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The $\hat W$-orbit of $ρ$, Kostant's formula for powers of the Euler product and affine Weyl groups as permutations of ZJul 29 2005Apr 08 2006Let an affine Weyl group $\hat W$ act as a group of affine transformations on a real vector space V. We analyze the $\hat W$-orbit of a regular element in V and deduce applications to Kostant's formula for powers of the Euler product and to the representations ... More

Spherical nilpotent orbits and abelian subalgebras in isotropy representationsJul 12 2016Nov 27 2016Let $G$ be a simply connected semisimple algebraic group with Lie algebra $\mathfrak g$, let $G_0 \subset G$ be the symmetric subgroup defined by an algebraic involution $\sigma$ and let $\mathfrak g_1 \subset \mathfrak g$ be the isotropy representation ... More

Kostant's pair of Lie type and conformal embeddingsFeb 08 2018We deal with some aspects of the theory of conformal embeddings of affine vertex algebras, providing a new proof of the Symmetric Space Theorem and a criterion for conformal embeddings of equal rank subalgebras. We finally study some examples of embeddings ... More

Conformal embeddings of affine vertex algebras in minimal $W$-algebras I: structural resultsFeb 15 2016Apr 17 2016We find all values of $k\in \mathbb C$, for which the embedding of the maximal affine vertex algebra in a simple minimal W-algebra $W_k(\mathfrak g,\theta)$ is conformal, where $\mathfrak g$ is a basic simple Lie superalgebra and $-\theta$ its minimal ... More

Casimir operators, abelian subspaces and u-cohomologyMay 15 2007Jun 05 2007This survey paper is an exposition of old and recent results of Kostant and al. on the relationships between the exterior algebra of a simple Lie algebra and the action of the Casimir operator on it. Our exposition relies on u-cohomology and it is basically ... More

The maximum cardinality of minimal inversion complete sets in finite reflection groupsDec 30 2013Sep 17 2014We compute for reflection groups of type $A,B,D,F_4,H_3$ and for dihedral groups a statistic counting the maximal cardinality of a set of elements in the group whose generalized inversions yield the full set of inversions and which are minimal with respect ... More

ad-nilpotent ideals containing a fixed number of simple root spacesJan 09 2004May 02 2009We give formulas for the number of ad-nilpotent ideals of a Borel subalgebra of a Lie algebra of type B or D containing a fixed number of root spaces attached to simple roots. This result solves positively a conjecture of Panyushev (cf. D. Panyushev, ... More

Abelian subalgebras in Z_2-graded Lie algebras and affine Weyl groupsNov 23 2003Mar 04 2004Let g=g_0+ g_1 be a simple Z_2-graded Lie algebra and let b_0 be a fixed Borel subalgebra of g_0. We describe and enumerate the abelian b_0-stable subalgebras of g_1.

Symmetries of abelian ideals of Borel subalgebrasJan 11 2013Jul 28 2013Elaborating on a paper by Suter, we provide a detailed description of the automorphism group of the poset of abelian ideals in a Borel subalgebra of a finite dimensional complex simple Lie algebra.

Spherical nilpotent orbits and abelian subalgebras in isotropy representationsJul 12 2016Jul 27 2016Let $G$ be a simply connected semisimple algebraic group with Lie algebra $\mathfrak g$, let $G_0 \subset G$ be the symmetric subgroup defined by an algebraic involution $\sigma$ and let $\mathfrak g_1 \subset \mathfrak g$ be the isotropy representation ... More

Denominator identities for finite-dimensional Lie superalgebras and Howe duality for compact dual pairsFeb 18 2011Jan 10 2012We provide formulas for the denominator and superdenominator of a basic classical type Lie superalgebra for any set of positive roots. We establish a connection between certain sets of positive roots and the theory of reductive dual pairs of real Lie ... More

On the Kernel of the affine Dirac operatorApr 22 2008Sep 14 2009Let L be a finite-dimensional semisimple Lie algebra with a non-degenerate invariant bilinear form, \sigma an elliptic automorphism of L leaving the form invariant, and A a \sigma-invariant reductive subalgebra of L, such that the restriction of the form ... More

Decomposition rules for conformal pairs associated to symmetric spaces and abelian subalgebras of Z_2-graded Lie algebrasJun 15 2005Jan 23 2006We give uniform formulas for the branching rules of level 1 modules over orthogonal affine Lie algebras for all conformal pairs associated to symmetric spaces. We also provide a combinatorial intepretation of these formulas in terms of certain abelian ... More

Conformal embeddings and simple current extensionsOct 24 2012Feb 18 2014In this paper we investigate the structure of intermediate vertex algebras associated with a maximal conformal embedding of a reductive Lie algebra in a semisimple Lie algebra of classical type.

Multiplets of representations, twisted Dirac operators and Vogan's conjecture in affine settingApr 25 2007Oct 02 2007We extend classical results of Kostant and al. on multiplets of representations of finite-dimensional Lie algebras and on the cubic Dirac operator to the setting of affine Lie algebras and twisted affine cubic Dirac operator. We prove in this setting ... More

Dirac operators and the Very Strange Formula for Lie superalgebrasMay 22 2013Aug 04 2013Using a super-affine version of Kostant's cubic Dirac operator, we prove a very strange formula for quadratic finite-dimensional Lie superalgebras with a reductive even subalgebra.

On the structure of Borel stable abelian subalgebras in infinitesimal symmetric spacesSep 21 2011Mar 31 2012Let g=g_0+g_1 be a Z_2-graded Lie algebra. We study the posets of abelian subalgebras of g_1 which are stable w.r.t. a Borel subalgebra of g_0. In particular, we find out a natural parametrization of maximal elements and dimension formulas for them. We ... More

Conformal embeddings of affine vertex algebras in minimal $W$-algebras II: decompositionsApr 04 2016May 20 2016This paper is a continuation of arXiv:1602.04687. We present methods for computing the explicit decomposition of the minimal simple affine $W$-algebra $W_k(\mathfrak g, \theta)$ at a conformal level $k$ as a module for its maximal affine subalgebra $\mathcal ... More

Finite vs infinite decompositions in conformal embeddingsSep 22 2015Apr 06 2016Building on work of the first and last author, we prove that an embedding of simple affine vertex algebras $V_{\mathbf{k}}(\mathfrak g^0)\subset V_{k}(\mathfrak g)$, corresponding to an embedding of a maximal equal rank reductive subalgebra $\mathfrak ... More

Replica equivalence in the Edwards-Anderson modelFeb 24 2003Sep 16 2003After introducing and discussing the "link-overlap" between spin configurations we show that the Edwards-Anderson model has a "replica-equivalent" quenched equilibrium state, a property introduced by Parisi in the description of the mean-field spin-glass ... More

Toward a Classification of Stochastically Stable Quenched MeasuresMay 27 2002In this short note we study the fourth order consequences of the stochastic stability property for mean field spin glass models introduced in previous paper by Aizenman and Contucci. We show that due to a remarkable cancellation mechanism it reduces to ... More

Approximated methods for the generation of dark matter halo catalogs in the age of precision cosmologyMay 25 2016Precision cosmology has recently triggered new attention on the topic of approximate methods for the clustering of matter on large scales, whose foundations date back to the period from late '60s to early '90s. Indeed, although the prospect of reaching ... More

Stochastic Stability: a Review and Some PerspectivesNov 05 2009Nov 19 2009A review of the stochastic stability property for the Gaussian spin glass models is presented and some perspectives discussed.

Critical exponents of the two dimensional Coulomb gas at the Berezinskii-Kosterlitz-Thouless transitionNov 10 2013Nov 25 2013The two dimensional Coulomb gas is the prototypical model of statistical mechanics displaying a special kind of phase transition, named after Berezinskii, Kosterlitz and Thouless. Physicists and mathematicians proposed several predictions about this system. ... More

Stochastic Stability and the Spin Glass Phase. The State of the Art for Mean Field and Finite Dimensional ModelsDec 01 2012Some invariances under perturbations of the spin glass phase are introduced, their proofs outlined and their consequences illustrated as factorisation rules for the overlap distribution. A comparison between the state of the art for mean field and finite ... More

Approximate methods for the generation of dark matter halo catalogs in the age of precision cosmologyMay 25 2016Oct 07 2016Precision cosmology has recently triggered new attention on the topic of approximate methods for the clustering of matter on large scales, whose foundations date back to the period from late '60s to early '90s. Indeed, although the prospect of reaching ... More

On special covariants in the exterior algebra of a simple Lie algebraApr 16 2014Sep 08 2014We study the subspace of the exterior algebra of a simple complex Lie algebra linearly spanned by the copies of the little adjoint representation or, in the case of the Lie algebra of traceless matrices, by the copies of the n-th symmetric power of the ... More

Local Order at Arbitrary Distances in Finite-Dimensional Spin-Glass ModelsSep 06 2004Oct 18 2004For a finite dimensional spin-glass model we prove local order at low temperatures for both local observables and for products of observables at arbitrary mutual distance. When the Hamiltonian includes the Edwards-Anderson interaction we prove "bond" ... More

Alienation in Italian cities. Social network fragmentation from collective dataOct 02 2014We study the structure of a social network of strong ties (trust network) investigating its property of connectedness versus fragmentation. To this purpose we analyse an extensive set of census data, about marrying or having children with immigrants, ... More

Optimal control of an Allen-Cahn equation with singular potentials and dynamic boundary conditionDec 11 2012Oct 24 2014In this paper, we investigate optimal control problems for Allen-Cahn equations with singular nonlinearities and a dynamic boundary condition involving singular nonlinearities and the Laplace-Beltrami operator. The approach covers both the cases of distributed ... More

The Ghirlanda-Guerra IdentitiesMay 20 2005If the variance of a Gaussian spin-glass Hamiltonian grows like the volume the model fulfills the Ghirlanda-Guerra identities in terms of the normalized Hamiltonian covariance.

Nonlinear diffusion equations as asymptotic limits of Cahn-Hilliard systemsNov 27 2015An asymptotic limit of a class of Cahn-Hilliard systems is investigated to obtain a general nonlinear diffusion equation. The target diffusion equation may reproduce a number of well-known model equations: Stefan problem, porous media equation, Hele-Shaw ... More

Correlation Inequalities for Spin Glass in one DimensionDec 22 2007Jan 07 2008We prove two inequalities for the direct and truncated correlation for the nearest-neighboor one-dimensional Edwards-Anderson model with symmetric quenched disorder. The second inequality has the opposite sign of the GKS inequality of type II. In the ... More

Toward a quantitative approach to migrants integrationOct 16 2009Migration phenomena and all the related issues, like integration of different social groups, are intrinsically complex problems since they strongly depend on several competitive mechanisms as economic factors, cultural differences and many others. By ... More

On a formula for the spectral flow and its applicationsJan 26 2008We consider a continuous path of bounded symmetric Fredholm bilinear forms with arbitrary endpoints on a real Hilbert space, and we prove a formula that gives the spectral flow of the path in terms of the spectral flow of the restriction to a finite codimensional ... More

Recent advances in bibliometric indexes and the PaperRank problemJul 26 2012Jan 10 2013Bibliometric indexes are customary used in evaluating the impact of scientific research, even though it is very well known that in different research areas they may range in very different intervals. Sometimes, this is evident even within a single given ... More

Existence of solutions for a model of microwave heatingMay 13 2015This paper is concerned with a system of differential equations related to a circuit model for microwave heating, complemented by suitable initial and boundary conditions. A RCL circuit with a thermistor is representing the microwave heating process with ... More

Convex Replica Simmetry Breaking From Positivity and Thermodynamic LimitJun 12 2003Consider a correlated Gaussian random energy model built by successively adding one particle (spin) into the system and imposing the positivity of the associated covariance matrix. We show that the validity of a recently isolated condition ensuring the ... More

Modeling Society with Statistical Mechanics: an Application to Cultural Contact and ImmigrationJun 07 2006We introduce a general modeling framework to predict the outcomes, at the population level, of individual psychology and behavior. The framework prescribes that researchers build a cost function that embodies knowledge of what trait values (opinions, ... More

Comment on OPERA neutrino velocity measurementOct 28 2011Nov 05 2011In this report a potential problem in the data analysis of the OPERA experiment is discussed: the main issue is that the quantity \partial t used in the maximum likelihood procedure is not a "true" parameter of the parent-distribution (called PDF in the ... More

A Hamiltonian approach to sufficiency in optimal control with minimal regularity conditions: Part IJul 14 2015In this paper we develop a Hamiltonian approach to sufficient conditions in optimal control problems. We extend the known conditions for $C^2$ maximised Hamiltonians into two directions: on the one hand we explain the role of a super Hamiltonian (i.e. ... More

On the Surface Pressure for the Edwards-Anderson ModelJun 03 2003Feb 13 2004For the Edwards-Anderson model we introduce an integral representation for the surface pressure (per unit surface) in terms of a quenched moment of the bond-overlap on the surface. We find upper and lower bounds uniformly in the volume and show that at ... More

Global solution to the Allen-Cahn equation with singular potentials and dynamic boundary conditionsJun 28 2012We prove well-posedness results for the solution to an initial and boundary-value problem for an Allen-Cahn type equation describing the phenomenon of phase transitions for a material contained in a bounded and regular domain. The dynamic boundary conditions ... More

Probabilistic Modeling and Simulation of Transmission Line Temperatures under Fluctuating Power FlowsNov 16 2014Increasing shares of fluctuating renewable energy sources induce higher and higher power flow variability at the transmission level. The question arises as to what extent existing networks can absorb additional fluctuating power injection without exceeding ... More

Variable-step finite difference schemes for the solution of Sturm-Liouville problemsJan 17 2014We discuss the solution of regular and singular Sturm-Liouville problems by means of High Order Finite Difference Schemes. We describe a code to define a discrete problem and its numerical solution by means of linear algebra techniques. Different test ... More

A phase-field approximation of the Willmore flow with volume constraintApr 02 2010The well-posedness of a phase-field approximation to the Willmore flow with volume constraint is established. The existence proof relies on the underlying gradient flow structure of the problem: the time discrete approximation is solved by a variational ... More

Factorization Properties in the 3D Edwards-Anderson ModelMar 07 2005Mar 21 2005Starting from the study of a linear combination of multi-overlaps which can be rigorously shown to vanish for large systems we numerically analyze the factorization properties of the link-overlaps multi-distribution for the 3D Gaussian Edward-Anderson ... More

Equation and dynamic boundary condition of Cahn-Hilliard type with singular potentialsFeb 18 2015The well-posedness of a system of partial differential equations and dynamic boundary conditions, both of Cahn-Hilliard type, is discussed. The existence of a weak solution and its continuous dependence on the data are proved using a suitable setting ... More

The Allen-Cahn equation with dynamic boundary conditions and mass constraintsMay 01 2014The Allen-Cahn equation, coupled with dynamic boundary conditions, has recently received a good deal of attention. The new issue of this paper is the setting of a rather general mass constraint which may involve either the solution inside the domain or ... More

Convergence properties for a generalization of the Caginalp phase field systemMay 28 2012We are concerned with a phase field system consisting of two partial differential equations in terms of the variables thermal displacement, that is basically the time integration of temperature, and phase parameter. The system is a generalization of the ... More

Early Telescopes and Ancient Scientific Instruments in the Paintings of Jan Brueghel the ElderDec 04 2015Ancient instruments of high interest for research on the origin and diffusion of early scientific devices in the late XVI - early XVII centuries are reproduced in three paintings by Jan Brueghel the Elder. We investigated the nature and the origin of ... More

Monotonicity and Thermodynamic Limit for Short Range Disordered ModelsFeb 06 2003Feb 12 2003If the variance of a short range Gaussian random potential grows like the volume its quenched thermodynamic limit is reached monotonically.

Correlation Inequalities for Spin GlassesDec 14 2006We prove a correlation type inequality for spin systems with quenched symmetric random interactions. This gives monotonicity of the pressure with respect to the strength of the interaction for a class of spin glass models. Consequences include existence ... More

Solution of the monomer-dimer model on locally tree-like graphs. Rigorous resultsMay 03 2013Jun 08 2013We consider the monomer-dimer model on sequences of random graphs locally convergent to trees. We prove that the monomer density converges almost surely, in the thermodynamic limit, to an analytic function of the monomer activity. We characterise this ... More

"Butterfly Effect" vs Chaos in Energy Futures MarketsAug 23 2016In this paper we test for the sensitive dependence on initial conditions (the so called "butterfly effect") of energy futures time series (heating oil, natural gas), and thus the determinism of those series. This paper is distinguished from previous studies ... More

A short comment on OPERA neutrino velocity measuerementNov 14 2011In this report a potential problem in the data analysis of the OPERA experiment is discussed: the main issue is that the quantity "\partialt" used in the maximum likelihood procedure is not a "true" parameter of the parent-distribution (called PDF in ... More

The class of Lucas-Lehmer polynomialsMar 07 2016In this paper we introduce a new sequence of polynomials, which follow the same recursive rule of the well-known Lucas-Lehmer integer sequence. We show the most important properties of this sequence, relating them to the Chebyshev polynomials of the first ... More

Scaling Limits for Multispecies Statistical Mechanics Mean-Field ModelsNov 14 2010Jul 06 2011We study the limiting thermodynamic behavior of the normalized sums of spins in multi-species Curie-Weiss models. We find sufficient conditions for the limiting random vector to be Gaussian (or to have an exponential distribution of higher order) and ... More

Thermodynamic Limit for Spin Glasses. Beyond the Annealed BoundSep 24 2008Oct 14 2008Using a correlation inequality of Contucci and Lebowitz for spin glasses, we demonstrate existence of the thermodynamic limit for short-ranged spin glasses, under weaker hypotheses than previously available, namely without the assumption of the annealed ... More

Modeling and analysis of water-hammer in coaxial pipesJan 29 2015The fluid-structure interaction is studied for a system composed of two coaxial pipes in an annular geometry, for both homogeneous isotropic metal pipes and fiber-reinforced (anisotropic) pipes. Multiple waves, traveling at different speeds and amplitudes, ... More

From the viscous Cahn-Hilliard equation to a regularized forward-backward parabolic equationMay 12 2016A rigorous proof is given for the convergence of the solutions of a viscous Cahn-Hilliard system to the solution of the regularized version of the forward-backward parabolic equation, as the coefficient of the diffusive term goes to 0. Non-homogenous ... More

The active and passive populations of Extremely Red ObjectsNov 27 2009Feb 05 2010[abridged] The properties of galaxies with the reddest observed R-K colors (Extremely Red Objects, EROs), including their apparent division into passive and obscured active objects with roughly similar number densities, are a known challenge for models ... More

Cahn-Hilliard equation with dynamic boundary conditions and mass constraint on the boundaryDec 05 2014The well-known Cahn-Hilliard equation entails mass conservation if a suitable boundary condition is prescribed. In the case when the equation is also coupled with a dynamic boundary condition, including the Laplace-Beltrami operator on the boundary, the ... More

Solvability and asymptotic analysis of a generalization of the Caginalp phase field systemJul 20 2011Aug 26 2011We study a diffusion model of phase field type, which consists of a system of two partial differential equations involving as variables the thermal displacement, that is basically the time integration of temperature, and the order parameter. Our analysis ... More

Parallel Factorizations in Numerical AnalysisDec 18 2009In this paper we review the parallel solution of sparse linear systems, usually deriving by the discretization of ODE-IVPs or ODE-BVPs. The approach is based on the concept of parallel factorization of a (block) tridiagonal matrix. This allows to obtain ... More

"Chaos" in energy futures markets: a controversial matterNov 05 2016In this paper we study the possible "chaotic" nature of some energy and commodity futures time series (like heating oil and natural gas, among the others). In particular the sensitive dependence on initial conditions (the so called "butterfly effect", ... More

A Mathematical Model for Signal's Energy at the Output of an Ideal DACNov 26 2015Mar 21 2016The presented research work considers a mathematical model for energy of the signal at the output of an ideal DAC, in presence of sampling clock jitter. When sampling clock jitter occurs, the energy of the signal at the output of ideal DAC does not satisfies ... More

Bipartite Mean Field Spin Systems. Existence and SolutionOct 03 2007A mean field spin system consisting two interacting groups each with homogeneous interaction coefficients is introduced and studied. Existence of the thermodynamic limit is shown by an asymptotic sub-addittivity method and factorization of correlation ... More

New formulas for $π$ involving infinite nested square roots and Gray codeJun 30 2016Jul 03 2016In previous papers we introduced a class of polynomials which follow the same recursive formula as the Lucas-Lehmer numbers, studying the distribution of their zeros and remarking that this distributions follows a sequence related to the binary Gray code. ... More

Stability theorems for the n-order hold modelsMay 05 2016Aug 08 2016We prove stability results for Gabor frames $\G(g, a,b)$ for a class of functions $g\in L^2(\R)$. Our results can be used to describe the effect of the timing jitters in the p-order hold models of signal reconstruction that are used in electronics and ... More

Ordering of nested square roots of 2 according to Gray codeApr 01 2016In this paper we discuss some relations between zeros of Lucas-Lehmer polynomials and Gray code. We study nested square roots of 2 applying a "binary code" that associates bits $0$ and $1$ to $\oplus$ and $\ominus$ signs in the nested form. This gives ... More

Bs mixing and lifetime difference measurements at CDFOct 13 2009We review latest experimental results on the Bs mixing and lifetime difference measurements at CDF. We report on the latest beta_s and dGamma_s results from Bs->J/psi phi. We also discuss flavor specific dGamma_s measurements, including information from ... More

Forecasting the Integration of ImmigrantsSep 17 2015This paper presents a quantitative framework for forecasting immigrant integration using immigrant density as the single driver. By comparing forecasted integration estimates based on data collected up to specific periods in time, with observed integration ... More

Joint Cosmological Formation of QSOs and Bulge-dominated GalaxiesJul 07 1999Aug 04 1999Older and more recent pieces of observational evidence suggest a strong connection between QSOs and galaxies; in particular, the recently discovered correlation between black hole and galactic bulge masses suggests that QSO activity is directly connected ... More

Griffiths inequalities for the Gaussian spin glassMar 25 2004Apr 30 2004The Griffiths inequalities for Ising spin-glass models with Gaussian randomness of non-vanishing mean are proved using properties of the Gaussian distribution and gauge symmetry of the system. These inequalities imply that correlation functions are non-negative ... More

Fast and Simple Computation of Top-k Closeness CentralitiesJul 06 2015Closeness is an important centrality measure widely used in the analysis of real-world complex networks. In particular, the problem of selecting the k most central nodes with respect to this measure has been deeply analyzed in the last decade. However, ... More

Global Existence of Weak Solutions to a Nonlocal Cahn-Hilliard-Navier-Stokes SystemJan 20 2011Feb 21 2011A well-known diffuse interface model consists of the Navier-Stokes equations nonlinearly coupled with a convective Cahn-Hilliard type equation. This system describes the evolution of an incompressible isothermal mixture of binary-fluids and it has been ... More

Commutative Languages and their Composition by Consensual MethodsMay 22 2014Commutative languages with the semilinear property (SLIP) can be naturally recognized by real-time NLOG-SPACE multi-counter machines. We show that unions and concatenations of such languages can be similarly recognized, relying on -- and further developing, ... More

Decision Fusion with Unknown Sensor Detection ProbabilityDec 08 2013In this correspondence we study the problem of channel-aware decision fusion when the sensor detection probability is not known at the decision fusion center. Several alternatives proposed in the literature are compared and new fusion rules (namely 'ideal ... More

Correlation Inequalities for Quantum Spin Systems with Quenched Centered DisorderJun 30 2009It is shown that random quantum spin systems with centered disorder satisfy correlation inequalities previously proved (arXiv:cond-mat/0612371) in the classical case. Consequences include monotone approach of pressure and ground state energy to the thermodynamic ... More

On Languages Accepted by P/T Systems Composed of joinsJul 29 2009Recently, some studies linked the computational power of abstract computing systems based on multiset rewriting to models of Petri nets and the computation power of these nets to their topology. In turn, the computational power of these abstract computing ... More

Recovering the Initial Condition of our Local Universe from NOG and PSCz CataloguesJan 30 2003We apply the ZTRACE algorithm to the optical NOG and infra-red PSCz galaxy catalogues to reconstruct the pattern of primordial fluctuations that have generated our local Universe. We check that the density fields traced by the two catalogues are well ... More

Universality of one-dimensional Fermi systems, II. The Luttinger liquid structureMar 15 2013We complete the proof started in "Universality of one-dimensional Fermi systems, I." of the universal Luttinger liquid relations for a general model of spinning fermions on a lattice, by making use of the Ward Identities due to asymptotically emerging ... More

On the Cahn-Hilliard equation with dynamic boundary conditions and a dominating boundary potentialMar 07 2014Sep 26 2014The Cahn-Hilliard and viscous Cahn-Hilliard equations with singular and possibly nonsmooth potentials and dynamic boundary condition are considered and some well-posedness and regularity results are proved. Key words: Cahn-Hilliard equation, dynamic boundary ... More

A boundary control problem for the pure Cahn-Hilliard equation with dynamic boundary conditionsMar 11 2015A boundary control problem for the pure Cahn-Hilliard equations with possibly singular potentials and dynamic boundary conditions is studied and first-order necessary conditions for optimality are proved. Key words: Cahn-Hilliard equation, dynamic boundary ... More

Path integral representations for the spin-pinned quantum XXZ chainJun 23 2003Sep 18 2003Two discrete path integral formulations for the ground state of a spin-pinned quantum anisotropic XXZ Heisenberg chain are introduced. Their properties are discussed and two recursion relations are proved.

A non-smooth regularization of a forward-backward parabolic equationAug 13 2015In this paper we introduce a model describing diffusion of species by a suitable regularization of a "forward-backward" parabolic equation. In particular, we prove existence and uniqueness of solutions, as well as continuous dependence on data, for a ... More

Asymptotic analysis of hierarchical martensitic microstructureJan 28 2015We consider a hierarchical nested microstructure, which also contains a point of singularity (disclination) at the origin, observed in lead orthovanadate. We show how to exactly compute the energy cost and associated displacement field within linearized ... More

Parameter Evaluation of a Simple Mean-Field Model of Social InteractionOct 16 2008Nov 20 2008The aim of this work is to implement a statistical mechanics theory of social interaction, generalizing econometric discrete choice models. A class of simple mean field discrete models is introduced and discussed both from the theoretical and phenomenological ... More

On a Cahn-Hilliard type phase field system related to tumor growthJan 23 2014Mar 21 2014The paper deals with a phase field system of Cahn-Hilliard type. For positive viscosity coefficients, the authors prove an existence and uniqueness result and study the long time behavior of the solution by assuming the nonlinearities to be rather general. ... More

The Formation of Supermassive Black Holes from Population III Seeds. I. Cosmic Formation HistoriesAug 15 2016Aug 27 2016We model the cosmic distributions in space and time of the formation sites of the first stars that may be the progenitors of supermassive black holes (SMBHs). Pop III.1 stars are defined to form in dark matter minihalos (i.e., with masses $\sim10^6\:M_\odot$) ... More

A Diffusive Strategic Dynamics for Social SystemsDec 08 2008Mar 10 2010We propose a model for the dynamics of a social system, which includes diffusive effects and a biased rule for spin-flips, reproducing the effect of strategic choices. This model is able to mimic some phenomena taking place during marketing or political ... More

An Axiomatic and an Average-Case Analysis of Algorithms and Heuristics for Metric Properties of GraphsApr 05 2016In recent years, researchers proposed several algorithms that compute metric quantities of real-world complex networks, and that are very efficient in practice, although there is no worst-case guarantee. In this work, we propose an axiomatic framework ... More

Sharp interface control in a Penrose-Fife modelMar 18 2014In this paper we study a singular control problem for a system of PDEs describing a phase-field model of Penrose-Fife type. The main novelty of this contribution consists in the idea of forcing a sharp interface separation between the states of the system ... More

The Formation of Supermassive Black Holes from Population III Seeds. I. Cosmic Formation HistoriesAug 15 2016Oct 06 2016We model the cosmic distributions in space and time of the formation sites of the first stars that may be the progenitors of supermassive black holes (SMBHs). Pop III.1 stars are defined to form in dark matter minihalos (i.e., with masses $\sim10^6\:M_\odot$) ... More

Global existence for a nonstandard viscous Cahn-Hilliard system with dynamic boundary conditionAug 02 2016In this paper, we study a model for phase segregation taking place in a spatial domain that was introduced by Podio-Guidugli in Ric. Mat. 55 (2006), pp. 105-118. The model consists of a strongly coupled system of nonlinear parabolic differential equations, ... More

Distributed optimal control of a nonstandard nonlocal phase field system with double obstacle potentialJul 07 2016This paper is concerned with a distributed optimal control problem for a nonlocal phase field model of Cahn-Hilliard type, which is a nonlocal version of a model for two-species phase segregation on an atomic lattice under the presence of diffusion. The ... More

The Ferromagnetic Heisenberg XXZ chain in a pinning fieldApr 06 2002Oct 01 2002We investigate the effect of a magnetic field supported at a single lattice site on the low-energy spectrum of the ferromagnetic Heisenberg XXZ chain. Such fields, caused by impurities, can modify the low-energy spectrum significantly by pinning certain ... More

A boundary control problem for the viscous Cahn-Hilliard equation with dynamic boundary conditionsJul 15 2014Feb 06 2015A boundary control problem for the viscous Cahn-Hilliard equations with possibly singular potentials and dynamic boundary conditions is studied and first order necessary conditions for optimality are proved. Key words: Cahn-Hilliard equation, dynamic ... More

Mean field behaviour of spin systems with orthogonal interaction matrixJun 21 2001Oct 24 2001For the long-range deterministic spin models with glassy behaviour of Marinari, Parisi and Ritort we prove weighted factorization properties of the correlation functions which represent the natural generalization of the factorization rules valid for the ... More