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Tropical complexesAug 17 2013Jun 08 2015We introduce tropical complexes, which are Delta-complexes together with additional numerical data. On a tropical complex, we define divisors and linear equivalence between divisors, analogous to the notions for algebraic varieties, and generalizing previous ... More

Excluded homeomorphism types for dual complexes of surfacesJun 15 2015We study an obstruction to prescribing the dual complex of a strict semistable degeneration of an algebraic surface. In particular, we show that if $\Delta$ is a complex homeomorphic to a 2-dimensional manifold with negative Euler characteristic, then ... More

Colored Eulerian Polynomials and the Colored PermutohedronMay 28 2016This paper introduces a colored generalization of the Eulerian polynomials, denoted the $\alpha$-colored Eulerian polynomials. We first compute these polynomials by taking the $h$-vector of the $\alpha$-colored permutohedron, a colored analog of the permutohedron ... More

unWISE: unblurred coadds of the WISE imagingMay 01 2014The Wide-Field Infrared Survey Explorer (WISE; Wright et al. 2010) satellite observed the full sky in four mid-infrared bands in the 2.8 to 28 micron range. The primary mission was completed in 2010. The WISE team have done a superb job of producing a ... More

A Reconstruction Procedure for Thermoacoustic Tomography in the Case of Limited Boundary DataMay 18 2009We derive an explicit method for reconstructing singularities of the initial data in a thermoacoustic tomography problem, in the case of variable sound speed and limited boundary data. In order to obtain this explicit formula we assume the metric induced ... More

A specialization inequality for tropical complexesNov 02 2015Aug 10 2018We prove a specialization inequality relating the dimension of the complete linear series on a variety to the tropical complex of a regular semistable degeneration. Our result extends Baker's specialization inequality to arbitrary dimension.

Tropical complexesAug 17 2013Jun 14 2018We introduce tropical complexes, as an enrichment of the dual complex of a degeneration with additional data from non-transverse intersection numbers. We define cycles, divisors, and linear equivalence on tropical complexes, analogous both to the corresponding ... More

Non-standard Symplectic Structures via Symplectic CohomologyNov 29 2014We examine how symplectic cohomology may be used as an invariant on symplectic structures, and investigate the non-uniqueness of these structures on Liouville domains, a field which has seen much development in the past decade. Notably, we prove the existence ... More

Connectivity of tropicalizationsApr 30 2012We show that the tropicalization of an irreducible variety over a complete or algebraically closed valued field is connected through codimension 1, giving an affirmative answer in all characteristics to a question posed by Einsiedler, Lind, and Thomas ... More

Causal Inference through the Method of Direct EstimationMar 16 2017Apr 01 2017The intersection of causal inference and machine learning is a rapidly advancing field. We propose a new approach, the method of direct estimation, that draws on both traditions in order to obtain nonparametric estimates of treatment effects. The approach ... More

Stabilizing inverse problems by internal data. II. Non-local internal data and generic linearized uniquenessJul 03 2014Nov 03 2014In the previous paper "Stabilizing Inverse Problems by Internal Data", the authors introduced a simple procedure that allows one to detect whether and explain why internal information arising in several novel coupled physics (hybrid) imaging modalities ... More

The Number of Eigenvalues of a TensorApr 28 2010May 14 2010Eigenvectors of tensors, as studied recently in numerical multilinear algebra, correspond to fixed points of self-maps of a projective space. We determine the number of eigenvectors and eigenvalues of a generic tensor, and we show that the number of normalized ... More

Open Gromov-Witten Theory and the Crepant Resolution ConjectureFeb 03 2011We compute open GW invariants for $\mathcal{K}_{\mathbb{P}^1}\oplus\mathcal{O}_{\mathbb{P}^1}$, open orbifold GW invariants for $[\C^3/\Z_2]$, formulate an open crepant resolution conjecture and verify it for this pair. We show that open invariants can ... More

Sigma Models and Phase Transitions for Complete IntersectionsNov 06 2015We study a one-parameter family of gauged linear sigma models (GLSMs) naturally associated to a complete intersection in weighted projective space. In the positive phase of the family we recover Gromov-Witten theory of the complete intersection, while ... More

Limit Points Badly Approximable by HoroballsJan 21 2012Apr 11 2012For a proper, geodesic, Gromov hyperbolic metric space X, a discrete subgroup of isometries \Gamma whose limit set is uniformly perfect, and a disjoint collection of horoballs {H_j}, we show that the set of limit points badly approximable by {H_j} is ... More

Explicit Matrices with the Restricted Isometry Property: Breaking the Square-Root BottleneckMar 13 2014Matrices with the restricted isometry property (RIP) are of particular interest in compressed sensing. To date, the best known RIP matrices are constructed using random processes, while explicit constructions are notorious for performing at the "square-root ... More

Three notions of tropical rank for symmetric matricesDec 08 2009We introduce and study three different notions of tropical rank for symmetric and dissimilarity matrices in terms of minimal decompositions into rank 1 symmetric matrices, star tree matrices, and tree matrices. Our results provide a close study of the ... More

The X-shaped Bulge of the Milky Way revealed by WISEFeb 29 2016The Milky Way bulge has a boxy/peanut morphology and an X-shaped structure. This X-shape has been revealed by the `split in the red clump' from star counts along the line of sight toward the bulge, measured from photometric surveys. This boxy, X-shaped ... More

Computer Generated Images for Quadratic Rational Maps with a Periodic Critical PointSep 17 2010We describe an algorithm for distinguishing hyperbolic components in the parameter space of quadratic rational maps with a periodic critical point. We then illustrate computer images of the hyperbolic components of the parameter spaces V1 - V4, which ... More

Random Polygon to Ellipse: A GeneralizationJun 26 2016This paper generalizes the result of Elmachtoub et al to any weighted barycenter, where a transformation is considered which takes an arbitrary point of division $\xi \in (0,1)$ of the segments of a polygon with $n$ vertices. We then consider connecting ... More

Intrinsic metrics on graphs: A surveyJul 28 2014Mar 24 2015A few years ago various disparities for Laplacians on graphs and manifolds were discovered. The corresponding results are mostly related to volume growth in the context of unbounded geometry. Indeed, these disparities can now be resolved by using so called ... More

On the spectral theory of operators on treesJan 15 2011We study a class of rooted trees with a substitution type structure. These trees are not necessarily regular, but exhibit a lot of symmetries. We consider nearest neighbor operators which reflect the symmetries of the trees. The spectrum of such operators ... More

DATR Theories and DATR ModelsMay 02 1995Evans and Gazdar introduced DATR as a simple, non-monotonic language for representing natural language lexicons. Although a number of implementations of DATR exist, the full language has until now lacked an explicit, declarative semantics. This paper ... More

Gauge-invariant two-point correlator of energy density in deconfining SU(2) Yang-Mills thermodynamicsJan 25 2008Dec 15 2008The thesis is considering aspects of SU(2) Yang-Mills thermodynamics in its deconfining high-temperature phase. We calculate the two-point correlation function of the energy density of the photon in a thermalized gas, at first in the conventional U(1) ... More

Rare events, exponential hitting times and extremal indices via spectral perturbationFeb 17 2012We discuss how an eigenvalue perturbation formula for transfer operators of dynamical systems is related to exponential hitting time distributions and extreme value theory for processes generated by chaotic dynamical systems. We also list a number of ... More

On triangulated orbit categoriesMar 13 2005Dec 05 2005We show that the category of orbits of the bounded derived category of a hereditary category under a well-behaved autoequivalence is canonically triangulated. This answers a question by A. Buan, R. Marsh and I. Reiten which appeared in their study with ... More

Tautness for sets of multiples and applications to $\mathcal B$-free dynamicsFeb 22 2018For any set $\mathcal B\subseteq\mathbb N=\{1,2,\dots\}$ one can define its \emph{set of multiples} $\mathcal M_{\mathcal B}:=\bigcup_{b\in\mathcal B}b\mathbb Z$ and the set of \emph{$\mathcal B$-free numbers} $\mathcal F_{\mathcal B}:=\mathbb Z\setminus\mathcal ... More

Erratum to "Deformed Calabi-Yau completions"Sep 02 2018We correct an error and some inaccuracies that occurred in "Deformed Calabi-Yau completions''. The most important point is that, as pointed out by W. K. Yeung, to show that the deformed Calabi-Yau completion has the Calabi-Yau property, one needs to assume ... More

A remark on a theorem by C. AmiotJun 02 2018C. Amiot has classified the connected triangulated k-categories with finitely many isoclasses of indecomposables satisfying suitable hypotheses. We remark that her proof shows that these triangulated categories are determined by their underlying k-linear ... More

Ricci iterations on Kahler classesSep 10 2007Sep 15 2007In this paper we consider the dynamical system involved by the Ricci operator on the space of K\"ahler metrics. A. Nadel has defined an iteration scheme given by the Ricci operator for Fano manifold and asked whether it has some nontrivial periodic points. ... More

A-infinity algebras, modules and functor categoriesOct 24 2005Feb 12 2006In this survey, we first present basic facts on A-infinity algebras and modules including their use in describing triangulated categories. Then we describe the Quillen model approach to A-infinity structures following K. Lefevre's thesis. Finally, starting ... More

Viscosity Solutions of Path-dependent Integro-differential EquationsDec 29 2014We extend the notion of viscosity solutions for path-dependent PDEs introduced by Ekren et al. [Ann. Probab. 42 (2014), no. 1, 204-236] to path-dependent integro-differential equations and establish well-posedness, i.e., existence, uniqueness, and stability, ... More

On cluster theory and quantum dilogarithm identitiesFeb 21 2011Oct 13 2011These are expanded notes from three survey lectures given at the 14th International Conference on Representations of Algebras (ICRA XIV) held in Tokyo in August 2010. We first study identities between products of quantum dilogarithm series associated ... More

Towards an Account of Extraposition in HPSGFeb 21 1995This paper investigates the syntax of extraposition in the HPSG framework. We present English and German data (partly taken from corpora), and provide an analysis using lexical rules and a nonlocal dependency. The condition for binding this dependency ... More

On The Probability of a Rational Outcome for Generalized Social Welfare Functions on Three AlternativesMay 26 2009Nov 19 2009In [G. Kalai, A Fourier-theoretic Perspective on the Condorcet Paradox and Arrow's Theorem, Adv. in Appl. Math. 29(3) (2002), pp. 412--426], Kalai investigated the probability of a rational outcome for a generalized social welfare function (GSWF) on three ... More

Generalized heredity in $\mathcal B$-free systemsApr 13 2017Sep 28 2017Let $\mathcal B\subseteq\mathbb N$ be a primitive set. We complement results on heredity of the $\mathcal B$-free subshift $X_\eta$ from [arxiv:1509.08010] in two directions: In the proximal case we prove that a subshift $X_\varphi$, which micht be slightly ... More

Singular Hochschild cohomology via the singularity categorySep 13 2018Dec 11 2018We show that the singular Hochschild cohomology (=Tate-Hochschild cohomology) of an algebra A is isomorphic, as a graded algebra, to the Hochschild cohomology of the differential graded enhancement of the singularity category of A. The existence of such ... More

Deformed Calabi-Yau CompletionsAug 24 2009Sep 29 2009We define and investigate deformed n-Calabi-Yau completions of homologically smooth differential graded (=dg) categories. Important examples are: deformed preprojective algebras of connected non Dynkin quivers, Ginzburg dg algebras associated to quivers ... More

An elementary proof for the dimension of the graph of the classical Weierstrass functionJun 13 2014May 02 2015Let $W_{\lambda,b}(x)=\sum_{n=0}^\infty\lambda^n g(b^n x)$ where $b\geqslant2$ is an integer and $g(u)=\cos(2\pi u)$ (classical Weierstrass function). Building on work by Ledrappier (1992), Bar\'ansky, B\'ar\'any and Romanowska (2013) and Tsujii (2001), ... More

Algèbres amassées et applicationsNov 15 2009Feb 16 2010Sergey Fomin and Andrei Zelevinsky have invented cluster algebras at the beginning of this decade with the aim of creating an algebraic framework for the study of canonical bases in quantum groups and total positivity in algebraic groups. It soon turned ... More

The essential spectrum of the Laplacian on rapidly branching tessellationsDec 21 2007Jan 17 2008In this paper we characterize emptiness of the essential spectrum of the Laplacian under a hyperbolicity assumption for general graphs. Moreover we present a characterization for emptiness of the essential spectrum for planar tessellations in terms of ... More

Vortex type equations and canonical metricsJan 19 2006Oct 10 2006We introduce a notion of Gieseker stability for a filtered holomorphic vector bundle $F$ over a projective manifold. We relate it to an analytic condition in terms of hermitian metrics on $F$ coming from a construction of the Geometric Invariant Theory ... More

Maximal equicontinuous generic factors and weak model setsOct 13 2016Regular model sets generated from a cut-and-project scheme given by a co-compact lattice $\mathcal L\subset G\times H$ and compact and aperiodic window $W\subseteq H$, have the maximal equicontinuous factor (MEF) $(G\times H)/\mathcal L$, if the window ... More

Theoretical Uncertainties Associated with the Extraction of M_W at Hadron CollidersApr 14 1998In this contribution I briefly summarize several topics related to the measurement of the W-boson mass, M_W, at hadron colliders.

Measuring the Gluon Helicity Difference Distribution Function of the Proton using Photoproduction ProcessesOct 26 1993Little information is known about the polarization of gluons inside a longitudinally polarized proton. I report on the sensitivity of photoproduction experiments to it. Both jet and heavy quark production are considered.

Bimodule complexes via strong homotopy actionsNov 01 1999We present a new and explicit method for lifting a tilting complex to a bimodule complex. The key ingredient of our method is the notion of a strong homotopy action in the sense of Stasheff.

Curvature, geometry and spectral properties of planar graphsJan 15 2011We introduce a curvature function for planar graphs to study the connection between the curvature and the geometric and spectral properties of the graph. We show that non-positive curvature implies that the graph is infinite and locally similar to a tessellation. ... More

Correspondence and translation principles for the Mandelbrot setOct 15 1997May 26 1999New insights into the combinatorial structure of the Mandelbrot set are given by `Correspondence' and `Translation' Principles both conjectured and partially proved by E. Lau and D. Schleicher. We provide complete proofs of these principles and discuss ... More

Globally coupled chaotic maps with bistable behaviour: Large deviationsApr 01 2010Sep 08 2010For a system of globally coupled chaotic maps with bistable behaviour we relate the rate function for large deviations in the system size at finite time to dynamical properties of the self consistent Perron-Frobenius operator (SCPFO) that describes the ... More

About projectivisation of Mumford semistable bundles over a curveJul 25 2014We study the existence of canonical K\"ahler metrics on the projectivisation of strictly Mumford semistable holomorphic vector bundles over a complex curve. We also provide an algebro-geometric characterization of these metrics.

The spectrogram expansion of Wigner functionsJul 01 2016Wigner functions generically attain negative values and hence are not probability densities. We prove an asymptotic expansion of Wigner functions in terms of Hermite spectrograms, which are probability densities. The expansion provides exact formulas ... More

Absolutely continuous spectrum for multi-type Galton Watson treesSep 09 2011Jan 25 2012We consider multi-type Galton Watson trees that are close to a tree of finite cone type in distribution. Moreover, we impose that each vertex has at least one forward neighbor. Then, we show that the spectrum of the Laplace operator exhibits almost surely ... More

Stability index, uncertainty exponent, and thermodynamic formalism for intermingled basins of chaotic attractorsOct 02 2015Skew product systems with monotone one-dimensional fibre maps driven by piecewise expanding Markov interval maps may show the phenomenon of intermingled basins. To quantify the degree of intermingledness the uncertainty exponent and the stability index ... More

On the Tate-Shafarevich group of Abelian schemes over higher dimensional bases over finite fieldsOct 20 2014May 25 2016We study analogues for the Tate-Shafarevich group for Abelian schemes with everywhere good reduction over higher dimensional bases over finite fields.

Cluster algebras, quiver representations and triangulated categoriesJul 12 2008Mar 19 2010This is an introduction to some aspects of Fomin-Zelevinsky's cluster algebras and their links with the representation theory of quivers and with Calabi-Yau triangulated categories. It is based on lectures given by the author at summer schools held in ... More

On The Influences of Variables on Boolean Functions in Product SpacesMay 26 2009In this paper we consider the influences of variables on Boolean functions in general product spaces. Unlike the case of functions on the discrete cube where there is a clear definition of influence, in the general case at least three definitions were ... More

The periodicity conjecture for pairs of Dynkin diagramsJan 10 2010Apr 14 2012We prove the periodicity conjecture for pairs of Dynkin diagrams using Fomin-Zelevinsky's cluster algebras and their (additive) categorification via triangulated categories.

Stability index for chaotically driven concave mapsSep 11 2012We study skew product systems driven by a hyperbolic base map S (e.g. a baker map or an Anosov surface diffeomorphism) and with simple concave fibre maps on an interval [0,a] like h(x)=g(\theta) tanh(x) where g(\theta) is a factor driven by the base map. ... More

Learning Boolean functions with concentrated spectraJul 15 2015This paper discusses the theory and application of learning Boolean functions that are concentrated in the Fourier domain. We first estimate the VC dimension of this function class in order to establish a small sample complexity of learning in this case. ... More

Partisan gerrymandering with geographically compact districtsDec 14 2017Bizarrely shaped voting districts are frequently lambasted as likely instances of gerrymandering. In order to systematically identify such instances, researchers have devised several tests for so-called geographic compactness (i.e., shape niceness). We ... More

The optimal packing of eight points in the real projective planeFeb 26 2019How can we arrange $n$ lines through the origin in three-dimensional Euclidean space in a way that maximizes the minimum interior angle between pairs of lines? Conway, Hardin and Sloane (1996) produced line packings for $n \leq 55$ that they conjectured ... More

Searching for comets on the World Wide Web: The orbit of 17P/Holmes from the behavior of photographersMar 30 2011Mar 28 2013We performed an image search for "Comet Holmes," using the Yahoo Web search engine, on 2010 April 1. Thousands of images were returned. We astrometrically calibrated---and therefore vetted---the images using the Astrometry.net system. The calibrated image ... More

Full Spark FramesOct 17 2011Apr 09 2012Finite frame theory has a number of real-world applications. In applications like sparse signal processing, data transmission with robustness to erasures, and reconstruction without phase, there is a pressing need for deterministic constructions of frames ... More

Extraction of Generalized Parton Distribution Observables from Deeply Virtual Electron Proton Scattering ExperimentsMar 13 2019We provide the general expression of the cross section for exclusive deeply virtual photon electroproduction from a spin 1/2 target using current parameterizations of the off-forward correlation function in a nucleon for different beam and target polarization ... More

A Multiple Hypothesis Testing Approach to Low-Complexity Subspace UnmixingAug 07 2014Subspace-based signal processing has a rich history in the literature. Traditional focus in this direction has been on problems involving a few subspaces. But a number of problems in different application areas have emerged in recent years that involve ... More

Numerical simulation of solutions and moments of the smoluchowski coagulation equationDec 27 2013Researchers have employed variations of the Smoluchowski coagulation equation to model a wide variety of both organic and inorganic phenomena and with relatively few known analytical solutions, numerical solutions play an important role in studying this ... More

Settling the feasibility of interference alignment for the MIMO interference channel: the symmetric square caseApr 05 2011Determining the feasibility conditions for vector space interference alignment in the K-user MIMO interference channel with constant channel coefficients has attracted much recent attention yet remains unsolved. The main result of this paper is restricted ... More

Towards building a Crowd-Sourced Sky MapJun 05 2014We describe a system that builds a high dynamic-range and wide-angle image of the night sky by combining a large set of input images. The method makes use of pixel-rank information in the individual input images to improve a "consensus" pixel rank in ... More

On the number of commutation classes of the longest element in the symmetric groupJan 25 2016Feb 29 2016Using the standard Coxeter presentation for the symmetric group $S_n$, two reduced expressions for the same group element are said to be commutation equivalent if we can obtain one expression from the other by applying a finite sequence of commutations. ... More

Brane backreactions and the Fischler-Susskind mechanism in conformal field theorySep 07 2007The backreaction of D-branes on closed string moduli is studied in perturbed conformal field theory. To this end we analyse the divergences in the modular integral of the annulus diagram. By the Fischler-Susskind mechanism, these divergences lead to additional ... More

Linear recurrence relations for cluster variables of affine quiversApr 05 2010Jun 16 2010We prove that the frieze sequences of cluster variables associated with the vertices of an affine quiver satisfy linear recurrence relations. In particular, we obtain a proof of a recent conjecture by Assem-Reutenauer-Smith.

A Tractable Extension of Linear Indexed GrammarsFeb 17 1995It has been shown that Linear Indexed Grammars can be processed in polynomial time by exploiting constraints which make possible the extensive use of structure-sharing. This paper describes a formalism that is more powerful than Linear Indexed Grammar, ... More

A Taxonomy for Attack Patterns on Information Flows in Component-Based Operating SystemsMar 05 2014We present a taxonomy and an algebra for attack patterns on component-based operating systems. In a multilevel security scenario, where isolation of partitions containing data at different security classifications is the primary security goal and security ... More

Cosmological Evolution of Fundamental Constants: From Theory to ExperimentOct 10 2014Dec 05 2014In this paper we discuss a possible cosmological time evolution of fundamental constants from the theoretical and experimental point of views. On the theoretical side, we explain that such a cosmological time evolution is actually something very natural ... More

Graded quiver varieties and derived categoriesMar 10 2013Mar 12 2013Inspired by recent work of Hernandez-Leclerc and Leclerc-Plamondon we investigate the link between Nakajima's graded affine quiver varieties associated with an acyclic connected quiver Q and the derived category of Q. As Leclerc-Plamondon have shown, ... More

Bump Cepheids and the Stellar Mass-Luminosity RelationFeb 12 2003We present the results of non-linear pulsation modeling of bump Cepheids in the LMC and SMC. By obtaining an optimal fit to the observed MACHO V and R lightcurves we can determine the fundamental parameters of each Cepheid, namely mass, luminosity, effective ... More

Rotation of Early B-type Stars in the Large Magellanic Cloud - The role of evolution and metallicityMay 07 2004I present measurements of the projected rotational velocities of a sample of 100 early B-type main-sequence stars in the Large Magellanic Cloud. This is the first extragalactic study of the distribution of stellar rotational velocities. The sample is ... More

Quantitative relation between noise sensitivity and influencesMar 09 2010A Boolean function $f:\{0,1\}^n \to \{0,1\}$ is said to be noise sensitive if inserting a small random error in its argument makes the value of the function almost unpredictable. Benjamini, Kalai and Schramm showed that if the sum of squares of influences ... More

A discrete Hopf-Rinow-theoremJul 26 2018We prove a version of the Hopf-Rinow-theorem with respect to path metrics on discrete spaces. The novel aspect is that we do not a priori assume local finiteness but isolate a local finiteness type condition, called essential local finiteness, that is ... More

A Multiple Hypothesis Testing Approach to Low-Complexity Subspace UnmixingAug 07 2014Nov 20 2016Subspace-based signal processing traditionally focuses on problems involving a few subspaces. Recently, a number of problems in different application areas have emerged that involve a significantly larger number of subspaces relative to the ambient dimension. ... More

Stochastic gradient descent methods for estimation with large data setsSep 22 2015We develop methods for parameter estimation in settings with large-scale data sets, where traditional methods are no longer tenable. Our methods rely on stochastic approximations, which are computationally efficient as they maintain one iterate as a parameter ... More

The Variational Gaussian ProcessNov 20 2015Apr 17 2016Variational inference is a powerful tool for approximate inference, and it has been recently applied for representation learning with deep generative models. We develop the variational Gaussian process (VGP), a Bayesian nonparametric variational family, ... More

Towards stability and optimality in stochastic gradient descentMay 10 2015Jun 07 2016Iterative procedures for parameter estimation based on stochastic gradient descent allow the estimation to scale to massive data sets. However, in both theory and practice, they suffer from numerical instability. Moreover, they are statistically inefficient ... More

Secant varieties of P^2 x P^n embedded by O(1,2)Sep 07 2010We describe the defining ideal of the rth secant variety of P^2 x P^n embedded by O(1,2), for arbitrary n and r at most 5. We also present the Schur module decomposition of the space of generators of each such ideal. Our main results are based on a more ... More

Equiangular tight frames from hyperovalsFeb 17 2016Jun 23 2016An equiangular tight frame (ETF) is a set of equal norm vectors in a Euclidean space whose coherence is as small as possible, equaling the Welch bound. Also known as Welch-bound-equality sequences, such frames arise in various applications, such as waveform ... More

Kirkman Equiangular Tight Frames and CodesJun 13 2013An equiangular tight frame (ETF) is a set of unit vectors in a Euclidean space whose coherence is as small as possible, equaling the Welch bound. Also known as Welch-bound-equality sequences, such frames arise in various applications, such as waveform ... More

Generalized solutions and spectrum for Dirichlet forms on graphsFeb 04 2010We study the connection of the existence of solutions with certain properties and the spectrum of operators in the framework of regular Dirichlet forms on infinite graphs. In particular we prove a version of the Allegretto-Piepenbrink theorem, which says ... More

Weighing of trapped ion crystals and its applicationsJun 14 2011Nov 04 2011We have developed a novel scheme to measure the secular motion of trapped ions. Employing pulsed excitation and analysis of the fluorescence of laser cooled ions, we have measured the centre-of-mass mode frequency of single as well as entire ion crystals ... More

Formal Deformations of Dirac StructuresJun 27 2006Jul 27 2006In this paper we set-up a general framework for a formal deformation theory of Dirac structures. We give a parameterization of formal deformations in terms of two-forms obeying a cubic equation. The notion of equivalence is discussed in detail. We show ... More

Piecewise Linear Phase TransitionsNov 26 2007It is shown how simple assumptions lead to piecewise linear behavior, which is observed in certain phase transitions.

On Large H-Intersecting FamiliesSep 07 2016A family $F$ of graphs on a fixed set of $n$ vertices is called triangle-intersecting if for any $G_1,G_2 \in F$, the intersection $G_1 \cap G_2$ contains a triangle. More generally, for a fixed graph $H$, a family $F$ is $H$-intersecting if the intersection ... More

A tight stability version of the Complete Intersection TheoremApr 20 2016Jul 09 2016A set family F is said to be t-intersecting if any two sets in F share at least t elements. The Complete Intersection Theorem of Ahlswede and Khachatrian (1997) determines the maximal size f(n,k,t) of a t-intersecting family of k-element subsets of {1,2,...,n}, ... More

General Cheeger inequalities for p-Laplacians on graphsSep 20 2015We prove Cheeger inequalities for p-Laplacians on finite and infinite weighted graphs. Unlike in previous works, we do not impose boundedness of the vertex degree, nor do we restrict ourselves to the normalized Laplacian and, more generally, we do not ... More

Modelling Creativity: Identifying Key Components through a Corpus-Based ApproachSep 12 2016Creativity is a complex, multi-faceted concept encompassing a variety of related aspects, abilities, properties and behaviours. If we wish to study creativity scientifically, then a tractable and well-articulated model of creativity is required. Such ... More

SafeMPI - Extending MPI for Byzantine Error Detection on Parallel ClustersMay 31 2005Modern high-performance computing relies heavily on the use of commodity processors arranged together in clusters. These clusters consist of individual nodes (typically off-the-shelf single or dual processor machines) connected together with a high speed ... More

Infrared Photometry of Red Supergiants in Young Clusters in the Magellanic CloudsMay 05 1999We present broad-band infrared photometry for 52 late-type supergiants in the young Magellanic Clouds clusters NGC 330, NGC 1818, NGC 2004 and NGC 2100. Standard models are seen to differ in the temperature they predict for the red supergiant population ... More

Quot-scheme limit of Fubini-Study metrics and Donaldson's functional for bundlesSep 22 2018For a holomorphic vector bundle $E$ over a polarised K\"ahler manifold, we establish a direct link between the slope stability of $E$ and the asymptotic behaviour of Donaldson's functional, by defining the Quot-scheme limit of Fubini-Study metrics. In ... More

On the lower bounds of the L^2-norm of the Hermitian scalar curvatureFeb 06 2017On a pre-quantized symplectic manifold, we show that the symplectic Futaki invariant, which is an obstruction to the existence of constant Hermitian scalar curvature almost-K\"ahler metrics, is actually an asymptotic invariant. This allows us to deduce ... More

Map Lattices coupled by collisionsNov 21 2008Dec 20 2008We introduce a new coupled map lattice model in which the weak interaction takes place via rare "collisions". By "collision" we mean a strong (possibly discontinuous) change in the system. For such models we prove uniqueness of the SRB measure and exponential ... More

A lower bound for the number of conjugacy classes of finite groupsAug 16 2007In 2000, L. H\'{e}thelyi and B. K\"{u}lshammer proved that if $p$ is a prime number dividing the order of a finite solvable group $G$, then $G$ has at least $2\sqrt{p-1}$ conjugacy classes. In this paper we show that if $p$ is large, the result remains ... More