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Torsional instability and sensitivity analysis in a suspension bridge model related to the Melan equationJul 19 2018Inspired by the Melan equation we propose a model for suspension bridges with two cables linked to a deck, through inextensible hangers. We write the energy of the system and we derive from variational principles two nonlinear and nonlocal hyperbolic ... More

On the first frequency of reinforced partially hinged platesApr 19 2019We consider a partially hinged rectangular plate and its normal modes. The dynamical properties of the plate are influenced by the spectrum of the associated eingenvalue problem. In order to improve the stability of the plate, it seems reasonable to place ... More

A new model for suspension bridges involving the convexification of the cablesOct 05 2018The final purpose of this paper is to show that, by inserting a convexity constraint on the cables of a suspension bridge, the torsional instability of the deck appears at lower energy thresholds. Since this constraint is suggested by the behavior of ... More

On a conjecture of Wilf about the Frobenius numberAug 22 2014May 20 2015Given coprime positive integers $a_1 < ...< a_d$, the Frobenius number $F$ is the largest integer which is not representable as a non-negative integer combination of the $a_i$. Let $g$ denote the number of all non-representable positive integers: Wilf ... More

The Tait conjecture in g(S^1xS^2)Feb 09 2016The Tait conjecture states that alternating reduced diagrams of links in S^3 have the minimal number of crossings. It has been proved in 1987 by M. Thistlethwaite, L. Kauffman and K. Murasugi studying the Jones polynomial. The author proved an analogous ... More

Charge Orbits and Moduli Spaces of Black Hole AttractorsDec 16 2010Dec 28 2010We report on the theory of "large" U-duality charge orbits and related "moduli spaces" of extremal black hole attractors in N = 2, d = 4 Maxwell-Einstein supergravity theories with symmetric scalar manifolds, as well as in N > 3-extended, d = 4 supergravities. ... More

Spin-Bits and N=4 SYMApr 24 2006May 04 2006We briefly review the spin-bit formalism, describing the non-planar dynamics of the $\mathcal{N}=4,d=4$ Super Yang-Mills SU(N) gauge theory. After considering its foundations, we apply such a formalism to the $su(2)$ sector of purely scalar operators. ... More

On a Coarse-Graining Concept in Colloidal Physics with Application to Fluid and Arrested Colloidal Suspensions in Shearing FieldsApr 13 2010We poorly understand the macroscopic properties of complex fluids and of amorphous bodies in general. This is mainly due to the interplay between phenomena at different levels and length-scales. In particular, it is not necessarily true that the microscopic ... More

Simple model for the static structure and the mean coordination of amorphous solidsMay 07 2009We propose a simple route to evaluate the static structure, in terms of average coordination, of completely disordered solids with spherical constituents, from ca. 55% volume fraction up to random close packing, in the absence of structural heterogeneities. ... More

Vanishing ideals of binary Hamming spheresFeb 08 2018We show how to efficiently obtain the Algebraic Normal Form of Boolean functions vanishing on Hamming spheres centred at zero. By exploiting the symmetry of the problem we obtain formulas for particular cases, and a computational method to address the ... More

Inference for Additive Models in the Presence of Infinite Dimensional Nuisance ParametersNov 07 2016A framework for hypothesis testing of functional restrictions against general alternatives is proposed. The parameter space is a reproducing kernel Hilbert space. The null the hypothesis does not necessarily define a parametric model. The tests allow ... More

Spectral theory for commutative algebras of differential operators on Lie groupsJul 29 2010The joint spectral theory of a system of pairwise commuting self-adjoint left-invariant differential operators L_1,...,L_n on a connected Lie group G is studied, under the hypothesis that the algebra generated by them contains a "weighted subcoercive ... More

Detecting multimode entanglement by symplectic uncertainty relationsAug 31 2005Aug 17 2006A hierarchy of multimode uncertainty relations on the second moments of n pairs of canonical operators is derived in terms of quantities invariant under linear canonical (i.e. symplectic) transformations. Conditions for the separability of multimode continuous ... More

On the Continuity of Center-Outward Distribution and Quantile FunctionsMay 13 2018To generalize the notion of distribution function to dimension $d\geq 2$, in the recent papers it was proposed a concept of center-outward distribution function based on optimal transportation ideas, and the inferential properties of the corresponding ... More

Weak Convergence of Laws on R^{K} with Common MarginalsJun 19 2006We present a result on topologically equivalent integral metrics (Rachev, 1991, Muller, 1997) that metrize weak convergence of laws with common marginals. This result is relevant for applications, as shown in a few simple examples.

Coupled nonlinear Schrodinger systems with potentialsJun 01 2005Coupled nonlinear Schrodinger systems describe some physical phenomena such as the propagation in birefringent optical fibers, Kerr-like photorefractive media in optics and Bose-Einstein condensates. In this paper, we study the existence of concentrating ... More

Semistable 3-fold flipsMay 31 1995We piece together ingredients, which are well known and documented in the literature, into a new proof of the existence of semistable 3-fold flips

Ground states for a system of nonlinear Schrodinger equations with three waves interactionOct 19 2009We consider a system of nonlinear Schrodinger equations with three waves interaction studying the existence of ground state solutions. In particular, we find a vector ground state, namely a ground state with the three components all different from zero. ... More

The $ω$-Borel invariant for representations into $SL(n,\mathbb{C}_ω)$Sep 22 2017Let $\Gamma$ be the fundamental group of a complete hyperbolic $3$-manifold $M$ with toric cusps. We define the $\omega$-Borel invariant $\beta_n^\omega(\rho_\omega)$ associated to a representation $\rho_\omega: \Gamma \rightarrow SL(n,\mathbb{C}_\omega)$, ... More

Stationary layered solutions for a system of Allen-Cahn type equationsNov 25 2012Dec 03 2012We consider a class of semilinear elliptic system of the form $-\Delta u(x,y)+\nabla W(u(x,y))=0,\quad (x,y)\in\R^{2}$ where $W:\R^{2}\to\R$ is a double well non negative symmetric potential. We show, via variational methods, that if the set of solutions ... More

Freudenthal Duality in Gravity: from Groups of Type E7 to Pre-Homogeneous SpacesSep 03 2015Sep 29 2015Freudenthal duality can be defined as an anti-involutive, non-linear map acting on symplectic spaces. It was introduced in four-dimensional Maxwell-Einstein theories coupled to a non-linear sigma model of scalar fields. In this short review, I will consider ... More

Finite generation of adjoint rings after Lazic: an introductionJun 26 2010An introduction to all the key ideas of Lazic's proof of the theorem on the finite generation of adjoint rings.

The shear modulus of metastable amorphous solids with strong central and bond-bending interactionsJul 23 2008Feb 17 2009We derive expressions for the shear modulus of deeply-quenched, glassy solids, in terms of a Cauchy-Born free energy expansion around a rigid (quenched) reference state, following the approach due to Alexander [Alexander, Phys. Rep. 296, 1998]. Continuum-limit ... More

A System of Interaction and StructureOct 28 1999Jan 27 2007This paper introduces a logical system, called BV, which extends multiplicative linear logic by a non-commutative self-dual logical operator. This extension is particularly challenging for the sequent calculus, and so far it is not achieved therein. It ... More

A characterization of the Arf property for quadratic quotients of the Rees algebraJun 12 2018Dec 06 2018We provide a characterization of the Arf property in both the numerical duplication of a numerical semigroup and in a member of a family of quotients of the Rees algebra studied in arXiv:1403.4200 [math.AC]

Rigidity at infinity for the Borel function of the tetrahedral reflection latticeJun 06 2019Let $\Gamma$ be a non-uniform lattice of $PSL(2,\mathbb{C})$. To every representation $\rho:\Gamma \rightarrow PSL(n,\mathbb{C})$ it is possible to associate a numerical invariant $\beta_n(\rho)$, called Borel invariant, which is constant on the $PSL(n,\mathbb{C})$-conjugancy ... More

Inference for Additive Models in the Presence of Possibly Infinite Dimensional Nuisance ParametersNov 07 2016Aug 20 2018A framework for estimation and hypothesis testing of functional restrictions against general alternatives is proposed. The parameter space is a reproducing kernel Hilbert space (RKHS). The null hypothesis does not necessarily define a parametric model. ... More

Asymptotic Structure and Bondi-Metzner-Sachs group in General RelativityJan 05 2018Jan 20 2019In this work the asymptotic structure of space-time and the main properties of the Bondi-Metzner-Sachs (BMS) group, which is the asymptotic symmetry group of asymptotically flat space-times, are analysed. Every chapter, except the fourth, begins with ... More

Asymptotically Moebius maps and rigidity for the hyperbolic planeJun 25 2019Let $S$ be a rank-one symmetric space of non-compact type and let $X$ be a $\text{CAT}(-1)$ space. A well-known result by Bourdon states that if a topological embedding $\varphi: \partial_\infty S \rightarrow \partial_\infty X$ respects cross ratios, ... More

Joint functional calculi and a sharp multiplier theorem for the Kohn Laplacian on spheresJan 18 2016Let $\Box_b$ be the Kohn Laplacian acting on $(0,j)$-forms on the unit sphere in $\mathbb{C}^n$. In a recent paper of Casarino, Cowling, Sikora and the author, a spectral multiplier theorem of Mihlin--H\"ormander type for $\Box_b$ is proved in the case ... More

The first elements of the quotient of a numerical semigroup by a positive integerDec 27 2013Apr 11 2015Given three pairwise coprime positive integers $a_1,a_2,a_3 \in \mathbb{Z}^+$ we show the existence of a relation between the sets of the first elements of the three quotients $\frac{\langle a_i,a_j \rangle}{a_k}$ that can be made for every $\{i.j,k\}=\{1,2,3\}$. ... More

Numerical semigroups with large embedding dimension satisfy Wilf's conjectureNov 08 2011Dec 17 2012We give an affirmative answer to Wilf's conjecture for numerical semigroups satisfying 2 \nu \geq m, where \nu and m are respectively the embedding dimension and the multiplicity of a semigroup. The conjecture is also proved when m \leq 8 and when the ... More

On the type of an almost Gorenstein monomial curveJul 21 2015Aug 22 2016We prove that the Cohen-Macaulay type of an almost Gorenstein monomial curve $\mathcal C \subseteq \mathbb{A}^4$ is at most $3$, and make some considerations on the general case.

Blowup algebras of rational normal scrollsOct 13 2016Sep 09 2018We determine the equations of the blowup of $\mathbb{P}^n$ along a $d$-fold rational normal scroll $S$, and we prove that the Rees ring and special fiber ring of $S \subseteq \mathbb{P}^n$ are Koszul algebras.

Greedy algorithms for predictionFeb 05 2016In many prediction problems, it is not uncommon that the number of variables used to construct a forecast is of the same order of magnitude as the sample size, if not larger. We then face the problem of constructing a prediction in the presence of potentially ... More

Minimal relations and the Diophantine Frobenius Problem in embedding dimension threeAug 22 2016Aug 24 2016This paper provides a formula for the minimal relations and the Frobenius number of a numerical semigroup minimally generated by three pairwise coprime positive integers.

Singularly perturbed Neumann problems with potentialsOct 08 2003We study the existence of concentrating solutions of a singularly perturbed Neumann problems with two potentials.

Algebras of differential operators on Lie groups and spectral multipliersJul 07 2010This thesis is devoted to the study of joint spectral multipliers for a system of pairwise commuting, self-adjoint left-invariant differential operators L_1,...,L_n on a connected Lie group G. Under the assumption that the algebra generated by L_1,...,L_n ... More

Generators of a fraction of a numerical semigroupFeb 20 2014May 30 2015Given a numerical semigroup $S$ and a positive integer $d$, the fraction $\frac{S}{d}=\{ x \in \mathbb{N} \ | \ dx \in S\}$ is again a numerical semigroup. In this paper we determine a generating set for $\frac{S}{d}$ in terms of the minimal generators ... More

On the least positive solution to a proportionally modular Diophantine inequalitDec 18 2013Feb 03 2014Given three positive integers $a,b,c$, a proportionally modular Diophantine inequality is an expression of the form $ax \mod{b} \le cx$. Our aim is to give a recursive formula for the least solution to such an inequality. We then use the formula to derive ... More

Spectral multipliers on Heisenberg-Reiter and related groupsDec 04 2012Let $L$ be a homogeneous sublaplacian on a 2-step stratified Lie group $G$ of topological dimension $d$ and homogeneous dimension $Q$. By a theorem due to Christ and to Mauceri and Meda, an operator of the form $F(L)$ is bounded on $L^p$ for $1 < p < ... More

Borel invariant for Zimmer cocycles of 3-manifold groupsJul 04 2019Let $\Gamma$ be a non-uniform lattice of $\text{PSL}(2,\mathbb{C})$. Given any representation $\rho:\Gamma \rightarrow \text{PSL}(n,\mathbb{C})$ we can define a numerical invariant $\beta_n(\rho)$, called Borel invariant, which remains constant along ... More

Generalized uncertainty inequalitiesApr 05 2008In this paper, Heisenberg-Pauli-Weyl-type uncertainty inequalities are obtained for a pair of positive-self adjoint operators on a Hilbert space, whose spectral projectors satisfy a ``balance condition'' involving certain operator norms. This result is ... More

On first attempts to reconcile quantum principles with gravitySep 26 2013In his 1916's first paper on gravitational waves Einstein began to speculate on interactions between the principles of the old quantum theory and his theory of gravitation. With this contribution Einstein has stimulated a lot of similar speculations, ... More

9 generators of the skein space of the 3-torusMar 31 2016We show that the skein vector space of the 3-torus is finitely generated. We show that it is generated by 9 elements: the empty set, some simple closed curves representing the non null elements of the first homology group with coefficients in \Z_2, and ... More

Shadows and quantum invariantsOct 15 2016This is a PhD thesis about low dimensional topology, in particular knot thory in 3-manifolds also different from the 3-sphere, topological applications of quantum invariants, and Turaev's shadows. There is an introduction and a survey for these topics. ... More

A Real-Time, GPU-Based, Non-Imaging Back-End for Radio TelescopesJan 31 2014Since the discovery of RRATs, interest in single pulse radio searches has increased dramatically. Due to the large data volumes generated by these searches, especially in planned surveys for future radio telescopes, such searches have to be conducted ... More

A true real-time success story: the case of collecting beauty-ful data at the LHCb experimentJun 22 2018Jun 25 2018The LHCb experiment at CERN is currently completing its first big data taking campaign at the LHC started in 2009. It has been collecting data at more than 2.5 times its nominal design luminosity value and with a global efficiency of ~92%. Even more striking, ... More

Feedback control in quantum optics: an overview of experimental breakthroughs and areas of applicationOct 15 2012Nov 22 2012We present a broad summary of research involving the application of quantum feedback control techniques to optical set-ups, from the early enhancement of optical amplitude squeezing to the recent stabilisation of photon number states in a microwave cavity, ... More

Patterns on the numerical duplication by their admissibility degreeJan 29 2019We develop the theory of patterns on numerical semigroups in terms of the admissibility degree. We prove that the Arf pattern induces every strongly admissible pattern, and determine all patterns equivalent to the Arf pattern. We study patterns on the ... More

Rigidity at infinity for lattices in rank-one Lie groupsNov 03 2017Jun 21 2018Let $\Gamma$ be a non-uniform lattice in $PU(p,1)$ without torsion and with $p\geq2 $. We introduce the notion of volume for a representation $\rho:\Gamma \rightarrow PU(m,1)$ where $m \geq p$. We use this notion to generalize the Mostow--Prasad rigidity ... More

s-Hankel hypermatrices and 2 x 2 determinantal idealsOct 16 2012Jun 11 2016We introduce the concept of s-Hankel hypermatrix, which generalizes both Hankel matrices and generic hypermatrices. We study two determinantal ideals associated to an s-Hankel hypermatrix: the ideal I<s,t> generated by certain 2 x 2 slice minors, and ... More

On the multiplicity of tangent cones of monomial curvesNov 29 2017Sep 09 2018Let $\Lambda$ be a numerical semigroup, $\mathcal{C}\subseteq \mathbb{A}^n$ the monomial curve singularity associated to $\Lambda$, and $\mathcal{T}$ its tangent cone. In this paper we provide a sharp upper bound for the least positive integer in $\Lambda$ ... More

Schrodinger equation with critical Sobolev exponentJan 22 2004In this paper we study the existence of solutions and their concentration phenomena of a singularly perturbed semilinear Schrodinger equation with the presence of the critical Sobolev exponent.

Del Pezzo surfaces over Dedekind schemesMay 31 1995Let S be a Dedekind scheme with fraction field K. We study the following problem: given a Del Pezzo surface X, defined over K, construct a distinguished integral model of X, defined over all of S. We provide a satisfactory answer if S is a smooth complex ... More

The symmetric signatureJun 10 2016This is the author's Ph.D. thesis. We introduce two related invariants for local (and standard graded) rings called differential and syzygy symmetric signature. These are defined by looking at the maximal free splitting of the module of K\"ahler differentials ... More

The LHCb UpgradeOct 01 2013The LHCb experiment is designed to perform high-precision measurements of CP violation and search for New Physics using the enormous flux involving beauty and charm quarks produced at the LHC. The operation and the results obtained from the data collected ... More

Weber's formula for the bitangents of a smooth plane quarticDec 06 2016In a section of his 1876 treatise Theorie der Abel'schen Functionen vom Geschlecht 3 Weber proved a formula that expresses the bitangents of a non-singular plane quartic in terms of Riemann theta constants (Thetanullwerte). The present note is devoted ... More

Blowup algebras of rational normal scrollsOct 13 2016We investigate the algebraic relations among the minors of a $2 \times c$ matrix with $d$ catalecticant blocks, which define a $d$-fold rational normal scroll $\mathcal{S}\subseteq \mathbb{P}^{c+d- 1}$. We determine the equations of the blowup of $\mathbb{P}^{c+d-1}$ ... More

On integers which are representable as sums of large squaresAug 06 2014Apr 11 2015We prove that the greatest positive integer that is not expressible as a linear combination with integer coefficients of elements of the set $\{n^2,(n+1)^2,\ldots \}$ is asymptotically $O(n^2)$, verifying thus a conjecture of Dutch and Rickett. Furthermore ... More

Consecutive cancellations in Tor modules over local ringsMay 17 2016Let $M, N$ be finite modules over a Noetherian local ring $R$, and let $G$ be the associated graded ring of $R$. We show that the bigraded Hilbert series of $gr(Tor^R(M,N))$ is obtained from that of $Tor^G(gr(M),gr(N))$ by negative consecutive cancellations, ... More

Oscillating solutions for prescribed mean curvature equations: Euclidean and Lorentz-Minkowski casesSep 20 2017Feb 25 2018This paper deals with the prescribed mean curvature equations both in the Euclidean case and in the Lorentz-Minkowski case in presence of a nonlinearity $g$ such that $g'(0)>0$. We show the existence of oscillating solutions, namely with an unbounded ... More

A characterization of the Arf property for quadratic quotients of the Rees algebraJun 12 2018May 13 2019We provide a characterization of the Arf property in both the numerical duplication of a numerical semigroup and in a member of a family of quotients of the Rees algebra studied in arXiv:1403.4200 [math.AC]

Analysis of joint spectral multipliers on Lie groups of polynomial growthOct 06 2010Dec 19 2010We study the problem of L^p-boundedness (1 < p < \infty) of operators of the form m(L_1,...,L_n) for a commuting system of self-adjoint left-invariant differential operators L_1,...,L_n on a Lie group G of polynomial growth, which generate an algebra ... More

Breaking of Goldstone modes in two component Bose-Einstein condensateSep 07 2016We study the decay rate $\Gamma(k)$ of density excitations of two-component Bose-Einstein condensates at zero temperature. Those excitations, where the two components oscillate in phase, include the Goldstone mode resulting from condensation. While within ... More

Weighted Plancherel estimates and sharp spectral multipliers for the Grushin operatorsApr 05 2012We study the Grushin operators acting on $\R^{d_1}_{x'}\times \R^{d_2}_{x"}$ and defined by the formula \[ L=-\sum_{\jone=1}^{d_1}\partial_{x'_\jone}^2 - (\sum_{\jone=1}^{d_1}|x'_\jone|^2) \sum_{\jtwo=1}^{d_2}\partial_{x"_\jtwo}^2. \] We obtain weighted ... More

Regularity of solutions to the parabolic fractional obstacle problemJan 26 2011In this paper we study a parabolic version of the fractional obstacle problem, proving almost optimal regularity for the solution. This problem is motivated by an American option model proposed by Menton which introduces, into the theory of option evaluation, ... More

The Cold Spot as a Large Void: Lensing Effect on CMB Two and Three Point Correlation FunctionsMay 07 2009Jul 01 2010The "Cold Spot" in the CMB sky could be due to the presence of an anomalous huge spherical underdense region - a "Void" - of a few hundreds Mpc/h radius. Such a structure would have an impact on the CMB two-point (power spectrum) and three-point (bispectrum) ... More

Inflation from the Higgs field false vacuum with hybrid potentialApr 18 2012Nov 20 2012We have recently suggested [1,2] that Inflation could have started in a local minimum of the Higgs potential at field values of about $10^{15}-10^{17}$ GeV, which exists for a narrow band of values of the top quark and Higgs masses and thus gives rise ... More

Detecting the Cold Spot as a Void with the Non-Diagonal Two-Point FunctionJul 01 2010Sep 03 2010The anomaly in the Cosmic Microwave Background known as the "Cold Spot" could be due to the existence of an anomalously large spherical (few hundreds Mpc/h radius) underdense region, called a "Void" for short. Such a structure would have an impact on ... More

A Cloud-Based and RESTful Internet of Things Platform to Foster Smart Grid Technologies Integration and Re-UsabilityJun 21 2016Jun 27 2016Currently, one of the hottest topics in the Internet of Things (IoT) research domain regards the issue to overcome the heterogeneity of proprietary technologies and systems so as to enable the integration of applications and devices developed for different ... More

On the genetic optimization of APSK constellations for satellite broadcastingJan 28 2015Both satellite transmissions and DVB applications over satellite present peculiar characteristics that could be taken into consideration in order to further exploit the optimality of the transmission. In this paper, starting from the state-of-the-art, ... More

On the stability of asynchronous Random Access SchemesJan 28 2015Slotted Aloha-based Random Access (RA) techniques have recently regained attention in light of the use of Interference Cancellation (IC) as a mean to exploit diversity created through the transmission of multiple burst copies per packet content (CRDSA). ... More

On the Proof Complexity of Deep InferenceSep 08 2007Apr 19 2009We obtain two results about the proof complexity of deep inference: 1) deep-inference proof systems are as powerful as Frege ones, even when both are extended with the Tseitin extension rule or with the substitution rule; 2) there are analytic deep-inference ... More

Matrix Norms, BPS Bounds and Marginal Stability in N=8 SupergravitySep 16 2010Dec 01 2010We study the conditions of marginal stability for two-center extremal black holes in N-extended supergravity in four dimensions, with particular emphasis on the N=8 case. This is achieved by exploiting triangle inequalities satisfied by matrix norms. ... More

Lecture notes on variational models for incompressible Euler equationsSep 17 2010These notes briefly summarize the lectures for the Summer School "Optimal transportation: Theory and applications" held by the second author in Grenoble during the week of June 22-26, 2009. Their goal is to describe some recent results on Brenier's variational ... More

Cosmological parameter estimation: impact of CMB aberrationOct 09 2012Jun 12 2013The peculiar motion of an observer with respect to the CMB rest frame induces an apparent deflection of the observed CMB photons, {\it i.e.} aberration, and a shift in their frequency, {\it i.e.} Doppler effect. Both effects distort the temperature multipoles ... More

A quantum Langevin model for non-equilibrium condensationMay 27 2014Nov 28 2014We develop a quantum model for non-equilibrium Bose-Einstein condensation of photons and polaritons in planar microcavity devices. The model builds upon laser theory and includes the spatial dynamics of the cavity field, a saturation mechanism and some ... More

Weighted GrassmanniansJun 03 2002Many classes of projective algebraic varieties can be studied in terms of graded rings. Gorenstein graded rings in small codimension have been studied recently from an algebraic point of view, but the geometric meaning of the resulting structures is still ... More

Pure spinor superstring in AdS_4 x CP^3 with unconstrained ghostsSep 17 2012We construct the action for the pure spinor superstring in the coset description of AdS_4 x CP^3 superspace, using the variables which solve the pure spinor condition. As a test of the consistency of the approach, we use the background field method to ... More

How to reconcile Information theory and Gibbs-Herz entropy for inverted populated systemsMar 10 2015In this paper we discuss about the validity of the Shannon entropy functional in connection with the correct Gibbs-Hertz probability distribution function. We show that there is no contradiction in using the Shannon-Gibbs functional and restate the validity ... More

Shadows, ribbon surfaces, and quantum invariantsApr 23 2014Mar 19 2015Eisermann has shown that the Jones polynomial of a $n$-component ribbon link $L\subset S^3$ is divided by the Jones polynomial of the trivial $n$-component link. We improve this theorem by extending its range of application from links in $S^3$ to colored ... More

A double-layer reduced model for fault flow on slipping domains with hybrid finite volume schemeSep 18 2017In this work we are interested in dealing with single-phase flows in fractured porous media for underground processes. We focus our attention on domains where the presence of faults, with thickness several orders of magnitude smaller than other characteristic ... More

Richness of Deep Echo State Network DynamicsMar 12 2019Reservoir Computing (RC) is a popular methodology for the efficient design of Recurrent Neural Networks (RNNs). Recently, the advantages of the RC approach have been extended to the context of multi-layered RNNs, with the introduction of the Deep Echo ... More

Long range correlations generated by phase separation. Exact results from field theoryJul 05 2016We consider near-critical planar systems with boundary conditions inducing phase separation. While order parameter correlations decay exponentially in pure phases, we show by direct field theoretical derivation how phase separation generates long range ... More

CMB all-scale blackbody distortions induced by linearizing temperatureOct 29 2015Aug 14 2016Cosmic Microwave Background (CMB) experiments, such as WMAP and Planck, measure intensity anisotropies and build maps using a linearized formula for relating them to the temperature blackbody fluctuations. However, this procedure also generates a signal ... More

On the proper kinetic quadrupole CMB removal and the quadrupole anomaliesApr 08 2015May 22 2015It has been pointed out recently that the quadrupole-octopole alignment in the CMB data is significantly affected by the so-called kinetic Doppler quadrupole (DQ), which is the temperature quadrupole induced by our proper motion. Assuming our velocity ... More

On the structure and applications of the Bondi-Metzner-Sachs groupSep 15 2017Jan 23 2019This work is a pedagogical review dedicated to a modern description of the Bondi-Metzner-Sachs group. The curved space-times that will be taken into account are the ones that suitably approach, at infinity, Minkowski space-time. In particular we will ... More

Universal origin of boson peak vibrational anomalies in ordered crystals and in amorphous materialsOct 22 2018Mar 22 2019The vibrational spectra of solids, both ordered and amorphous, in the low-energy regime, control the thermal and transport properties of materials, from heat capacity to heat conduction, electron-phonon couplings, conventional superconductivity etc. The ... More

On the fine structure of the free boundary for the classical obstacle problemSep 12 2017Nov 25 2017In the classical obstacle problem, the free boundary can be decomposed into "regular" and "singular" points. As shown by Caffarelli in his seminal papers \cite{C77,C98}, regular points consist of smooth hypersurfaces, while singular points are contained ... More

Prediction of Seasonal Temperature Using Soft Computing Techniques: Application in Benevento (Southern Italy) AreaNov 15 2016In this work two soft computing methods, Artificial Neural Networks and Genetic Programming, are proposed in order to forecast the mean temperature that will occur in future seasons. The area in which the soft computing techniques were applied is that ... More

Gradient stability for the Sobolev inequality: the case $p\geq 2$Oct 07 2015Oct 02 2016We prove a strong form of the quantitative Sobolev inequality in $\mathbb{R}^n$ for $p\geq 2$, where the deficit of a function $u\in \dot W^{1,p} $ controls $\| \nabla u -\nabla v\|_{L^p}$ for an extremal function $v$ in the Sobolev inequality.

From parabolic to loxodromic BMS transformationsJun 16 2018Oct 12 2018Half of the Bondi-Metzner-Sachs (BMS) transformations consist of orientation-preserving conformal homeomorphisms of the extended complex plane known as fractional linear (or Mobius) transformations. These can be of 4 kinds, i.e. they are classified as ... More

The complexity of MinRankMay 06 2019In this note, we leverage some of our results from arXiv:1706.06319 to produce a concise and rigorous proof for the complexity of the generalized MinRank Problem in the under-defined and well-defined case. Our main theorem recovers and extends previous ... More

A probabilistic interpretation of set-membership filtering: application to polynomial systems through polytopic boundingMay 05 2015Apr 12 2016Set-membership estimation is usually formulated in the context of set-valued calculus and no probabilistic calculations are necessary. In this paper, we show that set-membership estimation can be equivalently formulated in the probabilistic setting by ... More

A unified framework for deterministic and probabilistic D-stability analysis of uncertain polynomial matricesApr 07 2016Jun 17 2018Many problems in systems and control theory can be formulated in terms of robust D-stability analysis, which aims at verifying if all the eigenvalues of an uncertain matrix lie in a given region D of the complex plane. Robust D-stability analysis is an ... More

On systematic and GR effects on muon $g-2$ experimentsMay 09 2019We derive in full generality the equations that govern the time dependence of the energy ${\mathcal E}$ of the decay electrons in a muon $g-2$ experiment. We include both electromagnetic and gravitational effects and we estimate possible systematics on ... More

Spectral multiplier theorems of Euclidean type on new classes of 2-step stratified groupsJun 03 2013Apr 22 2014From a theorem of Christ and Mauceri and Meda it follows that, for a homogeneous sublaplacian $L$ on a $2$-step stratified group $G$ with Lie algebra $\mathfrak{g}$, an operator of the form $F(L)$ is of weak type $(1,1)$ and bounded on $L^p(G)$ for $1 ... More

Analytical theory of enhanced logarithmic Rayleigh scattering in amorphous solidsJun 02 2019The damping or attenuation coefficient of sound waves in solids due to impurities scales with the wavevector to the fourth power, also known as Rayleigh scattering. In amorphous solids, Rayleigh scattering may be enhanced by a logarithmic factor although ... More

On a class of singularly perturbed elliptic equations in divergence formMar 17 2003May 02 2003We prove the existence of one or more solutions to a singularly perturbed elliptic problema with two potential functions.