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The Algonauts Project: A Platform for Communication between the Sciences of Biological and Artificial IntelligenceMay 14 2019In the last decade, artificial intelligence (AI) models inspired by the brain have made unprecedented progress in performing real-world perceptual tasks like object classification and speech recognition. Recently, researchers of natural intelligence have ... More

A bound for the splitting of smooth Fano polytopes with many verticesSep 25 2014Aug 10 2015The classification of toric Fano manifolds with large Picard number corresponds to the classification of smooth Fano polytopes with large number of vertices. A smooth Fano polytope is a polytope that contains the origin in its interior such that the vertex ... More

Discriminants of stable rank two sheaves on some general type surfacesDec 05 2018Jan 10 2019We prove sharp bounds on the discriminants of stable rank two sheaves on surfaces in three-dimensional projective space. The key technical ingredient is to study them as torsion sheaves in projective space via tilt stability in the derived category. We ... More

Precision predictions for Z' production at the LHCMay 14 2008May 16 2008We present precision calculations of the transverse-momentum spectrum, the invariant-mass distribution and the total cross section for Z' production at hadron colliders. We implement joint resummation at the next-to-leading logarithmic accuracy and consistently ... More

The Heegner point Kolyvagin systemFeb 28 2012Perrin-Riou has formulated a form of the Iwasawa main conjecture, which relates Heegner points to the Selmer group of an elliptic curve as one goes up the anticyclotomic Z_p extension of a quadratic imaginary field K. Building on the earlier work of Bertolini ... More

Quantization of Perturbations in InflationFeb 21 2013Aug 15 2013The derivation of the angular spectrum of temperature perturbations of the cosmic microwave background relies on the quantization of field and metric perturbations in the inflationary phase. The quantization procedure thus deserves a close examination. ... More

An ACL2 Mechanization of an Axiomatic Framework for Weak MemoryJun 06 2014Proving the correctness of programs written for multiple processors is a challenging problem, due in no small part to the weaker memory guarantees afforded by most modern architectures. In particular, the existence of store buffers means that the programmer ... More

An elementary proof that subgroups of free groups are freeJun 19 2010We provide an elementary proof that subgroups of free groups are free via group actions.

The averaging trick and the Cerny conjectureOct 02 2009May 08 2010The results of several papers concerning the \v{C}ern\'y conjecture are deduced as consequences of a simple idea that I call the averaging trick. This idea is implicitly used in the literature, but no attempt was made to formalize the proof scheme axiomatically. ... More

Cerny's conjecture, synchronizing automata, group representation theoryAug 10 2008Let us say that a Cayley graph $\Gamma$ of a group $G$ of order $n$ is a Cerny Cayley graph if every synchronizing automaton containing $\Gamma$ as a subgraph with the same vertex set admits a synchronizing word of length at most $(n-1)^2$. In this paper ... More

A reconstruction theorem for abelian categories of twisted sheavesMay 11 2013Nov 02 2013We use an idea of Rosenberg to prove a reconstruction theorem for abelian categories of alpha-twisted quasi-coherent sheaves on quasi-compact and quasi-separated schemes X when alpha is in the Brauer group of X. By applying the work of To\"en on derived ... More

On the strength of proof-irrelevant type theoriesAug 28 2008Sep 25 2008We present a type theory with some proof-irrelevance built into the conversion rule. We argue that this feature is useful when type theory is used as the logical formalism underlying a theorem prover. We also show a close relation with the subset types ... More

Dynatomic cycles for morphisms of projective varietiesJan 23 2008Oct 22 2008We prove the effectivity of the dynatomic cycles for morphisms of projective varieties. We then analyze the degrees of the dynatomic cycles and multiplicities of formal periodic points and apply these results to the existence of periodic points with arbitrarily ... More

Unimodality Problems in Ehrhart TheoryMay 27 2015Ehrhart theory is the study of sequences recording the number of integer points in non-negative integral dilates of rational polytopes. For a given lattice polytope, this sequence is encoded in a finite vector called the Ehrhart $h^*$-vector. Ehrhart ... More

Exotic geometric structures on Kodaira surfacesJan 20 2012Oct 16 2012On all compact complex surfaces (modulo finite unramified coverings), we classify all of the locally homogeneous geometric structures which are locally isomorphic to the exotic homogeneous surfaces of Lie.

The Hot Bang state of massless fermionsApr 25 2005In 2002, a method has been proposed by Buchholz et al. in the context of Local Quantum Physics, to characterize states that are locally in thermodynamic equilibrium. It could be shown for the model of massless bosons that these states exhibit quite interesting ... More

Lower bounds for ballistic current and noise in non-equilibrium quantum steady statesOct 01 2014Let an infinite, homogeneous, many-body quantum system be unitarily evolved for a long time from a state where two halves are independently thermalized. One says that a non-equilibrium steady state emerges if there are nonzero steady currents in the central ... More

A comment on the OPERA result and CPTSep 26 2011Oct 19 2011We consider the possibility that the superluminal neutrino propagation reported by the OPERA collaboration originates from a violation of CPT. On this basis we compare our actual knowledge concerning the CPT theorem to the nuclear reaction chain between ... More

Spatially-sparse convolutional neural networksSep 22 2014Convolutional neural networks (CNNs) perform well on problems such as handwriting recognition and image classification. However, the performance of the networks is often limited by budget and time constraints, particularly when trying to train deep networks. ... More

Conformal or confining -- results from lattice gauge theory for higher-representation gauge theoriesJan 09 2013We have calculated the running coupling in SU(2), SU(3), and SU(4) gauge theories to see whether they have infrared fixed points. An infrared fixed point means no confinement: It means that the long-distance physics is conformal, without a mass scale ... More

Effective spin models for the confinement phase transitionSep 02 1998Oct 01 1998Spatial correlations - bubbles, domain walls, etc. - can best be studied by concentrating on the degrees of freedom most relevant to the problem. For the finite temperature confinement transition, I integrate out all gauge degrees of freedom, leaving ... More

Lattice gauge theory in technicolorJan 14 2009The methods of lattice gauge theory may be applied to gauge theories besides QCD, in fact to any gauge group and any representation of matter fields (as long as the coupling is not chiral). Such theories are useful for model building beyond the Standard ... More

Asymptotic Theory of the Sparse Group LASSONov 18 2016Nov 22 2016This paper proposes a general framework for penalized convex empirical criteria and a new version of the Sparse-Group LASSO (SGL, Simon and al., 2013), called the adaptive SGL, where both penalties of the SGL are weighted by preliminary random coefficients. ... More

Systematic studies of the centrality dependence of soft photon production in Au+Au collision with PHENIXAug 03 2014Since the earliest days of Heavy Ion Physics thermal soft photon radiation emitted during the reaction had been theorized as a smoking gun signal for formation of a quark-gluon plasma and as a tool to characterize its properties. In recent years the existence ... More

Selective orders in central simple algebras and isospectral families of arithmetic manifoldsSep 02 2014Let $k$ be a number field and $B$ be a central simple algebra over $k$ of dimension $p^2$ where $p$ is prime. In the case that $p=2$ we assume that $B$ is not totally definite. In this paper we study sets of pairwise nonisomorphic maximal orders of $B$ ... More

Decomposition theorems for Hilbert modular newformsJan 17 2011Let $\mathscr{S}_k^+(\cn,\Phi)$ denote the space generated by Hilbert modular newforms (over a fixed totally real field $K$) of weight $k$, level $\cn$ and Hecke character $\Phi$. We show how to decompose $\mathscr{S}_k^+(\cn,\Phi)$ into direct sums of ... More

Non-linear shrinkage estimation of large-scale structure covarianceDec 02 2016In many astrophysical settings covariance matrices of large datasets have to be determined empirically from a finite number of mock realisations. The resulting noise degrades inference and precludes it completely if there are fewer realisations than data ... More

Better Runtime Guarantees Via Stochastic DominationJan 13 2018Apart from few exceptions, the mathematical runtime analysis of evolutionary algorithms is mostly concerned with expected runtimes. In this work, we argue that stochastic domination is a notion that should be used more frequently in this area. Stochastic ... More

Saturated Actions on C*-algebra Suspensions and Joins by Finite Cyclic GroupsOct 14 2015Mar 24 2016We present proofs of a C*-algebraic conjecture of Dabrowski, and certain topological cases of conjectures by Baum, Dabrowski, and Hajac, that generalize the Borsuk-Ulam theorem. We also formulate a different type of noncommutative join than the previous ... More

The WAGASCI detector as an off-axis near detector of the T2K and Hyper-Kamiokande experimentsOct 20 2016In the search for CP violation at the T2K and future Hyper-Kamiokande experiments, it is crucial to reduce the present systematic uncertainties. The current T2K near detector, ND280, reduces the uncertainties coming from the neutrino beam and cross-section ... More

Reconstruction for multiwave imaging in attenuating media with large damping coefficientApr 20 2016Oct 16 2016In this article we study the reconstruction problem in TAT/PAT on an attenuating media. Namely, we prove a reconstruction procedure of the initial condition for the damped wave equation via Neumann series that works for arbitrary large smooth attenuation ... More

Homogenization of Hamilton-Jacobi equations with rough time dependenceFeb 16 2016Nov 10 2016We consider viscosity solutions of Hamilton-Jacobi equations with oscillatory spatial dependence and rough time dependence. The time dependence is in the form of the derivative of a continuous path that converges to a possibly nowhere-differentiable path, ... More

Constructing mutually unbiased bases from quantum Latin squaresMay 28 2016We introduce orthogonal quantum Latin squares, which restrict to traditional orthogonal Latin squares, and investigate their application in quantum information science. We use quantum Latin squares to build maximally entangled bases, and show how mutually ... More

Perron's method for stochastic viscosity solutionsMay 03 2016In this paper we use Perron's method to construct stochastic viscosity solutions of fully nonlinear second order SPDEs. The result holds for smooth Hamiltonians and for a single, real-valued path, and relies on the finite speed of propagation property ... More

Smooth Surfaces in Smooth Fourfolds with Vanishing First Chern ClassOct 13 2016Oct 25 2016Hartshorne conjectured and Ellingsrud and Peskine proved that the smooth rational surfaces in $\mathbb{P}^4$ belong to only finitely many families. We formulate and study a collection of analogous problems in which $\mathbb{P}^4$ is replaced by a smooth ... More

Tate objects in stable $(\infty,1)$-categoriesJun 17 2016Tate objects have been studied by many authors. They allow us to deal with infinite dimensional spaces by identifying some more structure. In this article, we set up the theory of Tate objects in stable $(\infty,1)$-categories, while the literature only ... More

Thermalization and pseudolocality in extended quantum systemsDec 11 2015Feb 07 2016Recently, it was understood that modified concepts of locality played an important role in the study of extended quantum systems out of equilibrium, in particular in so-called generalized Gibbs ensembles. In this paper, we rigorously study pseudolocal ... More

Dual-Fitting Approximation Algorithms for Network Connectivity ProblemsAug 23 2015We consider the NP-complete network connectivity problem of Dual Power Assignment (DPA). This models an ad hoc networks where each node can either operate at high or low power. The goal is to produce a minimum power strongly connected network. We give ... More

G2 manifolds of cohomogeneity twoNov 25 2003Aug 06 2005This paper has been withdrawn by the author, due to errors in Groebner basis calculations in the cases of five and six dimensional groups.

Revisiting the tree edit distance and its backtracing: A tutorialMay 17 2018Oct 26 2018Almost 30 years ago, Zhang and Shasha (1989) published a seminal paper describing an efficient dynamic programming algorithm computing the tree edit distance, that is, the minimum number of node deletions, insertions, and replacements that are necessary ... More

Tree Edit Distance Learning via Adaptive Symbol Embeddings: Supplementary Materials and ResultsMay 18 2018Metric learning has the aim to improve classification accuracy by learning a distance measure which brings data points from the same class closer together and pushes data points from different classes further apart. Recent research has demonstrated that ... More

Subspace-Invariant AC$^0$ FormulasJun 13 2018Jan 12 2019We consider the action of a linear subspace $U$ of $\{0,1\}^n$ on the set of AC$^0$ formulas with inputs labeled by literals in the set $\{X_1,\overline X_1,\dots,X_n,\overline X_n\}$, where an element $u \in U$ acts on formulas by transposing the $i$th ... More

EKR sets for large $n$ and $r$Oct 28 2012Let $\A\subset\binom{[n]}{r}$ be a compressed, intersecting family and let $X\subset[n]$. Let $\A(X)={A\in\A:A\cap X\ne\emptyset}$ and $\S_{n,r}=\binom{[n]}{r}({1})$. Motivated by the Erd\H{o}s-Ko-Rado theorem, Borg asked for which $X\subset[2,n]$ do ... More

Formulas vs. Circuits for Small Distance ConnectivityDec 02 2013We give the first super-polynomial separation in the power of bounded-depth boolean formulas vs. circuits. Specifically, we consider the problem Distance $k(n)$ Connectivity, which asks whether two specified nodes in a graph of size $n$ are connected ... More

Rigid geometry on projective varietiesMar 12 2006Nov 25 2010We prove rigidity of various types of holomorphic parabolic geometry on smooth complex projective varieties.

Iterated functions and the Cantor set in one dimensionNov 03 2013In this paper we consider the long-term behavior of points in ${\mathbb R}$ under iterations of continuous functions. We show that, given any Cantor set $\Lambda^*$ embedded in ${\mathbb R}$, there exists a continuous function $F^*:{\mathbb R}\to{\mathbb ... More

On the Maintenance of Classic Modula-2 CompilersSep 19 2018The classic Modula-2 language was specified in [Wir78] by N.Wirth at ETH Z\"urich in 1978. The last revision [Wir88] was published in 1988. Many computer science books of that era used Modula-2 in programming examples. Many of these are still valuable ... More

Sparse Multivariate ARCH Models: Finite Sample PropertiesAug 16 2018Feb 21 2019We provide finite sample properties of sparse multivariate ARCH processes, where the linear representation of ARCH models allows for an ordinary least squares estimation. Under the restricted strong convexity of the unpenalized loss function, regularity ... More

An Exponential Lower Bound for the Runtime of the cGA on Jump FunctionsApr 17 2019In the first runtime analysis of an estimation-of-distribution algorithm (EDA) on the multi-modal jump function class, Hasen\"ohrl and Sutton (GECCO 2018) proved that the runtime of the compact genetic algorithm with suitable parameter choice on jump ... More

Families of Explicit Isogenies of Hyperelliptic JacobiansSep 29 2009We construct three-dimensional families of hyperelliptic curves of genus 6, 12, and 14, two-dimensional families of hyperelliptic curves of genus 3, 6, 7, 10, 20, and 30, and one-dimensional families of hyperelliptic curves of genus 5, 10 and 15, all ... More

The Q-curve construction for endomorphism-accelerated elliptic curvesSep 16 2014Mar 24 2015We give a detailed account of the use of $\mathbb{Q}$-curve reductions to construct elliptic curves over $\mathbb{F}\_{p^2}$ with efficiently computable endomorphisms, which can be used to accelerate elliptic curve-based cryptosystems in the same way ... More

Families of fast elliptic curves from Q-curvesMay 23 2013We construct new families of elliptic curves over \(\FF_{p^2}\) with efficiently computable endomorphisms, which can be used to accelerate elliptic curve-based cryptosystems in the same way as Gallant-Lambert-Vanstone (GLV) and Galbraith-Lin-Scott (GLS) ... More

Heavy Flavor TheoryOct 13 2009Oct 16 2009This is a limited review and update of the status of Heavy Flavor Physics. After we review the flavor problem we discuss a number of topics: recent puzzles in purely leptonic D and B decays and their possible resolutions, mixing in neutral B and D mesons, ... More

The SSC: Programme and Searches for New ParticlesOct 14 1992Oct 15 1992Talk presented at the Trieste Workshop on the Search for New Elementary Particles: Status and Prospects.

An Introduction to Heavy MesonsAug 04 1995Introductory lectures (delivered at the VI Mexican School of Particles and Fields) on heavy quarks and heavy quark effective field theory. Applications to inclusive semileptonic decays and to interactions with light mesons are covered in detail.

Light-Quark, Heavy-Quark Systems: An UpdateOct 27 1993We review many of the recently developed applications of Heavy Quark Effective Theory techniques. After a brief update on Luke's theorem, we describe striking relations between heavy baryon form factors, and how to use them to estimate the accuracy of ... More

Morphisms of Cartan connectionsFeb 11 2008Sep 28 2010We define what we call morphisms of Cartan connections. We generalize the main theorems on Cartan connections to theorems on morphisms. Many of the known constructions involving Cartan connections turn out to be examples of morphisms. We prove some basic ... More

Complete toric varieties with reductive automorphism groupJul 28 2004We give equivalent and sufficient criteria for the automorphism group of a complete toric variety, respectively a Gorenstein toric Fano variety, to be reductive. In particular we show that the automorphism group of a Gorenstein toric Fano variety is reductive, ... More

Presentations for Generalized nilHecke AlgebrasAug 26 2012Dec 01 2014In this note presentations are given for the nilHecke algebras implicit in the work of Bressler and Evens on Schubert calculus for generalized cohomology theories. Such algebras do not usually satisfy the braid relation. Here the obstruction to the braid ... More

Formal Contact CategoriesNov 15 2015Jul 23 2018To each oriented surface S, we associate a differential graded category Ko(S). The homotopy category Ho(Ko(S)) is a triangulated category which satisfies properties akin to those of the contact categories studied by K. Honda. These categories are also ... More

Some Categorical Representations of the Modular GroupSep 11 2012Dec 01 2014Examples of SL(2, Z) actions on differential graded categories are defined and explored.

Lifting Commuting 3-Isometric TuplesAug 06 2015An operator $T$ is called a 3-isometry if there exists operators $B_1(T^*,T)$ and $B_2(T^*,T)$ such that \[Q(n)=T^{*n}T^n=1+nB_1(T^*,T)+n^2 B_2(T^*,T)\] for all natural numbers $n$. An operator $J$ is a Jordan operator of order $2$ if $J=U+N$ where $U$ ... More

Finite, fiber- and orientation-preserving actions on orientable Seifert manifolds with non-orientable base spaceNov 09 2018Apr 29 2019This paper extends the results from the author's previous paper to consider finite, fiber- and orientation- preserving group actions on closed, orientable Seifert manifolds $M$ that fiber over a non-orientable base space. An orientable base space double ... More

Finite, fiber- and orientation-preserving group actions on totally orientable Seifert manifoldsOct 25 2018May 08 2019In this paper we consider the finite groups that act fiber- and orientation-preservingly on closed, compact, and orientable Seifert manifolds that fiber over an orientable base space. We establish a method of constructing such group actions and then show ... More

Note on the diophantine equation X^t+Y^t=BZ^tMar 16 2010In this paper, we obtain new results on the integers solutions X, Y, Z of the diophantine equation X^t+Y^t=BZ^t for a rationnal integer B and a prime number t verifying some conditions explained in the paper.

On the welded Tube mapAug 23 2014Mar 08 2016This note investigates the so-called Tube map which connects welded knots, that is a quotient of the virtual knot theory, to ribbon torus-knots, that is a restricted notion of fillable knotted tori in the 4-sphere. It emphasizes the fact that ribbon torus-knots ... More

Cartan matrices and Brauer's k(B)-conjectureDec 20 2010We show (among other things) that Brauer's k(B)-conjecture holds for defect groups with are central extensions of metacyclic 2-groups by cyclic groups. The same holds for defect groups which contain a central cyclic subgroup of index at most 9. In particular ... More

Triviality of Equivariant Maps in Crossed Products and Matrix AlgebrasDec 19 2016Mar 18 2018We consider a "twisted" noncommutative join procedure for unital $C^*$-algebras which admit actions by a compact abelian group $G$ and its discrete abelian dual $\Gamma$, so that we may investigate an analogue of Baum-Dabrowski-Hajac noncommutative Borsuk-Ulam ... More

Anticommutation in the Presentations of Theta-Deformed SpheresApr 29 2016We consider an analogue of the theta-deformed even spheres, modifying the relations demanded of the self-adjoint generator x in the usual presentation. In this analogue, x is given anticommutation relations with all of the other generators, as opposed ... More

Geometry of the EOS(R) Radiographic ScannerApr 14 2019The EOS(R) scanner is a radiographic system that captures PA and lateral images in standing posture. The system is widely used in diagnosis and assessment of scoliosis, as it provides a low-dose alternative to traditional X-ray and can capture full-body ... More

Fusion systems on metacyclic 2-groupsAug 06 2009Oct 19 2010Let P be a finite metacyclic 2-group and F a fusion system on P. We prove that F is nilpotent unless P has maximal class or P is homocyclic, i.e. P is a direct product of two isomorphic cyclic groups. As a consequence we obtain the numerical invariants ... More

On the Square Peg Problem and some RelativesDec 31 2009The Square Peg Problem asks whether every continuous simple closed planar curve contains the four vertices of a square. This paper proves this for the largest so far known class of curves. Furthermore we solve an analogous Triangular Peg Problem affirmatively, ... More

Rooted Graph Minors and Reducibility of Graph PolynomialsApr 15 2017In 2009, Brown gave a set of conditions which when satisfied imply that a Feynman integral evaluates to a multiple zeta value. One of these conditions is called reducibility, which loosely says there is an order of integration for the Feynman integral ... More

The mixed degree of families of lattice polytopesAug 10 2017The degree of a lattice polytope is a notion in Ehrhart theory that was studied quite intensively over the previous years. It is well-known that a lattice polytope has normalized volume one if and only if its degree is zero. Recently, Esterov and Gusev ... More

On polarization types of Lagrangian fibrationsJan 19 2015Apr 26 2016The generic fiber of a Lagrangian fibration on an irreducible holomorphic symplectic manifold is an abelian variety. Associate a polarization type to such Lagrangian fibrations coming from polarizations on a generic fiber. We prove that this polarization ... More

Global model structures for $*$-modulesJul 01 2016Feb 28 2018We extend Schwede's work on the unstable global homotopy theory of orthogonal spaces and $\mathcal{L}$-spaces to the category of $*$-modules (i.e., unstable $S$-modules). We prove a theorem which transports model structures and their properties from $\mathcal{L}$-spaces ... More

Isogenies and the Discrete Logarithm Problem in Jacobians of Genus 3 Hyperelliptic CurvesJun 18 2008Feb 27 2009We describe the use of explicit isogenies to translate instances of the Discrete Logarithm Problem (DLP) from Jacobians of hyperelliptic genus 3 curves to Jacobians of non-hyperelliptic genus 3 curves, where they are vulnerable to faster index calculus ... More

Local means and atoms in vector-valued function spacesMar 31 2011The first part of this paper deals with the topic of finding equivalent norms and characterizations for vector-valued Besov and Triebel-Lizorkin spaces. We will deduce general criteria by transferring and extending a theorem of Bui, Paluszynski and Taibleson ... More

Global well-posedness and scattering for the mass critical nonlinear Schr{ö}dinger equation with mass below the mass of the ground stateApr 06 2011Apr 20 2011In this paper we prove that the focusing, $d$-dimensional mass critical nonlinear Schr{\"o}dinger initial value problem is globally well-posed and scattering for $u_{0} \in L^{2}(\mathbf{R}^{d})$, $\| u_{0} \|_{L^{2}(\mathbf{R}^{d})} < \| Q \|_{L^{2}(\mathbf{R}^{d})}$, ... More

Global well-posedness and scattering for nonlinear Schr{ö}dinger equations with algebraic nonlinearity when $d = 2, 3$, $u_{0}$ radialMay 01 2014In this paper we discuss global well - posedness and scattering for some initial value problems that are $L^{2}$ supercritical and $\dot{H}^{1}$ subcritical, with radial data. We prove global well - posedness and scattering for radial data in $H^{s}$, ... More

Global well-posedness and scattering for the defocusing, $L^{2}$-critical, nonlinear Schr{ö}dinger equation when $d \geq 3$Dec 13 2009Mar 18 2011In this paper we prove that the defocusing, $d$-dimensional mass critical nonlinear Schr{\"o}dinger initial value problem is globally well-posed and scattering for $u_{0} \in L^{2}(\mathbf{R}^{d})$ and $d \geq 3$. To do this, we will prove a frequency ... More

Rational Periodic Points for Degree Two Polynomial Morphisms on Projective SpaceNov 19 2008Aug 04 2009This article addresses the existence of $\Q$-rational periodic points for morphisms of projective space. In particular, we construct an infinitely family of morphisms on $\P^N$ where each component is a degree 2 homogeneous form in $N+1$ variables which ... More

An Approximate Version of the Jordan von Neumann Theorem for Finite Dimensional Real Normed SpacesMay 13 2013Sep 04 2013It is known that any normed vector space which satisfies the parallelogram law is actually an inner product space. For finite dimensional normed vector spaces over R, we formulate an approximate version of this theorem: if a space approximately satisfies ... More

Eigenvalue Fluctuations of Symmetric Group Permutation Representations on k-tuples and k-subsetsOct 28 2018Let the term $k$-representation refer to the permutation representations of the symmetric group $\mathfrak{S}_n$ on $k$-tuples and $k$-subsets as well as the $S^{(n-k,1^k)}$ irreducible representation of $\mathfrak{S}_n$. Endow $\mathfrak{S}_n$ with the ... More

A Lower Bound for the Discrepancy of a Random Point SetOct 01 2012Oct 05 2013We show that there is a constant $K > 0$ such that for all $N, s \in \N$, $s \le N$, the point set consisting of $N$ points chosen uniformly at random in the $s$-dimensional unit cube $[0,1]^s$ with probability at least $1-\exp(-\Theta(s))$ admits an ... More

Computing the Cech cohomology of decomposition spacesDec 03 2017A line pattern in a free group $F$ is defined by a malnormal collection of cyclic subgroups. Otal defined a decomposition space $\mathcal{D}$ associated to a line pattern. We provide an algorithm that computes a presentation for the \v{C}ech cohomology ... More

A Combinatorial Identity for Rooted Labelled ForestsFeb 18 2019In this brief note a purely combinatorial proof for an identity related to rooted forests and unordered set partitions is provided. Furthermore, references that put this type of identity in the context of forest volumes are given.

Inverse zero-sum problems in finite Abelian p-groupsDec 10 2008In this paper, we study the minimal number of elements of maximal order within a zero-sumfree sequence in a finite Abelian p-group. For this purpose, in the general context of finite Abelian groups, we introduce a new number, for which lower and upper ... More

Etale twists in noncommutative algebraic geometry and the twisted Brauer spaceNov 26 2012Apr 17 2013This paper studies etale twists of derived categories of schemes and associative algebras. A general method, based on a new construction called the twisted Brauer space, is given for classifying etale twists, and a complete classification is carried out ... More

Cech approximation to the Brown-Gersten spectral sequenceDec 18 2009Feb 07 2011In this paper, we show that the etale index of a torsion cohomological Brauer class is divisible by the period of the class. The tool used to make this computation is the Cech approximation of the title. To create the approximation, we use the folklore ... More

Inequalities for generalized minorsMar 11 2013It is a classical result that the absolute value of any $k$-minor of an $r\times s$ real or complex matrix is bounded by the product of its first $k$ singular values. We generalize this statement to the context of real or complex simple Jordan pairs with ... More

The Category-Theoretic Arithmetic of InformationMar 25 2008Jul 21 2008We highlight the underlying category-theoretic structure of measures of information flow. We present an axiomatic framework in which communication systems are represented as morphisms, and information flow is characterized by its behavior when communication ... More

Minimal positive stencils in meshfree finite difference methods for the Poisson equationFeb 19 2008Jul 10 2008Meshfree finite difference methods for the Poisson equation approximate the Laplace operator on a point cloud. Desirable are positive stencils, i.e. all neighbor entries are of the same sign. Classical least squares approaches yield large stencils that ... More

Path-by-path well-posedness of nonlinear diffusion equations with multiplicative noiseJul 11 2018We prove the path-by-path well-posedness of stochastic porous media and fast diffusion equations driven by linear, multiplicative noise. As a consequence, we obtain the existence of a random dynamical system. This solves an open problem raised in [Barbu, ... More

Quantum spin pumping with adiabatically modulated magnetic barrier'sMar 29 2003Dec 09 2003A quantum pump device involving magnetic barriers produced by the deposition of ferro magnetic stripes on hetero-structure's is investigated. The device for dc- transport does not provide spin-polarized currents, but in the adiabatic regime, when one ... More

On smooth Gorenstein polytopesMar 08 2013A Gorenstein polytope of index r is a lattice polytope whose r-th dilate is a reflexive polytope. These objects are of interest in combinatorial commutative algebra and enumerative combinatorics, and play a crucial role in Batyrev's and Borisov's computation ... More

The Cartan-Hadamard Theorem for Metric Spaces with Local Geodesic BicombingsSep 23 2015Nov 07 2016Local-to-global principles are spread all-around in mathematics. The classical Cartan-Hadamard Theorem from Riemannian geometry was generalized by W. Ballmann for metric spaces with non-positive curvature, and by S. Alexander and R. Bishop for locally ... More

Long wave approximation for water waves under a Coriolis forcing and the Ostrovsky equationMar 29 2016Sep 09 2016This paper is devoted to the study of the long wave approximation for water waves under the influence of the gravity and a Coriolis forcing. We start by deriving a generalization of the Boussinesq equations in 1D (in space) and we rigorously justify them ... More

Blue hypertext is a perfect design decision: No perceptual disadvantage in reading and successful highlighting of relevant informationJan 13 2016Highlighted text in the Internet (i.e. Hypertext) is predominantly blue and underlined. The percept of these hypertext characteristics were heavily questioned by applied research and empirical tests resulted in inconclusive results. The ability to identify ... More

Coriolis effect on water wavesNov 23 2015Sep 09 2016This paper is devoted to the study of water waves under the influence of the gravity and the Coriolis force. It is quite common in the physical literature that the rotating shallow water equations are used to study such water waves. We prove a local wellposedness ... More