Results for "Alessandro Umbrico"

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Timeline-based Planning and Execution with Uncertainty: Theory, Modeling Methodologies and PracticeMay 14 2019Automated Planning is one of the main research field of Artificial Intelligence since its beginnings. Research in Automated Planning aims at developing general reasoners (i.e., planners) capable of automatically solve complex problems. Broadly speaking, ... More
A Cesàro Average of Goldbach numbersJun 01 2012Let $\Lambda$ be the von Mangoldt function and (r_G(n) = \sum_{m_1 + m_2 = n} \Lambda(m_1) \Lambda(m_2)) be the counting function for the Goldbach numbers. Let $N \geq 2$ be an integer. We prove that &\sum_{n \le N} r_G(n) \frac{(1 - n/N)^k}{\Gamma(k ... More
Short intervals asymptotic formulae for binary problems with primes and powers, II: density $1$Apr 18 2015Nov 28 2015We prove that suitable asymptotic formulae in short intervals hold for the problems of representing an integer as a sum of a prime square and a square, or a prime square. Such results are obtained both assuming the Riemann Hypothesis and in the unconditional ... More
Short intervals asymptotic formulae for binary problems with primes and powers, I: density $3/2$Apr 09 2015Nov 28 2015We prove that suitable asymptotic formulae in short intervals hold for the problems of representing an integer as a sum of a prime and a square, or a prime square. Such results are obtained both assuming the Riemann Hypothesis and in the unconditional ... More
On the constant in the Mertens product for arithmetic progressions. I. IdentitiesJun 19 2007Sep 26 2008The aim of the paper is the proof of new identities for the constant in the Mertens product for arithmetic progressions. We deal with the problem of the numerical computation of these constants in another paper.
The number of Goldbach representations of an integerNov 14 2010We prove the following result: Let $N \geq 2$ and assume the Riemann Hypothesis (RH) holds. Then \[ \sum_{n=1}^{N} R(n) =\frac{N^{2}}{2} -2 \sum_{\rho} \frac{N^{\rho + 1}}{\rho (\rho + 1)} + O(N \log^{3}N), \] where $\rho=1/2+i\gamma$ runs over the non-trivial ... More
Explicit relations between primes in short intervals and exponential sums over primesDec 22 2012Dec 29 2012Under the assumption of the Riemann Hypothesis (RH), we prove explicit quantitative relations between hypothetical error terms in the asymptotic formulae for truncated mean-square average of exponential sums over primes and in the mean-square of primes ... More
Cesàro average in short intervals for Goldbach numbersJun 02 2016We prove that a suitable explicit formula for the Cesaro-averaged number of representations of an integer as a sum of two primes holds in short intervals.
Effective non-linear spinor dynamics in a spin-1 Bose-Einstein condensateMar 14 2018Sep 03 2018We derive from first principles the experimentally observed effective dynamics of a spinor Bose gas initially prepared as a Bose-Einstein condensate and then left free to expand ballistically. In spinor condensates, which represent one of the recent frontiers ... More
Computing the Mertens and Meissel-Mertens constants for sums over arithmetic progressionsJun 11 2009We give explicit numerical values with 100 decimal digits for the Mertens constant involved in the asymptotic formula for $\sum\limits_{\substack{p\leq x p\equiv a \bmod{q}}}1/p$ and, as a by-product, for the Meissel-Mertens constant defined as $\sum_{p\equiv ... More
Short intervals asymptotic formulae for binary problems with prime powersJun 14 2018Jun 21 2018We prove results about the asymptotic formulae in short intervals for the average number of representations of integers of the forms $n=p_{1}^{\ell_1}+p_{2}^{\ell_2}$, with $\ell_1, \ell_2\in\{2,3\}$, $\ell_1+\ell_2\le 5$ are fixed integers, and $n=p^{\ell_1} ... More
On a ternary Diophantine problem with mixed powers of primesJun 01 2012Jul 30 2012Let $1 < k < 33 / 29$. We prove that if $\lambda_1$, $\lambda_2$ and $\lambda_3$ are non-zero real numbers, not all of the same sign and that $\lambda_1 / \lambda_2$ is irrational and $\varpi$ is any real number, then for any $\eps > 0$ the inequality ... More
A Diophantine problem with a prime and three squares of primesJun 01 2012We prove that if $\lambda_1$, $\lambda_2$, $\lambda_3$ and $\lambda_4$ are non-zero real numbers, not all of the same sign, $\lambda_1 / \lambda_2$ is irrational, and $\varpi$ is any real number then, for any $\eps > 0$ the inequality $ \bigl|\lambda_1 ... More
Blowdown of hydrocarbons pressure vessel with partial phase separationJan 05 2011We propose a model for the simulation of the blowdown of vessels containing two-phase (gas-liquid) hydrocarbon fluids, considering non equilibrium between phases. Two phases may be present either already at the beginning of the blowdown process (for instance ... More
A Cesàro Average of generalised Hardy-Littlewood numbersJun 13 2018Jan 04 2019We continue our recent work on additive problems with prime summands: we already studied the \emph{average} number of representations of an integer as a sum of two primes, and also considered individual integers. Furthermore, we dealt with representations ... More
Short-depth circuits for efficient expectation value estimationMay 20 2019The evaluation of expectation values $Tr\left[\rho O\right]$ for some pure state $\rho$ and Hermitian operator $O$ is of central importance in a variety of quantum algorithms. Near optimal techniques developed in the past require a number of measurements ... More
Gross-Pitaevskii non-linear dynamics for pseudo-spinor condensatesApr 01 2017Oct 18 2017We derive the equations for the non-linear effective dynamics of a so called pseudo-spinor Bose-Einstein condensate, which emerges from the linear many-body Schr\"odinger equation at the leading order in the number of particles. The considered system ... More
A Cesàro Average of Hardy-Littlewood numbersJun 01 2012Let $\Lambda$ be the von Mangoldt function and (r_{\textit{HL}}(n) = \sum_{m_1 + m_2^2 = n} \Lambda(m_1),) be the counting function for the Hardy-Littlewood numbers. Let $N$ be a sufficiently large integer. We prove that \sum_{n \le N} r_{\textit{HL}}(n) ... More
Sum of one prime and two squares of primes in short intervalsJun 13 2014Jul 30 2015Assuming the Riemann Hypothesis we prove that the interval $[N, N + H]$ contains an integer which is a sum of a prime and two squares of primes provided that $H \ge C (\log N)^{4}$, where $C > 0$ is an effective constant.
Sums of many primesJan 18 2011Assuming that the Generalized Riemann Hypothesis (GRH) holds, we prove an explicit formula for the number of representations of an integer as a sum of $k\geq 5$ primes. Our error terms in such a formula improve by some logarithmic factors an analogous ... More
A Diophantine problem with prime variablesJun 01 2012We study the distribution of the values of the form $\lambda_1 p_1 + \lambda_2 p_2 + \lambda_3 p_3^k$, where $\lambda_1$, $\lambda_2$ and $\lambda_3$ are non-zero real number not all of the same sign, with $\lambda_1 / \lambda_2$ irrational, and $p_1$, ... More
A Credal Extension of Independent Choice LogicJun 21 2018We propose an extension of Poole's independent choice logic based on a relaxation of the underlying independence assumptions. A credal semantics involving multiple joint probability mass functions over the possible worlds is adopted. This represents a ... More
Short intervals asymptotic formulae for binary problems with prime powers, IIOct 26 2018We improve some results about the asymptotic formulae in short intervals for the average number of representations of integers of the forms $n=p_{1}^{\ell_1}+p_{2}^{\ell_2}$ and $n=p^{\ell_1} + m^{\ell_2}$, where $\ell_1, \ell_2\ge 2$ are fixed integers, ... More
Mean-field quantum dynamics for a mixture of Bose-Einstein condensatesMar 08 2016Sep 12 2016We study the effective time evolution of a large quantum system consisting of a mixture of different species of identical bosons in interaction. If the system is initially prepared so as to exhibit condensation in each component, we prove that condensation ... More
A Diophantine approximation problem with two primes and one $k$-th power of a primeMay 31 2017Feb 13 2018We refine a result of the last two Authors of [8] on a Diophantine approximation problem with two primes and a $k$-th power of a prime which was only proved to hold for $1<k<4/3$. We improve the $k$-range to $1<k\le 3$ by combining Harman's technique ... More
Positive operator measures, generalised imprimitivity theorem, and their applicationsMay 30 2005Given a topological group $G$ and a unitary representation $U$ of $G$, we consider the problem of classifying the positive operator measures which are based on a $G$-homogeneous space $X$ and covariant with respect to the representation $U$. We completely ... More
Order Parameter for the Transition from Phase to Amplitude TurbulenceAug 06 1996The maximal conserved phase gradient is introduced as an order parameter to characterize the transition from phase- to defect-turbulence in the complex Ginzburg-Landau equation. It has a finite value in the phase-turbulent regime and decreases to zero ... More
Ab initio calculations on nuclear matter properties including the effects of three-nucleons interactionOct 01 2012In this thesis, the ground state properties of nuclear matter, namely the energy per particle and the response to weak probes, are computed, studying the effects of three nucleon interactions. Both the variational approach, based on the formalism of correlated ... More
Thermal production of axino Dark MatterMar 30 2010Jun 24 2010We reconsider thermal production of axinos in the early universe, adding: a) missed terms in the axino interaction; b) production via gluon decays kinematically allowed by thermal masses; c) a precise modeling of reheating. We find an axino abunance a ... More
Theory summary of Moriond Electro-Weak 2015Apr 30 2015I summarise the theoretical talks at Moriond 2015, with emphasis on naturalness.
Naturalness of supersymmetric modelsApr 06 1999After presenting a simple procedure for testing naturalness (similar to Bayesian inference and not more subjective than it) we show that LEP2 experiments pose a naturalness problem for `conventional' supersymmetric models. About 95% of the parameter space ... More
Resonant Activation in Asymmetric PotentialsMay 15 2008Oct 23 2008The resonant activation effect (RA) has been well studied in different ways during the last two decades. It consists in the presence of a minimum in the mean time spent by a Brownian particle to exit from a potential well in the presence of a fluctuating ... More
Multi-azimuthal-angle effects in self-induced supernova neutrino flavor conversions without axial symmetryAug 06 2013Oct 16 2013The flavor evolution of neutrinos emitted by a supernova (SN) core is strongly affected by the refractive effects associated with the neutrino-neutrino interactions in the deepest stellar regions. Till now, all numerical studies have assumed the axial ... More
Finite Size Corrections for DimersAug 10 2012In this paper we derive the finite size corrections to the energy eigenvalues of the energy for 2D dimers on a square lattice. These finite size corrections, as in the case of Critical Dense Polymers, are proportional to the eigenvalues of the Local Integrals ... More
Cosmology Rounding the CapeApr 16 2002A survey is made of the present observational status on cosmological parameters from microwave background anisotropies. I then move to some non-standard aspect of parameter extraction like quintessence, extra-background of relativistic particles and variations ... More
Gravitational recoil in nonspinning black hole binaries: the span of test-mass resultsJun 26 2013Dec 16 2013We consider binary systems of coalescing, nonspinning, black holes of masses $m_{1}$ and $m_{2}$ and show that the gravitational recoil velocity for any mass ratio can be obtained accurately by extrapolating the waveform of the test-mass limit case. The ... More
A proof of the Bekenstein bound for any strength of gravity through holographyMar 02 2009Jul 09 2010The universal entropy bound of Bekenstein is considered, at any strength of the gravitational interaction. A proof of it is given, provided the considered general-relativistic spacetimes allow for a meaningful and inequivocal definition of the quantities ... More
A note on the connection between the universal relaxation bound and the covariant entropy boundJul 02 2008Jun 24 2009A recently proposed universal lower-bound to the characteristic relaxation times of perturbed thermodynamic systems, derived from quantum information theory and (classical) thermodynamics and known to be saturated for (certain) black holes, is investigated ... More
On the statistical-mechanical meaning of the Bousso boundMar 18 2008Jun 04 2008The Bousso entropy bound, in its generalized form, is investigated for the case of perfect fluids at local thermodynamic equilibrium and evidence is found that the bound is satisfied if and only if a certain local thermodynamic property holds, emerging ... More
From Unruh temperature to generalized Bousso boundAug 28 2007Nov 28 2007In a classical spacetime satisfying Einstein's equation and the null convergence condition, the same quantum mechanical effects that cause black holes to have a temperature are found to imply, if joined to the macroscopic nature of entropy, the covariant ... More
(A class of) Hodge duality operators over the quantum SU(2)Apr 03 2011Oct 03 2012On the exterior algebra over the quantum SU(2) coming from the four dimensional bicovariant calculus \`a la Woronowicz we introduce, using sesquilinear contraction maps, a class of metrics and Hodge duality operators, and compare this formulation with ... More
Applications of the Weyl-Wigner formalism to noncommutative geometryMay 31 2005In this dissertation the Weyl-Wigner approach is presented as a map between functions on a real cartesian symplectic vector space and a set of operators on a Hilbert space, to analyse some aspects of the relations between quantum and classical formalism, ... More
Separable and tree-like asymptotic cones of groupsOct 06 2010Mar 06 2011Using methods from nonstandard analysis, we will discuss which metric spaces can be realized as asymptotic cones. Applying the results we will find in the context of groups, we will prove that a group with "a few" separable asymptotic cones is virtually ... More
Steinitz classes of tamely ramified Galois extensions of algebraic number fieldsOct 27 2009The Steinitz class of a number field extension K/k is an ideal class in the ring of integers O_k of k, which, together with the degree [K:k] of the extension determines the O_k-module structure of O_K. We call rt(k,G) the classes which are Steinitz classes ... More
Dynamical evolution of planetary systemsJun 21 2011The apparent regularity of the motion of the giant planets of our solar system suggested for decades that said planets formed onto orbits similar to the current ones and that nothing dramatic ever happened during their lifetime. The discovery of extra-solar ... More
Cluster variation - Pade` approximants method for the simple cubic Ising modelOct 20 1999Jun 06 2000The cluster variation - Pade` approximant method is a recently proposed tool, based on the extrapolation of low/high temperature results obtained with the cluster variation method, for the determination of critical parameters in Ising-like models. Here ... More
Transverse-momentum-dependent parton distributions (TMDs)Dec 10 2010Transverse-momentum-dependent parton distributions (TMDs) provide three-dimensional images of the partonic structure of the nucleon in momentum space. We made impressive progress in understanding TMDs, both from the theoretical and experimental point ... More
What can we learn from TMD measurements?Feb 16 2009Transverse-momentum-dependent parton distribution and fragmentation functions describe the partonic structure of the nucleon in a three-dimensional momentum space. They are subjects of flourishing theoretical and experimental activity. They provide novel ... More
The analog of the Hawking effect in BECsNov 28 2014The observation of the Hawking effect from black holes in the astrophysical context is unlikely. However, the analog of this effect is present in condensed matter systems. We focus on Bose-Einstein condensates, and on a proposal to detect it through correlation ... More
Generic finiteness of minimal surfaces with bounded Morse indexSep 23 2015Jun 13 2016Given a compact 3-manifold N without boundary, we prove that for a bumpy metric of positive scalar curvature the space of minimal surfaces having a uniform upper bound on the Morse index is always finite unless the manifold itself contains an embedded ... More
Ultraproducts, weak equivalence and sofic entropySep 10 2015In this work, we study pmp actions of countable groups on arbitrary diffuse probability spaces under the point of view of weak equivalence. We will show that any such an action is weakly equivalent to an action on a standard probability space. We also ... More
Statistical Mechanics of Quantum-Classical Systems with Holonomic ConstraintsNov 15 2005The statistical mechanics of quantum-classical systems with holonomic constraints is formulated rigorously by unifying the classical Dirac bracket and the quantum-classical bracket in matrix form. The resulting Dirac quantum-classical theory, which conserves ... More
Linear Collisionless Landau Damping in Hilbert SpaceDec 16 2014The equivalence between the Laplace transform [Landau L., J. Phys. USSR, 10 (1946), 25] and Hermite transform [Zocco and Schekochihin, Phys. Plasmas, 18, 102309 (2011)] solutions of the linear collisionless Landau damping problem is proven.
A note on the computation of the Euler-Kronecker constants for cyclotomic fieldsMar 13 2019Mar 22 2019The goal of this note is to introduce an alternative method to compute the Euler-Kronecker constants for cyclotomic fields and to compare it with other two different ways of computing the same quantity. The new algorithm requires the values of the generalised ... More
Bilinear quantum systems on compact graphs: well-posedness and global exact controllabilityOct 16 2017Jul 12 2018We consider the bilinear Schr\"odinger equations on compact quantum graphs. We prove the well-posedness and the global exact controllability according to the structure of the graph. We apply the main results to examples involving star graphs and tadpole ... More
On a solution to display non-filled-in quaternionic Julia setsAug 01 2006Aug 01 2006During early 1980s, the so-called `escape time' method, developed to display the Julia sets for complex dynamical systems, was exported to quaternions in order to draw analogous pictures in this wider numerical field. Despite of the fine results in the ... More
Playing with the critical point. An experiment with the Mandelbrot set connectivityAug 15 2006By means of a graphical journey across the Mandelbrot set for the classic quadratic iterator $f(z):z^2+q$, we illustrate how connectivity breaks as the seed $z_0$ is no longer at the critical point of $f(z)$. Finally we suggest an attack to the MLC conjecture. ... More
Molecular Modeling of Self-assembling Hybrid Materials (PhD Thesis)Jun 04 2010Lattice Monte Carlo simulations are used to study the phase behavior of self-assembling ordered mesoporous materials formed by an organic template with amphiphilic properties and an inorganic precursor in a model solvent. Three classes of inorganic precursors ... More
Alexandrov curvature of Kaehler curvesJun 11 2008Jul 21 2008We study the intrinsic geometry of a one-dimensional complex space provided with a Kaehler metric in the sense of Grauert. We show that if K is an upper bound for the Gaussian curvature on the regular locus, then the intrinsic metric has curvature at ... More
On the universal abelian variety of dimension 4Nov 25 2007Aug 08 2008Let A be the moduli space of principally polarized abelian varieties of dimension 4 over an algebraically closed field k of characteristic different from 2,3. It is proved that the universal principally polarized abelian variety over A, as well as the ... More
On Whitney numbers of the Order Ideals of Generalized Fences and CrownsMay 30 2005Jun 17 2005We solve some recurrences given by E. Munarini and N. Zagaglia Salvi proving explicit closed formulas for Whitney numbers of the distributive lattices of order ideals of the fence poset and crown poset. Moreover, we get explicit closed formulas for Whitney ... More
Néron models of $Pic^0$ via $Pic^0$Sep 22 2015We provide a new description of the N\'eron model of the Jacobian of a smooth curve $C_K$ with stable reduction $C_R$ on a discrete valuation ring $R$ with field of fractions $K$. Instead of the regular semistable model, our approach uses the regular ... More
Rigidity ConjecturesDec 04 2018We prove several rigidity results for corona $\mathrm{C}^*$-algebras and \v{C}ech-Stone remainders under the assumption of Forcing Axioms. In particular, we prove that a strong version of Todor\v{c}evi\'c's OCA and Martin's Axiom at level $\aleph_1$ imply: ... More
Logic and $\mathrm{C}^*$-algebras: set theoretical dichotomies in the theory of continuous quotientsJun 20 2017Given a nonunital $\mathrm{C}^*$-algebra $A$ one constructs its corona algebra $\mathcal M(A)/A$. This is the noncommutative analog of the \v{C}ech-Stone remainder of a topological space. We analyze the two faces of these algebras: the first one is given ... More
Holomorphic functions and regular quaternionic functions on the hyperkähler space HNov 28 2007Let H be the space of quaternions, with its standard hypercomplex structure. Let R(D) be the module of regular functions on D. For every unitary vector p in S^2, R(D) contains the space of holomorphic functions w.r.t. the complex structure J_p induced ... More
Zero-groups and maximal toriNov 07 2005We give a presentation of various results on zero-groups in o-minimal structures together with some new observations. In particular we prove that if G is a definably connected definably compact group in an o-minimal expansion of a real closed field, then ... More
Normal projectivity of complete symmetric varietiesMay 16 2006Chiriv\`{\i} and Maffei \cite{CM II} have proved that the multiplication of sections of any two ample spherical line bundles on the wonderful symmetric variety $X=\bar{G/H}$ is surjective. We have proved two criterions that allows ourselves to reduce ... More
Simultaneous global exact controllability in projection of infinite 1D bilinear Schrödinger equationsMar 02 2017Jun 03 2019The aim of this work is to study the controllability of infinite bilinear Schr\"odinger equations (BSE) on a segment. First, we show that simultaneously controlling infinite (BSE) by projecting onto suitable N dimensional spaces is equivalent to the simultaneous ... More
Asymptotic analysis for radial sign-changing solutions of the Brezis-Nirenberg problemDec 20 2013We study the asymptotic behavior, as $\lambda \rightarrow 0$, of least energy radial sign-changing solutions $u_\lambda$, of the Brezis-Nirenberg problem \begin{equation*} \begin{cases} -\Delta u = \lambda u + |u|^{2^* -2}u & \hbox{in}\ B_1\\ u=0 & \hbox{on}\ ... More
An artificial neural network to find correlation patterns in an arbitrary number of variablesJun 21 2016Jun 30 2017Methods to find correlation among variables are of interest to many disciplines, including statistics, machine learning, (big) data mining and neurosciences. Parameters that measure correlation between two variables are of limited utility when used with ... More
Is psychosis caused by defective dissociation? An Artificial Life model for schizophreniaOct 11 2016Mar 09 2017Both neurobiological and environmental factors are known to play a role in the origin of schizophrenia, but no model has been proposed that accounts for both. This work presents a functional model of schizophrenia that merges psychodynamic elements with ... More
Boolean constraint satisfaction problems for reaction networksAug 13 2019This Thesis presents research at the boundary between Statistical Physics and Biology. First, we have devised a class of Boolean constraint satisfaction problems (CSP) whose solutions describe the feasible operational states of a chemical reaction network. ... More
Stochastic filtering and optimal control of pure jump Markov processes with noise-free partial observationMar 16 2018Jan 03 2019We consider an infinite horizon optimal control problem for a pure jump Markov process $X$, taking values in a complete and separable metric space $I$, with noise-free partial observation. The observation process is defined as $Y_t = h(X_t)$, $t \geq ... More
Optimal control of continuous-time Markov chains with noise-free observationJul 22 2017Nov 30 2017We consider an infinite horizon optimal control problem for a continuous-time Markov chain $X$ in a finite set $I$ with noise-free partial observation. The observation process is defined as $Y_t = h(X_t)$, $t \geq 0$, where $h$ is a given map defined ... More
Geometry of genus 8 Nikulin surfaces and rationality of their moduliSep 10 2015Let S be a general complex Nikulin surface of genus 8, a geometric construction of S is given as follows. Consider a smooth 3-fold linear section T of the Grassmannian G(1,4) and the Hilbert scheme of rational normal sextic curves of T. In it consider ... More
Tracking rates of random walksMay 23 2013We show that simple random walks on (non-trivial) relatively hyperbolic groups stay $O(\log(n))$-close to geodesics, where $n$ is the number of steps of the walk. Using similar techniques we show that simple random walks in mapping class groups stay $O(\sqrt{n\log(n)})$-close ... More
On a generalized Sturm theoremMay 24 2007May 23 2009Sturm oscillation theorem for second order differential equations was generalized to systems and higher order equations with positive leading coefficient by several authors. What we propose here is a Sturm oscillation theorem for systems of even order ... More
The Selberg integral and a new pair-correlation function for the zeros of the Riemann zeta-functionMar 09 2016The present paper is a report on joint work with Alessandro Languasco and Alberto Perelli on our recent investigations on the Selberg integral and its connections to Montgomery's pair-correlation function. We introduce a more general form of the Selberg ... More
Special Lagrangian Geometry in irreducible symplectic 4-foldsJan 11 2000Having fixed a Kaehler class and the unique corresponding hyperkaehler metric, we prove that all special Lagrangian submanifolds of an irreducible symplectic 4-fold X are bi-Lagrangian and that they are obtained by complex submanifolds via a sort of "hyperkaehler ... More
Post-merger analytic templates for GW150914Jun 13 2016Following the new analytic description of the postmerger (ringdown) waveform of coalescing, nonprecessing, spinning, black hole binaries (BBHs) introduced in Phys.~Rev.~D~90, 024054 (2014), we propose an analytic, closed form, time-domain, representation ... More
Brief communication. An indefinite Sturm theoryDec 10 2008Sturm theory for second order differential equations was generalized to systems and higher order equations with positive leading coefficient by several authors. Here we propose a Sturm oscillation theorem for indefinite systems of even order and with ... More
Steinitz classes of some abelian and nonabelian extensions of even degreeJan 15 2010The Steinitz class of a number field extension K/k is an ideal class in the ring of integers O_k of k, which, together with the degree [K:k] of the extension determines the O_k-module structure of O_K. We call R_t(k,G) the classes which are Steinitz classes ... More
Examples of Hodge Laplacians on quantum spheresSep 07 2011Using a non canonical braiding over the 3d left covariant calculus we present a family of Hodge operators on the quantum SU(2) and its homogeneous quantum two-sphere.
Tree-graded asymptotic conesApr 03 2012We study the bilipschitz equivalence type of tree-graded spaces, showing that asymptotic cones of relatively hyperbolic groups (resp. asymptotic cones of groups containing a cut-point) only depend on the bilipschitz equivalence types of the pieces in ... More
3-manifold groups have unique asymptotic conesSep 21 2011We describe the (minimal) tree-graded structure of asymptotic cones of non-geometric graph manifold groups, and as a consequence we show that all said asymptotic cones are bilipschitz equivalent. Combining this with geometrization and other known results ... More
Projections and relative hyperbolicityOct 21 2010Apr 03 2012We give an alternative definition of relative hyperbolicity based on properties of closest-point projections on peripheral subgroups. We also derive a distance formula for relatively hyperbolic groups, similar to the one for mapping class groups.
Long range order for lattice dipolesMar 25 2008We consider a system of classical Heisenberg spins on a cubic lattice in dimensions three or more, interacting via the dipole-dipole interaction. We prove that at low enough temperature the system displays orientational long range order, as expected by ... More
Cluster Variation Method in Statistical Physics and Probabilistic Graphical ModelsAug 09 2005The cluster variation method (CVM) is a hierarchy of approximate variational techniques for discrete (Ising--like) models in equilibrium statistical mechanics, improving on the mean--field approximation and the Bethe--Peierls approximation, which can ... More
CVM ANALYSIS OF CROSSOVER IN THE SEMI-INFINITE ISING MODELFeb 03 1995Feb 06 1995The crossover behavior of the semi--infinite three dimensional Ising model is investigated by means of Pad\'e approximant analysis of cluster variation method results. We give estimates for ordinary critical as well as for multicritical exponents, which ... More
Black Holes in Galactic Nuclei: the Promise and the FactsJan 30 2002It has long been suspected that Active Galactic Nuclei are powered by accretion of matter onto massive black holes and this belief implies their presence in the nuclei of most nearby galaxies as "relics" of past activity. Just a few years ago this was ... More
Lattice Integrals of Motion of the Ising Model on the CylinderOct 21 2010Mar 27 2012We consider the 2D critical Ising model with spatially periodic boundary conditions. It is shown that for a suitable reparametrization of the known Boltzmann weights the transfer matrix becomes a polynomial in the variable $\csc(4u)$, being $u$ the spectral ... More
The Baxter Q Operator of Critical Dense PolymersMay 04 2009Sep 07 2009We consider critical dense polymers ${\cal L}_{1,2}$, corresponding to a logarithmic conformal field theory with central charge $c=-2$. An elegant decomposition of the Baxter $Q$ operator is obtained in terms of a finite number of lattice integrals of ... More
Free Field realization of the $\hat{\mathcal{D}}_q$ Algebra for the $η$-$ξ$ system, Integrals of Motion and CharactersNov 12 2012We introduce a free field realization of the central extension of the Lie algebra $\mathcal{D}_q$ of difference operators on the circle in terms of the fermionic $\eta$-$\xi$ system. This realization admits a nontrivial Jordan block structure. We also ... More
Classical behavior in quantum systems: the case of straight tracks in a cloud chamberMay 10 2009The aim of this review is to discuss in a pedagogical way the problem of the emergence of a classical behavior in certain physical systems which, in principle, are correctly described by quantum mechanics. It is stressed that the limit $\hbar \to 0$ is ... More
On the computation of the entropy in the microcanonical ensemble for mean-field-like systemsMar 28 2006Two recently proposed expressions for the computation of the entropy in the microcanonical ensemble are compared, and their equivalence is proved. These expressions are valid for a certain class of statistical mechanics systems, that can be called mean-field-like ... More
Multiple Peaks in the CMBJan 15 2002Recent measurements of the Cosmic Microwave Background Anisotropy have provided evidence for the presence of oscillations in the angular power spectrum. These oscillations are a wonderful confirmation of the standard cosmological scenario and allow us ... More
The existence of a minimum wavelength for photonsAug 25 2011The holographic property of entropy plays a key role in the thermodynamic description of gravitational field equations. It remains unclear, we argue, whether this property is necessarily interwoven with gravity itself or can be understood instead as a ... More
Gravity from the entropy of lightFeb 05 2010Jan 25 2011The holographic principle, considered in a semiclassical setting, is shown to have direct consequences on physics at a fundamental level. In particular, a certain relation is pointed out to be the expression of holography in basic thermodynamics. It is ... More
A stability result for Neumann problems in dimension $N \ge 3$May 08 2002We give a sufficient condition in dimension $N \ge 3$ in order to obtain the stability of a sequence of Neumann problems on fractured domains.
K-Theory, D-Branes and Ramond-Ramond FieldsDec 03 2008This thesis is dedicated to the study of K-theoretical properties of D-branes and Ramond-Ramond fields. We construct abelian groups which define a homology theory on the category of CW-complexes, and prove that this homology theory is equivalent to the ... More