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Generalized Approximate Survey Propagation for High-Dimensional EstimationMay 13 2019In Generalized Linear Estimation (GLE) problems, we seek to estimate a signal that is observed through a linear transform followed by a component-wise, possibly nonlinear and noisy, channel. In the Bayesian optimal setting, Generalized Approximate Message ... More

Finite Size Corrections to Disordered Systems : mean field results and applications to finite dimensional modelsFeb 09 2015Feb 19 2015This PhD thesis has the following structure: Chapter 1 - General introduction; Chapter 2 - Preliminaries; Chapter 3 - The Replicated Transfer Matrix; Chapter 4 - Finite Size Corrections On Random Graphs; Chapter 5 - The Random Field Ising Model; Chapter ... More

The statistical mechanics of random set packing and a generalization of the Karp-Sipser algorithmNov 13 2013We analyse the asymptotic behaviour of random instances of the Maximum Set Packing (MSP) optimization problem, also known as Maximum Matching or Maximum Strong Independent Set on Hypergraphs. We give an analytical prediction of the MSPs size using the ... More

One-dimensional disordered Ising models by replica and cavity methodsJan 20 2014Aug 01 2014Using a formalism based on the spectral decomposition of the replicated transfer matrix for disordered Ising models, we obtain several results that apply both to isolated one-dimensional systems and to locally tree-like graph and factor graph (p-spin) ... More

One-loop diagrams in the Random Euclidean Matching ProblemSep 29 2016Oct 01 2016The matching problem is a notorious combinatorial optimization problem that has attracted for many years the attention of the statistical physics community. Here we analyze the Euclidean version of the problem, i.e. the optimal matching problem between ... More

Learning may need only a few bits of synaptic precisionFeb 12 2016May 27 2016Learning in neural networks poses peculiar challenges when using discretized rather then continuous synaptic states. The choice of discrete synapses is motivated by biological reasoning and experiments, and possibly by hardware implementation considerations ... More

Local entropy as a measure for sampling solutions in Constraint Satisfaction ProblemsNov 18 2015Feb 25 2016We introduce a novel Entropy-driven Monte Carlo (EdMC) strategy to efficiently sample solutions of random Constraint Satisfaction Problems (CSPs). First, we extend a recent result that, using a large-deviation analysis, shows that the geometry of the ... More

Subdominant Dense Clusters Allow for Simple Learning and High Computational Performance in Neural Networks with Discrete SynapsesSep 18 2015We show that discrete synaptic weights can be efficiently used for learning in large scale neural systems, and lead to unanticipated computational performance. We focus on the representative case of learning random patterns with binary synapses in single ... More

The Random Fractional Matching ProblemFeb 08 2018We consider two formulations of the random-link fractional matching problem, a relaxed version of the more standard random-link (integer) matching problem. In one formulation, we allow each node to be linked to itself in the optimal matching configuration. ... More

The Random Fractional Matching ProblemFeb 08 2018May 04 2018We consider two formulations of the random-link fractional matching problem, a relaxed version of the more standard random-link (integer) matching problem. In one formulation, we allow each node to be linked to itself in the optimal matching configuration. ... More

Scaling hypothesis for the Euclidean bipartite matching problemFeb 27 2014Aug 22 2014We propose a simple yet very predictive form, based on a Poisson's equation, for the functional dependence of the cost from the density of points in the Euclidean bipartite matching problem. This leads, for quadratic costs, to the analytic prediction ... More

On the role of synaptic stochasticity in training low-precision neural networksOct 26 2017Mar 20 2018Stochasticity and limited precision of synaptic weights in neural network models are key aspects of both biological and hardware modeling of learning processes. Here we show that a neural network model with stochastic binary weights naturally gives prominence ... More

Unreasonable Effectiveness of Learning Neural Networks: From Accessible States and Robust Ensembles to Basic Algorithmic SchemesMay 20 2016Oct 06 2016In artificial neural networks, learning from data is a computationally demanding task in which a large number of connection weights are iteratively tuned through stochastic-gradient-based heuristic processes over a cost-function. It is not well understood ... More

Anomalous finite size corrections in random field modelsJun 25 2014The presence of a random magnetic field in ferromagnetic systems leads, in the broken phase, to an anomalous $O(\sqrt{1/N})$ convergence of some thermodynamic quantities to their asymptotic limits. Here we show a general method, based on the replica trick, ... More

Finite size corrections to disordered Ising models on Random Regular GraphsMar 24 2014Aug 01 2014We derive the analytical expression for the first finite size correction to the average free energy of disordered Ising models on random regular graphs. The formula can be physically interpreted as a weighted sum over all non self-intersecting loops in ... More

Loop expansion around the Bethe approximation through the $M$-layer constructionJul 26 2017For every physical model defined on a generic graph or factor graph, the Bethe $M$-layer construction allows building a different model for which the Bethe approximation is exact in the large $M$ limit and it coincides with the original model for $M=1$. ... More

Finite size corrections to disordered systems on Erdös-Rényi random graphsMay 14 2013Oct 01 2013We study the finite size corrections to the free energy density in disorder spin systems on sparse random graphs, using both replica theory and cavity method. We derive an analytical expressions for the $O(1/N)$ corrections in the replica symmetric phase ... More

Signal propagation in continuous approximations of binary neural networksFeb 01 2019The training of stochastic neural network models with binary ($\pm1$) weights and activations via a deterministic and continuous surrogate network is investigated. We derive, using mean field theory, a set of scalar equations describing how input signals ... More

Higher-order corrections for the deflection of light around a massive objectJan 16 2017Jan 18 2017From the Schwarzschild metric we obtain the higher-order terms (up to 20-th order) for the deflection of light around a massive object using the Lindstedt-Poincar\'e method to solve the equation of motion of a photon around the stellar object. Additionally, ... More

Foliations and Polynomial Diffeomorphisms of $\mathbb{R}^{3}$Jul 17 2006Let $Y=(f,g,h):\mathbb{R}^{3} \to \mathbb{R}^{3}$ be a $C^{2}$ map and let $\spec(Y)$ denote the set of eigenvalues of the derivative $DY_p$, when $p$ varies in $\mathbb{R}^3$. We begin proving that if, for some $\epsilon>0,$ $\spec(Y)\cap (-\epsilon,\epsilon)=\emptyset,$ ... More

An Ergodic Dilation of Completely Positive MapsJul 20 2011We shall prove the following Stinespring-type theorem: there exists a triple $(\pi,\mathcal{H},\mathbf{V})$ associated with an unital completely positive map $\Phi:\mathfrak{A}\rightarrow \mathfrak{A}$ on C* algebra $\mathfrak{A}$ with unit, where $\mathcal{H}$ ... More

Pure Subspaces, Generalizing the Concept of Pure SpinorsOct 01 2013May 16 2014The concept of pure spinor is generalized, giving rise to the notion of pure subspaces, spinorial subspaces associated to isotropic vector subspaces of non-maximal dimension. Several algebraic identities concerning the pure subspaces are proved here, ... More

Transcendental Liuville inequalities on projective varietiesSep 14 2016Let $p$ be an algebraic point of a projective variety $X$ defined over a number field. Liouville inequality tells us that the norm at $p$ of a non vanishing integral global section of an hermitian line bundle over $X$ is either zero or it cannot be too ... More

The dangers of non-empirical confirmationSep 02 2016In the book "String Theory and the Scientific Method", Richard Dawid describes a few of the many non-empirical arguments that motivate theoretical physicists' confidence in a theory, taking string theory as case study. I argue that excessive reliance ... More

Classification of Random Boolean NetworksAug 01 2002We provide the first classification of different types of Random Boolean Networks (RBNs). We study the differences of RBNs depending on the degree of synchronicity and determinism of their updating scheme. For doing so, we first define three new types ... More

A stochastic maximum principle with dissipativity conditionsSep 30 2013In this paper we prove a version of the maximum principle, in the sense of Pontryagin, for the optimal control of a finite dimensional stochastic differential equation, driven by a multidimensional Wiener process. We drop the usual Lipschitz assumption ... More

A Simulated Annealing Approach to Bayesian InferenceSep 17 2015A generic algorithm for the extraction of probabilistic (Bayesian) information about model parameters from data is presented. The algorithm propagates an ensemble of particles in the product space of model parameters and outputs. Each particle update ... More

Relative information at the foundation of physicsOct 31 2013Shannon's notion of relative information between two physical systems can function as foundation for statistical mechanics and quantum mechanics, without referring to subjectivism or idealism. It can also represent a key missing element in the foundation ... More

Strings, loops and others: a critical survey of the present approaches to quantum gravityMar 05 1998Apr 07 1998I review the present theoretical attempts to understand the quantum properties of spacetime. In particular, I illustrate the main achievements and the main difficulties in: string theory, loop quantum gravity, discrete quantum gravity (Regge calculus, ... More

An argument against the realistic interpretation of the wave functionAug 22 2015Sep 02 2015Testable predictions of quantum mechanics are invariant under time reversal. But the change of the quantum state in time is not so, neither in the collapse nor in the no-collapse interpretations of the theory. This fact challenges the realistic interpretation ... More

Lorentzian Connes Distance, Spectral Graph Distance and Loop GravityAug 14 2014Sep 09 2014Connes' formula defines a distance in loop quantum gravity, via the spinfoam Dirac operator. A simple notion of spectral distance on a graph can be extended do the discrete Lorentzian context, providing a physically natural example of Lorentzian spectral ... More

"Forget time"Mar 23 2009Mar 27 2009Following a line of research that I have developed for several years, I argue that the best strategy for understanding quantum gravity is to build a picture of the physical world where the notion of time plays no role. I summarize here this point of view, ... More

Spectral noncommutative geometry and quantization: a simple exampleApr 13 1999We explore the relation between noncommutative geometry, in the spectral triple formulation, and quantum mechanics. To this aim, we consider a dynamical theory of a noncommutative geometry defined by a spectral triple, and study its quantization. In particular, ... More

Light Sterile Neutrinos: Status and PerspectivesDec 15 2015Jan 05 2016The indications in favor of the existence of light sterile neutrinos at the eV scale found in short-baseline neutrino oscillation experiments is reviewed. The future perspectives of short-baseline neutrino oscillation experiments and the connections with ... More

Comment on the Neutrino-Mixing Interpretation of the GSI Time AnomalyJan 30 2008Apr 17 2008It is shown that neutrino mixing cannot explain the GSI time anomaly, refuting recent claims in this direction. Addendum 1: Remarks on arXiv:0801.1465. Addendum 2: Quantum effects in GSI nuclear decay.

Double Beta Decay and the Absolute Neutrino Mass ScaleAug 20 2003After a short review of the current status of three-neutrino mixing, the implications for the values of neutrino masses are discussed. The bounds on the absolute scale of neutrino masses from Tritium beta-decay and cosmological data are reviewed. Finally, ... More

The GSI Time Anomaly: Facts and FictionMay 28 2009The claims that the GSI time anomaly is due to the mixing of neutrinos in the final state of the observed electron-capture decays of hydrogen-like heavy ions are refuted with the help of an analogy with a double-slit experiment. It is a consequence of ... More

Fractal geometry of non-uniformly hyperbolic horseshoesNov 06 2013This article is an expanded version of some notes for my talk at the ``Ergodic Theory and Dynamical Systems Workshop'' (from March 22 to March 25, 2012) held at the Department of Mathematics of the University of North Carolina at Chapel Hill. In the aforementioned ... More

Phenomenology of a New Supersymmetric Standard Model: The $μν$SSMSep 28 2009The $\mu\nu$SSM solves the $\mu$ problem of the MSSM and explains the origin of neutrino masses by simply using right-handed neutrino superfields. The solution implies the breaking of R-parity. The properties and phenomenology of the model are briefly ... More

The $μν$SSM and gravitino dark matterSep 25 2009We consider the phenomenological implications of gravitino dark matter in the context of the $\mu\nu$SSM. The latter is an R-parity breaking model which provides a solution to the $\mu$-problem of the MSSM and explains the origin of neutrino masses by ... More

Charge and Color Breaking in Supersymmetry and SuperstringsSep 12 1997Charge and color breaking minima in SUSY theories might make the standard vacuum unstable. In this talk a brief review of this issue is performed. When a complete analysis of all the potentially dangerous directions in the field space of the theory is ... More

Counting words with vector spacesDec 16 2013The sequence 2,5,15,51,187,... with the form (2^n+1)(2^(n-1)+1)/3 has two interpretations in terms of the dimension of the universal embedding of the symplectic polar space and the density of a language with four letters. This article presents a way to ... More

The classifying space of the 1+1 dimensional G-cobordism categoryNov 09 2012Nov 29 2013The 1+1 G-cobordism category, with G a finite group, is important in the construction of G-topological field theories which are completely determined by a G-Frobenius algebra. We give a description of the classifying space of this category generalizing ... More

On Maximal-Acceleration, Strings and the Group of Minimal Planck-Area Relativity TheoryNov 07 2002Recently we have presented a new physical model that links the maximum speed of light with the minimal Planck scale into a maximal-acceleration Relativity principle in phase spaces . The maximal proper-acceleration bound is $a = c^2/ \Lambda$ where $ ... More

Noncommutative Geometry, Negative Probabilities and Cantorian-Fractal SpacetimeJul 27 2000A straightforward explanation of the Young's two-slit experiment of a quantum particle is obtained within the framework of the Noncommutative Geometric associated with El Naschie's Cantorian-Fractal transfinite Spacetime continuum.

p-Brane Quantum Mechanical Wave EquationsDec 21 1998Dec 22 1998Several quantum mechanical wave equations for $p$-branes are proposed based on the role that the volume-preserving diffeomorphisms group has on the physics of extended objects. The $p$-brane quantum mechanical wave equations determine the quantum dynamics ... More

p-Branes as Composite Antisymmetric Tensor Field TheoriesMar 17 1996Apr 09 1996$p'$-brane solutions to rank $p+1$ composite antisymmetric tensor field theories of the kind developed by Guendelman, Nissimov and Pacheva are found when the dimensionality of spacetime is $D=(p+1)+(p'+1)$. These field theories posses an infinite dimensional ... More

W-Geometry from Fedosov's Deformation QuantizationFeb 05 1998May 25 1998A geometric derivation of $W_\infty$ Gravity based on Fedosov's deformation quantization of symplectic manifolds is presented. To lowest order in Planck's constant it agrees with Hull's geometric formulation of classical nonchiral $W_\infty$ Gravity. ... More

A Moyal Quantization of the Continuous Toda FieldMar 13 1997May 19 1997Since the lightcone self dual spherical membrane, moving in flat target backgrounds, has a direct correspondence with the $SU(\infty)$ Nahm equations and the continuous Toda theory, we construct the Moyal deformations of the self dual membrane in terms ... More

Incorporating the Scale-Relativity Principle in String Theory and Extended ObjectsNov 29 1996Dec 03 1996First steps in incorporating Nottale's scale-relativity principle to string theory and extended objects are taken. Scale Relativity is to scales what motion Relativity is to velocities. The universal, absolute, impassible, invariant scale under dilatations, ... More

String Theory, Scale Relativity and the Generalized Uncertainty PrincipleDec 07 1995Nov 06 1996Extensions (modifications) of the Heisenberg Uncertainty principle are derived within the framework of the theory of Special Scale-Relativity proposed by Nottale. In particular, generalizations of the Stringy Uncertainty Principle are obtained where the ... More

On $C^r-$closing for flows on 2-manifoldsNov 23 1999For some full measure subset B of the set of iet's (i.e. interval exchange transformations) the following is satisfied: Let X be a $C^r$, $1\le r\le \infty$, vector field, with finitely many singularities, on a compact orientable surface M. Given a nontrivial ... More

Algebraic aspects of higher nonabelian Hodge theoryFeb 10 1999Mar 02 1999We look more closely at the higher nonabelian de Rham cohomology of a smooth projective variety or family of varieties that had been defined in some previous papers. We formalize using $n$-stacks the notion of shape underlying this nonabelian cohomology. ... More

Secondary Kodaira-Spencer classes and nonabelian Dolbeault cohomologyDec 18 1997Jan 06 1998If $X$ is a smooth projective variety moving in a family, we define a secondary Kodaira-Spencer class for nonabelian Dolbeault cohomology $Hom(X_{Dol}, T)$ of $X$ with coefficients in the complexified 2-sphere $T=S^2\otimes \cc$ (which is a 3-stack on ... More

Next-to-Leading-Order Corrections to the Production of Heavy-Flavour Jets in e+e- CollisionsFeb 26 1998In this thesis we describe the calculation of the process e+ e- --> Z/gamma -> Q Qbar + X, where Q is a heavy quark, X is anything else at order alpha_s^2.

Information-Geometric Indicators of Chaos in Gaussian Models on Statistical Manifolds of Negative Ricci CurvatureFeb 14 2007Oct 25 2008A new information-geometric approach to chaotic dynamics on curved statistical manifolds based on Entropic Dynamics (ED) is proposed. It is shown that the hyperbolicity of a non-maximally symmetric 6N-dimensional statistical manifold M_{s} underlying ... More

The Information Geometry of ChaosJan 28 2016Feb 09 2016We present a new theoretical information-geometric framework (IGAC, Information Geometrodynamical Approach to Chaos) suitable to characterize chaotic dynamical behavior of arbitrary complex systems.

Reggeization in High Energy QCDMar 23 2001We study QCD in the regime of high parton density arising in hadronic collisions at large center-of-mass energy. The n-gluon amplitudes of the generalized leading logarithmic approximation are investigated. We find identities relating amplitudes with ... More

Bipartite entanglement of localized separated systemsDec 09 2011The main part of this Thesis is devoted to the dynamics of entanglement in matter-radiation interaction and circuit QED systems, and its relationship with the notion of causality. Results on non-RWA effects in circuit QED and quantum simulations of relativistic ... More

Running couplings with a vanishing scale anomalySep 04 2013Jan 03 2014Running couplings can be understood as arising from the spontaneous breaking of an exact scale invariance in appropriate effective theories with no dilatation anomaly. Any ordinary quantum field theory, even if it has massive fields, can be embedded into ... More

Mapping curved spacetimes into Dirac spinorsJul 29 2016We show how to transform a Dirac equation in curved spacetime into a Dirac equation in flat spacetime. In particular, we show that any solution of the free massless Dirac equation in a 1+1 dimensional flat spacetime can be transformed via a local phase ... More

Stochastic growth equations on growing domainsJan 18 2009Jun 28 2009The dynamics of linear stochastic growth equations on growing substrates is studied. The substrate is assumed to grow in time following the power law $t^\gamma$, where the growth index $\gamma$ is an arbitrary positive number. Two different regimes are ... More

Dynamics of curved interfacesNov 02 2008Jun 28 2009Stochastic growth phenomena on curved interfaces are studied by means of stochastic partial differential equations. These are derived as counterparts of linear planar equations on a curved geometry after a reparametrization invariance principle has been ... More

Particle Statistics and Population DynamicsDec 30 2004We study a master equation system modelling a population dynamics problem in a lattice. The problem is the calculation of the minimum size of a refuge that can protect a population from hostile external conditions, the so called critical patch size problem. ... More

Stochastic growth of radial clusters: weak convergence to the asymptotic profile and implications for morphogenesisJan 19 2010Jan 16 2012The asymptotic shape of randomly growing radial clusters is studied. We pose the problem in terms of the dynamics of stochastic partial differential equations. We concentrate on the properties of the realizations of the stochastic growth process and in ... More

Dynamics of Generalized Hydrodynamics: Hyperbolic and Pseudohyperbolic Burgers EquationsDec 14 2009The equations of continuum hydrodynamics can be derived from the Boltzmann equation, which describes rarefied gas dynamics at the kinetic level, by means of the Chapman-Enskog expansion. This expansion assumes a small Knudsen number, and as a consequence, ... More

Shock wave formation in Rosenau's extended hydrodynamicsDec 30 2004We study the extended hydrodynamics proposed by Philip Rosenau [Phys. Rev. A 40, 7193 (1989)] in the context of a regularization of the Chapman-Enskog expansion. We are able to prove that shock waves appear in finite time in Rosenau's extended Burgers' ... More

The subtle unphysical hypothesis of the firewall theoremFeb 10 2019Feb 12 2019The black-hole firewall theorem derives a suspicious consequence (large energy-momentum density on the horizon of a black hole) from a set of seemingly reasonable hypotheses. I point out the hypothesis which is likely to be unrealistic---a hypothesis ... More

Design and Analysis of a Single-Camera Omnistereo Sensor for Quadrotor Micro Aerial Vehicles (MAVs)Oct 03 2015We describe the design and 3D sensing performance of an omnidirectional stereo-vision system (omnistereo) as applied to Micro Aerial Vehicles (MAVs). The proposed omnistereo model employs a monocular camera that is co-axially aligned with a pair of hyperboloidal ... More

New surfaces with $K^2=7$ and $p_g=q\leq 2$Jun 30 2015We construct smooth minimal complex surfaces of general type with $K^2=7$ and: $p_g=q=2,$ Albanese map of degree $2$ onto a $(1,2)$-polarized abelian surface; $p_g=q=1$ as a double cover of a quartic Kummer surface; $p_g=q=0$ as a double cover of a numerical ... More

Viewpoint: Black Hole Evolution Traced Out with Loop Quantum GravityJan 15 2019Loop Quantum gravity predicts that black holes evolve into white holes.

Jump sets in local fieldsOct 23 2018We show how to use the combinatorial notion of jump sets to parametrize the possible structures of the group of principal units of local fields, viewed as filtered modules. We establish a natural bijection between the set of jump sets and the orbit space ... More

Large deviations for interacting particle systems: joint mean-field and small-noise limitOct 30 2018We consider a system of stochastic interacting particles in $\mathbb{R}^d$ and we describe large deviations asymptotics in a joint mean-field and small-noise limit. Precisely, a large deviations principle (LDP) is established for the empirical measure ... More

"Space is blue and birds fly through it"Dec 08 2017Jan 29 2018Quantum mechanics is not about 'quantum states': it is about values of physical variables. I give a short fresh presentation and update on the $relational$ perspective on the theory, and a comment on its philosophical implications.

Some bidouble planes with $p_g=q=0$ and $4\leq K^2\leq 7$Mar 15 2011Apr 12 2013We give a list of possibilities for surfaces of general type with $p_g=0$ having an involution $i$ such that the bicanonical map of $S$ is not composed with $i$ and $S/i$ is not rational. Some examples with $K^2=4,...,7$ are constructed as double coverings ... More

Involutions on surfaces with $p_g=q=0$ and $K^2=3$Jul 28 2010We study surfaces of general type $S$ with $p_g=0$ and $K^2=3$ having an involution $i$ such that the bicanonical map of $S$ is not composed with $i$. It is shown that, if $S/i$ is not rational, then $S/i$ is birational to an Enriques surface or it has ... More

Involutions on surfaces with $p_g=q=1$May 29 2008In this paper some numerical restrictions for surfaces with an involution are obtained. These formulas are used to study surfaces of general type $S$ with $p_g=q=1$ having an involution $i$ such that $S/i$ is a non-ruled surface and such that the bicanonical ... More

New 2--critical sets in the abelian 2--groupDec 13 2006In this paper we determine a class of critical sets in the abelian {2--group} that may be obtained from a greedy algorithm. These new critical sets are all 2--critical (each entry intersects an intercalate, a trade of size 4) and completes in a top down ... More

Is Weyl unified theory wrong or incomplete?Aug 15 2015Aug 25 2015In 1918, H. Weyl proposed a unified theory of gravity and electromagnetism based on a generalization of Riemannian geometry. In spite of its elegance and beauty, a serious objection was raised by Einstein, who argued that Weyl's theory was not suitable ... More

Generation and analysis of lamplighter programsJul 09 2017Oct 22 2018We consider a programming language based on the lamplighter group that uses only composition and iteration as control structures. We derive generating functions and counting formulas for this language and special subsets of it, establishing lower and ... More

On the sum of digits of the factorialSep 17 2014Let b > 1 be an integer and denote by s_b(m) the sum of the digits of the positive integer m when is written in base b. We prove that s_b(n!) > C_b log n log log log n for each integer n > e, where C_b is a positive constant depending only on b. This ... More

A Model Existence Theorem for Infinitary Formulas in Metric SpacesFeb 24 1998We prove a Model Existence Theorem for a fully infinitary logic for metric structures. This result is based on a generalization of the notions of approximate formulas and approximate truth in normed structures introduced by Henson and studied in different ... More

Knowledge Extraction and Knowledge Integration governed by Łukasiewicz LogicsApr 11 2016The development of machine learning in particular and artificial intelligent in general has been strongly conditioned by the lack of an appropriate interface layer between deduction, abduction and induction. In this work we extend traditional algebraic ... More

Some answers to certain questions established by Jose Adem concerning nonsingular bilinear mapsNov 08 2018The present article contains some constructions of new nonsingular real bilinear maps, using the commutator inside the octonion numbers. As a consequence, we answer certain questions established by J. Adem in 1971.

A defect action for Wilson loopsMar 26 2018Apr 10 2018An effective action is proposed to compute the expectation value of Wilson loops in $(S)U(N)$ gauge theories. The action consists of fermions localized on the loop and an Abelian gauge field that fixes the representation. The discussion is limited to ... More

First derivatives at the optimum analysis (\textit{fdao}): An approach to estimate the uncertainty in nonlinear regression involving stochastically independent variablesFeb 25 2018Jan 20 2019An important problem of optimization analysis surges when parameters such as $ \{\theta_j\}_{j=1,\, \dots \,,k }$, determining a function $ y=f(x\given\{\theta_j\}) $, must be estimated from a set of observables $ \{ x_i,y_i\}_{i=1,\, \dots \,,m} $. Where ... More

Ideals on countable sets: a survey with questionsFeb 22 2019An ideal on a set $X$ is a collection of subsets of $X$ closed under the operations of taking finite unions and subsets of its elements. Ideals are a very useful notion in topology and set theory and have been studied for a long time. We present a survey ... More

On some differences between number fields and function fieldsJun 21 2016The analogy between the arithmetic of varieties over number fields and the arithmetic of varieties over function fields is a leading theme in arithmetic geometry. This analogy is very powerful but there are some gaps. In this note we will show how the ... More

On numbers divisible by the product of their nonzero base $b$ digitsSep 14 2018For each integer $b \geq 3$ and every $x \geq 1$, let $\mathcal{N}_{b,0}(x)$ be the set of positive integers $n \leq x$ which are divisible by the product of their nonzero base $b$ digits. We prove bounds of the form $x^{\rho_{b,0} + o(1)} < \#\mathcal{N}_{b,0}(x) ... More

An isoperimetric result for the fundamental frequency via domain derivativeJan 25 2012Jan 30 2012The Faber-Krahn deficit $\delta\lambda$ of an open bounded set $\Omega$ is the normalized gap between the values that the first Dirichlet Laplacian eigenvalue achieves on $\Omega$ and on the ball having same measure as $\Omega$. For any given family of ... More

On the additivity of geometric invariants in Grothendieck categoriesJul 26 2010Jul 28 2010We study the additivity of various geometric invariants involved in Reimann-Roch type formulas and defined via the trace map. To do so in a general context we prove that given any Grothendieck category A, the derived category D(A) has a compatible triangulation ... More

Generic flows on 3-manifoldsNov 27 2012We provide a combinatorial presentation of the set F of 3-dimensional generic flows, namely the set of pairs (M,v) with M a compact oriented 3-manifold and v a nowhere-zero vector field on M having generic behaviour along the boundary of M, with M viewed ... More

3D vortex approximation construction and $\varepsilon$-level estimates for the Ginzburg-Landau functionalDec 20 2017We provide a quantitative three-dimensional vortex approximation construction for the Ginzburg-Landau functional. This construction gives an approximation of vortex lines coupled to a lower bound for the energy, optimal to leading order, analogous to ... More

A lower bound for the r-order of a matrix modulo NOct 09 2006Dec 06 2006For a positive integer $N$, we define the N-rank of a non singular integer $d\times d$ matrix $A$ to be the maximum integer $r$ such that there exists a minor of order $r$ whose determinant is not divisible by $N$. Given a positive integer $r$, we study ... More

Algorithmic construction and recognition of hyperbolic 3-manifolds, links, and graphsMar 24 2010This survey article describes the algorithmic approaches successfully used over the time to construct hyperbolic structures on 3-dimensional topological "objects" of various types, and to classify several classes of such objects using such structures. ... More

On the number of distinct exponents in the prime factorization of an integerFeb 25 2019Let $f(n)$ be the number of distinct exponents in the prime factorization of the natural number $n$. We prove some results about the distribution of $f(n)$. In particular, for any positive integer $k$, we obtain that $$ \#\{n \leq x : f(n) = k\} \sim ... More

On transverse invariants from Khovanov-type homologiesMay 09 2017Feb 08 2018In this article we introduce a family of transverse invariants arising from the deformations of Khovanov homology. This family includes the invariants introduced by Plamenevskaya and by Lipshitz, Ng, and Sarkar. Then, we investigate the invariants arising ... More

An Itô type formula for the additive stochastic heat equationMar 05 2018Feb 05 2019We use the theory of regularity structures to develop an It\^o formula for $u$, the solution of the one dimensional stochastic heat equation driven by space-time white noise with periodic boundary conditions. In particular for any smooth enough function ... More

Non-commutative Probability Theory for Topological Data AnalysisAug 21 2017Sep 08 2017Recent developments have found unexpected connections between non-commutative probability theory and algebraic topology. In particular, Boolean cumulants functionals seem to be important for describing morphisms of homotopy operadic algebras. We provide ... More

Oscillations Beyond Three-Neutrino MixingSep 15 2016The current status of the phenomenology of short-baseline neutrino oscillations induced by light sterile neutrinos in the framework of 3+1 mixing is reviewed.