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On lattice path matroid polytopes: integer points and Ehrhart polynomialJan 19 2017Oct 25 2017In this paper we investigate the number of integer points lying in dilations of lattice path matroid polytopes. We give a characterization of such points as polygonal paths in the diagram of the lattice path matroid. Furthermore, we prove that lattice ... More

Depth with respect to a family of convex setsDec 11 2016We propose a notion of depth with respect to a finite family $\mathcal{F}$ of convex sets in $\mathbb{R}^d$ which we call $\text{dep}_\mathcal{F}$. We begin showing that $\text{dep}_\mathcal{F}$ satisfies some expected properties for a measure of depth ... More

Regularity properties of fiber derivatives associated with higher-order mechanical systemsFeb 08 2016Jul 16 2016The aim of this work is to study fiber derivatives associated to Lagrangian and Hamiltonian functions describing the dynamics of a higher-order autonomous dynamical system. More precisely, given a function in $T^*T^{(k-1)}Q$, we find necessary and sufficient ... More

Bounding a global red-blue proportion using local conditionsJan 09 2017Apr 20 2017We study the following local-to-global phenomenon: Let $B$ and $R$ be two finite sets of (blue and red) points in the Euclidean plane $\mathbb{R}^2$. Suppose that in each "neighborhood" of a red point, the number of blue points is at least as large as ... More

Constants of motion for the magnetic force: the angular momentum and the Laplace-Runge-Lenz vectorOct 09 2013Oct 25 2013It is well-known that an electric charge under a uniform magnetic field has a bidimensional motion if its initial position and velocity are perpendicular to this magnetic field. Although some constants of motion, as the energy and angular momentum, have ... More

Singularities and internal rotational dynamics of electron beamsAug 02 2016We study the internal rotational dynamics of electronic beams in relation to the phase singularities of their wave functions. Given their complex singularity structure, Hermite-Gaussian beams and other superpositions of Laguerre-Gaussian modes are studied ... More

A Tutte polynomial inequality for lattice path matroidsOct 02 2015Jun 20 2016Let $M$ be a matroid without loops or coloops and let $T(M;x,y)$ be its Tutte polynomial. In 1999 Merino and Welsh conjectured that $$\max(T(M;2,0), T(M;0,2))\geq T(M;1,1)$$ holds for graphic matroids. Ten years later, Conde and Merino proposed a multiplicative ... More

Further Consequences of the Colorful Helly HypothesisMar 16 2018Let $\mathcal{F}$ be a family of convex sets in ${\mathbb R}^d$, which are colored with $d+1$ colors. We say that $\mathcal{F}$ satisfies the Colorful Helly Property if every rainbow selection of $d+1$ sets, one set from each color class, has a non-empty ... More

A sunflower anti-Ramsey theorem and its applicationsMay 19 2015A $h$-sunflower in a hypergraph is a family of edges with $h$ vertices in common. We show that if we colour the edges of a complete hypergraph in such a way that any monochromatic $h$-sunflower has at most $\lambda$ petals, then it contains a large rainbow ... More

A Tutte polynomial inequality for lattice path matroidsOct 02 2015Oct 27 2016Let $M$ be a matroid without loops or coloops and let $T(M;x,y)$ be its Tutte polynomial. In 1999 Merino and Welsh conjectured that $$\max(T(M;2,0), T(M;0,2))\geq T(M;1,1)$$ holds for graphic matroids. Ten years later, Conde and Merino proposed a multiplicative ... More

Unified formalism for the generalized kth-order Hamilton-Jacobi problemOct 03 2013May 19 2014The geometric formulation of the Hamilton-Jacobi theory enables us to generalize it to systems of higher-order ordinary differential equations. In this work we introduce the unified Lagrangian-Hamiltonian formalism for the geometric Hamilton-Jacobi theory ... More

Inclusive Single Hadron Production in Neutral Current Deep-Inelastic Scattering at Next-to-Leading OrderAug 06 2009A study of inclusive production of single hadrons with finite transverse momentum in neutral current deep-inelastic scattering has been carried out. Cross sections have been calculated using perturbative Quantum Chromodynamics at next-to-leading order ... More

HAWC Upgrade with a Sparse Outrigger ArraySep 14 2015The High Altitude Water Cherenkov (HAWC) high-energy gamma-ray observatory has recently been completed on the slopes of the Sierra Negra volcano in central Mexico. HAWC consists of 300 Water Cherenkov Detectors, each containing 180 m$^3$ of ultra-purified ... More

IDTxl: The Information Dynamics Toolkit xl: a Python package for the efficient analysis of multivariate information dynamics in networksJul 27 2018Feb 19 2019The Information Dynamics Toolkit xl (IDTxl) is a comprehensive software package for efficient inference of networks and their node dynamics from multivariate time series data using information theory. IDTxl provides functionality to estimate the following ... More

Complete Kneser TransversalsNov 04 2015Aug 12 2016Let $k,d,\lambda\geqslant1$ be integers with $d\geqslant\lambda $. Let $m(k,d,\lambda)$ be the maximum positive integer $n$ such that every set of $n$ points (not necessarily in general position) in $\mathbb{R}^{d}$ has the property that the convex hulls ... More

Triangle areas determined by arrangements of planar linesFeb 08 2019A widely investigated subject in combinatorial geometry, originated from Erd\H{o}s, is the following. Given a point set $P$ of cardinality $n$ in the plane, how can we describe the distribution of the determined distances? This has been generalized in ... More

Codimension two and three Kneser TransversalsJan 04 2016Sep 27 2016Let $k,d,\lambda \geqslant 1$ be integers with $d\geqslant \lambda $ and let $X\subset\mathbb{R}^{d}$ be a finite set. A $(d-\lambda)$-plane $L$ transversal to the convex hull of all $k$-sets of $X$ is called Kneser transversal. If in addition $L$ contains ... More

Codimension two and three Kneser TransversalsJan 04 2016Nov 15 2017Let $k,d,\lambda \geqslant 1$ be integers with $d\geqslant \lambda $ and let $X$ be a finite set of points in $\mathbb{R}^{d}$. A $(d-\lambda)$-plane $L$ transversal to the convex hulls of all $k$-sets of $X$ is called Kneser transversal. If in addition ... More

Dynamics in two networks based on stocks of the US stock marketAug 07 2014Sep 01 2014We follow the main stocks belonging to the New York Stock Exchange and to Nasdaq from 2003 to 2012, through years of normality and of crisis, and study the dynamics of networks built on two measures expressing relations between those stocks: correlation, ... More

The Singularities of the Wave Trace of the Basic Laplacian of a Riemannian FoliationAug 14 2006We apply techniques of microlocal analysis to the study of the transverse geometry of Riemannian foliations in order to analyze spectral invariants of the basic Laplacian acting on functions on a Riemannian foliation with a bundle-like metric. In particular, ... More

A geometric Hall-type theoremDec 20 2014Jan 14 2015We introduce a geometric generalization of Hall's marriage theorem. For any family $F = \{X_1, \dots, X_m\}$ of finite sets in $\mathbb{R}^d$, we give conditions under which it is possible to choose a point $x_i\in X_i$ for every $1\leq i \leq m$ in such ... More

Differential Calculus on Iso_q (N), Quantum Poincare' Algebra and q - GravityDec 22 1993Jan 06 1994We present a general method to deform the inhomogeneous algebras of the $B_n,C_n,D_n$ type, and find the corresponding bicovariant differential calculus. The method is based on a projection from $B_{n+1}, C_{n+1}, D_{n+1}$. For example we obtain the (bicovariant) ... More

Asymptotically hyperbolic manifolds with polyhomogeneous metricNov 27 2008Sep 08 2009We analyze the resolvent and define the scattering matrix for asymptotically hyperbolic manifolds with metrics which have a polyhomogeneous expansion near the boundary, and also prove that there is always an essential singularity of the resolvent in this ... More

Some arithmetic proerties of Lame operators with dihedral monodromyMar 17 2004In this paper, we describe some arithmetic properties of Lame operators with finite dihedral projective monodromy. We take advantage of the deep link with Grothendieck's theory of dessins d'enfants. We focus more particularly on the case of projective ... More

Some Results on Infinite Dimensional Riemannian GeometryApr 18 2003Apr 29 2003In this paper we will investigate the global properties of complete Hilbert manifolds with upper and lower bounded sectional curvature. We shall prove the Focal Index Lemma that we will allow us to extend some classical results of finite dimensional Riemannian ... More

On the essential spectrum of the Laplacian and the drifted LaplacianFeb 07 2013Apr 26 2013This paper concerns the $L^2$ essential spectrum of the Laplacian $\Delta$ and the drift Laplacian $\Delta_f$ on complete Riemannian manifolds endowed with a weighted measure $e^{-f}d\;vol_g$. We prove that the essential spectrum of the drift Laplacian ... More

Super-renormalizable Quantum GravityJul 12 2011In this paper we study perturbatively an extension of the Stelle higher derivative gravity involving an infinite number of derivative terms. We know that the usual quadratic action is renormalizable but suffers of the unitarity problem because of the ... More

OSp(1|4) supergravity and its noncommutative extensionJan 08 2013Jul 24 2013We review the OSp(1|4)-invariant formulation of N=1, D=4 supergravity and present its noncommutative extension, based on a star-product originating from an abelian twist with deformation parameter \theta. After use of a geometric generalization of the ... More

Analysis of the anomalous-dimension matrix of n-jet operators at 4 loopsDec 14 2011Recently, an all-order conjecture for the anomalous-dimension matrix of n-jet operators in SCET was proposed, which allows one to predict the structure of the infrared divergences of dimensionally regularized, massless gauge-theory scattering amplitudes ... More

Helium-4 Synthesis in an Anisotropic UniverseDec 09 2011Dec 30 2011We calculate the 4He abundance in a universe of Bianchi type I whose cosmic anisotropy is dynamically generated by a fluid with anisotropic equation of state. Requiring that the relative variation of mass fraction of 4He is less than 4% with respect to ... More

Bouligand-Severi $k$-tangents and strongly semisimple MV-algebrasJul 22 2013An algebra $A$ is said to be strongly semisimple if every principal congruence of $A$ is an intersection of maximal congruences. We give a geometrical characterisation of strongly semisimple MV-algebras in terms of Bouligand-Severi $k$-tangents. The latter ... More

Obtaining a New Representation for the Golden Ratio by Solving a Biquadratic EquationAug 27 2002Nov 11 2014In the present work we show how different ways to solve biquadratic equations can lead us to different representations of its solutions. A particular equation which has the golden ratio and its reciprocal as solutions is shown as an example.

Super Star Clusters in the Blue Dwarf Galaxy UM 462Jul 03 2003I present optical observations of the Blue Compact Dwarf Galaxy UM 462. The images of this galaxy show several bright compact sources. A careful study of these sources has revealed their nature of young Super Star Clusters. The ages determined from the ... More

Noncommutative geometry and physics: a review of selected recent resultsMay 23 2000Aug 02 2000This review is based on two lectures given at the 2000 TMR school in Torino. We discuss two main themes: i) Moyal-type deformations of gauge theories, as emerging from M-theory and open string theories, and ii) the noncommutative geometry of finite groups, ... More

On G/H geometry and its use in M-theory compactificationsDec 30 1999The Riemannian geometry of coset spaces is reviewed, with emphasis on its applications to supergravity and M-theory compactifications. Formulae for the connection and curvature of rescaled coset manifolds are generalized to the case of nondiagonal Killing ... More

The Lagrangian of q-Poincare' GravityFeb 07 1994Feb 17 1994The gauging of the q-Poincar\'e algebra of ref. hep-th 9312179 yields a non-commutative generalization of the Einstein-Cartan lagrangian. We prove its invariance under local q-Lorentz rotations and, up to a total derivative, under q-diffeomorphisms. The ... More

On the quantum Poincare' groupDec 02 1992The inhomogeneous quantum groups $IGL_q(n)$ are obtained by means of a particular projection of $GL_q(n+1)$. The bicovariant differential calculus on $GL_q(n)$ is likewise projected into a consistent bicovariant calculus on $IGL_q(n)$. Applying the same ... More

Gauge theories of quantum groupsMay 28 1992We find two different q-generalizations of Yang-Mills theories. The corresponding lagrangians are invariant under the q-analogue of infinitesimal gauge transformations. We explicitly give the lagrangian and the transformation rules for the bicovariant ... More

Choosing the Right Relativity for QFTFeb 09 2009Jan 30 2012When speaking of the unification of quantum mechanics and relativity, one normally refers to special relativity (SR) or to Einstein general relativity (GR). The Dirac and Klein-Gordon wave equations are an example of unification of quantum concepts and ... More

A combinatorial formula for the coefficient of $q$ in Kazhdan-Lusztig polynomialsNov 20 2018We propose a combinatorial interpretation of the coefficient of $q$ in Kazhdan- Lusztig polynomials and we prove it for finite simply-laced Weyl groups.

An energy functional on the universal spinor bundleDec 18 2017Jan 02 2018We study an energy functional on the universal spinor bundle over a closed $n$-dimensional spin manifold $M$. The critical points of this functional, which is modelled on the total torsion functional of $G_2$-structures in seven dimensions, are pairs ... More

A Pragmatic Smoothing Method for Improving the Quality of the Results in Atomic SpectroscopyMar 07 2016A new smoothing method for the improvement on the identification and quantification of spectral functions based on the previous knowledge of the signals that are expected to be quantified, is presented. These signals are used as weighted coefficients ... More

Hierarchy from BaryogenesisJul 21 2005Feb 19 2006We study a recently proposed mechanism to solve the hierarchy problem in the context of the landscape, where the solution of the hierarchy problem is connected to the requirement of having baryons in our universe via Electroweak Baryogenesis. The phase ... More

Extended Lie derivatives and a new formulation of D=11 supergravityApr 28 2006Apr 30 2006Introducing an extended Lie derivative along the dual of A, the three-form field of d=11 supergravity, the full diffeomorphism algebra of d=11 supergravity is presented. This algebra suggests a new formulation of the theory, where the three-form field ... More

Differential calculi on finite groupsMay 23 2000A brief review of bicovariant differential calculi on finite groups is given, with some new developments on diffeomorphisms and integration. We illustrate the general theory with the example of the nonabelian finite group S_3.

Study of the young stellar population of NGC 4214 using the Hubble Space TelescopeAug 26 2007We present an original study of the dwarf starburst galaxy NGC 4214. We use archival optical and UV images obtained with WFPC2 and STIS on-board the Hubble Space Telescope. We explain the process followed to obtain high-quality photometry and astrometry ... More

Archetypes, Causal Description and Creativity in Natural WorldJul 10 2006The idea, formulated for the first time by Pauli, of a "creativity" of natural processes on a quantum scale is briefly investigated, with particular reference to the phenomena, common throughout the biological world, involved in the amplification of microscopic ... More

On the moment map on symplectic manifoldsMay 10 2006Sep 28 2006We consider a connected symplectic manifold $M$ acted on by a connected Lie group $G$ in a Hamiltonian fashion. If $G$ is compact, we prove give an Equivalence Theorem for the symplectic manifolds whose squared moment map $\parallel \mu \parallel^2$ is ... More

Coisotropic and polar actions on compact irreducible Hermitian symmetric spacesAug 30 2004Jan 18 2006We obtain the full classification of coisotropic and polar actions of compact Lie group on irreducible Hermitian symmetric spaces.

Higher-order Variational Calculus on Lie algebroidsJan 26 2015The equations for the critical points of the action functional defined by a Lagrangian depending on higher-order derivatives of admissible curves on a Lie algebroid are found. The relation with Euler-Poincar\'e and Lagrange Poincar\'e type equations is ... More

Linearization of nonlinear connections on vector and affine bundles, and some applicationsNov 18 2017A linear connection is associated to a nonlinear connection on a vector bundle by a linearization procedure. Our definition is intrinsic in terms of vector fields on the bundle. For a connection on an affine bundle our procedure can be applied after homogenization ... More

Lie derivatives along antisymmetric tensors, and the M-theory superalgebraAug 29 2005Aug 31 2005Free differential algebras (FDA's) provide an algebraic setting for field theories with antisymmetric tensors. The "presentation" of FDA's generalizes the Cartan-Maurer equations of ordinary Lie algebras, by incorporating p-form potentials. An extended ... More

Gravity on Finite GroupsSep 07 1999Jul 06 2000Gravity theories are constructed on finite groups G. A self-consistent review of the differential calculi on finite G is given, with some new developments. The example of a bicovariant differential calculus on the nonabelian finite group S_3 is treated ... More

Bicovariant Differential Calculus on the Quantum D=2 Poincare GroupJan 09 1992Feb 26 1992We present a bicovariant differential calculus on the quantum Poincare group in two dimensions. Gravity theories on quantum groups are discussed.

Tilted Ghost InflationJun 07 2004May 22 2005In a ghost inflationary scenario, we study the observational consequences of a tilt in the potential of the ghost condensate. We show how the presence of a tilt tends to make contact between the natural predictions of ghost inflation and the ones of slow ... More

Recent progress on chiral symmetry breaking in QCDNov 27 2015I review recent progress achieved on the lattice in the quantitative comprehension of chiral symmetry breaking in QCD. Emphasis is given to the recent precise computations of the spectral density of the Dirac operator in the continuum limit, and of the ... More

AdS/CFT and its proofAug 22 2018Mar 03 2019In this letter we examine some structural aspects of the AdS/CFT such as the way of obtaining the expectation value of product of operators of the CFT, and ideas that should be considered when a proof of AdS/CFT is under consideration.

Lectures on InflationSep 02 2016Planning to explore the beginning of the Universe? A lightweight introductory guide to the theory of Inflation.

On the self-similarity of nonhelical magnetohydrodynamic turbulenceNov 20 2015Sep 19 2016We re-analyze the Olesen arguments on the self-similarity properties of freely evolving, nonhelical magnetohydrodynamic turbulence. We find that a necessary and sufficient condition for the kinetic and magnetic energy spectra to evolve self-similarly ... More

History operators in quantum mechanicsOct 08 2018Oct 19 2018It is convenient to describe a quantum system at all times by means of a "history operator" $C$, encoding measurements and unitary time evolution between measurements. These operators naturally arise when computing the probability of measurement sequences, ... More

Second-order constrained variational problems on Lie algebroids: applications to optimal controlJan 17 2017The aim of this work is to study, from an intrinsic and geometric point of view, second-order constrained variational problems on Lie algebroids, that is, optimization problems defined by a cost functional which depends on higher-order derivatives of ... More

Scalar Fields in Particle PhysicsAug 05 2016Extending the scalar sector helps in studying the Higgs mechanism and some Standard Model problems. We implement the correspondence between the gauge-dependent elementary states and the non-perturbative non-abelian gauge-invariant asymptotic states, necessary ... More

Finitary Process Evolution I: Information Geometry of Configuration Space and the Process-Replicator DynamicsJul 12 2018Jul 25 2018This report presents some fundamental mathematical results towards elucidating the information-geometric underpinnings of evolutionary modelling schemes for (quasi-)stationary discrete stochastic processes. The model class under consideration is that ... More

Thermodynamic interpretation of reactive processes in Ni-Al nanolayers from atomistic simulationsSep 10 2013Dec 28 2013Metals which can form intermetallic compounds by an exothermic reaction constitute a class of reactive materials with multiple applications. Ni-Al laminates of thin alternating layers are being considered as model nanometric metallic multilayers for studying ... More

Cosmological bulk viscosity, the Burnett regime, and the BGK equationOct 25 2002Einstein's field equations in FRW space-times are coupled to the BGK equation in order to derive the stress energy tensor including dissipative effects up to second order in the thermodynamical forces. The space-time is assumed to be matter-dominated, ... More

The thermal and kinematic Sunyaev-Zel'dovich effects revisitedOct 16 2003This paper shows that a simple convolution integral expression based on the mean value of the isotropic frequency distribution corresponding to photon scattering off electrons leads to useful analytical expressions describing the thermal Sunyaev-Zel'dovich ... More

Note on the Sunyaev-Zel'dovich thermal effectMay 08 2003Jun 12 2003In a previous publication we have derived an expression for the full distorted spectrum arising when the photons of the cosmic background radiation are absorbed and emitted by an optically thin gas. The expression simply adds up the effects of the joint ... More

Points defining triangles with distinct circumradiiFeb 25 2014Paul Erdos asked if, among sufficiently many points in general position, there are always $k$ points such that all the circles through $3$ of these $k$ points have different radii. He later proved that this is indeed the case. However, he overlooked a ... More

Scalar Resonances in Axially Symmetric SpacetimesMar 12 2015We study properties of resonant solutions to the scalar wave equation in several axially symmetric spacetimes. We prove that non-axial resonant modes do not exist neither in the Lanczos dust cylinder, the $(2+1)$ extreme BTZ spacetime nor in a class of ... More

Leaf Space Isometries of Singular Riemannian Foliations and Their Spectral PropertiesAug 28 2017Jan 07 2019In this paper, the authors consider leaf spaces of singular Riemannian foliations $\mathcal{F}$ on compact manifolds $M$ and the associated $\mathcal{F}$-basic spectrum on $M$, $spec_B(M, \mathcal{F}),$ counted with multiplicities. Recently, a notion ... More

Electron correlations in a C$_{20}$ fullerene cluster: A lattice density-functional study of the Hubbard modelApr 29 2005The ground-state properties of C$_{20}$ fullerene clusters are determined in the framework of the Hubbard model by using lattice density-functional theory (LDFT) and scaling approximations to the interaction-energy functional. Results are given for the ... More

Density-Matrix functional theory of strongly-correlated lattice fermionsJul 17 2002A density functional theory (DFT) of lattice fermion models is presented, which uses the single-particle density matrix gamma_{ij} as basic variable. A simple, explicit approximation to the interaction-energy functional W[gamma] of the Hubbard model is ... More

Semiclassical propagator of the Wigner functionAug 06 2005Jan 24 2006Propagation of the Wigner function is studied on two levels of semiclassical propagation, one based on the van-Vleck propagator, the other on phase-space path integration. Leading quantum corrections to the classical Liouville propagator take the form ... More

A convolution integral representation of the thermal Sunyaev-Zel'dovich effectAug 23 2002Feb 27 2003Analytical expressions for the non-relativistic and relativistic Sunyaev-Zel'dovich effect (SZE) are derived by means of suitable convolution integrals. The establishment of these expressions is based on the fact that the SZE disturbed spectrum, at high ... More

A causality analysis of the linearized relativistic Navier-Stokes equationsJan 27 2010It is shown by means of a simple analysis that the linearized system of transport equations for a relativistic, single component ideal gas at rest obeys the \textit{antecedence principle}, which is often referred to as causality principle. This task is ... More

Remarks on relativistic kinetic theory to first order in the gradientsJan 20 2009Aug 03 2010In this paper we emphasize some conceptual points related to the kinetic foundations of relativistic hydrodynamics. We summarize previous work and focus on the construction of the heat flux from a kinetic theory point of view. A thorough discussion addressing ... More

Hydrodynamic time correlation functions in the presence of a gravitational fieldJan 24 2003Apr 10 2003This paper shows that the ordinary Brillouin spectrum peaks associated to scattered radiation off acoustic modes in a fluid suffer a shift in their values due to gravitational effects. The approach is based in the ordinary linearized Navier-Stokes equations ... More

Relativistic non-equilibrium thermodynamics revisitedMar 11 2005Mar 16 2005Relativistic irreversible thermodynamics is reformulated following the conventional approach proposed by Meixner in the non-relativistic case. Clear separation between mechanical and non-mechanical energy fluxes is made. The resulting equations for the ... More

Formation of Nanotwin Networks during High-Temperature Crystallization of Amorphous GermaniumJul 14 2015Germanium is an extremely important material used for numerous functional applications in many fields of nanotechnology. In this paper, we study the crystallization of amorphous Ge using atomistic simulations of critical nano-metric nuclei at high temperatures. ... More

Thermodynamics of ultracold trapped gases. Generalized mechanical variables, equation of state and heat capacitySep 27 2008The thermodynamics framework of an interacting quantum gas trapped by an arbitrary external potential is reviewed. We show that for each confining potential, in the thermodynamic limit, there emerge "generalized" volume and pressure variables ${\cal V}$ ... More

Magnetised accretion discs in Kerr spacetimesDec 01 2014We study the effect caused by external magnetic fields on the observed thermal spectra and iron line profiles of thin accretion discs formed around Kerr black holes and naked singularities. We aim to provide a tool that can be used to estimate the presence ... More

A Calabi's Type CorrespondenceJan 31 2019Calabi observed that there is a natural correspondence between the solutions of the minimal surface equation in $\mathbb{R}^3$ with those of the maximal spacelike surface equation in $\mathbb{L}^3$. We are going to show how this correspondence can be ... More

Overcoming experimental limitations in a non-linear two-qubit gate through postselectionAug 17 2016We introduce a modular-value two-qubit gate and explore its advantages in experimentally-limited situations. The gate is defined such that the final state of a target qubit is fully controlled by a pre- and post-selection procedure in a control qubit ... More

Semisimple coadjoint orbits and cotangent bundlesAug 20 2014Semisimple (co)adjoint orbits through real hyperbolic elements are well-known to be symplectomorphic to cotangent bundles. We provide a new proof of this fact based on elementary results on both Lie theory and symplectic geometry, thus shedding some new ... More

Proper Lie groupoids are real analyticDec 29 2016Jul 25 2017We show that any proper Lie groupoid admits a compatible (real) analytic structure.

The GC-content of a family of cyclic codes with applications to DNA-codesMar 08 2019Given a prime power $q$ and a positive integer $r>1$ we say that a cyclic code of length $n$, $C\subseteq F_{q^r}^n$, is Galois supplemented if for any non-trivial element $\sigma$ in the Galois group of the extension $ F_{q^r}/ F_q$, $C+C^\sigma= F_{q^r}^n$, ... More

Markovianness and Conditional Independence in Annotated Bacterial DNANov 18 2013We explore the probabilistic structure of DNA in a number of bacterial genomes and conclude that a form of Markovianness is present at the boundaries between coding and non-coding regions, that is, the sequence of START and STOP codons annotated for the ... More

Generalized chordality, vertex separators and hyperbolicity on graphsAug 21 2017Let $G$ be a graph with the usual shortest-path metric. A graph is $\delta$-hyperbolic if for every geodesic triangle $T$, any side of $T$ is contained in a $\delta$-neighborhood of the union of the other two sides. A graph is chordal if every induced ... More

Sums of binomial determinants, non-intersecting lattice paths and positivity of Chern-Schwartz-MacPherson classesFeb 19 2007We give a combinatorial interpretation of a certain positivity conjecture of Chern-Schwartz-MacPherson classes, as stated by P. Aluffi and the author in a previous paper. It translates into a positivity property for a sum of p by p determinants consisting ... More

Bosonic and fermionic behavior in gravitational configurationsMay 20 2002We extend Dirac's approach about the quantization of the electric charge to the case of gravitational configurations. The spacetime curvature is used to define a phase-like object which allows us to extract information about the behavior of the corresponding ... More

On the viscosity solutions to a degenerate parabolic differential equationOct 09 2013In this work, we study some properties of the viscosity solutions to a degenerate parabolic equation involving the non-homogeneous infinity-Laplacian.

An Eigenvalue problem for the Infinity-LaplacianNov 13 2012Feb 01 2013We study an eigenvalue problem for the infinity-Laplacian on bounded domains. We prove the existence of the principal eigenvalue and a corresponding positive eigenfunction. The work also contains existence results when the parameter, in the equation, ... More

Positivity in equivariant quantum Schubert CalculusJul 14 2004We prove a positivity result in (T-)equivariant quantum cohomology of the homogeneous space G/P, generalizing Graham's positivity in equivariant cohomology.

Polynomial description of inhomogeneous topological superconducting wiresJul 04 2017Jul 25 2017We present universal features of the topological invariant of p-wave superconducting wires after the inclusion of spatial inhomogeneities. Three classes of distributed potentials are studied, a single- impurity, a commensurate and an incommensurate model ... More

Universal secure rank-metric coding schemes with optimal communication overheadsMay 30 2017Aug 25 2017We study the problem of reducing the communication overhead from a noisy wire-tap channel or storage system where data is encoded as a matrix, when more columns (or their linear combinations) are available. We present its applications to reducing communication ... More

Subgroup posets, Bredon cohomology and equivariant Euler characteristicsNov 16 2011Feb 24 2012For a discrete group $\Gamma$ satisfying some finiteness conditions we give a Bredon projective resolution of the trivial module in terms of projective covers of the chain complex associated to certain posets of subgroups. We use this to give new results ... More

Abelian fibrations and SYZ mirror conjectureMar 14 2011Aug 01 2012SYZ mirror conjecture predicts that a Calabi-Yau manifold $X$ consists of a family of tori which are dual to a family of special lagrangian tori on the mirror dual manifold $\hat{X}$. Here we consider a fibration of polarized abelian varieties and we ... More

A new characterisation of groups amongst monoidsJun 08 2016We prove that a monoid $M$ is a group if and only if, in the category of monoids, all points over $M$ are strong. This sharpens and greatly simplifies a result of Montoli, Rodelo and Van der Linden which characterises groups amongst monoids as the protomodular ... More

An arithmetic Bernštein-Kušnirenko inequalitySep 02 2016Jun 14 2018We present an upper bound for the height of the isolated zeros in the torus of a system of Laurent polynomials over an adelic field satisfying the product formula. This upper bound is expressed in terms of the mixed integrals of the local roof functions ... More

STIT Tessellations -- Ergodic Limit Theorems and Bounds for the Speed of ConvergenceSep 05 2016We consider homogeneous STIT tessellations in the $\ell$-dimensional Euclidean space ${\mathbb R}^\ell$. Based on results for the spatial $\beta$-mixing coefficient an upper bound for the variance of additive functionals of tessellations is derived, using ... More