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Counting multi-quadratic number fields of bounded discriminantFeb 08 2019Feb 15 2019We prove an asymptotic formula for the number of multi-quadratic number fields of bounded discriminant with a power-saving error term. Furthermore, we explicitly calculate the leading coefficient and extend our result to totally real multi-quadratic number ... More

Counting multi-quadratic number fields of bounded discriminantFeb 08 2019We prove an asymptotic formula for the number of multi-quadratic number fields of bounded discriminant with a power-saving error term. Furthermore, we explicitly calculate the leading coefficient and extend our result to totally real multi-quadratic number ... More

Matter wave speckle observed in an out-of-equilibrium quantum fluidJun 06 2016Jan 23 2019We report the results of a direct comparison of a freely expanding turbulent Bose-Einstein condensate and the propagation of an optical speckle pattern. We found remarkably similar statistical properties underlying the spatial propagation of both phenomena. ... More

Chiral approach to nuclear matter: Role of explicit short-range NN-termsDec 16 2003We extend a recent chiral approach to nuclear matter by including the most general (momentum-independent) NN-contact interaction. Iterating this two-parameter contact-vertex with itself and with one-pion exchange the emerging energy per particle exhausts ... More

Proximity effect in superconductor/conical magnet heterostructuresSep 01 2014The presence of a spin-flip potential at the interface between a superconductor and a ferromagnetic metal allows for the generation of equal-spin spin-triplet Cooper pairs. These Cooper pairs are compatible with the exchange interaction within the ferromagnetic ... More

Lambda DeterminantsApr 27 2013In this paper we prove a homogenous generalization of the lambda determinant formula of Mills, Robbins and Rumsey. In our formula the parameters depends on two indices. Our result also extends a recent formula of Di Francesco.

Planetary Nebulae as Probes of Stellar PopulationsMay 02 2006Planetary nebulae (PNe) have the potential to revolutionize our understanding of extragalactic stellar populations. Indeed, in many systems, bright PNe are the only individual objects identifiable from the ground, and, even more often, they are the only ... More

Quantum and classical dynamics of methane scatteringJun 05 2001The dissociation of methane on transition metals is an important reaction in catalysis. It is the rate limiting step in steam reforming to produce syngas. Molecular beam experiments have shown that the energy in the internal vibrations are about as effective ... More

On Rao's Theorems and the Lazarsfeld-Rao PropertyFeb 07 2003Let $X$ be an integral projective scheme satisfying the condition $S_3$ of Serre and $H^1({\mathcal O}_X(n)) = 0$ for all $n \in {\mathbb Z}$. We generalize Rao's theorem by showing that biliaison equivalence classes of codimension two subschemes without ... More

A Shuffle that Mixes Sets of any Fixed Size much Faster than it Mixes the Whole DeckApr 02 2004Consider an n by n array of cards shuffled in the following manner. An element x of the array is chosen uniformly at random; Then with probability 1/2 the rectangle of cards above and to the left of x is rotated 180 degrees, and with probability 1/2 the ... More

Anomalous photon noise levels predicted for CMB measurements made by the Planck satellite missionMay 21 2009A fundamental assumption inherent in the standard Lambda+CDM Hot Big Bang (HBB) model is that photons lose energy as they are redshifted due to the expansion of the universe. We show that for the Quasi-Static Universe (QSU) model, in which photon energy ... More

Scale invariant gravity and the quasi-static universeMar 19 2002Apr 13 2002We highlight the fact that the lack of scale invariance in the gravitational field equations of General Relativity results from the underlying assumption that the appropriate scale for the gravitational force should be linked to the atomic scale. We show ... More

Machian General Relativity: a possible solution to the Dark Energy problem, and a replacement for Big Bang cosmologyJun 04 2001Jun 17 2001Observations of an apparent acceleration in the expansion rate of the universe, derived from measurements of high-redshift supernovae, have been used to support the hypothesis that the universe is permeated by some form of dark energy. We show that an ... More

Franklin's argument proves an identity of ZagierSep 04 2000Recently Zagier proved a remarkable q-series identity. We show that this identity can also be proved by modifying Franklin's classical proof of Euler's pentagonal number theorem.

A survey of random processes with reinforcementOct 02 2006Feb 23 2007The models surveyed include generalized P\'{o}lya urns, reinforced random walks, interacting urn models, and continuous reinforced processes. Emphasis is on methods and results, with sketches provided of some proofs. Applications are discussed in statistics, ... More

Questions of Connectedness of the Hilbert Scheme of Curves in ${\mathbb P}^3$Apr 27 2001We review the present state of the problem, for each degree $d$ and genus $g$, is the Hilbert scheme of locally Cohen--Macaulay curves in ${\mathbb P}^3$ connected?

Fast rate of convergence in high dimensional linear discriminant analysisSep 11 2009Feb 19 2010This paper gives a theoretical analysis of high dimensional linear discrimination of Gaussian data. We study the excess risk of linear discriminant rules. We emphasis on the poor performances of standard procedures in the case when dimension p is larger ... More

Cubic identities for theta series in three variablesSep 20 2000We introduce three-variable analogues of the theta series of Borwein and Borwein. We prove various identities involving these theta series including a generalization of the cubic identity of Borwein and Borwein.

Potentially diagonalisable lifts with controlled Hodge--Tate weightsDec 05 2018Mar 16 2019Motivated by the weight part of Serre's conjecture we consider the following question. Let $K/\mathbb{Q}_p$ be a finite extension and suppose $\overline{\rho} \colon G_K \rightarrow \operatorname{GL}_n(\overline{\mathbb{F}}_p)$ admits a crystalline lift ... More

Massey products and the Golod property for simplicially resolvable ringsJun 20 2018We apply algebraic Morse theory to the Taylor resolution of a monomial ring $R = S/I$ to obtain an $A_{\infty}$-structure on the minimal free resolution of $R$. Using this structure we describe the vanishing of higher Massey products in case the minimal ... More

Multisided Fairness for RecommendationJul 01 2017Jul 08 2017Recent work on machine learning has begun to consider issues of fairness. In this paper, we extend the concept of fairness to recommendation. In particular, we show that in some recommendation contexts, fairness may be a multisided concept, in which fair ... More

Inversion, Iteration, and the Art of Dual WieldingApr 02 2019The humble $\dagger$ ("dagger") is used to denote two different operations in category theory: Taking the adjoint of a morphism (in dagger categories) and finding the least fixed point of a functional (in categories enriched in domains). While these two ... More

Atmospheric heat redistribution and collapse on tidally locked rocky planetsDec 17 2014Atmospheric collapse is likely to be of fundamental importance to tidally locked rocky exoplanets but remains understudied. Here, general results on the heat transport and stability of tidally locked terrestrial-type atmospheres are reported. First, the ... More

The Planetary Nebula Luminosity Function at the Dawn of GaiaMar 25 2012The [O III] 5007 Planetary Nebula Luminosity Function (PNLF) is an excellent extragalactic standard candle. In theory, the PNLF method should not work at all, since the luminosities of the brightest planetary nebulae (PNe) should be highly sensitive to ... More

Choosing a Spanning Tree for the Integer Lattice UniformlyApr 02 2004Consider the nearest neighbor graph for the integer lattice Z^d in d dimensions. For a large finite piece of it, consider choosing a spanning tree for that piece uniformly among all possible subgraphs that are spanning trees. As the piece gets larger, ... More

Local-entire cyclic cocycles for graded quantum field netsJun 26 2013Feb 17 2014In a recent paper we studied general properties of super-KMS functionals on graded quantum dynamical systems coming from graded translation-covariant quantum field nets over R, and we carried out a detailed analysis of these objects on certain models ... More

On the Banach-Mazur Type for Normed SpacesDec 11 2008Jan 05 2009In order to measure qualitative properties we introduce a notion of a type for arbitrary normed spaces which measures the worst possible growth of partial sums of sequences weakly converging to zero. The ideas can be traced back to Banach and Mazur who ... More

A proof of Hadjicostas's conjectureMay 25 2004Jun 15 2004We prove a recent conjecture of Hadjicostas concerning a double integral formula involving the zeta and the gamma functions.

Clifford Index of ACM Curves in ${\mathbb P}^3$Apr 27 2001In this paper we review the notions of gonality and Clifford index of an abstract curve. For a curve embedded in a projective space, we investigate the connection between the \ci of the curve and the \gc al properties of its \emb. In particular if $C$ ... More

Some Remarks on the Hyperkähler ReductionJan 10 2017We consider a hyperk\"ahler reduction and describe it via frame bundles. Tracing the connection through the various reductions, we recover the results of Gocho and Nakajima. In addition, we show that the fibers of such a reduction are necessarily totally ... More

Classification of virtual string links up to cobordismFeb 24 2019Cobordism of virtual string links on $n$ strands is a combinatorial generalization of link cobordism. There exists a bijection between virtual string links up to cobordisms and elements of the group $\mathbb{Z}^{n(n-1)}$. This paper also shows that virtual ... More

A note on strong-form stability for the Sobolev inequalityJan 25 2019In this note, we establish a strong form of the quantitive Sobolev inequality in Euclidean space for $p \in (1,n)$. Given any function $u \in \dot W^{1,p}(\mathbb{R}^n)$, the gap in the Sobolev inequality controls $\| \nabla u -\nabla v\|_{p}$, where ... More

Cohomology of a Quaternionic ComplexJul 18 1995We investigate the cohomology of a certain elliptic complex defined on a compact quaternionic-K\"{a}hler manifold with negative scalar curvature. We show that this particular complex is exact, with the possible exception of one term.

Birkhoff's theorem in Lovelock gravityMay 03 2005We show that the generic solutions of the Lovelock equations with spherical, planar or hyperbolic symmetry are locally isometric to the corresponding static Lovelock black hole. As a consequence, these solutions are locally static: they admit an additional ... More

Decay of currents for strong interactionsMar 25 2011Jul 26 2011The decay of current autocorrelation functions is investigated for quantum systems featuring strong 'interactions'. Here, the term interaction refers to that part of the Hamiltonian causing the (major) decay of the current. On the time scale before the ... More

The Planetary Nebula Luminosity FunctionJul 14 2004The [O III] 5007 planetary nebula luminosity function (PNLF) occupies an important place on the extragalactic distance ladder: it is the only standard candle that can be applied to all the large galaxies of the Local Supercluster. We review the method's ... More

The Planetary Nebula Luminosity Function: Pieces of the PuzzleSep 24 2009Extragalactic surveys in the emission line of [O III] 5007 have provided us with the absolute line strengths of large, homogeneous sets of planetary nebulae. These data have been used to address a host of problems, from the measurement of the extragalactic ... More

Geometry of arithmetically Gorenstein curves in ${\mathbb P}^4$Jan 15 2003We characterize the postulation character of arithmetically Gorenstein curves in ${\mathbb P}^4$. We give conditions under which the curve can be realized in the form $mH-K$ on some ACM surface. Finally, we strengthen a theorem of Watanabe by showing ... More

Algebraic TopologyApr 30 2013Sep 10 2013The chapter provides an introduction to the basic concepts of Algebraic Topology with an emphasis on motivation from applications in the physical sciences. It finishes with a brief review of computational work in algebraic topology, including persistent ... More

Generalized Divisors and BiliaisonJan 15 2003Nov 29 2006We extend the theory of generalized divisors so as to work on any scheme $X$ satisfying the condition $S_2$ of Serre. We define a generalized notion of Gorenstein biliaison for schemes in projective space. With this we give a new proof in a stronger form ... More

Reassessment of the GZK cutoff in the spectrum of UHE cosmic rays in a universe with low photon-baryon ratioSep 29 2003A prediction of standard Big Bang cosmology is that the observed UHECR (ultra-high-energy cosmic rays) spectrum will exhibit a cutoff at the GKZ limit, resulting from interaction with the photons that constitute the cosmic microwave background. We show ... More

Homotopy Bott-Taubes integrals and the Taylor tower for spaces of knots and linksFeb 11 2011Jun 02 2015This work continues the study of a homotopy-theoretic construction of the author inspired by the Bott-Taubes integrals. Bott and Taubes constructed knot invariants by integrating differential forms along the fiber of a bundle over the space of knots. ... More

Inhomogeneous Parabolic Neumann ProblemsAug 31 2011We study second order parabolic equations on Lipschitz domains subject to inhomogeneous Neumann (or, more generally, Robin) boundary conditions. We prove existence and uniqueness of weak solutions and their continuity up to the boundary of the parabolic ... More

Conference matrices and unimodular latticesJul 19 2000Conference matrices are used to define complex structures on real vector spaces. Certain lattices in these spaces become modules for rings of quadratic integers. Multiplication of these lattices by non-principal ideals yields simple constructions of further ... More

A strong form of the quantitative Wulff inequalityMar 23 2015Mar 26 2016Quantitative isoperimetric inequalities for anisotropic surface energies are shown where the isoperimetric deficit controls both the Fraenkel asymmetry and a measure of the oscillation of the boundary with respect to the boundary of the corresponding ... More

QPEL: Quantum Program and Effect LanguageDec 30 2014We present the syntax and rules of deduction of QPEL (Quantum Program and Effect Language), a language for describing both quantum programs, and properties of quantum programs - effects on the appropriate Hilbert space. We show how semantics may be given ... More

Geometric construction of quasiconformal mappings in the Heisenberg groupDec 05 2016In this paper, we are interested in the construction of quasiconformal mappings between domains of the Heisenberg group H that minimise a mean distortion functional. We propose to construct such mappings by considering a corresponding problem between ... More

Building reverse plane partitions with rim-hook-shaped bricksDec 12 2016Jan 23 2017The generating function of reverse plane partitions of a fixed shape factors into a product featuring the hook-lengths of this shape. This result, which was first obtained by Stanley, can be explained bijectively using the Hillman-Grassl correspondence ... More

Lower bound on entanglement in subspaces defined by Young diagramsMay 01 2018Jan 29 2019Eigenvalues of 1-particle reduced density matrices of $N$-fermion states are upper bounded by $1/N$, resulting in a lower bound on entanglement entropy. We generalize these bounds to all other subspaces defined by Young diagrams in the Schur-Weyl decomposition ... More

Cancellation of homothetic modulesJan 07 2018Let R be a commutative ring, M an R-module, and N a finitely presented R-module such that the intersection of Max(R) and Supp(N) is finite-dimensional and Noetherian. Suppose also that N is homothetic; in other words, suppose that the natural ring homomorphism ... More

Representation Learning for Recommender Systems with Application to the Scientific LiteratureFeb 28 2019The scientific literature is a large information network linking various actors (laboratories, companies, institutions, etc.). The vast amount of data generated by this network constitutes a dynamic heterogeneous attributed network (HAN), in which new ... More

Local convergence of large critical multi-type Galton-Watson trees and applications to random mapsDec 22 2014Aug 01 2016We show that large critical multi-type Galton-Watson trees, when conditioned to be large, converge locally in distribution to an infinite tree which is analoguous to Kesten's infinite monotype Galton-Watson tree. This is proven when we condition on the ... More

QCD Sum Rule Studies of Heavy Quarkonium-like StatesJul 08 2014The research presented here uses QCD sum rules (QSR) to study exotic hadrons. There are several themes in this work. First is the use of QSR to predict the masses of exotic hadrons that may exist among the heavy quarkonium-like states. The second theme ... More

Inserting rim-hooks into reverse plane partitionsOct 26 2017May 21 2018A new algorithm for inserting rim-hooks into reverse plane partitions is presented. The insertion is used to define a bijection between reverse plane partitions of a fixed shape and multi-sets of rim-hooks. In turn this yields a bijective proof of the ... More

Linear Logic without UnitsMay 09 2013We study categorical models for the unitless fragment of multiplicative linear logic. We find that the appropriate notion of model is a special kind of promonoidal category. Since the theory of promonoidal categories has not been developed very thoroughly, ... More

Quantum Multiple ScatteringMar 12 2010The quest for Anderson localization of light is at the center of many experimental and the- oretical activities. Atomic vapors play a particular role in this research field, as they show a number of specific properties which makes them quite different ... More

Distances from Planetary NebulaeJan 15 2003The [O III] 5007 planetary nebula luminosity function (PNLF) occupies an important place on the extragalactic distance ladder. Since it is the only method that is applicable to all the large galaxies of the Local Supercluster, it is uniquely useful for ... More

Causal Models for Estimating the Effects of Weight Gain on MortalityFeb 04 2008Suppose, contrary to fact, in 1950, we had put the cohort of 18 year old non-smoking American men on a stringent mandatory diet that guaranteed that no one would ever weigh more than their baseline weight established at age 18. How would the counter-factual ... More

The International Epsilon Aurigae Campaign 2009-2011. A description of the campaign and early results to May 2010Jan 07 2011In early 2009, immediately following the end of the WR140 periastron campaign (see these proceedings), I turned my telescope back to epsilon Aurigae in time for the start of the eclipse. As well as being an interesting object in its own right, the Pro-Am ... More

N-Gram Cluster Identification During Empirical Knowledge Representation GenerationDec 05 1994This paper presents an overview of current research concerning knowledge extraction from technical texts. In particular, the use of empirical techniques during the identification and generation of a semantic representation is considered. A key step is ... More

PL3: Structure FunctionsJan 14 1998Recent measurements of unpolarised and polarised nucleon structure functions and F_2(gamma) are reviewed. The implications for QCD and the gluon momentum distribution are discussed. The status of the understanding of the total virtual-photon proton total ... More

Risk bounds for purely uniformly random forestsJun 15 2010Random forests, introduced by Leo Breiman in 2001, are a very effective statistical method. The complex mechanism of the method makes theoretical analysis difficult. Therefore, a simplified version of random forests, called purely random forests, which ... More

Experiments with Gorenstein LiaisonJun 28 2001We give some experimental data of Gorenstein liaison, working with points in ${\mathbb P}^3$ and curves in ${\mathbb P}^4$, to see how far the familiar situation of liaison, biliaison, and Rao modules of curves in ${\mathbb P}^3$ will extend to subvarieties ... More

Lambda-Free Logical FrameworksApr 11 2008Nov 18 2008We present the definition of the logical framework TF, the Type Framework. TF is a lambda-free logical framework; it does not include lambda-abstraction or product kinds. We give formal proofs of several results in the metatheory of TF, and show how it ... More

Enumeration of Cylindric Plane Partitions - part IApr 20 2012Cylindric plane partitions may be thought of as a natural generalization of reverse plane partitions. A generating series for the enumeration of cylindric plane partitions was recently given by Borodin. The first result of this paper is a $(q,t)$-analog ... More

General Fragmentation TreesMar 27 2013Mar 31 2013We show that the genealogy of any self-similar fragmentation process can be encoded in a compact measured real tree. Under some Malthusian hypotheses, we compute the fractal Hausdorff dimension of this tree through the use of a natural measure on the ... More

Periodic points of quadratic polynomials in Galois extensionsOct 04 2016Oct 13 2016For quadratic polynomials with coefficients in a field $k$ of characteristic zero, we seek to understand the periodic points under the actions of its iteration and the absolute Galois group $\mathrm{Gal}(\bar{k}/k)$. Supported by previous numerical work, ... More

A-infinity resolutions and the Golod property for monomial ringsDec 08 2016Let R=S/I be a monomial ring whose minimal free resolution F is rooted. We describe an A-infinity algebra structure on F. Using this structure, we show that R is Golod if and only if the product on Tor^S(R,k) vanishes. Furthermore, we give a necessary ... More

Tree-indexed processesApr 05 2004This article examines a recent body of work on stochastic processes indexed by a tree. Emphasis is on the application of this new framework to existing probability models. Proofs are largely omitted, with references provided.

Super-KMS functionals for graded-local conformal netsApr 23 2012Jul 16 2014Motivated by a few preceding papers and a question of R. Longo, we introduce super-KMS functionals for graded translation-covariant nets over R with superderivations, roughly speaking as a certain supersymmetric modification of classical KMS states on ... More

A note on the implicit function theorem for quasi-linear eigenvalue problemsSep 23 2011We consider the quasi-linear eigenvalue problem $-\Delta_p u = \lambda g(u)$ subject to Dirichlet boundary conditions on a bounded open set $\Omega$, where $g$ is a locally Lipschitz continuous functions. Imposing no further conditions on $\Omega$ or ... More

Approximation of the Semigroup generated by the Robin Laplacian in terms of the Gaussian SemigroupJul 09 2008For smooth bounded open sets in euclidean space, we construct corresponding contractive linear extension operators for the space of continuous functions which preserve regularity of functions in the domain of the Robin Laplacian. We also prove a Trotter-like ... More

Combinatorial proofs of q-series identitiesSep 03 2001We provide combinatorial proofs of some of the q-series identities considered by Andrews, Jimenez-Urroz and Ono [q-series identities and values of certain $L$-functions. Duke Math. J. 108 (2001), no. 3, 395--419].

Bott-Taubes/Vassiliev cohomology classes by cut-and-paste topologyDec 21 2015Oct 12 2018Bott and Taubes used integrals over configuration spaces to produce finite-type (a.k.a. Vassiliev) knot invariants. Their techniques were then used to construct "Vassiliev classes" in the real cohomology spaces of knots and links in higher-dimensional ... More

Time and place of the maximum for one-dimensional diffusion bridges and meandersJul 23 2018For three constrained Brownian motions, the excursion, the meander, and the reflected bridge, the densities of the maximum and of the time to reach it were expressed as double series by Majumdar, Randon-Furling, Kearney, and Yor (2008). Some of these ... More

Differential forms on three dimensional CR manifoldsJul 20 2018We are dealing with differential forms on $3$-dimensional strictly pseudoconvex CR manifolds. Considering Rumin complex introduced in \cite {Rum} and its decomposition (see \cite{GL}), we are able to define two objects. The first one is a differential ... More

Investigation of Algorithms for Highly Nonlinear Model Fitting on Big DatasetsDec 18 2017Dec 19 2017This thesis investigates algorithms regarding their applicability for highly nonlinear model fitting on big datasets. Various mathematical methods are presented with which a model fit using the least squares criterion is possible. Special requirements ... More

Some Comments on Multiple Discovery in MathematicsDec 11 2014Among perhaps many things common to Kuratowski's Theorem in graph theory, Reidemeister's Theorem in topology, and Cook's Theorem in theoretical computer science is this: all belong to the phenomenon of simultaneous discovery in mathematics. We are interested ... More

Hyperbolicity and stable polynomials in combinatorics and probabilityOct 11 2012This was the basis of two lectures in the Current Developments in Mathematics conference in 2011. These lectures survey the theory of hyperbolic and stable polynomials, from their origins in the theory of linear PDE's to their present uses in combinatorics ... More

Rational Shi tableaux and the skew length statisticDec 14 2015Sep 15 2016We define two refinements of the skew length statistic on simultaneous core partitions. The first one relies on hook lengths and is used to prove a refined version of the theorem stating that the skew length is invariant under conjugation of the core. ... More

Spin transport in the XXZ model at high temperatures: Classical dynamics versus quantum S=1/2 autocorrelationsOct 30 2011Feb 14 2012The transport of magnetization is analyzed for the classical Heisenberg chain at and especially above the isotropic point. To this end, the Hamiltonian equations of motion are solved numerically for initial states realizing harmonic-like magnetization ... More

Self-gravitating branes of codimension 4 in Lovelock gravityJan 15 2008We construct a familly of exact solutions of Lovelock equations describing codimension four branes with discrete symmetry in the transverse space. Unlike what is known from pure Einstein gravity, where such brane solutions of higher codimension are singular, ... More

An optimal quantum algorithm for the oracle identification problemNov 29 2013Jan 06 2014In the oracle identification problem, we are given oracle access to an unknown N-bit string x promised to belong to a known set C of size M and our task is to identify x. We present a quantum algorithm for the problem that is optimal in its dependence ... More

Some Examples of Gorenstein Liaison in Codimension ThreeMar 22 2001Oct 02 2001Gorenstein liaison seems to be the natural notion to generalize to higher codimension the well-known results about liaison of varieties of codimension~2 in projective space. In this paper we study points in ${\mathbb P}^3$ and curves in ${\mathbb P}^4$ ... More

Potentially diagonalisable lifts with controlled Hodge--Tate weigthsDec 05 2018Motivated by the weight part of Serre's conjecture we consider the following question. Let $K/\mathbb{Q}_p$ be a finite extension and suppose $\overline{\rho} \colon G_K \rightarrow \operatorname{GL}_n(\overline{\mathbb{F}}_p)$ admits a crystalline lift ... More

Towards a theory of negative dependenceApr 05 2004The FKG theorem says that the POSITIVE LATTICE CONDITION, an easily checkable hypothesis which holds for many natural families of events, implies POSITIVE ASSOCIATION, a very useful property. Thus there is a natural and useful theory of positively dependent ... More

The Milnor triple-linking number of string links by cut-and-paste topologySep 27 2012Oct 29 2013Bott and Taubes constructed knot invariants by integrating differential forms along the fiber of a bundle over the space of knots, generalizing the Gauss linking integral. Their techniques were later used to construct real cohomology classes in spaces ... More

Symmetry properties of the Novelli-Pak-Stoyanovskii algorithmMar 20 2014The number of standard Young tableaux of a fixed shape is famously given by the hook-length formula due to Frame, Robinson and Thrall. A bijective proof of Novelli, Pak and Stoyanovskii relies on a sorting algorithm akin to jeu-de-taquin which transforms ... More

Regularity of Solutions of Linear Second Order Elliptic and Parabolic Boundary Value Problems on Lipschitz DomainsJun 29 2009For a linear, strictly elliptic second order differential operator in divergence form with bounded, measurable coefficients on a Lipschitz domain $\Omega$ we show that solutions of the corresponding elliptic problem with Robin and thus in particular with ... More

Betti number signatures of homogeneous Poisson point processesSep 22 2006The Betti numbers are fundamental topological quantities that describe the k-dimensional connectivity of an object: B_0 is the number of connected components and B_k effectively counts the number of k-dimensional holes. Although they are appealing natural ... More

Finite Products are Biproducts in a Compact Closed CategoryApr 25 2006May 02 2007If a compact closed category has finite products or finite coproducts then it in fact has finite biproducts, and so is semi-additive.

Low degree hypersurfaces of projective toric varieties defined over a $C_1$ field have a rational pointJul 25 2014Aug 20 2014Quasi algebraically closed fields, or $C_1$ fields, are defined in terms of a low degree condition. Namely, the field $K$ is $C_1$ if every degree $d$ hypersurface of the projective space $\mathbb{P}_K^n$ contains a $K$-point as soon as $d\leq n$. In ... More

The Climate of Early MarsJun 09 2016The nature of the early Martian climate is one of the major unanswered questions of planetary science. Key challenges remain, but a new wave of orbital and in situ observations and improvements in climate modeling have led to significant advances over ... More

Nearly optimal separations between communication (or query) complexity and partitionsDec 03 2015We show a nearly quadratic separation between deterministic communication complexity and the logarithm of the partition number, which is essentially optimal. This improves upon a recent power 1.5 separation of G\"o\"os, Pitassi, and Watson (FOCS 2015). ... More

A property relating the Galois theory and arithmetic dynamics of unicritical polynomialsOct 04 2016Aug 31 2018For the polynomial $\phi_c(z) := z^2 + c$ with rational $c$, Vivaldi and Hatjispyros demonstrated that a subgroup of the Galois group of the $N$-th dynatomic polynomial $\Phi_N$ mimics the action of $\phi_c$ on periodic points of exact period $N$ whenever ... More

Surjective and splitting capacitiesOct 16 2017Jan 08 2018Let R be a commutative ring, S a module-finite R-algebra, M a right S-module, and N a finitely generated right S-module such that the intersection of Max(R) and Supp(N) is finite-dimensional and Noetherian. Working under various combinations of additional ... More

Inertial and Hodge--Tate weights of crystalline representationsNov 26 2018Let $K$ be an unramified extension of $\mathbb{Q}_p$ and $\rho\colon G_K \rightarrow \operatorname{GL}_n(\overline{\mathbb{Z}}_p)$ a crystalline representation. If the Hodge--Tate weights of $\rho$ differ by at most $p$ then we show that these weights ... More

Chiral Dynamics and Nuclear MatterMay 22 2001We calculate the equation of state of isospin-symmetric nuclear matter in the three-loop approximation of chiral perturbation theory. The contributions to the energy per particle $\bar E(k_f)$ from one- and two-pion exchange diagrams are ordered in powers ... More

Nuclear mean field from chiral pion-nucleon dynamicsAug 06 2001Using the two-loop approximation of chiral perturbation theory, we calculate the momentum and density dependent single particle potential of nucleons in isospin-symmetric nuclear matter. The contributions from one- and two-pion exchange diagrams give ... More

Incomplete graphical model inference via latent tree aggregationMay 26 2017Mar 21 2018Graphical network inference is used in many fields such as genomics or ecology to infer the conditional independence structure between variables, from measurements of gene expression or species abundances for instance. In many practical cases, not all ... More