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Quantitative a Priori Estimates for Fast Diffusion Equations with Caffarelli-Kohn-Nirenberg weights. Harnack inequalities and Hölder continuityApr 10 2018Oct 29 2018We study a priori estimates for a class of non-negative local weak solution to the weighted fast diffusion equation $u_t = |x|^{\gamma} \nabla\cdot (|x|^{-\beta} \nabla u^m)$, with $0 < m <1$ posed on cylinders of $(0,T)\times{\mathbb R}^N$. The weights ... More

Sharp Extinction Rates for Fast Diffusion Equations on Generic Bounded DomainsFeb 08 2019We investigate the homogeneous Dirichlet problem for the Fast Diffusion Equation $u_t=\Delta u^m$, posed in a smooth bounded domain $\Omega\subset \mathbb{R}^N$, in the exponent range $m_s=(N-2)_+/(N+2)<m<1$. It is known that bounded positive solutions ... More

A Priori Estimates for Fractional Nonlinear Degenerate Diffusion Equations on bounded domainsNov 27 2013We investigate quantitative properties of the nonnegative solutions $u(t,x)\ge 0$ to the nonlinear fractional diffusion equation, $\partial_t u + {\mathcal L} (u^m)=0$, posed in a bounded domain, $x\in\Omega\subset {\mathbb R}^N$ with $m>1$ for $t>0$. ... More

Sharp global estimates for local and nonlocal porous medium-type equations in bounded domainsOct 31 2016Nov 25 2017This paper provides a quantitative study of nonnegative solutions to nonlinear diffusion equations of porous medium-type of the form $\partial_t u + {\mathcal L}u^m=0$, $m>1$, where the operator ${\mathcal L}$ belongs to a general class of linear operators, ... More

Non-existence and instantaneous extinction of solutions for singular nonlinear fractional diffusion equationsMay 12 2015We show non-existence of solutions of the Cauchy problem in $\mathbb{R}^N$ for the nonlinear parabolic equation involving fractional diffusion $\partial_t u + (-\Delta)^s \phi(u)= 0,$ with $0<s<1$ and very singular nonlinearities $\phi$ . More precisely, ... More

Total Variation Flow and Sign Fast Diffusion in one dimensionJul 11 2011Aug 17 2011We consider the dynamics of the Total Variation Flow (TVF) $u_t=\div(Du/|Du|)$ and of the Sign Fast Diffusion Equation (SFDE) $u_t=\Delta\sign(u)$ in one spatial dimension. We find the explicit dynamic and sharp asymptotic behaviour for the TVF, and we ... More

Positivity, local smoothing, and Harnack inequalities for very fast diffusion equationsMay 30 2008Dec 01 2008We investigate qualitative properties of local solutions $u(t,x)\ge 0$ to the fast diffusion equation, $\partial_t u =\Delta (u^m)/m$ with $m<1$, corresponding to general nonnegative initial data. Our main results are quantitative positivity and boundedness ... More

Fractional Nonlinear Degenerate Diffusion Equations on Bounded Domains Part I. Existence, Uniqueness and Upper BoundsAug 31 2015Sep 30 2015We investigate quantitative properties of nonnegative solutions $u(t,x)\ge 0$ to the nonlinear fractional diffusion equation, $\partial_t u + \mathcal{L}F(u)=0$ posed in a bounded domain, $x\in\Omega\subset \mathbb{R}^N$, with appropriate homogeneous ... More

Quantitative Local and Global A Priori Estimates for Fractional Nonlinear Diffusion EquationsOct 09 2012Oct 07 2013We establish quantitative estimates for solutions $u(t,x)$ to the fractional nonlinear diffusion equation, $\partial_t u +(-\Delta)^s (u^m)=0$ in the whole range of exponents $m>0$, $0<s<1$. The equation is posed in the whole space $x\in\mathbb{R}^d$. ... More

Sharp global estimates for local and nonlocal porous medium-type equations in bounded domainsOct 31 2016This paper provides a quantitative study of nonnegative solutions to nonlinear diffusion equations of porous medium-type of the form $\partial_t u + \mathcal{L} u^m=0$, $m>1$, where the operator $\mathcal{L}$ belongs to a general class of linear operators, ... More

Special fast diffusion with slow asymptotics. Entropy method and flow on a Riemannian manifoldMay 30 2008May 27 2009We consider the asymptotic behaviour of positive solutions $u(t,x)$ of the fast diffusion equation $u_t=\Delta (u^{m}/m)={\rm div} (u^{m-1}\nabla u)$ posed for $x\in\RR^d$, $t>0$, with a precise value for the exponent $m=(d-4)/(d-2)$. The space dimension ... More

Optimal Existence and Uniqueness Theory for the Fractional Heat EquationJun 02 2016Aug 29 2016We construct a theory of existence, uniqueness and regularity of solutions for the fractional heat equation $\partial_t u +(-\Delta)^s u=0$, $0<s<1$, posed in the whole space $\mathbb{R}^N$ with data in a class of locally bounded Radon measures that are ... More

Existence, Uniqueness and Asymptotic behaviour for fractional porous medium equations on bounded domainsApr 24 2014Jul 24 2014We consider nonlinear diffusive evolution equations posed on bounded space domains, governed by fractional Laplace-type operators, and involving porous medium type nonlinearities. We establish existence and uniqueness results in a suitable class of solutions ... More

Quantitative Local Bounds for Subcritical Semilinear Elliptic EquationsJan 27 2012The purpose of this paper is to prove local upper and lower bounds for weak solutions of semilinear elliptic equations of the form $-\Delta u= c u^p$, with $0<p<p_s=(d+2)/(d-2)$, defined on bounded domains of $\RR^d$, $d\ge 3$, without reference to the ... More

Sharp boundary behaviour of solutions to semilinear nonlocal elliptic equationsOct 07 2017Feb 12 2018We investigate quantitative properties of nonnegative solutions $u(x)\ge 0$ to the semilinear diffusion equation $\mathcal{L} u= f(u)$, posed in a bounded domain $\Omega\subset {\mathbb R}^N$ with appropriate homogeneous Dirichlet or outer boundary conditions. ... More

Behaviour near extinction for the Fast Diffusion Equation on bounded domainsDec 03 2010We consider the Fast Diffusion Equation $u_t=\Delta u^m$ posed in a bounded smooth domain $\Omega\subset \RR^d$ with homogeneous Dirichlet conditions; the exponent range is $m_s=(d-2)_+/(d+2)<m<1$. It is known that bounded positive solutions $u(t,x)$ ... More

Infinite speed of propagation and regularity of solutions to the fractional porous medium equation in general domainsOct 13 2015Jun 21 2016We study the positivity and regularity of solutions to the fractional porous medium equations $u_t+(-\Delta)^su^m=0$ in $(0,\infty)\times\Omega$, for $m>1$ and $s\in (0,1)$ and with Dirichlet boundary data $u=0$ in $(0,\infty)\times({\mathbb R}^N\setminus\Omega)$, ... More

Weighted fast diffusion equations (Part II): Sharp asymptotic rates of convergence in relative error by entropy methodsFeb 26 2016Jun 20 2016This paper is the second part of the study. In Part~I, self-similar solutions of a weighted fast diffusion equation (WFD) were related to optimal functions in a family of subcritical Caffarelli-Kohn-Nirenberg inequalities (CKN) applied to radially symmetric ... More

Weighted fast diffusion equations (Part I): Sharp asymptotic rates without symmetry and symmetry breaking in Caffarelli-Kohn-Nirenberg inequalitiesFeb 26 2016Jun 20 2016In this paper we consider a family of Caffarelli-Kohn-Nirenberg interpolation inequalities (CKN), with two radial power law weights and exponents in a subcritical range. We address the question of symmetry breaking: are the optimal functions radially ... More

Classification of radial solutions to the Emden-Fowler equation on the hyperbolic spaceApr 19 2011May 01 2011We study the Emden-Fowler equation $-\Delta u=|u|^{p-1}u$ on the hyperbolic space ${\mathbb H}^n$. We are interested in radial solutions, namely solutions depending only on the geodesic distance from a given point. The critical exponent for such equation ... More

Sharp rates of decay of solutions to the nonlinear fast diffusion equation via functional inequalitiesJul 17 2009The goal of this note is to state the optimal decay rate for solutions of the nonlinear fast diffusion equation and, in self-similar variables, the optimal convergence rates to Barenblatt self-similar profiles and their generalizations. It relies on the ... More

Asymptotics of the fast diffusion equation via entropy estimatesApr 18 2007We consider non-negative solutions of the fast diffusion equation $u_t=\Delta u^m$ with $m \in (0,1)$, in the Euclidean space R^d, d?3, and study the asymptotic behavior of a natural class of solutions, in the limit corresponding to $t\to\infty$ for $m\ge ... More

Clustering dynamics in a class of normalised generalised gamma dependent priorsAug 02 2016Normalised generalised gamma processes are random probability measures that induce nonparametric prior distributions widely used in Bayesian statistics, particularly for mixture modelling. We construct a class of dependent normalised generalised gamma ... More

Embedded hyper-parameter tuning by Simulated AnnealingJun 04 2019We propose a new metaheuristic training scheme that combines Stochastic Gradient Descent (SGD) and Discrete Optimization in an unconventional way. Our idea is to define a discrete neighborhood of the current SGD point containing a number of "potentially ... More

Clustering dynamics in a class of normalised generalised gamma dependent priorsAug 02 2016Nov 04 2016Normalised generalised gamma processes are random probability measures that induce nonparametric prior distributions widely used in Bayesian statistics, particularly for mixture modelling. We construct a class of dependent normalised generalised gamma ... More

Common factors, trends, and cycles in large datasetsSep 05 2017Nov 07 2017This paper considers a non-stationary dynamic factor model for large datasets to disentangle long-run from short-run co-movements. We first propose a new Quasi Maximum Likelihood estimator of the model based on the Kalman Smoother and the Expectation ... More

The fractional Laplacian in power-weighted $L^p$ spaces: integration-by-parts formulas and self-adjointnessDec 05 2015Aug 08 2016We consider the fractional Laplacian operator $(-\Delta)^s$ (let $ s \in (0,1) $) on Euclidean space and investigate the validity of the classical integration-by-parts formula that connects the $ L^2(\mathbb{R}^d) $ scalar product between a function and ... More

Proof diagrams for multiplicative linear logicJun 29 2016Sep 14 2016The original idea of proof nets can be formulated by means of interaction nets syntax. Additional machinery as switching, jumps and graph connectivity is needed in order to ensure correspondence between a proof structure and a correct proof in sequent ... More

Weak fiber products in a bicategory of fractionsDec 10 2014We fix any pair $(\mathbf{\mathscr{C}},\mathbf{W})$ consisting of a bicategory and a class of morphisms in it, admitting a bicalculus of fractions, i.e. a "localization" of $\mathbf{\mathscr{C}}$ with respect to the class $\mathbf{W}$. In the resulting ... More

Automatic Synthesis of Test Cases to Identify Software RedundancyNov 16 2014Software system can include redundant implementation elements, such as, different methods that can produce indistinguishable results. This type of redundancy is called intrinsic if it is already available in the software, although not intentionally planned. ... More

Minimum relative entropy distributions with a large mean are GaussianMay 26 2016We consider the following frustrated optimization problem: given a prior probability distribution $q$, find the distribution $p$ minimizing the relative entropy with respect to $q$ such that $\textrm{mean}(p)$ is fixed and large. We show that solutions ... More

On the large $Ω$-deformations in the Nekrasov-Shatashvili limit of $\mathcal N=2^{*}$ SYMApr 30 2016May 14 2016We study the multi-instanton partition functions of the $\Omega$-deformed $\mathcal N =2^{*}$ $SU(2) $ gauge theory in the Nekrasov-Shatashvili (NS) limit. They depend on the deformation parameters $\epsilon_{1}$, the scalar field expectation value $a$, ... More

An Improved Upper Bound for the Ground State Energy of Fermion Lattice ModelsMay 23 2001We present an improved upper bound for the ground state energy of lattice fermion models with sign problem. The bound can be computed by numerical simulation of a recently proposed family of deformed Hamiltonians with no sign problem. For one dimensional ... More

The Lyman-alpha forest as a probe of fundamental physicsApr 28 2005We use LUQAS, a sample of 27 high resolution high signal-to-noise UVES quasar (QSO) spectra (Kim et al. 2004), and the Croft et al. (2002) sample together with a set of high resolution large box size hydro-dynamical simulations run with the code GADGET-II ... More

Elementary Thermal Operations and the Universality of Thermodynamic ConstraintsJul 01 2016To what extent is the resource theory approach to thermodynamics relevant for realistic experimental scenarios? We deconstruct this framework, showing that each transition among incoherent states allowed in the theory can be obtained by sequentially applying ... More

On high dimensional directed polymer in random mediaMay 16 1995Aug 10 1995Directed polymers in random media are studied using results of the asymptotic theory of extreme statistics. Despite the strong correlation, one can recover the behavior of independent random variables for high dimensions, using a result which requires ... More

On Heavy Quarks Photoproduction and c -> D* Fragmentation FunctionsAug 07 1997The state of the art of the theoretical calculations for heavy quarks photoproduction is reviewed. The full fixed order next-to-leading order massive calculation and the resummation of large log(p_T/m) terms for differential cross sections are described. ... More

Heavy Quark Production: Theory vs. ExperimentDec 15 2003The current status of the comparisons between some experimental results and theoretical predictions for heavy quark production is reviewed. It is shown that the combination of new theoretical tools and better experimental input allows for a good description ... More

Phenomenology of quarkonia production in fixed target experiments and at the Tevatron and HERA collidersJun 16 1997The phenomenology of heavy quarkonia production in fixed target experiments and at the Tevatron and HERA colliders is reviewed. The latest theoretical results are presented and compared with data, with emphasis on the predictions of the factorization ... More

Explicit bounds on exceptional zeroes of Dirichlet $L$-functionsSep 14 2018The aim of this paper is to improve the upper bound for the exceptional zeroes $\beta_0$ of Dirichlet $L$-functions. We do this by improving on explicit estimate for $L'(\sigma, \chi)$ for $\sigma$ close to unity.

Trispectrum from Co-dimension 2(n) GalileonsMar 20 2013Dec 14 2013A generalized theory of multi-field galileons has been recently put forward. This model stems from the ongoing effort to embed generic galileon theories within brane constructions. Such an approach has proved very useful in connecting interesting and ... More

Search for new physics in dijet final states in ATLAS and CMSSep 14 2017Events containing a pair of high energy hadronic jet can provide clear signatures in the search for new physics at high energy hadron colliders. The ATLAS and CMS experiments collected the data from LHC collisions at $\sqrt{s}$= 13 TeV during 2015 and ... More

The Hunt for Primordial Interactions in the Large Scale Structures of the UniverseJun 28 2019Aug 09 2019The understanding of the primordial mechanism that seeded the cosmic structures we observe today in the sky is one of the major goals in cosmology. The leading paradigm for such a mechanism is provided by the inflationary scenario, a period of violent ... More

Double scaling limit of N=2 chiral correlators with Maldacena-Wilson loopOct 24 2018We consider $\mathcal N=2$ conformal QCD in four dimensions and the one-point correlator of a class of chiral primaries with the circular $\frac{1}{2}$-BPS Maldacena-Wilson loop. We analyze a recently introduced double scaling limit where the gauge coupling ... More

Localisation in 2+1 dimensional SU(3) pure gauge theory at finite temperatureMar 12 2019May 30 2019I study the localisation properties of low Dirac eigenmodes in 2+1 dimensional SU(3) pure gauge theory, both in the low-temperature, confined and chirally-broken phase and in the high-temperature, deconfined and chirally-restored phase, by means of numerical ... More

Guessing models and generalized Laver diamondDec 10 2010Oct 10 2011We analyze the notion of guessing model, a way to assign combinatorial properties to arbitrary regular cardinals. Guessing models can be used, in combination with inaccessibility, to characterize various large cardinals axioms, ranging from supercompactness ... More

A family of covering properties for forcing axioms and strongly compact cardinalsMar 03 2007This paper presents the main results in my Ph.D. thesis. In what follows several proofs of SCH are presented introducing a family of covering properties which implies both SCH and the failure of various forms of square. These covering properties are also ... More

Proof Diagrams for Multiplicative Linear Logic: Syntax and SemanticsFeb 01 2017Proof nets are a syntax for linear logic proofs which gives a coarser notion of proof equivalence with respect to syntactic equality together with an intuitive geometrical representation of proofs. In this paper we give an alternative $2$-dimensional ... More

Two-orbit convex polytopes and tilingsMar 10 2014We classify the convex polytopes whose symmetry groups have two orbits on the flags. These exist only in two or three dimensions, and the only ones whose combinatorial automorphism group is also two-orbit are the cuboctahedron, the icosidodecahedron, ... More

Dispersive deformations of the Hamiltonian structure of Euler's equationsSep 01 2015Euler's equations for a two-dimensional system can be written in Hamiltonian form, where the Poisson bracket is the Lie-Poisson bracket associated to the Lie algebra of divergence free vector fields. We show how to derive the Poisson brackets of 2d hydrodynamics ... More

Trakhtenbrot theorem and first-order axiomatic extensions of MTLMar 04 2014Jul 09 2014In 1950, B.A. Trakhtenbrot showed that the set of first-order tautologies associated to finite models is not recursively enumerable. In 1999, P. H\'ajek generalized this result to the first-order versions of \L ukasiewicz, G\"odel and Product logics. ... More

First-order Nilpotent Minimum Logics: first stepsMar 30 2011Jul 02 2012Following the lines of the analysis done in [BPZ07, BCF07] for first-order G\"odel logics, we present an analogous investigation for Nilpotent Minimum logic NM. We study decidability and reciprocal inclusion of various sets of first-order tautologies ... More

Arbitrage and Hedging in model-independent markets with frictionsDec 04 2015Aug 25 2016We provide a Fundamental Theorem of Asset Pricing and a Superhedging Theorem for a model independent discrete time financial market with proportional transaction costs. We consider a probability-free version of the Robust No Arbitrage condition introduced ... More

On the Cooperation of Independent RegistriesJul 21 2010Registries play a key role in service-oriented applications. Originally, they were neutral players between service providers and clients. The UDDI Business Registry (UBR) was meant to foster these concepts and provide a common reference for companies ... More

Følner functions and the generic Word Problem for finitely generated amenable groupsMar 12 2017Jul 03 2018We introduce and investigate different definitions of effective amenability, in terms of computability of F{\o}lner sets, Reiter functions, and F{\o}lner functions. As a consequence, we prove that recursively presented amenable groups have subrecursive ... More

On hereditarily just infinite profinite groups obtained via iterated wreath productsMay 30 2015We study a generalisation of the family of non-(virtually pro-$p$) hereditarily just infinite profinite groups introduced by J.\! S.\! Wilson in 2010. We prove that this family contains groups of finite lower rank. We also show that many groups in this ... More

Fine regularity results for Mumford-Shah minimizers: porosity, higher integrability and the Mumford-Shah conjectureOct 12 2016We review some classical results and more recent insights about the regularity theory for local minimizers of the Mumford and Shah energy and their connections with the Mumford and Shah conjecture. We discuss in details the links among the latter, the ... More

Some insights on bicategories of fractions: representations and compositions of 2-morphismsOct 15 2014Apr 20 2016In this paper we investigate the construction of bicategories of fractions originally described by D. Pronk: given any bicategory $\mathcal{C}$ together with a suitable class of morphisms $\mathbf{W}$, one can construct a bicategory $\mathcal{C}[\mathbf{W}^{-1}]$, ... More

Cosmology with the lyman-alpha forest in the WMAP eraOct 15 2003In the WMAP era of high precision cosmology an accurate determination of the matter power spectrum from lyman-alpha forest data becomes crucial. When combining the matter power spectrum derived from CMB experiments with that inferred from lyman-alpha ... More

The coherent interaction between matter and radiation - A tutorial on the Jaynes-Cummings modelNov 04 2011The Jaynes-Cummings (JC) model is a milestone in the theory of coherent interaction between a two-level system and a single bosonic field mode. This tutorial aims to give a complete description of the model, analyzing the Hamiltonian of the system, its ... More

On the strong coupling expansion in the su(1|1) sector of N=4 SYMMay 08 2008May 12 2008We consider the anomalous dimension of the fermionic highest states Tr(psi^L) in the su(1|1) sector of N=4 SYM at strong coupling. In the thermodynamical L->OO limit it is described by a BES-like integral equation recently proposed by Rej, Staudacher ... More

Universality of three gaugino anomalous dimensions in N=4 SYMMay 04 2007May 05 2007We study maximal helicity three gaugino operators in N=4 Super Yang-Mills theory. We show that the lowest anomalous dimension of scaling operators with generic finite spin can be expressed in terms of the universal anomalous dimension appearing at twist-2. ... More

Anomalous dimensions at twist-3 in the sl(2) sector of N=4 SYMApr 26 2007We consider twist-3 operators in the sl(2) sector of N=4 SYM built out of three scalar fields with derivatives. We extract from the Bethe Ansatz equations of this sector the exact lowest anomalous dimension gamma(s) of scaling fields for several values ... More

Wave functions for Hamiltonian Lattice Gauge TheoryMar 21 2000We study four dimensional SU(2) lattice gauge theory in the Hamiltonian formalism by Green's Function Monte Carlo methods. A trial ground state wave function is introduced to improve the configuration sampling and we discuss the interplay between its ... More

Ultraluminous X-ray sources: three exciting yearsOct 19 2015The extreme extragalactic sources known as Ultraluminous X-ray Sources (ULX) represent a unique testing environment for compact objects population studies and the accretion process. Their nature has long been disputed. Their luminosity, well above the ... More

Hadronic Production of Heavy QuarksOct 29 1997We review the status of theoretical evaluations of heavy quark and heavy quarkonium hadroproduction cross sections and their comparisons with experimental data.

Jet Areas, and What They are Good ForJun 19 2007We introduce the concept of the area of a jet, and show how it can be used to perform the subtraction of even a large amount of diffuse noise from hard jets.

pQCD Calculations of Heavy Quark and J/psi ProductionFeb 20 2007We review the present status of theoretical predictions for both closed (J/psi) and open heavy quark production in high energy collisions, and their comparisons to experimental data.

QCD Predictions for Charm and Bottom Production at RHICDec 20 2005We present up-to-date QCD predictions for open charm and bottom production at RHIC in nucleon-nucleon collisions at \sqrt{S} = 200 GeV. The electron spectrum resulting from heavy flavor decays is also evaluated for direct comparison to the PHENIX and ... More

Rise and Fall of the Bottom Quark Production ExcessJul 16 2004We review the history of comparisons between bottom production measurements and QCD predictions. We challenge the existence of a `significant discrepancy', and argue that standard approaches to QCD calculations do a good job in describing the experimental ... More

An equilibrated fluxes approach to the Certified Descent Algorithm for shape optimization using conforming Finite Element and Discontinuous Galerkin discretizationsNov 10 2016The Certified Descent Algorithm (CDA) is a gradient-based method for shape optimization which certifies that the direction computed using the shape gradient is a genuine descent direction for the objective functional under analysis. It relies on the computation ... More

Gravity, holography and applications to condensed matterOct 09 2016Oct 17 2016Momentum relaxation is an ever-present and unavoidable ingredient of any realistic condensed matter system. In real-world materials the presence of a lattice, impurities or disorder forces momentum to dissipate and leads to relevant physical effects such ... More

Stress-corrosion mechanisms in silicate glassesJan 19 2009Apr 01 2009The present review is intended to revisit the advances and debates in the comprehension of the mechanisms of subcritical crack propagation in silicate glasses almost a century after its initial developments. Glass has inspired the initial insights of ... More

Localisation in 2+1 dimensional SU(3) pure gauge theory at finite temperatureMar 12 2019I study the localisation properties of low Dirac eigenmodes in 2+1 dimensional SU(3) pure gauge theory, both in the low-temperature, confined and chirally-broken phase and in the high-temperature, deconfined and chirally-restored phase, by means of numerical ... More

Chemically-exfoliated single-layer MoS$_2$ : stability, lattice dynamics and catalytic adsorption from first principlesDec 05 2013Chemically and mechanically exfoliated MoS$_2$ single-layer samples have substantially different properties. While mechanically exfoliated single-layers are mono-phase (1H polytype with Mo in trigonal prismatic coordination), the chemically exfoliated ... More

A Law of Large Numbers for an Interacting Particle System with Confining PotentialJan 03 2007In this paper we consider an interacting particle system modeled as a system of $N$ stochastic differential equations driven by Brownian motions with a drift term including a confining potential acting on each particle, and an interaction potential modeling ... More

Contracting rigid germs in higher dimensionsSep 30 2011Jan 09 2013Following Favre, we define a holomorphic germ f:(C^d,0) -> (C^d,0) to be rigid if the union of the critical set of all iterates has simple normal crossing singularities. We give a partial classification of contracting rigid germs in arbitrary dimensions ... More

A Poincaré-Dulac renormalization theorem for attracting rigid germs in $\mathbb{C}^d$Mar 14 2011Sep 30 2011Studying the dynamics of attracting rigid germs $f:(\mathbb{C}^d, 0) \rightarrow (\mathbb{C}^d, 0)$ in dimension $d \geq 3$, a new phenomenon arise: principal resonances. The resonances of the classic Poincar\'e-Dulac theory are given by (multiplicative) ... More

Thermal properties of a string bit model at large NSep 06 2017We study the finite temperature properties of a recently introduced string bit model designed to capture some features of the emergent string in the tensionless limit. The model consists of a pair of bosonic and fermionic bit operators transforming in ... More

A temporal semantics for Nilpotent Minimum logicOct 22 2013In [Ban97] a connection among rough sets (in particular, pre-rough algebras) and three-valued {\L}ukasiewicz logic {\L}3 is pointed out. In this paper we present a temporal like semantics for Nilpotent Minimum logic NM ([Fod95, EG01]), in which the logic ... More

On the classification of complete area-stationary and stable surfaces in the sub-Riemannian Sol manifoldMay 25 2013Aug 17 2013We study the classification of area-stationary and stable $C^2$ regular surfaces in the space of the rigid motions of the Minkowski plane E(1,1), equipped with its sub-Riemannian structure. We construct examples of area-stationary surfaces that are not ... More

Filtrations on graph complexes and the Grothendieck-Teichmüller Lie algebra in depth twoJul 03 2017We establish an isomorphism between the Grothendieck-Teichm\"uller Lie algebra $\mathfrak{grt}_1$ in depth two modulo higher depth and the cohomology of the two-loop part of the graph complex of internally connected graphs $\mathsf{ICG}(1)$. In particular, ... More

Internally connected graphs and the Kashiwara-Vergne Lie algebraDec 09 2016Dec 19 2017It is conjectured that the Kashiwara-Vergne Lie algebra $\widehat{\mathfrak{krv}}_2$ is isomorphic to the direct sum of the Grothendieck-Teichm\"uller Lie algebra $\mathfrak{grt}_1$ and a one-dimensional Lie algebra. In this paper, we use the graph complex ... More

Verification of Reachability Problems for Time Basic Petri NetsSep 09 2014Time-Basic Petri nets, is a powerful formalism for model- ing real-time systems where time constraints are expressed through time functions of marking's time description associated with transition, representing possible firing times. We introduce a technique ... More

Lyapunov exponents, holomorphic flat bundles and de Rham moduli spaceOct 30 2018We consider Lyapunov exponents for flat bundles over hyperbolic curves defined via parallel transport over the geodesic flow. We refine a lower bound obtained by Eskin, Kontsevich, Moeller and Zorich showing that the sum of the first k exponents is greater ... More

Top production at large p_t at NLO+NLL accuracySep 18 2018We introduce a new version of the FONLL code, now capable of calculating differential distributions for top quark production with next-to-leading-log resummation of log(p_t/m) terms. Numerical results for LHC and FCC kinematics are presented. In the transverse ... More

Thermodynamic laws for populations and quantum coherence: A self-contained introduction to the resource theory approach to thermodynamicsJul 30 2018In these notes I give a self-contained introduction to the resource theory approach to quantum thermodynamics. I will introduce in an elementary manner the technical machinery necessary to unpack and prove the core statements of the theory. The topics ... More

Note on Calderón's inverse problem for measurable conductivitiesMar 19 2018Jun 25 2019The unique determination of a measurable conductivity from the Dirichlet-to-Neumann map of the equation $\mathrm{div} (\sigma \nabla u) = 0$ is the subject of this note. A new strategy, based on Clifford algebras and a higher dimensional analogue of the ... More

On a homotopy version of the Duflo isomorphismDec 19 2017For a finite dimensional Lie algebra $\mathfrak{g}$, the Duflo map $S\mathfrak{g}\rightarrow U\mathfrak{g}$ defines an isomorphism of $\mathfrak{g}$-modules. On $\mathfrak{g}$-invariant elements it gives an isomorphism of algebras. Moreover, it induces ... More

The classification of isotrivially fibred surfaces with p_g=q=2Apr 08 2009Jul 29 2010An isotrivially fibred surface is a smooth projective surface endowed with a morphism onto a curve such that all the smooth fibres are isomorphic to each other. The first goal of this paper is to classify the isotrivially fibred surfaces with $p_g=q=2$ ... More

Radial and cylindrical symmetry of solutions to the Cahn-Hilliard equationFeb 01 2019The paper is devoted to the classification of entire solutions to the Cahn-Hilliard equation $-\Delta u = u-u^3-\delta$ in $\R^N$, with particular interest in those solutions whose nodal set is either bounded or contained in a cylinder. The aim is to ... More

A bicategory of reduced orbifolds from the point of view of differential geometry - IApr 25 2013Jan 09 2015We describe a bicategory $(\mathcal{R}ed\,\mathcal{O}rb)$ of reduced orbifolds in the framework of classical differential geometry (i.e. without any explicit reference to notions of Lie groupoids or differentiable stacks, but only using orbifold atlases, ... More

$Γ$-convergence for high order phase field fracture: continuum and isogeometric formulationsJul 23 2019We consider second order phase field functionals, in the continuum setting, and their discretization with isogeometric tensor product B-splines. We prove that these functionals, continuum and discrete, $\Gamma$-converge to a brittle fracture energy, defined ... More

Combinatorially two-orbit convex polytopesNov 06 2014Feb 19 2015Any convex polytope whose combinatorial automorphism group has two orbits on the flags is isomorphic to one whose group of Euclidean symmetries has two orbits on the flags (equivalently, to one whose automorphism group and symmetry group coincide.) Hence, ... More

Finite generation of iterated wreath products in product actionMay 30 2015Jun 21 2015Let $\mathcal{S}$ be a sequence of finite perfect transitive permutation groups with uniformly bounded number of generators. We prove that the infinitely iterated wreath product in product action of the groups in $\mathcal{S}$ is topologically finitely ... More

Viral Search algorithmJun 14 2016The article, after a brief introduction on genetic algorithms and their functioning, presents a kind of genetic algorithm called Viral Search. We present the key concepts, we formally derive the algorithm and we perform numerical tests designed to illustrate ... More

Some insights on bicategories of fractions - IIOct 19 2014Nov 21 2014We fix any bicategory $\mathscr{A}$ together with a class of morphisms $\mathbf{W}_{\mathscr{A}}$, such that there is a bicategory of fractions $\mathscr{A}[\mathbf{W}_{\mathscr{A}}^{-1}]$. Given another such pair $(\mathscr{B},\mathbf{W}_{\mathscr{B}})$ ... More

Computability of Følner setsJun 14 2016We define the notion of computability of F\o lner sets for finitely generated amenable groups. We prove, by an explicit description, that the Kharlampovich group, a finitely presented solvable group with unsolvable word problem, has computable F\o lner ... More

The generalized scaling function of AdS/CFT and semiclassical string theoryJun 23 2008Recently, Freyhult, Rej and Staudacher (FRS) proposed an integral equation determining the leading logarithmic term of the anomalous dimension of sl(2) twist-operators in N=4 SYM for large Lorentz spin M and twist L at fixed j = L/log(M). We discuss the ... More

Three loop anomalous dimensions of twist-3 gauge operators in N=4 SYMJul 11 2007We propose a closed expression for the three loop anomalous dimension of a class of twist-3 operators built with gauge fields and covariant derivatives. To this aim, we solve the long-range Bethe Ansatz equations at finite spin and provide a consistent ... More