quasi-order is a binary, reflexive and transitive relation. In the Journal of Pure and Applied Algebra 45 (1987), S.M. Fakhruddin introduced the notion of (totally) quasi-ordered fields and showed that each such field is either an ordered field or else ... More

Complex structures on nilpotent Lie algebrasAug 05 1998Dec 13 2000We classify real 6-dimensional nilpotent Lie algebras for which the corresponding Lie group has a left-invariant complex structure, and estimate the dimensions of moduli spaces of such structures.

Regular polygraphs and the Simpson conjectureJul 07 2018We prove Carlos Simpson's "semi-strictification" (or "weak unit") conjecture in the case of infinity-groupoids. More precisely, we introduce two precise versions of the conjecture, the "general" and the "regular" conjecture, involving two different notions ... More

Fine Structure of the Zeros of Orthogonal Polynomials, II. OPUC With Competing Exponential DecayNov 17 2004We present a complete theory of the asymptotics of the zeros of OPUC with Verblunsky coefficients $\alpha_n = \sum_{\ell=1}^L C_\ell b_\ell^n + O((b\Delta)^n)$ where $\Delta <1$ and $\abs{b_\ell} = b<1$.

Orthogonal polynomials on the unit circle: New resultsMay 06 2004We announce numerous new results in the theory of orthogonal polynomials on the unit circle.

The Christoffel-Darboux KernelJun 09 2008A review of the uses of the CD kernel in the spectral theory of orthogonal polynomials, concentrating on recent results.

Relative Zeta Determinants and the Quillen MetricOct 27 1999We compute the relative zeta-function metric on the determinant line bundle for a family of elliptic boundary value problems of Dirac-type. To do this we prove a general formula relating the zeta-determinant to a Fredholm determinant over the boundary ... More

Defending the future: An MSc module in End User Computing Risk ManagementSep 28 2010This paper describes the rationale, curriculum and subject matter of a new MSc module being taught on an MSc Finance and Information Management course at the University of Wales Institute in Cardiff. Academic research on spreadsheet risks now has some ... More

Computing Cup-Products in integral cohomology of Hilbert schemes of points on K3 surfacesOct 30 2014Jan 18 2016We study cup products in integral cohomology of the Hilbert scheme of $n$ points on a K3 surface and present a computer program for this purpose. In particular, we deal with the question, which classes can be represented by products of lower degrees.

Singular cotangent bundle reduction and spin Calogero-Moser systemsNov 03 2004Oct 30 2008We develop a bundle picture for the case that the configuration manifold has only a single isotropy type, and give a formula for the reduced symplectic form in this setting. Furthermore, as an application of this bundle picture we consider Calogero-Moser ... More

On the remote interaction of biological objects with identical genetic structuresJul 03 2002The paper puts forward an unusual prediction that cultivating a clone can curtail the lifespan of the clone donor. Neither the arrangement of this suggested empirical study nor the analyses of the anticipated outcomes rely on the accompanying theoretical ... More

Empirical AUC for evaluating probabilistic forecastsAug 22 2015Scoring functions are used to evaluate and compare partially probabilistic forecasts. We investigate the use of rank-sum functions such as empirical Area Under the Curve (AUC), a widely-used measure of classification performance, as a scoring function ... More

The asymmetric sandwich theoremAug 29 2011Sep 22 2011We discuss the asymmetric sandwich theorem, a generalization of the Hahn-Banach theorem. As applications, we derive various results on the existence of linear functionals that include bivariate, trivariate and quadrivariate generalizations of the Fenchel ... More

Quadrivariate existence theorems and strong representabilitySep 01 2008Feb 22 2011In this paper, we give conditions under which we can compute the conjugate of a convex function on the product of two Frechet spaces defined in terms of another convex function on the product of two (possibly different) Frechet spaces. We use this result ... More

Higher-Derivative Quantum CosmologyNov 06 1999Nov 10 1999The quantum cosmology of a higher-derivative derivative gravity theory arising from the heterotic string effective action is reviewed. A new type of Wheeler-DeWitt equation is obtained when the dilaton is coupled to the quadratic curvature terms. Techniques ... More

A Proof of the Odd Perfect Number ConjectureJan 08 2004May 31 2008It is sufficient to prove that there is an excess of prime factors in the product of repunits with odd prime bases defined by the sum of divisors of the integer $N=(4k+1)^{4m+1}\prod_{i=1}^\ell ~ q_i^{2\alpha_i}$ to establish that there do not exist any ... More

Complementarity and Scientific RationalityDec 24 2004Bohr's interpretation of quantum mechanics has been criticized as incoherent and opportunistic, and based on doubtful philosophical premises. If so Bohr's influence, in the pre-war period of 1927-1939, is the harder to explain, and the acceptance of his ... More

A new approach to inverse spectral theory, I. Fundamental formalismJun 17 1999Nov 01 1999We present a new approach (distinct from Gel'fand-Levitan) to the theorem of Borg-Marchenko that the m-function (equivalently, spectral measure) for a finite interval or half-line Schr\"odinger operator determines the potential. Our approach is an analog ... More

Equilibrium measures and capacities in spectral theoryNov 16 2007This is a comprehensive review of the uses of potential theory in studying the spectral theory of orthogonal polynomials. Much of the article focuses on the Stahl-Totik theory of regular measures, especially the case of OPRL and OPUC. Links are made to ... More

Weak convergence of CD kernels and applicationsJul 17 2007We prove a general result on equality of the weak limits of the zero counting measure, $d\nu_n$, of orthogonal polynomials (defined by a measure $d\mu$) and $\frac{1}{n} K_n(x,x) d\mu(x)$. By combining this with Mate--Nevai and Totik upper bounds on $n\lambda_n(x)$, ... More

The Classical Moment Problem as a Self-Adjoint Finite Difference OperatorJun 08 1999This is a comprehensive exposition of the classical moment problem using methods from the theory of finite difference operators. Among the advantages of this approach is that the Nevanlinna functions appear as elements of a transfer matrix and convergence ... More

Four Fermion Models at Non-Zero DensityJun 22 1998I review the properties of the three-dimensional Gross-Neveu model formulated with non-zero chemical potential and temperature, focussing on results obtained by lattice Monte Carlo simulation.

Log Triviality in the Nambu -- Jona-Lasinio ModelSep 15 1997Results are presented from a Monte Carlo simulation of the Nambu -- Jona-Lasinio model with SU(2)xSU(2) chiral symmetry and N_f=2 flavors of fermion. We show that fits to the equation of state are sensitive to the shape and extent of the assumed scaling ... More