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Predictive Active Set Selection Methods for Gaussian ProcessesFeb 22 2011Jun 23 2011We propose an active set selection framework for Gaussian process classification for cases when the dataset is large enough to render its inference prohibitive. Our scheme consists of a two step alternating procedure of active set update rules and hyperparameter ... More

A Theory of Solving TAP Equations for Ising Models with General Invariant Random MatricesSep 03 2015Mar 28 2016We consider the problem of solving TAP mean field equations by iteration for Ising model with coupling matrices that are drawn at random from general invariant ensembles. We develop an analysis of iterative algorithms using a dynamical functional approach ... More

Perturbative Corrections for Approximate Inference in Gaussian Latent Variable ModelsJan 12 2013Oct 25 2013Expectation Propagation (EP) provides a framework for approximate inference. When the model under consideration is over a latent Gaussian field, with the approximation being Gaussian, we show how these approximations can systematically be corrected. A ... More

Attend, Copy, Parse - End-to-end information extraction from documentsDec 18 2018Document information extraction tasks performed by humans create data consisting of a PDF or document image input, and extracted string outputs. This end-to-end data is naturally consumed and produced when performing the task because it is valuable in ... More

An Adaptive Resample-Move Algorithm for Estimating Normalizing ConstantsApr 07 2016Aug 15 2016The estimation of normalizing constants is a fundamental step in probabilistic model comparison. Sequential Monte Carlo methods may be used for this task and have the advantage of being inherently parallelizable. However, the standard choice of using ... More

Dynamical Functional Theory for Compressed SensingMay 11 2017We introduce a theoretical approach for designing generalizations of the approximate message passing (AMP) algorithm for compressed sensing which are valid for large observation matrices that are drawn from an invariant random matrix ensemble. By design, ... More

Self-Averaging Expectation PropagationAug 23 2016We investigate the problem of approximate Bayesian inference for a general class of observation models by means of the expectation propagation (EP) framework for large systems under some statistical assumptions. Our approach tries to overcome the numerical ... More

BIVA: A Very Deep Hierarchy of Latent Variables for Generative ModelingFeb 06 2019With the introduction of the variational autoencoder (VAE), probabilistic latent variable models have received renewed attention as powerful generative models. However, their performance in terms of test likelihood and quality of generated samples has ... More

End-to-End Information Extraction without Token-Level SupervisionJul 16 2017Most state-of-the-art information extraction approaches rely on token-level labels to find the areas of interest in text. Unfortunately, these labels are time-consuming and costly to create, and consequently, not available for many real-life IE tasks. ... More

Convolutional LSTM Networks for Subcellular Localization of ProteinsMar 06 2015Machine learning is widely used to analyze biological sequence data. Non-sequential models such as SVMs or feed-forward neural networks are often used although they have no natural way of handling sequences of varying length. Recurrent neural networks ... More

Sparse Linear Identifiable Multivariate ModelingApr 29 2010Jun 23 2011In this paper we consider sparse and identifiable linear latent variable (factor) and linear Bayesian network models for parsimonious analysis of multivariate data. We propose a computationally efficient method for joint parameter and model inference, ... More

Tractable approximations for probabilistic models: The adaptive TAP mean field approachFeb 15 2001We develop an advanced mean field method for approximating averages in probabilistic data models that is based on the TAP approach of disorder physics. In contrast to conventional TAP, where the knowledge of the distribution of couplings between the random ... More

Teaching computers to fold proteinsSep 22 2003A new general algorithm for optimization of potential functions for protein folding is introduced. It is based upon gradient optimization of the thermodynamic stability of native folds of a training set of proteins with known structure. The iterative ... More

Protein Secondary Structure Prediction with Long Short Term Memory NetworksDec 25 2014Jan 04 2015Prediction of protein secondary structure from the amino acid sequence is a classical bioinformatics problem. Common methods use feed forward neural networks or SVMs combined with a sliding window, as these models does not naturally handle sequential ... More

Scalable Bayesian Modelling of Paired SymbolsSep 09 2014Sep 10 2014We present a novel, scalable and Bayesian approach to modelling the occurrence of pairs of symbols (i,j) drawn from a large vocabulary. Observed pairs are assumed to be generated by a simple popularity based selection process followed by censoring using ... More

S-AMP for Non-linear Observation ModelsJan 25 2015Recently we extended Approximate message passing (AMP) algorithm to be able to handle general invariant matrix ensembles. In this contribution we extend our S-AMP approach to non-linear observation models. We obtain generalized AMP (GAMP) algorithm as ... More

S-AMP: Approximate Message Passing for General Matrix EnsemblesMay 12 2014In this work we propose a novel iterative estimation algorithm for linear observation systems called S-AMP whose fixed points are the stationary points of the exact Gibbs free energy under a set of (first- and second-) moment consistency constraints in ... More

Deep Belief Nets for Topic ModelingJan 18 2015Applying traditional collaborative filtering to digital publishing is challenging because user data is very sparse due to the high volume of documents relative to the number of users. Content based approaches, on the other hand, is attractive because ... More

CloudScan - A configuration-free invoice analysis system using recurrent neural networksAug 24 2017We present CloudScan; an invoice analysis system that requires zero configuration or upfront annotation. In contrast to previous work, CloudScan does not rely on templates of invoice layout, instead it learns a single global model of invoices that naturally ... More

Sequential Neural Models with Stochastic LayersMay 24 2016How can we efficiently propagate uncertainty in a latent state representation with recurrent neural networks? This paper introduces stochastic recurrent neural networks which glue a deterministic recurrent neural network and a state space model together ... More

Bayesian leave-one-out cross-validation approximations for Gaussian latent variable modelsDec 23 2014May 23 2016The future predictive performance of a Bayesian model can be estimated using Bayesian cross-validation. In this article, we consider Gaussian latent variable models where the integration over the latent values is approximated using the Laplace method ... More

Spatio-temporal Spike and Slab Priors for Multiple Measurement Vector ProblemsAug 19 2015We are interested in solving the multiple measurement vector (MMV) problem for instances, where the underlying sparsity pattern exhibit spatio-temporal structure motivated by the electroencephalogram (EEG) source localization problem. We propose a probabilistic ... More

Auxiliary Deep Generative ModelsFeb 17 2016Jun 16 2016Deep generative models parameterized by neural networks have recently achieved state-of-the-art performance in unsupervised and semi-supervised learning. We extend deep generative models with auxiliary variables which improves the variational approximation. ... More

Accurate switching intensities and length scales in quasi-phase-matched materialsJan 30 2001We consider unseeded Type I second-harmonic generation in quasi-phase-matched (QPM) quadratic nonlinear materials and derive an accurate analytical expression for the evolution of the average intensity. The intensity-dependent nonlinear phase mismatch ... More

Sequential Neural Models with Stochastic LayersMay 24 2016Nov 13 2016How can we efficiently propagate uncertainty in a latent state representation with recurrent neural networks? This paper introduces stochastic recurrent neural networks which glue a deterministic recurrent neural network and a state space model together ... More

Machine learning methods for nanolaser characterizationNov 10 2016Nanocavity lasers, which are an integral part of an on-chip integrated photonic network, are setting stringent requirements on the sensitivity of the techniques used to characterize the laser performance. Current characterization tools cannot provide ... More

Recurrent Spatial Transformer NetworksSep 17 2015We integrate the recently proposed spatial transformer network (SPN) [Jaderberg et. al 2015] into a recurrent neural network (RNN) to form an RNN-SPN model. We use the RNN-SPN to classify digits in cluttered MNIST sequences. The proposed model achieves ... More

Bayesian inference for spatio-temporal spike and slab priorsSep 15 2015Sep 18 2015In this work we address the problem of solving a series of underdetermined linear inverse problems subject to a sparsity constraint. We generalize the spike and slab prior distribution to encode a priori correlation of the support of the solution in both ... More

A Disentangled Recognition and Nonlinear Dynamics Model for Unsupervised LearningOct 16 2017Oct 30 2017This paper takes a step towards temporal reasoning in a dynamically changing video, not in the pixel space that constitutes its frames, but in a latent space that describes the non-linear dynamics of the objects in its world. We introduce the Kalman variational ... More

Menger 1934 revisitedOct 07 2011Karl Menger's 1934 paper on the St. Petersburg paradox contains mathematical errors that invalidate his conclusion that unbounded utility functions, specifically Bernoulli's logarithmic utility, fail to resolve modified versions of the St. Petersburg ... More

Six problems in frame theoryAug 23 2013We discuss various problems in frame theory that have been open for some years. A short discussion of frame theory is also provided, but it only contains the information that is necessary in order to understand the open problems and their role.

Galaxy cluster strong lensing: image deflections from density fluctuations along the line of sightOct 24 2011Dec 08 2011A standard method to study the mass distribution in galaxy clusters is through strong lensing of background galaxies in which the positions of multiple images of the same source constrain the surface mass distribution of the cluster. However, current ... More

Optimal leverage from non-ergodicityFeb 17 2009Aug 09 2010In modern portfolio theory, the balancing of expected returns on investments against uncertainties in those returns is aided by the use of utility functions. The Kelly criterion offers another approach, rooted in information theory, that always implies ... More

Interactive Tools and Tasks for the Hebrew BibleMar 14 2016Ancient texts can support intertextuality in different ways through digital tools for databases and for tasks that scholars and students do, when they interac twith the texts in new ways. This contribution explores how the corpus of the Hebrew Bible created ... More

Reconstruction from Representations: Jacobi via CohomologyNov 15 2016May 16 2017A subalgebra of a Lie algebra $\mathfrak{h}\subset\mathfrak{g}$ determines $\mathfrak{h}$-representation $\rho$ on $\mathfrak{m}=\mathfrak{g}/\mathfrak{h}$. In this note we discuss how to reconstruct $\mathfrak{g}$ from $(\mathfrak{h},\mathfrak{m},\rho)$. ... More

Debian Astro: An open computing platform for astronomyNov 22 2016Debian Astro is a Debian Pure Blend that aims to distribute the available astronomy software within the Debian operating system. Using Debian as the foundation has unique advantages for end-users and developers such as an easy installation and upgrading ... More

Measurement of the dark matter velocity anisotropy profile in galaxy clustersOct 20 2008Dark matter particles form halos that contribute the major part of the mass of galaxy clusters. The formation of these cosmological structures have been investigated both observationally and in numerical simulations, which have confirmed the existence ... More

Non-degenerate Para-Complex Structures in 6D with Large Symmetry GroupsNov 17 2016For an almost product structure $J$ on a manifold $M$ of dimension $6$ with non-degenerate Nijenhuis tensor $N_J$, we show that the automorphism group $G=Aut(M,J)$ has dimension at most 14. In the case of equality $G$ is the exceptional Lie group $G_2^*$. ... More

Submaximally Symmetric Quaternion Hermitian StructuresDec 28 2018We consider and resolve the gap problem for almost quaternion-Hermitian structures, i.e. we determine the maximal and submaximal symmetry dimensions, both for Lie algebras and Lie groups, in the class of almost quaternion-Hermitian manifolds. We classify ... More

A deep learning approach to identify local structures in atomic-resolution transmission electron microscopy imagesFeb 08 2018Recording atomic-resolution transmission electron microscopy (TEM) images is becoming increasingly routine. A new bottleneck is then analyzing this information, which often involves time-consuming manual structural identification. We have developed a ... More

Neural Machine Translation with Characters and Hierarchical EncodingOct 20 2016Most existing Neural Machine Translation models use groups of characters or whole words as their unit of input and output. We propose a model with a hierarchical char2word encoder, that takes individual characters both as input and output. We first argue ... More

Autoencoding beyond pixels using a learned similarity metricDec 31 2015Feb 10 2016We present an autoencoder that leverages learned representations to better measure similarities in data space. By combining a variational autoencoder with a generative adversarial network we can use learned feature representations in the GAN discriminator ... More

Local coderivatives and approximation of Hodge Laplace problemsOct 25 2016Sep 23 2017The standard mixed finite element approximations of Hodge Laplace problems associated with the de Rham complex are based on proper discrete subcomplexes. As a consequence, the exterior derivatives, which are local operators, are computed exactly. However, ... More

Ladder Variational AutoencodersFeb 06 2016May 27 2016Variational Autoencoders are powerful models for unsupervised learning. However deep models with several layers of dependent stochastic variables are difficult to train which limits the improvements obtained using these highly expressive models. We propose ... More

Ascent Properties of Auslander CategoriesSep 23 2005Feb 16 2006Let R be a homomorphic image of a Gorenstein local ring. Recent work has shown that there is a bridge between Auslander categories and modules of finite Gorenstein homological dimensions over R. We use Gorenstein dimensions to prove new results about ... More

Totally acyclic complexes and locally Gorenstein ringsFeb 09 2017A commutative noetherian ring with a dualizing complex is Gorenstein if and only if every acyclic complex of injective modules is totally acyclic. We extend this characterization, which is due to Iyengar and Krause, to arbitrary commutative noetherian ... More

A Bass equality for Gorenstein injective dimension of modules finite over homomorphismsFeb 16 2019Let $R \to S$ be a local ring homomorphism and $N$ a finitely generated $S$-module. We prove that if the Gorenstein injective dimension of $N$ over $R$ is finite, then it equals the depth of $R$.

The bubble transform: A new tool for analysis of finite element methodsDec 05 2013The purpose of this paper is to discuss the construction of a linear operator, referred to as the bubble transform, which maps scalar functions defined on a bounded domain $\Omega$ in $\mathbb{R}^n$ into a collection of functions with local support. In ... More

Acyclicity over local rings with radical cube zeroMay 22 2006Nov 23 2006This paper studies infinite acyclic complexes of finitely generated free modules over a commutative noetherian local ring $(R,m)$ with $m^3=0$. Conclusive results are obtained on the growth of the ranks of the modules in acyclic complexes, and new sufficient ... More

Ergodicity breaking in geometric Brownian motionSep 20 2012Mar 14 2013Geometric Brownian motion (GBM) is a model for systems as varied as financial instruments and populations. The statistical properties of GBM are complicated by non-ergodicity, which can lead to ensemble averages exhibiting exponential growth while any ... More

The evolutionary advantage of cooperationJun 10 2015The present study asks how cooperation and consequently structure can emerge in many different evolutionary contexts. Cooperation, here, is a persistent behavioural pattern of individual entities pooling and sharing resources. Examples are: individual ... More

Solvable lattice models labelled by Dynkin diagramsJan 08 1993An equivalence between generalised restricted solid-on-solid (RSOS) models, associated with sets of graphs, and multi-colour loop models is established. As an application we consider solvable loop models and in this way obtain new solvable families of ... More

The sl_3 Selberg integralJan 27 2009Jun 17 2010Using an extension of the well-known evaluation symmetry, a new Cauchy-type identity for Macdonald polynomials is proved. After taking the classical limit this yields a new sl_3 generalisation of the famous Selberg integral. Closely related results obtained ... More

Neutron to proton mass difference, parton distribution functions and baryon resonances from dynamics on the Lie group u(3)Sep 22 2011Jun 25 2012We present a hamiltonian structure on the Lie group u(3) to describe the baryon spectrum. The ground state is identified with the proton. From this single fit we calculate approximately the relative neutron to proton mass shift to within half a percentage ... More

On the Sidon Constant for Dirichlet PolynomialsJun 03 2013Dec 10 2013We estimate the error term in the asymptotic formula of the Sidon constant for (ordinary) Dirichlet polynomials by providing explicit lower and upper bounds. The lower bound is already implicitly known, but we supply the necessary computations to make ... More

Remarks on the paper "Skew Pieri rules for Hall-Littlewood functions" by Konvalinka and LauveAug 20 2012In a recent paper Konvalinka and Lauve proved several skew Pieri rules for Hall-Littlewood polynomials. In this note we show that q-analogues of these rules are encoded in a q-binomial theorem for Macdonald polynomials due to Lascoux and the author.

Self-organized Criticality and Absorbing States: Lessons from the Ising ModelNov 29 2004We investigate a suggested path to self-organized criticality. Originally, this path was devised to "generate criticality" in systems displaying an absorbing-state phase transition, but closer examination of the mechanism reveals that it can be used for ... More

On variational eigenvalue approximation of semidefinite operatorsMay 12 2010Oct 26 2011Eigenvalue problems for semidefinite operators with infinite dimensional kernels appear for instance in electromagnetics. Variational discretizations with edge elements have long been analyzed in terms of a discrete compactness property. As an alternative, ... More

Local bounded cochain projectionNov 26 2012We construct projections from the space of differential k-forms which belong to L2 and whose exterior derivative also belongs to L2, to finite dimensional subspaces of piecewise polynomial differential forms defined on a simplicial mesh. These projections ... More

Algebras that satisfy Auslander's condition on vanishing of cohomologyJan 02 2008Jan 21 2009Auslander conjectured that every Artin algebra satisfies a certain condition on vanishing of cohomology of finitely generated modules. The failure of this conjecture - by a 2003 counterexample due to Jorgensen and Sega - motivates the consideration of ... More

Comment on 'Comparative study of beta-decay data for eight nuclides measured at the Physikalisch-Technische Bundesanstalt' [Astropart. Phys., 50, 47-58]Aug 22 2014We would like to comment on a recent paper by Sturrock et al. [1] in which the authors analyze decay data acquired by an ionization chamber in our institute. They interpret the variations in the data as solar-driven changes in the decay rates of the radionuclides ... More

Lensing by Groups of GalaxiesSep 17 1999Sep 18 1999A large fraction of known galaxy-lens systems require a component of external shear to explain the observed image geometries. In most cases, this shear can be attributed to a nearby group of galaxies. We discuss how the dark-matter mass distribution of ... More

Highly sensitive refractometer with photonic crystal fiber long-period gratingNov 19 2007We present highly sensitive refractometers based on a long-period grating in a large mode area PCF. The maximum sensitivity is 1500 nm/RIU at a refractive index of 1.33, the highest reported for any fiber grating. The minimal detectable index change is ... More

Quantum speed limits and optimal Hamiltonians for driven systems in mixed statesDec 21 2013Apr 28 2014Inequalities of Mandelstam-Tamm and Margolus-Levitin type provide lower bounds on the time it takes for a quantum system to evolve from one state into another. Knowledge of such bounds, called quantum speed limits, is of utmost importance in virtually ... More

Summation formulae for elliptic hypergeometric seriesSep 15 2003Several new identities for elliptic hypergeometric series are proved. Remarkably, some of these are elliptic analogues of identities for basic hypergeometric series that are balanced but not very-well-poised.

Ramanujan's {_1ψ_1} summationJun 12 2012Nov 05 2012This paper gives a short but reasonably comprehensive review of Ramanujan's {_1\psi_1} summation and its generalisations. It covers the history of Ramanujan's summation, simple applications to sums of squares and orthogonal polynomials, non-commutative ... More

Proof of the Flohr-Grabow-Koehn conjectures for characters of logarithmic conformal field theoryApr 24 2007In a recent paper Flohr, Grabow and Koehn conjectured that the characters of the logarithmic conformal field theory c_{k,1}, of central charge c=1-6(k-1)^2/k, admit fermionic representations labelled by the Lie algebra D_k. In this note we provide a simple ... More

Extensions of the well-poised and elliptic well-poised Bailey lemmaSep 15 2003We establish a number of extensions of the well-poised Bailey lemma and elliptic well-poised Bailey lemma. As application we prove some new transformation formulae for basic and elliptic hypergeometric series, and embed some recent identities of Andrews, ... More

The generalized Borwein conjecture. I. The Burge transformNov 27 2000Given an arbitrary ordered pair of coprime integers (a,b) we obtain a pair of identities of the Rogers--Ramanujan type. These identities have the same product side as the (first) Andrews--Gordon identity for modulus 2ab\pm 1, but an altogether different ... More

Rogers-Szego polynomials and Hall-Littlewood symmetric functionsAug 22 2007We use Rogers-Szego polynomials to unify some well-known identities for Hall-Littlewood symmetric functions due to Macdonald and Kawanaka.

A Selberg integral for the Lie algebra A_nAug 08 2007A new q-binomial theorem for Macdonald polynomials is employed to prove an A_n analogue of the celebrated Selberg integral. This confirms the g=A_n case of a conjecture by Mukhin and Varchenko concerning the existence of a Selberg integral for every simple ... More

Refined q-trinomial coefficients and character identitiesMay 12 2000A refinement of the q-trinomial coefficients is introduced, which has a very powerful iterative property. This ``T-invariance'' is applied to derive new Virasoro character identities related to the exceptional simply-laced Lie algebras E_6,E_7 and E_8. ... More

Local-field study of phase conjugation in metallic quantum wells with probe fields of both propagating and evanescent characterOct 10 1999The phase conjugated response from nonmagnetic multi-level metallic quantum wells is analyzed and an essentially complete analytical solution is presented and discussed. The description is based on a semi-classical local-field theory for degenerate four-wave ... More

Disproof of solar influence on the decay rates of 90Sr/90YJul 09 2014A custom-built liquid scintillation counter was used for long-term measurements of 90Sr/90Y sources. The detector system is equipped with an automated sample changer and three photomultiplier tubes, which makes the application of the triple-to-double ... More

A Higgs mass at 125 GeV calculated from neutron to proton decay in a u(3) Lie group Hamiltonian frameworkFeb 07 2013May 01 2014We investigate the neutron to proton decay via a Higgs mechanism in the framework of a reinterpreted Kogut-Susskind Hamiltonian on the Lie group u(3). We calculate expressions for a scalar Higgs mass, an electroweak energy scale, and vector gauge boson ... More

Sensitivity of photonic crystal fiber grating sensors: biosensing, refractive index, strain, and temperature sensingAug 31 2007We study the sensitivity of fiber grating sensors in the applications of strain, temperature, internal label-free biosensing, and internal refractive index sensing. It is shown that optical dispersion plays a central role in determining the sensitivity, ... More

50 Years of Bailey's lemmaOct 12 2009Oct 14 2009This is a paper published in 2001 based on a talk given in 1999 celebrating the 50th anniversary of W. N. Bailey's influential q-series paper "Identities of the Rogers-Ramanujan type". In no more than 13 pages I give a brief but reasonably complete overview ... More

On the generalised Selberg integral of Richards and ZhengAug 22 2007In a recent paper Richards and Zheng compute the determinant of a matrix whose entries are given by beta-type integrals, thereby generalising an earlier result by Dixon and Varchenko. They then use their result to obtain a generalisation of the famous ... More

Tuning- and order parameter in the SOC ensembleDec 11 2009The one-dimensional Oslo model is studied under self-organized criticality (SOC) conditions and under absorbing state (AS) conditions. While the activity signals the phase transition under AS conditions by a sudden increase, this is not the case under ... More

Solitons in coupled atomic-molecular Bose-Einstein condensates in a trapMay 16 2006Mar 26 2008We consider coupled atomic-molecular Bose-Einstein condensate system in a quasi-one-dimensional trap. In the vicinity of a Feshbach resonance the system can reveal soliton-like behavior. We analyze bright soliton solutions for the system in the trap and ... More

Bisymmetric functions, Macdonald polynomials and sl_3 basic hypergeometric seriesNov 14 2005Jul 24 2007A new type of sl_3 basic hypergeometric series based on Macdonald polynomials is introduced. Besides a pair of Macdonald polynomials attached to two different sets of variables, a key-ingredient in the sl_3 basic hypergeometric series is a bisymmetric ... More

On the electron to proton mass ratio and the proton structureMar 19 2013Apr 22 2014We derive an expression for the electron to nucleon mass ratio from a reinterpreted lattice gauge theory Hamiltonian to describe interior baryon dynamics. We use the classical electron radius as our fundamental length scale. Based on expansions on trigonometric ... More

Dimension of graphoids of rational vector-functionsAug 10 2011Let $F$ be a countable family of rational functions of two variables with real coefficients. Each rational function $f\in F$ can be thought as a continuous function $f:dom(f)\to\bar R$ taking values in the projective line $\bar R=R\cup\{\infty\}$ and ... More

Testing for simultaneous jumps in case of asynchronous observationsJun 23 2016This paper proposes a novel test for simultaneous jumps in a bivariate It\^o semimartingale when observation times are asynchronous and irregular. Inference is built on a realized correlation coefficient for the jumps of the two processes which is estimated ... More

Reply to "Comment on `Self-organized Criticality and Absorbing States: Lessons from the Ising Model'"Apr 04 2008In [Braz. J. Phys. 30, 27 (2000)] Dickman et al. suggested that self-organized criticality can be produced by coupling the activity of an absorbing state model to a dissipation mechanism and adding an external drive. We analyzed the proposed mechanism ... More

Growth in the minimal injective resolution of a local ringDec 26 2008Jul 06 2009Let R be a commutative noetherian local ring with residue field k and assume that it is not Gorenstein. In the minimal injective resolution of R, the injective envelope E of the residue field appears as a summand in every degree starting from the depth ... More

Homotopy categories of totally acyclic complexes with applications to the flat-cotorsion theoryDec 11 2018We introduce a notion of total acyclicity associated to a subcategory of an abelian category and consider the Gorenstein objects they define. These Gorenstein objects form a Frobenius category, whose induced stable category is equivalent to the homotopy ... More

Solitons in nonlocal nonlinear media: exact resultsJun 19 2000We investigate the propagation of one-dimensional bright and dark spatial solitons in a nonlocal Kerr-like media, in which the nonlocality is of general form. We find an exact analytical solution to the nonlinear propagation equation in the case of weak ... More

Rational insurance with linear utility and perfect informationJul 16 2015We present a mathematical solution to the insurance puzzle. Our solution only uses time-average growth rates and makes no reference to risk preferences. The insurance puzzle is this: according to the expectation value of wealth, buying insurance is only ... More

Optimal strategies for fighting persistent bugsDec 01 2005Jul 12 2010Some microbial organisms are known to randomly slip into and out of hibernation, irrespective of environmental conditions [1]. In a (genetically) uniform population a typically very small subpopulation becomes metabolically inactive whereas the majority ... More

Partial theta functions. I. Beyond the lost notebookMay 01 2001It is shown how many of the partial theta function identities in Ramanujan's lost notebook can be generalized to infinite families of such identities. Key in our construction is the Bailey lemma and a new generalization of the Jacobi triple product identity. ... More

q-Hypergeometric proofs of polynomial analogues of the triple product identity, Lebesgue's identity and Euler's pentagonal number theoremMar 22 2002We present alternative, q-hypergeometric proofs of some polynomial analogues of classical q-series identities recently discovered by Alladi and Berkovich, and Berkovich and Garvan.

The generalized Borwein conjecture. II. Refined q-trinomial coefficientsOct 29 2001Transformation formulas for four-parameter refinements of the q-trinomial coefficients are proven. The iterative nature of these transformations allows for the easy derivation of several infinite series of q-trinomial identities, and can be applied to ... More

Zeros of functions in Bergman-type Hilbert spaces of Dirichlet SeriesFeb 18 2014Jun 24 2014For a real number $\alpha$ the Hilbert spaces $\mathscr{D}_\alpha$ consists of those Dirichlet series $\sum_{n=1}^\infty a_n/n^s$ for which $\sum_{n=1}^\infty |a_n|^2/[d(n)]^\alpha < \infty$, where $d(n)$ denotes the number of divisors of $n$. We extend ... More

The kinematical structure of gravitationally lensed arcsNov 07 2005In this paper the expected properties of the velocity fields of strongly lensed arcs behind galaxy clusters are investigated. The velocity profile along typical lensed arcs is determined by ray tracing light rays from a model source galaxy through parametric ... More

The A_{2n}^{(2)} Rogers-Ramanujan identitiesSep 20 2013Nov 05 2013The famous Rogers-Ramanujan and Andrews--Gordon identities are embedded in a doubly-infinite family of Rogers-Ramanujan-type identities labelled by positive integers m and n. For fixed m and n the product side corresponds to a specialised character of ... More

Laws of large numbers for Hayashi-Yoshida-type functionalsMar 15 2018In high-frequency statistics and econometrics sums of functionals of increments of stochastic processes are commonly used and statistical inference is based on the asymptotic behaviour of these sums as the mesh of the observation times tends to zero. ... More

Building modules from the singular locusSep 28 2012Nov 19 2014A finitely generated module over a commutative noetherian ring of finite Krull dimension can be built from the prime ideals in the singular locus by iteration of three procedures: taking extensions, direct summands, and cosyzygies. In 2003 Schoutens gave ... More

Descent via Koszul extensionsDec 12 2006Mar 01 2008Let R be a commutative noetherian local ring with completion R^. We apply differential graded (DG) algebra techniques to study descent of modules and complexes from R^ to R' where R' is either the henselization of R or a pointed \'etale neighborhood of ... More