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The failure of the Classical Nucleation Theory at low temperatures resolvedFeb 08 2019A relevant observation about crystal nucleation kinetics in glass-forming substances has been a matter of intense debate for several decades. The Classical Nucleation Theory (CNT) allegedly fails to describe the temperature dependence of the homogeneous ... More

A mechanical autonomous stochastic heat engineJan 27 2016Stochastic heat engines are devices that generate work from random thermal motion using a small number of highly fluctuating degrees of freedom. Proposals for such devices have existed for more than a century and include the Maxwell demon and the Feynman ... More

SU Uma stars: Rebrightenings after superoutburstApr 02 2015SU Uma stars after their long superoutbursts often show single or multiple rebrightenings. We show how this phenomenon can be understood as repeated reflections of transition waves which mediate changes between the hot and the cool state of the accretion ... More

Broad iron emission lines in Seyfert Galaxies - re-condensation of gas onto an inner disk below the ADAFJan 25 2011Recent observations of Seyfert 1 AGN with Chandra, XMM-Newton and Suzaku revealed broad iron K_alpha emission lines, some relativistically blurred. For galactic black hole X-ray binaries XMM-Newton spectra during hard state also reveal the presence of ... More

The formation of the coronal flow/ADAFMar 24 2003We develop a new method to describe the accretion flow in the corona above a thin disk around a black hole in vertical and radial extent. The model is based on the same physics as the earlier one-zone model, but now modified including inflow and outflow ... More

The effect of disk magnetic fields on the truncation of geometrically thin disks in AGNJul 26 2002We suggest that magnetic fields in the accretion disks of AGN reach into the coronae above and have a profound effect on the mass flow rate in the corona. This strongly affects the location where the accretion flow changes from a geometrically thin disk ... More

A limit for the mass transfer rate in soft X-ray transientsMar 03 2000Many black hole X-ray transients are in a low state for several decades until an outburst occurs. We interpret this outburst behaviour as a marginal occurrence of a dwarf nova type disk instability in the cool outer accretion disk. We compute the disk ... More

A disk in the Galactic Center in the past ?Oct 04 2004We raise the question whether in the past a disk could have existed in our Galactic Center which has disappeared now. Our model for the interaction of a cool disk and a hot corona above (Liu et al. 2004) allows to estimate an upper limit for the mass ... More

Evaporation: The change from accretion via a thin disk to a coronal flowJul 07 2000We present a model for a corona above a geometrically thin standard disk around a black hole. This corona is fed by matter from the thin disk which evaporates from the cool layers underneath. An equilibrium establishes between the cool accretion stream ... More

The SiC problem: astronomical and meteoritic evidenceJan 11 1999Pre-solar grains of silicon carbide found in meteorites and interpreted as having had an origin around carbon stars from their isotopic composition, have all been found to be of the beta-SiC polytype. Yet to date fits to the 11.3 microns SiC emission ... More

Re-condensation from an ADAF into an inner disk - the intermediate state of black hole accretion?Nov 15 2006Context: Accretion onto galactic and supermassive black holes occurs in different modes, which are documented in hard and soft spectral states, commonly attributed to an advection-dominated flow (ADAF) inside a truncated disk and standard disk accretion, ... More

Black hole X-ray binaries: A new view on soft-hard spectral transitionsFeb 02 2000The theory of coronal evaporation predicts the formation of an inner hole in the cool thin accretion disk for mass accretion rates below a certain value (~ 1/50 of the Eddington mass accretion rate) and the sudden disappearance of this hole when the mass ... More

WZ Sagittae - an old dwarf novaSep 23 1998We model the evolution of the accretion disk of WZ Sagittae during the long quiescence. We find that the large amount of mass in the disk derived from the outburst luminosity is a severe constraint and demands values of $\alpha_c$ $\approx$ 0.001 in contradiction ... More

Low heat conduction in white dwarf boundary layers?Mar 13 2008X-ray spectra of dwarf novae in quiescence observed by Chandra and XMM-Newton provide new information on the boundary layers of their accreting white dwarfs. Comparison of observations and models allows us to extract estimates for the thermal conductivity ... More

Riemann Hypothesis and Random Walks: the Zeta caseJan 05 2016Feb 05 2016In previous work it was shown that if certain series based on sums over primes of non-principal Dirichlet characters have a conjectured random walk behavior, then the Euler product formula for its $L$-function is valid to the right of the critical line ... More

Quantum statistical mechanics of gases in terms of dynamical filling fractions and scattering amplitudesNov 17 2006We develop a finite temperature field theory formalism in any dimension that has the filling fractions as the basic dynamical variables. The formalism efficiently decouples zero temperature dynamics from the quantum statistical sums. The zero temperature ... More

Quantum critical spin liquids and superconductivity in the cupratesOct 30 2006Nov 17 2006We describe a new kind of quantum critical point in the context of quantum anti-ferromagnetism in 2d that can be understood as a quantum critical spin liquid. Based on the comparison of exponents with previous numerical work, we argue it describes a transition ... More

An asymptotic upper bound on prime gapsJun 10 2015Oct 07 2015The Cram\'er-Granville conjecture is an upper bound on prime gaps, $g_n = p_{n+1} - p_n < \cCramer \, \log^2 p_n$ for some constant $\cCramer \geq 1$. Using a formula of Selberg, we first prove the weaker summed version: $\sum_{n=1}^N g_n < \sum_{n=1}^N ... More

Superconductivity in the two-dimensional Hubbard model based on the exact pair potentialAug 30 2010Sep 09 2010We analyze solutions to a superconducting gap equation based on the two-dimensional Hubbard model with nearest and next-to-nearest neighbor hopping. The Cooper pair potential can be calculated exactly and expressed in terms of elliptic functions. The ... More

3D Ising and other models from symplectic fermionsOct 30 2006Nov 06 2012We study a model of N component symplectic fermions in D spacetime dimensions. It has an infra-red stable fixed point in 2<D<4 dimensions referred to as Sp{2N}{D}. Based on the comparison of exponents, we conjecture that the critical exponents for the ... More

The Froissart bound for inelastic cross-sectionsApr 23 2009Aug 14 2009We prove that while the total cross{}-section is bounded by $(\pi/m_\pi^2) \ln^2 s$, where $s$ is the square of the c.m. energy and $m_\pi$ the mass of the pion, the total inelastic cross{}-section is bounded by $(1/4)(\pi/m_\pi^2) \ln^2 s$, which is ... More

The rigorous analyticity-unitarity program and its successesJun 16 1999We show how the combination of analyticity properties derived from local field theory and the unitarity condition (in particular positivity) leads to non-trivial physical results, including the proof of the "Froissart bound" from first principles and ... More

Representations of surface groups in the projective general linear groupJan 15 2009Aug 14 2010Given a closed, oriented surface X of genus g>1, and a semisimple Lie group G, let R_G be the moduli space of reductive representations of the fundamental group of X in G. We determine the number of connected components of R_PGL(n,R), for n>=4 even. In ... More

Hyperbolicity and Cubulability Are Preserved Under Elementary EquivalenceJan 29 2018The following properties are preserved under elementary equivalence, among finitely generated groups: being hyperbolic (possibly with torsion), being hyperbolic and cubulable, and being a subgroup of a hyperbolic group. In other words, if a finitely generated ... More

The general 1D Schrödinger equation as an exactly solvable problemDec 14 2004We review an exact WKB resolution method for the stationary 1D Schr\"odinger equation with a general polynomial potential. This contribution covers already published material: we supply a commented summary here, stressing a few aspects which were less ... More

Atomic quantum gases in periodically driven optical latticesJun 26 2016Time periodic forcing in the form of coherent radiation is a standard tool for the coherent manipulation of small quantum systems like single atoms. In the last years, periodic driving has more and more also been considered as a means for the coherent ... More

On the viscosity to entropy density ratio for unitary Bose and Fermi GasesDec 27 2010Jul 08 2011We calculate the ratio of the viscosity to the entropy density for both Bose and Fermi gases in the unitary limit using a new approach to the quantum statistical mechanics of gases based on the S-matrix. In the unitary limit the scattering length diverges ... More

Quantum critical spin liquids and conformal field theory in 2+1 dimensionsOct 23 2006Jan 12 2007We describe new conformal field theories based on symplectic fermions that can be extrapolated between 2 and 4 dimensions. The critical exponents depend continuously on the number of components N of the fermions and the dimension D. In the context of ... More

Chiral stabilization of the renormalization group for flavor and color anisotropic current interactionsMay 10 2001Aug 29 2001We propose an all-orders beta function for current-current interactions in 2d with flavor anisotropy. When the number of left-moving and right-moving flavors are unequal, the beta function has a non-trivial fixed point at finite values of the couplings. ... More

Macroscopic limit of the Becker-Döring equation via gradient flowsJul 29 2016This work considers gradient structures for the Becker-D\"oring equation and its macroscopic limits. The result of Niethammer [16] is extended to proof the convergence not only for solutions of the Becker-D\"oring equation towards the Lifshitz-Slyozov-Wagner ... More

A new convergence proof for the higher-order power method and generalizationsJul 17 2014Jan 23 2015A proof for the point-wise convergence of the factors in the higher-order power method for tensors towards a critical point is given. It is obtained by applying established results from the theory of \L{}ojasiewicz inequalities to the equivalent, unconstrained ... More

On the Kodaira-Spencer map of abelian schemesJun 12 2016Let $A$ be an abelian scheme over a smooth affine complex variety $S$, $\varOmega_A$ the $\sO_S$-module of $1$-forms of the first kind on $A$, $\sD_S\varOmega_A$ the $\sD_S$-module spanned by $\varOmega_A$ in the first algebraic De Rham cohomology module, ... More

Uniform sheaves and differential equationsJul 14 2012Real blow-ups and more refined "zooms" play a key role in the analysis of singularities of complex-analytic differential modules. They do not change the underlying topology, but the uniform structure. This suggests to revisit the cohomology theory of ... More

Discretized Keiper/Li approach to the Riemann HypothesisMar 08 2017Jul 17 2017The Keiper--Li sequence $\{ \lambda _n \}$ is most sensitive to the Riemann Hypothesis asymptotically ($n \to \infty$), but highly elusive both analytically and numerically. We deform it to fully explicit sequences, simpler to analyze and to compute (up ... More

Simplifications of the Keiper/Li approach to the Riemann HypothesisFeb 10 2016The Keiper/Li constants $\{\lambda_n\}_{n=1,2,\ldots}$ are asymptotically ($n \to \infty$) sensitive to the Riemann Hypothesis, but highly elusive analytically and difficult to compute numerically. We present quite explicit variant sequences that stay ... More

Viterbi Algorithm Generalized for n-Tape Best-Path SearchDec 07 2006We present a generalization of the Viterbi algorithm for identifying the path with minimal (resp. maximal) weight in a n-tape weighted finite-state machine (n-WFSM), that accepts a given n-tuple of input strings (s_1,... s_n). It also allows us to compile ... More

Acronym-Meaning Extraction from Corpora Using Multi-Tape Weighted Finite-State MachinesDec 06 2006The automatic extraction of acronyms and their meaning from corpora is an important sub-task of text mining. It can be seen as a special case of string alignment, where a text chunk is aligned with an acronym. Alternative alignments have different cost, ... More

Critical points of 2d disordered Dirac fermions: the Quantum Hall Transitions revisitedOct 22 2007May 30 2008We propose a resolution of the renormalization group flow for the disordered Dirac fermion theories describing the quantum Hall transition (QHT) and spin Quantum Hall transition (SQHT), which previously revealed no perturbative fixed points at 1-loop ... More

The gl(1|1) super-current algebra: the role of twist and logarithmic fieldsOct 16 2007A free field representation of the gl(1|1)_k current algebra at arbitrary level k is given in terms of two scalar fields and a symplectic fermion. The primary fields for all representations are explicitly constructed using the twist and logarithmic fields ... More

Usage-based vs. Citation-based Methods for Recommending Scholarly Research ArticlesMar 28 2013Mar 29 2013There are two principal data sources for collaborative filtering recommenders in scholarly digital libraries: usage data obtained from harvesting a large, distributed collection of Open URL web logs and citation data obtained from the journal articles. ... More

Recent Progress on Singularities of Lagrangian Mean Curvature FlowDec 09 2010We survey some of the state of the art regarding singularities in Lagrangian mean curvature flow. Some open problems are suggested at the end.

Idées galoisiennesJul 14 2012Classical applications of Galois theory concern algebraic numbers and algebraic functions. Still, the night before his duel, Galois wrote that his last mathematical thoughts had been directed toward applying his "theory of ambiguity to transcendental ... More

Structure des connexions méromorphes formelles de plusieurs variables et semi-continuité de l'irrégularitéJan 30 2007We prove Malgrange's conjecture on the absence of confluence phenomena for integrable meromorphic connections. More precisely, if $ Y\to X$ is a complex-analytic fibration by smooth curves, $Z$ a hypersurface of $Y$ finite over $X$, and $\nabla$ an integrable ... More

Dynamic Logics of Dynamical SystemsMay 22 2012We survey dynamic logics for specifying and verifying properties of dynamical systems, including hybrid systems, distributed hybrid systems, and stochastic hybrid systems. A dynamic logic is a first-order modal logic with a pair of parametrized modal ... More

Zeta-regularisation for exact-WKB resolution of a general 1D Schrödinger equationFeb 14 2012Apr 06 2012We review an exact analytical resolution method for general one-dimensional (1D) quantal anharmonic oscillators: stationary Schr\"odinger equations with polynomial potentials. It is an exact form of WKB treatment involving spectral (usual) vs "classical" ... More

On octahedraliy and Müntz spacesNov 05 2018We show that every M\"untz space can be written as a direct sum of Banach spaces X and Y , where Y is almost isometric to a subspace of c and X is finite dimensional. We apply this to show that no M\"untz space is locally octahedral or almost square.

Function call overhead benchmarks with MATLAB, Octave, Python, Cython and CFeb 13 2012We consider the overhead of function calls in the programming languages MATLAB/Octave, Python, Cython and C. In many applications a function has to be called very often inside a loop. One such application in numerical analysis is the finite element method ... More

Interacting Bose and Fermi gases in low dimensions and the Riemann hypothesisNov 17 2006Sep 18 2007We apply the S-matrix based finite temperature formalism to non-relativistic Bose and Fermi gases in 1+1 and 2+1 dimensions. In the 2+1 dimensional case, the free energy is given in terms of Roger's dilogarithm in a way analagous to the relativistic 1+1 ... More

An electrostatic depiction of the validity of the Riemann Hypothesis and a formula for the N-th zero at large NMay 12 2013Sep 18 2013We construct a vector field E from the real and imaginary parts of an entire function xi (z) which arises in the quantum statistical mechanics of relativistic gases when the spatial dimension d is analytically continued into the complex z plane. This ... More

Energy loss mechanism for suspended micro- and nanoresonators due to the Casimir forceMay 11 2011A so far not considered energy loss mechanism in suspended micro- and nanoresonators due to noncontact acoustical energy loss is investigated theoretically. The mechanism consists on the conversion of the mechanical energy from the vibratory motion of ... More

Baryons made of heavy quarks at the LHCSep 29 2014Oct 08 2014Baryons made of heavy quarks are extremely interesting and could be seen at the LHC.

The Herschel View of Star FormationSep 30 2013Recent studies of the nearest star-forming clouds of the Galaxy at submillimeter wavelengths with the Herschel Space Observatory have provided us with unprecedented images of the initial conditions and early phases of the star formation process. The Herschel ... More

From exact-WKB toward singular quantum perturbation theory IIMar 17 2006Following earlier studies, several new features of singular perturbation theory for one-dimensional quantum anharmonic oscillators are computed by exact WKB analysis; former results are thus validated.

A sharpening of Li's criterion for the Riemann HypothesisApr 10 2004Apr 15 2004Exact and asymptotic formulae are displayed for the coefficients $\lambda_n$ used in Li's criterion for the Riemann Hypothesis. In particular, we argue that if (and only if) the Hypothesis is true, $\lambda_n \sim n(A \log n +B)$ for $n \to \infty$ (with ... More

On nef and semistable hermitian lattices, and their behaviour under tensor productAug 09 2010We study the behaviour of semistability under tensor product in various settings: vector bundles, euclidean and hermitian lattices (alias Humbert forms or Arakelov bundles), multifiltered vector spaces. One approach to show that semistable vector bundles ... More

Approximations for the free evolution of self-gravitating quantum particlesMar 09 2015Aug 01 2016The evolution of the centre-of-mass wave-function for a mesoscopic particle according to the Schr\"odinger-Newton equation can be approximated by a harmonic potential, if the wave-function is narrow compared to the size of the particle. It was noticed ... More

Coherent pairs of measures and Markov-Bernstein inequalitiesMay 11 2016All the coherent pairs of measures associated to linear functionals $c_0$ and $c_1$, introduced by Iserles et al in 1991, have been given by Meijer in 1997. There exist seven kinds of coherent pairs. All these cases are explored in order to give three ... More

Filtrations de type Hasse-Arf et monodromie p-adiqueMar 23 2002One proves the Crew-Tsuzuki "p-adic local monodromy conjecture" (for local fields of characteristic p>0).

Différentielles non commutatives et théorie de Galois différentielle ou aux différencesMar 26 2002We show how the Galois-Picard_Vessiot theory of differential equations and difference equations, and the theory of holonomy groups in differential geometry, are different aspects of a unique Galois theory. The latter is based upon the construction and ... More

Phenomenological modeling of long range noncontact friction in micro- and nanoresonatorsApr 14 2011Oct 05 2011Motivated by the results of an experiment using atomic force microscopy performed by Gotsmann and Fuchs [Phys. Rev. Lett. {\bf 86}, 2597 (2001)], where a strong energy loss due to the tip-sample interaction was measured, we investigate the potential implications ... More

Possible Cooper instabilities in pair Green functions of the two-dimensional Hubbard modelJul 26 2011Nov 06 2012In analogy with ordinary BCS superconductivity, we identify possible pairing instabilities with poles in a certain class of Green functions of the two-dimensional repulsive Hubbard model, which normally signify bound states. Relating the gap to the location ... More

Analytical analysis of Lyot coronographsNov 30 2006Dec 18 2006We derive an analytical solution to the computation of the output of a Lyot coronagraph for a given complex amplitude on the pupil plane. This solution, which does not require any simplifying assumption, relies on an expansion of the entrance complex ... More

Sharpenings of Li's criterion for the Riemann HypothesisJun 16 2005Jan 25 2006Exact and asymptotic formulae are displayed for the coefficients $\lambda_n$ used in Li's criterion for the Riemann Hypothesis. For $n \to \infty$ we obtain that if (and only if) the Hypothesis is true, $\lambda_n \sim n(A \log n +B)$ (with $A>0$ and ... More

Atomic quantum gases in periodically driven optical latticesJun 26 2016Nov 03 2016Time periodic forcing in the form of coherent radiation is a standard tool for the coherent manipulation of small quantum systems like single atoms. In the last years, periodic driving has more and more also been considered as a means for the coherent ... More

Lyapunov Exponents of Rank 2-Variations of Hodge Structures and Modular EmbeddingsMar 05 2013Aug 22 2013If the monodromy representation of a VHS over a hyperbolic curve stabilizes a rank two subspace, there is a single non-negative Lyapunov exponent associated with it. We derive an explicit formula using only the representation in the case when the monodromy ... More

Zeta functions over zeros of Zeta functions and an exponential-asymptotic view of the Riemann HypothesisMar 18 2014Jul 26 2014We review generalized zeta functions built over the Riemann zeros (in short: "superzeta" functions). They are symmetric functions of the zeros that display a wealth of explicit properties, fully matching the much more elementary Hurwitz zeta function. ... More

A Uniform Substitution Calculus for Differential Dynamic LogicMar 06 2015Jul 30 2015This paper introduces a new proof calculus for differential dynamic logic (dL) that is entirely based on uniform substitution, a proof rule that substitutes a formula for a predicate symbol everywhere. Uniform substitutions make it possible to rely on ... More

Identification of coronal holes and filament channels in SDO/AIA 193Å images via geometrical classification methodsAug 12 2014In this study, we describe and evaluate shape measures for distinguishing between coronal holes and filament channels as observed in Extreme Ultraviolet (EUV) images of the Sun. For a set of well-observed coronal hole and filament channel regions extracted ... More

The Dependence of the Peak Velocity of High-Speed Solar Wind Streams as Measured in the Ecliptic by ACE and the STEREO satellites on the Area and Co-Latitude of their Solar Source Coronal HolesApr 25 2018Apr 26 2018We study the properties of 115 coronal holes in the time-range from 2010/08 to 2017/03, the peak velocities of the corresponding high-speed streams as measured in the ecliptic at 1 AU, and the corresponding changes of the Kp index as marker of their geo-effectiveness. ... More

The Mean/Max Statistic in Extreme Value AnalysisJun 29 2016Most extreme events in real life can be faithfully modeled as random realizations from a Generalized Pareto distribution, which depends on two parameters: the scale and the shape. In many actual situations, one is mostly concerned with the shape parameter, ... More

Electromagnetic absorption of quasi-1D Majorana nanowiresJun 24 2015Jul 17 2015We calculate the electromagnetic absorption cross section of long and narrow nanowires, in the so-called quasi-1D limit. We consider only two transverse bands and compute the dipole absorption cross section taking into account quasiparticle transitions ... More

Quasi-particle current in planar Majorana nanowiresJun 23 2015Jul 17 2015We calculate the local quasi-particle current of a Majorana state in a planar hybrid (superconductor-semiconductor) nanowire. In absence of perpendicular components of the magnetic field the current flows in circular trajectories without a preferred orientation. ... More

Majorana states and magnetic orbital motion in planar hybrid nanowiresJan 27 2015Jul 17 2015The Majorana phase boundaries in planar 2D hybrid (semiconductor-superconductor) nanowires are modified by orbital effects due to off plane magnetic components. We show that Majorana zero modes survive sizable vertical field tiltings, uncovering a remarkable ... More

Two-temperature coronal flow above a thin diskApr 10 2002We extended the disk corona model (Meyer & Meyer-Hofmeister 1994; Meyer, Liu, & Meyer-Hofmeister 2000a) to the inner region of galactic nuclei by including different temperatures in ions and electrons as well as Compton cooling. We found that the mass ... More

Rainbow Matchings: existence and countingApr 14 2011A perfect matching M in an edge-colored complete bipartite graph K_{n,n} is rainbow if no pair of edges in M have the same color. We obtain asymptotic enumeration results for the number of rainbow matchings in terms of the maximum number of occurrences ... More

A minimization approach to hyperbolic Cauchy problemsOct 25 2013Developing an original idea of De Giorgi, we introduce a new and purely variational approach to the Cauchy Problem for a wide class of defocusing hyperbolic equations. The main novel feature is that the solutions are obtained as limits of functions that ... More

On the number of monochromatic solutions of integer linear systems on Abelian groupsMar 11 2012Let $G$ be a finite abelian group with exponent $n$, and let $r$ be a positive integer. Let $A$ be a $k\times m$ matrix with integer entries. We show that if $A$ satisfies some natural conditions and $|G|$ is large enough then, for each $r$--coloring ... More

Top Quark Compositeness: Feasibility and ImplicationsJun 19 2008Oct 06 2008In models of electroweak symmetry breaking in which the SM fermions get their masses by mixing with composite states, it is natural to expect the top quark to show properties of compositeness. We study the phenomenological viability of having a mostly ... More

Resonant Anderson localization in segmented wiresDec 02 2015We discuss a model of random segmented wire, with linear segments of 2D wires joined by circular bends. The joining vertices act as scatterers on the propagating electron waves. The model leads to resonant Anderson localization when all segments are of ... More

Verification of high-speed solar wind stream forecasts using operational solar wind modelsJul 24 2016High-speed solar wind streams emanating from coronal holes are frequently impinging on the Earth's magnetosphere causing recurrent, medium-level geomagnetic storm activity. Modeling high-speed solar wind streams is thus an essential element of successful ... More

Supervised Learning in Spiking Neural Networks for Precise Temporal EncodingJan 14 2016Oct 28 2016Precise spike timing as a means to encode information in neural networks is biologically supported, and is advantageous over frequency-based codes by processing input features on a much shorter time-scale. For these reasons, much recent attention has ... More

On the Origin of the High Helium Sequence in $ω$ CentauriJan 19 2006The blue Main Sequence (bMS) of $\omega$ Cen implies a ratio of helium to metal enrichment $\Delta Y/\Delta Z \approx 70$, which is a major enigma. We show that rotating models of low metallicity stars, which account for the anomalous abundance ratios ... More

Projective Pseudodifferential Analysis and Harmonic AnalysisMay 05 2006We consider pseudodifferential operators on functions on $\R^{n+1}$ which commute with the Euler operator, and can thus be restricted to spaces of functions homogeneous of some given degree. Their symbols can be regarded as functions on a reduced phase ... More

Scalable Inference of Customer Similarities from Interactions Data using Dirichlet ProcessesDec 21 2010Under the sociological theory of homophily, people who are similar to one another are more likely to interact with one another. Marketers often have access to data on interactions among customers from which, with homophily as a guiding principle, inferences ... More

Asymptotics of prediction in functional linear regression with functional outputsOct 16 2009Feb 10 2011We study prediction in the functional linear model with functional outputs : $Y=SX+\epsilon $ where the covariates $X$ and $Y$ belong to some functional space and $S$ is a linear operator. We provide the asymptotic mean square prediction error with exact ... More

Some Riemann Hypotheses from Random Walks over PrimesSep 11 2015Apr 17 2016The aim of this article is to investigate how various Riemann Hypotheses would follow only from properties of the prime numbers. To this end, we consider two classes of $L$-functions, namely, non-principal Dirichlet and those based on cusp forms. The ... More

Transcendental equations satisfied by the individual zeros of Riemann $ζ$, Dirichlet and modular $L$-functionsFeb 20 2015We consider the non-trivial zeros of the Riemann $\zeta$-function and two classes of $L$-functions; Dirichlet $L$-functions and those based on level one modular forms. We show that there are an infinite number of zeros on the critical line in one-to-one ... More

On the $L^p$ index of spin Dirac operators on conical manifoldsJul 02 2004We compute the index of the Dirac operator on spin Riemannian manifolds with conical singularities, acting from $L^p(\Sigma^+)$ to $L^q(\Sigma^-)$ with $p,q>1$. When $1+\frac{n}{p}-\frac{n}{q}>0$ we obtain the usual Atiyah-Patodi-Singer formula, but with ... More

Translating solutions to Lagrangian mean curvature flowNov 27 2007We prove some non-existence theorems for translating solutions to Lagrangian mean curvature flow. More precisely, we show that translating solutions with an $L^2$ bound on the mean curvature are planes and that almost-calibrated translating solutions ... More

Parallel Repetition of Entangled Games with Exponential Decay via the Superposed Information CostOct 29 2013Oct 02 2014In a two-player game, two cooperating but non communicating players, Alice and Bob, receive inputs taken from a probability distribution. Each of them produces an output and they win the game if they satisfy some predicate on their inputs/outputs. The ... More

On the stability of the solitary waves to the (generalized) kawahara equationNov 28 2016In this paper we investigate the orbital stability of solitary waves to the (generalized) Kawahara equation (gKW) which is a fifth order dispersive equation. For some values of the power of the nonlinearity, we prove the orbital stability in the energy ... More

Stop the tests: Opinion bias and statistical testsNov 20 2016When statisticians quarrel about hypothesis testing, the debate usually focus on which method is the correct one. The fundamental question of whether we should test hypothesis at all tends to be forgotten. This lack of debate has its roots on our desire ... More

The Top Mass: Interpretation and Theoretical UncertaintiesDec 11 2014Currently the most precise LHC measurements of the top quark mass are determinations of the top quark mass parameter of Monte-Carlo (MC) event generators reaching uncertainties of well below $1$ GeV. However, there is an additional theoretical problem ... More

On the Born-Oppenheimer approximation of diatomic molecular resonancesJun 25 2015We give a new reduction of a general diatomic molecular Hamiltonian, without modifying it near the collision set of nuclei. The resulting effective Hamiltonian is the sum of a smooth semiclassical pseudodifferential operator (the semiclassical parameter ... More

Widths of highly excited resonances in multidimensional molecular predissociationJun 19 2018Sep 25 2018We investigate the simple resonances of a 2 by 2 matrix of n-dimensional semiclassical Shr\"odinger operators that interact through a first order differential operator. We assume that one of the two (analytic) potentials admits a well with non empty interior, ... More

A Human-Checkable Four-Color Theorem ProofJun 06 2017Nov 09 2018This paper presents a short and simple proof of the Four-Color Theorem, which can be utterly checkable by human mathematicians, without computer assistance. The new key idea that has permitted it is presented in the Introduction.

Analysis of the implicit upwind finite volume scheme with rough coefficientsFeb 08 2017Nov 06 2017We study the implicit upwind finite volume scheme for numerically approximating the linear continuity equation in the low regularity DiPerna-Lions setting. That is, we are concerned with advecting velocity fields that are spatially Sobolev regular and ... More

Expected reliability of communication protocolsMay 18 2017We consider the problem of sending a message from a sender $s$ to a receiver $r$ through an unreliable network by specifying in a protocol what each vertex is supposed to do if it receives the message from one of its neighbors. A protocol for routing ... More

Modular System for Shelves and Coasts (MOSSCO v1.0) - a flexible and multi-component framework for coupled coastal ocean ecosystem modellingJun 13 2017Shelf and coastal sea processes extend from the atmosphere through the water column and into the sea bed. These processes are driven by physical, chemical, and biological interactions at local scales, and they are influenced by transport and cross strong ... More

Selectable linear or quadratic coupling in an optomechanical systemDec 04 2012There has been much interest recently in the analysis of optomechanical systems incorporating dielectric nano- or microspheres inside a cavity field. We analyse here the situation when one of the mirrors of the cavity itself is also allowed to move. We ... More