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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

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

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

Semi-Supervised Generation with Cluster-aware Generative ModelsApr 03 2017Deep generative models trained with large amounts of unlabelled data have proven to be powerful within the domain of unsupervised learning. Many real life data sets contain a small amount of labelled data points, that are typically disregarded when training ... 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

Hash Embeddings for Efficient Word RepresentationsSep 12 2017We present hash embeddings, an efficient method for representing words in a continuous vector form. A hash embedding may be seen as an interpolation between a standard word embedding and a word embedding created using a random hash function (the hashing ... 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

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

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

Recurrent Relational NetworksNov 21 2017Nov 29 2018This paper is concerned with learning to solve tasks that require a chain of interdependent steps of relational inference, like answering complex questions about the relationships between objects, or solving puzzles where the smaller elements of a solution ... 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

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

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

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

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

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

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

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

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

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

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

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

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

Bayesian inference for spatio-temporal spike-and-slab priorsSep 15 2015Dec 01 2017In 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 ... 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

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

Interactive Tools and Tasks for the Hebrew BibleMar 14 2016Oct 24 2017This contribution to a special issue on "Computer-aided processing of intertextuality" in ancient texts will illustrate how using digital tools to interact with the Hebrew Bible offers new promising perspectives for visualizing the texts and for performing ... More

C-projective symmetries of submanifolds in quaternionic geometryJan 22 2018The generalized Feix--Kaledin construction shows that c-projective $2n$-manifolds with curvature of type $(1,1)$ are precisely the submanifolds of quaternionic $4n$-manifolds which are fixed points set of a special type of quaternionic $S^1$ action $v$. ... 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

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.

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

The direct limit closure of perfect complexesJan 04 2013Jun 11 2013Every projective module is flat. Conversely, every flat module is a direct limit of finitely generated free modules; this was proved independently by Govorov and Lazard in the 1960s. In this paper we prove an analogous result for complexes of modules, ... 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

Injective Modules under Faithfully Flat Ring ExtensionsJun 30 2014Apr 16 2015Let R be a commutative ring and S be an R-algebra. It is well-known that if N is an injective R-module, then Hom(S,N) is an injective S-module. The converse is not true, not even if R is a commutative noetherian local ring and S is its completion, but ... 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

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 $R$.

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

Pure-minimal chain complexesDec 31 2017Oct 03 2018We introduce a notion of pure-minimality for chain complexes of modules and show that it coincides with (homotopic) minimality in standard settings, while being a more useful notion for complexes of flat modules. As applications, we characterize von Neumann ... More

The Golod property of powers of the maximal ideal of a local ringAug 09 2017Jan 09 2018We identify minimal cases in which a power $m^i\not=0$ of the maximal ideal of a local ring $R$ is not Golod, i.e.\ the quotient ring $R/m^i$ is not Golod. Complementary to a 2014 result by Rossi and \c{S}ega, we prove that for a generic artinian Gorenstein ... 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

A deep learning approach to identify local structures in atomic-resolution transmission electron microscopy imagesFeb 08 2018Feb 09 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

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

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

Vanishing of cohomology over Cohen--Macaulay ringsJun 04 2010Feb 23 2012A 2003 counterexample to a conjecture of Auslander brought attention to a family of rings - colloquially called AC rings - that satisfy a natural condition on vanishing of cohomology. Several results attest to the remarkable homological properties of ... 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

Gorenstein dimension of modules over homomorphismsApr 16 2005Nov 18 2005Given a homomorphism of commutative noetherian rings R --> S and an S-module N, it is proved that the Gorenstein flat dimension of N over R, when finite, may be computed locally over S. When, in addition, the homomorphism is local and N is finitely generated ... More

Local rings of embedding codepth 3: a classification algorithmFeb 17 2014Sep 25 2014Let I be an ideal of a regular local ring Q with residue field k. The length of the minimal free resolution of R=Q/I is called the codepth of R. If it is at most 3, then the resolution carries a structure of a differential graded algebra, and the induced ... More

Local rings of embedding codepth 3. ExamplesSep 19 2012Nov 14 2012A complete local ring of embedding codepth 3 has a minimal free resolution of length 3 over a regular local ring. Such resolutions carry a differential graded algebra structure, based on which one can classify local rings of embedding codepth 3. We give ... More

Simultaneous Object Detection and Semantic SegmentationMay 06 2019Both object detection in and semantic segmentation of camera images are important tasks for automated vehicles. Object detection is necessary so that the planning and behavior modules can reason about other road users. Semantic segmentation provides for ... 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

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

Dynamic shear suppression in quantum phase spaceAug 01 2017Jan 21 2019Classical phase space flow is inviscid. Here we show that in quantum phase space Wigner's probability current J can be effectively viscous. This results in shear suppression in quantum phase space dynamics which enforces Zurek's limit for the minimum ... More

Quantum Kerr oscillators' evolution in phase space: Wigner current, symmetries, shear suppression and special statesNov 07 2018Mar 19 2019The creation of quantum coherences requires a system to be anharmonic. The simplest such continuous 1D quantum system is the Kerr oscillator. It has a number of interesting symmetries we derive. Its quantum dynamics is best studied in phase space, using ... More

Hall--Littlewood functions and the A_2 Rogers--Ramanujan identitiesOct 28 2004Jun 17 2005We prove an identity for Hall--Littlewood symmetric functions labelled by the Lie algebra A_2. Through specialization this yields a simple proof of the A_2 Rogers--Ramanujan identities of Andrews, Schilling and the author.

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.

N-conserving Bogoliubov vacuum of a two component Bose-Einstein condensate: Density fluctuations close to a phase separation conditionJan 10 2007Mar 26 2008Two-component Bose-Einstein condensates are considered within a number conserving version of the Bogoliubov theory. We show that the Bogoliubov vacuum state can be obtained in the particle representation in a simple form. We predict considerable density ... More

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

Revisiting topology optimization with buckling constraintsSep 14 2018Sep 22 2018We review some features of topology optimization with a lower bound on the critical load factor, as computed by linearized buckling analysis. The change of the optimized design, the competition between stiffness and stability requirements and the activation ... More

Operator representations of frames: boundedness, duality, and stabilityApr 28 2017The purpose of the paper is to analyze frames $\{f_k\}_{k\in \mathbf Z}$ having the form $\{T^kf_0\}_{k\in\mathbf Z}$ for some linear operator $T: \mbox{span} \{f_k\}_{k\in \mathbf Z} \to \mbox{span}\{f_k\}_{k\in \mathbf Z}$. A key result characterizes ... 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

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

Charge and orbital order in transition metal oxidesAug 15 2010A short introduction to the complex phenomena encountered in transition metal oxides with either charge or orbital or joint charge-and-orbital order, usually accompanied by magnetic order, is presented. It is argued that all the types of above ordered ... More

The Bailey lemma and Kostka polynomialsJul 03 2002Using the theory of Kostka polynomials, we prove an A_{n-1} version of Bailey's lemma at integral level. Exploiting a new, conjectural expansion for Kostka numbers, this is then generalized to fractional levels, leading to a new expression for admissible ... 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

A Fast Route to Non-Linear Clustering Statistics in Modified Gravity TheoriesMar 25 2014Jun 19 2015We propose a simple and computationally fast method for performing N-body simulations for a large class of modified gravity theories with a screening mechanism such as chameleons, symmetrons and galileons. By combining the linear Klein-Gordon equation ... 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

Nonconforming tetrahedral mixed finite elements for elasticityOct 23 2012May 21 2013This paper presents a nonconforming finite element approximation of the space of symmetric tensors with square integrable divergence, on tetrahedral meshes. Used for stress approximation together with the full space of piecewise linear vector fields for ... More

Gorenstein dimensions of unbounded complexes and faithfully flat change of base (With an appendix by Driss Bennis)Dec 03 2015May 12 2016For a commutative ring R and a faithfully flat R-algebra S we prove, under mild extra assumptions, that an R-module M is Gorenstein flat if and only if the left S-module S\otimes M is Gorenstein flat, and that an R-module N is Gorenstein injective if ... More

Assessing non-linear models for galaxy clustering III: Theoretical accuracy for Stage IV surveysMay 13 2019We provide in depth MCMC comparisons of two different models for the halo redshift space power spectrum, namely a variant of the commonly applied Taruya-Nishimichi-Saito (TNS) model and an effective field theory of large scale structure (EFTofLSS) inspired ... 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

Quasiparticle band structure engineering in van der Waals heterostructures via dielectric screeningMar 09 2017The idea of combining different two-dimensional (2D) crystals in van der Waals heterostructures (vdWHs) has led to a new paradigm for band structure engineering with atomic precision. Due to the weak interlayer couplings, the band structures of the individual ... 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

A Cohen-Macaulay algebra has only finitely many semidualizing modulesApr 20 2007Nov 16 2007We prove the result stated in the title, which answers the equicharacteristic case of a question of Vasconcelos.

Tate (co)homology via pinched complexesMay 11 2011Nov 14 2011For complexes of modules we study two new constructions, which we call the pinched tensor product and the pinched Hom. They provide new methods for computing Tate homology and Tate cohomology, which lead to conceptual proofs of balancedness of Tate (co)homology ... More

Transfer of Gorenstein dimensions along ring homomorphismsJul 04 2008Aug 10 2009A central problem in the theory of Gorenstein dimensions over commutative noetherian rings is to find resolution-free characterizations of the modules for which these invariants are finite. Over local rings, this problem was recently solved for the Gorenstein ... More

Trimming a Gorenstein idealDec 09 2015Jan 19 2017Let Q be a regular local ring of dimension 3. We show how to trim a Gorenstein ideal in Q to obtain an ideal that defines a quotient ring that is close to Gorenstein in the sense that its Koszul homology algebra is a Poincare duality algebra P padded ... 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

Hydrodynamic behavior of non-interacting quantum particles in presence of dephasingJul 18 2018Jul 24 2018In solids and organic materials, environment-induced dephasing of particles and long-lived excitations leads to the crossover in their transport properties between quantum wave-like propagation and classical diffusive motion. In this work, we demonstrate ... 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

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

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.

Structures far below sub-Planck scale in quantum phase-space through superoscillationsApr 26 2017In 2001, Zurek derived the generic minimum scale $a_{Z}$ for the area of structures of Wigner's quantum phase distribution. Here we show by construction, using superoscillatory functions, that the Wigner distribution can locally show regular spotty structures ... More

Gabor frames in $\ell^2(\mathbf Z)$ and linear dependenceOct 23 2017We prove that an overcomplete Gabor frame in $ \ell^2(\mathbf Z)$ by a finitely supported sequence is always linearly dependent. This is a particular case of a general result about linear dependence versus independence for Gabor systems in $\ell^2(\mathbf ... More

An open problem concerning operator representations of framesMay 01 2017Recent research has shown that the properties of overcomplete Gabor frames and frames arising from shift-invariant systems form a precise match with certain conditions that are necessary for a frame in $L^2(\mathbf R)$ to have a representation $\{T^k ... 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

The Vainshtein mechanism beyond the quasi-static approximationMay 13 2015Theories of modified gravity, in both the linear and fully non-linear regime, are often studied under the assumption that the evolution of the new (often scalar) degree of freedom present in the theory is quasi-static. This approximation significantly ... More

The dynamics of the local group as a probe of Dark Energy and Modified GravityDec 21 2016Jan 11 2017In this work we study the dynamics of the Local Group (LG) within the context of cosmological models beyond General Relativity (GR). Using observable kinematic quantities to identify candidate pairs we build up samples of simulated LG-like objects drawing ... More