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Distributed methods for synchronization of orthogonal matrices over graphsJan 25 2017Apr 07 2017This paper addresses the problem of synchronizing orthogonal matrices over directed graphs. For synchronized transformations (or matrices), composite transformations over loops equal the identity. We formulate the synchronization problem as a least-squares ... More

Synchronisation of Partial Multi-Matchings via Non-negative FactorisationsMar 16 2018Jul 12 2018In this work we study permutation synchronisation for the challenging case of partial permutations, which plays an important role for the problem of matching multiple objects (e.g. images or shapes). The term synchronisation refers to the property that ... More

Systems Aliasing in Dynamic Network Reconstruction: Issues on Low Sampling FrequenciesMay 27 2016Oct 29 2018Network reconstruction of dynamical continuous-time (CT) systems is motivated by applications in many fields. Due to experimental limitations, especially in biology, data could be sampled at low frequencies, leading to significant challenges in network ... More

Identification of Sparse Continuous-Time Linear Systems with Low Sampling Rate: Optimization ApproachesMay 30 2016Apr 17 2018This paper addresses identification of sparse linear and noise-driven continuous-time state-space systems, i.e., the right-hand sides in the dynamical equations depend only on a subset of the states. The key assumption in this study, is that the sample ... More

Linear system identification from ensemble snapshot observationsMar 15 2019Developments in transcriptomics techniques have caused a large demand in tailored computational methods for modelling gene expression dynamics from experimental data. Recently, so-called single-cell experiments have revolutionised genetic studies. These ... More

Linear identification of nonlinear systems: A lifting technique based on the Koopman operatorMay 14 2016Aug 27 2016We exploit the key idea that nonlinear system identification is equivalent to linear identification of the socalled Koopman operator. Instead of considering nonlinear system identification in the state space, we obtain a novel linear identification technique ... More

Dynamical Structure Functions for the Estimation of LTI Networks with Limited InformationOct 03 2006This research explores the role and representation of network structure for LTI Systems. We demonstrate that transfer functions contain no structural information without more assumptions being made about the system, assumptions that we believe are unreasonable ... More

Bayesian variable selection in linear dynamical systemsFeb 15 2018We develop a method for reconstructing regulatory interconnection networks between variables evolving according to a linear dynamical system. The work is motivated by the problem of gene regulatory network inference, that is, finding causal effects between ... More

Koopman-based lifting techniques for nonlinear systems identificationSep 06 2017Nov 21 2018We develop a novel lifting technique for nonlinear system identification based on the framework of the Koopman operator. The key idea is to identify the linear (infinitedimensional) Koopman operator in the lifted space of observables, instead of identifying ... More

Data-driven Discovery of Cyber-Physical SystemsOct 01 2018Cyber-physical systems (CPSs) embed software into the physical world. They appear in a wide range of applications such as smart grids, robotics, intelligent manufacture and medical monitoring. CPSs have proved resistant to modeling due to their intrinsic ... More

Equilibrium Fluctuations for the Totally Asymmetric Zero Range processFeb 23 2009We prove a Central Limit Theorem for the empirical measure in the one-dimensional Totally Asymmetric Zero-Range Process in the hyperbolic scaling $N$, starting from the equilibrium measure $\nu_{\rho}$. We also show that when taking the direction of the ... More

Network Reconstruction from Intrinsic NoiseOct 01 2013Dec 19 2014This paper considers the problem of inferring an unknown network of dynamical systems driven by unknown, intrinsic, noise inputs. Equivalently we seek to identify direct causal dependencies among manifest variables only from observations of these variables. ... More

Towards Almost Global Synchronization on the Stiefel ManifoldMar 14 2018Jul 25 2018A graph $\mathcal{G}$ is referred to as $\mathsf{S}^1$-synchronizing if, roughly speaking, the Kuramoto-like model whose interaction topology is given by $\mathcal{G}$ synchronizes almost globally. The Kuramoto model evolves on the unit circle, \ie the ... More

Dynamic controllers for column synchronization of rotation matrices: a QR-factorization approachAug 11 2017Jan 08 2018In the multi-agent systems setting, this paper addresses continuous-time distributed synchronization of columns of rotation matrices. More precisely, k specific columns shall be synchronized and only the corresponding k columns of the relative rotations ... More

An Approach to Sparse Continuous-time System Identification from Unevenly Sampled DataFeb 28 2018In this work, we address the problem of identifying sparse continuous-time dynamical systems when the spacing between successive samples (the sampling period) is not constant over time. The proposed approach combines the leave-one-sample-out cross-validation ... More

Intrinsic almost global consensus on the n-sphereSep 16 2016Oct 06 2016This paper provides a novel analysis of the global convergence properties of a large class of consensus protocols for multi-agent systems that evolve in continuous time on the n-sphere. The feedback laws are intrinsic in the sense of not rely on a protocol ... More

High-dimensional Kuramoto models on Stiefel manifolds synchronize complex networks almost globallyJul 26 2018Jan 22 2019The Kuramoto model of a system of coupled phase oscillators describe synchronization phenomena in nature. We propose a generalization of the Kuramoto model where each oscillator state lives on the compact, real Stiefel manifold St(p,n). Previous work ... More

A Full Bayesian Approach to Sparse Network Inference using Heterogeneous DatasetsJan 04 2019Network inference has been attracting increasing attention in several fields, notably systems biology, control engineering and biomedicine. To develop a therapy, it is essential to understand the connectivity of biochemical units and the internal working ... More

High Precision Variational Bayesian Inference of Sparse Linear NetworksJan 03 2019Sparse networks can be found in a wide range of applications, such as biological and communication networks. Inference of such networks from data has been receiving considerable attention lately, mainly driven by the need to understand and control internal ... More

Correlating Pedestrian Flows and Search Engine QueriesJun 19 2012An important challenge for ubiquitous computing is the development of techniques that can characterize a location vis-a-vis the richness and diversity of urban settings. In this paper we report our work on correlating urban pedestrian flows with Google ... More

On Transitive Consistency for Linear Invertible Transformations between Euclidean Coordinate SystemsSep 02 2015Transitive consistency is an intrinsic property for collections of linear invertible transformations between Euclidean coordinate frames. In practice, when the transformations are estimated from data, this property is lacking. This work addresses the ... More

Inverse Problems for Matrix Exponential in System Identification: System AliasingMay 23 2016This note addresses identification of the $A$-matrix in continuous time linear dynamical systems on state-space form. If this matrix is partially known or known to have a sparse structure, such knowledge can be used to simplify the identification. We ... More

Shaping Pulses to Control Bistable Monotone Systems Using Koopman OperatorMay 20 2016In this paper, we further develop a recently proposed control method to switch a bistable system between its steady states using temporal pulses. The motivation for using pulses comes from biomedical and biological applications (e.g. synthetic biology), ... More

The problem of almost global consensus on the n-sphereSep 16 2016This paper provides a novel analysis of the global convergence properties of a large class of consensus protocol for multi-agent systems that evolve in continuous time on the n-sphere. It is shown that, for any connected undirected graph topology and ... More

Consensus and Formation Control on SE(3) for Switching TopologiesNov 01 2015This paper addresses the consensus problem and the formation problem on SE(3) in multi-agent systems with directed and switching interconnection topologies. Several control laws are introduced for the consensus problem. By a simple transformation, it ... More

Situationally-Induced Impairments and Disabilities ResearchApr 12 2019Research has shown that various environmental factors impact smartphone interaction and lead to Situationally-Induced Impairments and Disabilities. In this work we discuss the importance of thoroughly understanding the effects of these situational impairments ... More

Free path groupoid grading on Leavitt path algebrasNov 17 2015In this work we realize Leavitt path algebras as partial skew groupoid rings. This yields a free path groupoid grading on Leavitt path algebras. Using this grading we characterize free path groupoid graded isomorphisms of Leavitt path algebras that preserves ... More

Minimal realization of the dynamical structure function and its application to network reconstructionSep 17 2012Network reconstruction, i.e., obtaining network structure from data, is a central theme in systems biology, economics and engineering. In some previous work, we introduced dynamical structure functions as a tool for posing and solving the problem of network ... More

Synchronisation of Partial Multi-Matchings via Non-negative FactorisationsMar 16 2018Mar 25 2019In this work we study permutation synchronisation for the challenging case of partial permutations, which plays an important role for the problem of matching multiple objects (e.g. images or shapes). The term synchronisation refers to the property that ... More

Linear Dynamic Network Reconstruction from Heterogeneous DatasetsDec 06 2016This paper addresses reconstruction of linear dynamic networks from heterogeneous datasets. Those datasets consist of measurements from linear dynamical systems in multiple experiment subjected to different experimental conditions, e.g., changes/perturbations ... More

Experimental design trade-offs for gene regulatory network inference: an in silico study of the yeast Saccharomyces cerevisiae cell cycleDec 14 2017Time-series of high throughput gene sequencing data intended for gene regulatory network (GRN) inference are often short due to the high costs of sampling cell systems. Moreover, experimentalists lack a set of quantitative guidelines that prescribe the ... More

A state-space approach to sparse dynamic network reconstructionNov 21 2018Dynamic network reconstruction has been shown to be challenging due to the requirements on sparse network structures and network identifiability. The direct parametric method (e.g., using ARX models) requires a large amount of parameters in model selection. ... More

Linear Shape Deformation Models with Local Support Using Graph-based Structured Matrix FactorisationOct 28 2015May 11 2016Representing 3D shape deformations by linear models in high-dimensional space has many applications in computer vision and medical imaging, such as shape-based interpolation or segmentation. Commonly, using Principal Components Analysis a low-dimensional ... More

Dynamic Network Reconstruction from Heterogeneous DatasetsDec 06 2016Feb 04 2019Performing multiple experiments is common when learning internal mechanisms of complex systems. These experiments can include perturbations to parameters or external disturbances. A challenging problem is to efficiently incorporate all collected data ... More

A Lifting method for analyzing distributed synchronization on the unit sphereMay 07 2018Jun 07 2018This paper introduces a new lifting method for analyzing convergence of continuous-time distributed synchronization/consensus systems on the unit sphere. Points on the d-dimensional unit sphere are lifted to the (d+1)-dimensional Euclidean space. The ... More

Identification of Sparse Continuous-Time Linear Systems with Low Sampling Rate: Optimization ApproachesMay 30 2016Jun 07 2016This paper addresses identification of sparse linear and noise-driven continuous-time state-space systems, i.e., the right-hand sides in the dynamical equations depend only on a subset of the states. The key assumption in this study, is that the sample ... More

Identification of Sparse Continuous-Time Linear Systems with Low Sampling Rate: Exploring Matrix LogarithmsMay 27 2016May 30 2016A continuous time linear dynamic in state space form has an $A$-matrix that reveals the connection between the states. Many dynamical systems allow a a sparse structure for this matrix. This means that the right-hand sides of the dynamical equations depend ... More

Continuous time Gaussian process dynamical models in gene regulatory network inferenceAug 24 2018One of the focus areas of modern scientific research is to reveal mysteries related to genes and their interactions. The dynamic interactions between genes can be encoded into a gene regulatory network (GRN), which can be used to gain understanding on ... More

Compressed Sensing for Network ReconstructionNov 15 2014The problem of identifying sparse solutions for the link structure and dynamics of an unknown linear, time-invariant network is posed as finding sparse solutions x to Ax=b. If the sensing matrix A satisfies a rank condition, this problem has a unique, ... More

No-horizon theorem for spacetimes with spacelike G1 isometry groupsDec 30 2003We consider four-dimensional spacetimes $(M,{\mathbf g})$ which obey the Einstein equations ${\mathbf G}={\mathbf T}$, and admit a global spacelike $G_{1}={\mathbb R}$ isometry group. By means of dimensional reduction and local analyis on the reduced ... More

Shear-free gravitational collapse is strongly censoredDec 30 2003We consider spherically symmetric spacetimes with matter whose timelike flow is assumed to be shear-free. A number of results on the formation and visibility of spacetime singularities is proven, with the main one being that shear-free collapse cannot ... More

Naked singularities in Tolman-Bondi-de Sitter collapseDec 07 2000We study the formation of central naked singularities in spherical dust collapse with a cosmological constant. We find that the central curvature singularity is locally naked, Tipler strong, and generic, in the sense that it forms from a non-zero-measure ... More

Black hole formation from massive scalar field collapse in the Einstein-de Sitter universeAug 15 2000We study the spherically symmetric collapse of a real, minimally coupled, massive scalar field in an asymptotically Einstein-de Sitter spacetime background. By means of an eikonal approximation for the field and metric functions, we obtain a simple analytical ... More

Epidemics scenarios in the "Romantic network"Aug 09 2012The structure of sexual contacts, its contacts network and its temporal interactions, play an important role in the spread of sexually transmitted infections. Unfortunately, that kind of data is very hard to obtain. One of the few exceptions is the "Romantic ... More

Anyons in 1+1 DimensionsMar 20 1995The possibility of excitations with fractional spin and statististics in $1+1$ dimensions is explored. The configuration space of a two-particle system is the half-line. This makes the Hamiltonian self-adjoint for a family of boundary conditions parametrized ... More

Distributed Kalman filtering with minimum-time consensus algorithmMar 16 2017Fueled by applications in sensor networks, these years have witnessed a surge of interest in distributed estimation and filtering. A new approach is hereby proposed for the Distributed Kalman Filter (DKF) by integrating a local covariance computation ... More

Identifying Biochemical Reaction Networks From Heterogeneous DatasetsSep 17 2015Sep 18 2015In this paper, we propose a new method to identify biochemical reaction networks (i.e. both reactions and kinetic parameters) from heterogeneous datasets. Such datasets can contain (a) data from several replicates of an experiment performed on a biological ... More

A Solution for Multi-Alignment by Transformation SynchronisationOct 30 2014Apr 14 2015The alignment of a set of objects by means of transformations plays an important role in computer vision. Whilst the case for only two objects can be solved globally, when multiple objects are considered usually iterative methods are used. In practice ... More

Scalar perturbations and the possible self-destruction of the phantom menaceMar 07 2006Some analysis of the supernovae type Ia observational data seems to indicate that the Universe today is dominated by a phantom field, for which all energy conditions are violated. Such phantom field may imply a singularity in a future finite time, called ... More

Weakly harmonic oscillators perturbed by a conservative noiseNov 09 2016We consider a chain of weakly harmonic coupled oscillators perturbed by a conservative noise. We show that by tuning accordingly the coupling constant energy can diffuse like a Brownian motion or superdiffuse like a maximally 3/2-stable asymmetric L{\'e}vy ... More

The longitudinal dynamic correlation and dynamic susceptibility of the isotropic XY-model on the 1d alternating superlatticeNov 20 2001The dynamic susceptibility $\chi_{Q}^{zz}(\omega)$ of the isotropic XY-model (s=1/2) on the alternating superlattice (closed chain) in a transverse field $h$ is obtained exactly at arbitrary temperatures. It is determined from the results obtained for ... More

The structure and stability of molecular cloud cores in external radiation fieldsAug 22 2002We have considered the thermal equilibrium in pre-protostellar cores in the approximation where the dust temperature is independent of interactions with the gas and where the gas is heated both by collisions with dust grains and ionization by cosmic rays. ... More

Gravitational waves in a stringlike fluid cosmologyJun 03 1998The coupling of a stringlike fluid with ordinary matter and gravity may lead to a closed Universe with the dynamic of an open one. This can provide an alternative solution for the age and horizon problems. A study of density perturbations of the stringlike ... More

Soft-excess in ULX spectra: the chilled-disk scenarioNov 05 2006Soft X-ray spectra of ULXs show small deviations from a power-law model, that can be attributed to reprocessing in a fast, ionized outflow, or to thermal emission from a cool disk. If it is thermal emission, the cool peak temperature can be explained ... More

On the Structure of the Solution Set of a Sign Changing Perturbation of the p-Laplacian under Dirichlet Boundary ConditionOct 21 2013In a recent paper D. D. Hai showed that the equation $ -\Delta_{p} u = \lambda f(u) \mbox{in} \Omega$, under Dirichlet boundary condition, where $\Omega \subset {\bf R^N}$ is a bounded domain with smooth boundary $\partial\Omega$, $\Delta_{p}$ is the ... More

Non-equilibrium work relationsNov 03 2005This is a brief review of recently derived relations describing the behaviour of systems far from equilibrium. They include the Fluctuation Theorem, Jarzynski's and Crooks' equalities, and an extended form of the Second Principle for general steady states. ... More

Recent theories of glasses as out of equilibrium systemsNov 07 2000We discuss a theoretical approach to structural glasses as they happen in real situations. Older ideas based on `configurational entropy', on `fictive temperatures' and on Edwards' `compactivity' are sharpened and unified in an out of equilibrium context. ... More

Supersymmetry, replica and dynamic treatments of disordered systems: a parallel presentationSep 17 2002Sep 23 2002I briefly review the three nonperturbative methods for the treatment of disordered systems -- supersymmetry, replicas and dynamics -- with a parallel presentation that highlights their connections and differences.

Emergence of macroscopic temperatures in systems that are not thermodynamical microscopically: towards a thermodynamical description of slow granular rheologySep 21 1999Oct 18 1999A scenario for systems with slow dynamics is characterised by stating that there are several temperatures coexisting in the sample, with a single temperature shared by all observables at each (widely separate) time-scale. In preparation for the study ... More

Chern-Simons Forms in Gravitation TheoriesAug 16 2012The Chern-Simons (CS) form evolved from an obstruction in mathematics into an important object in theoretical physics. In fact, the presence of CS terms in physics is more common than one may think: they seem to play an important role in high Tc superconductivity ... More

Ricci flow of homogeneous manifoldsDec 26 2011Mar 02 2012We present in this paper a general approach to study the Ricci flow on homogeneous manifolds. Our main tool is a dynamical system defined on a subset H(q,n) of the variety of (q+n)-dimensional Lie algebras, parameterizing the space of all simply connected ... More

Ricci soliton solvmanifoldsFeb 02 2010All known examples of nontrivial homogeneous Ricci solitons are left-invariant metrics on simply connected solvable Lie groups whose Ricci operator is a multiple of the identity modulo derivations (called solsolitons, and nilsolitons in the nilpotent ... More

A canonical compatible metric for geometric structures on nilmanifoldsOct 27 2004Let (N,g) be a nilpotent Lie group endowed with an invariant geometric structure (cf. symplectic, complex, hypercomplex or any of their `almost' versions). We define a left invariant Riemannian metric on N compatible with g to be minimal, if it minimizes ... More

Spontaneous superconducting islands and Hall voltage in clean superconductorsSep 10 2004Oct 27 2004We study a clean superconductor in the Hall configuration, in the framework of a purely dissipative time-dependent Ginzburg--Landau theory. We find situations in which the order parameter differs significantly from zero in a set of islands that appear ... More

A Formal Model for Dynamically Adaptable ServicesNov 11 2010The growing complexity of software systems as well as changing conditions in their operating environment demand systems that are more flexible, adaptive and dependable. The service-oriented computing paradigm is in widespread use to support such adaptive ... More

The last sunset on mainland EuropeAug 09 2014This paper documents the places in mainland Europe at which the sun sets latest, by Coordinated Universal Time (UTC), on any given day (distortion due to differences in local standard times is ignored). In contradiction to the na\"ive assumption that ... More

On the extended loop calculusDec 05 1995Some features of extended loops are considered. In particular, the behaviour under diffeomorphism transformations of the wavefunctions with support on the extended loop space are studied. The basis of a method to obtain analytical expressions of diffeomorphism ... More

$K \rightarrow π\ell^+ \ell^-$: Status and updateNov 22 2016$K \rightarrow \pi \ell^+ \ell^-$ decays, $\ell = e, \mu$, will be one of the goals of future kaon facilities, like NA62 (CERN) and K$^0$TO (J-PARC). We review briefly the theoretical status of those processes.

Historical Comments on Monge's Ellipsoid and the Configuration of Lines of Curvature on Surfaces Immersed in ${\mathbb R}^3$Nov 18 2004This is an essay on the historical landmarks leading to the study of principal configurations on surfaces, their structural stability and further generalizations. Here it is pointed out that in the work of Monge, 1796, are found elements of the qualitative ... More

A contribution for a mathematical classification of square tilesJun 16 2012In this article we study some geometric properties of a non-trivial square tile (a non-trivial square tile is a non-constant function on a square). Consider infinitely many copies of this single square tile and cover the plane with them, without gaps ... More

Ginzburg-Landau equations with consistent Langevin terms for nonuniform wiresMay 03 2006Apr 04 2007Many analyses based on the time-dependent Ginzburg--Landau model are not consistent with statistical mechanics, because thermal fluctuations are not taken correctly into account. We use the fluctuation-dissipation theorem in order to establish the appropriate ... More

Nonlinearity of the field induced by a rotating superconducting shellApr 06 2004For a thin superconducting shell with cylindrical symmetry, the magnetic field generated by its rotation is easily evaluated in the Ginzburg-Landau framework. We compare this field with the result that is obtained by using the London theory.

Flux transitions in a superconducting ringJun 17 2002Dec 11 2002We perform a numeric study of the flux transitions in a superconducting ring at fixed temperature, while the applied field is swept at an ideally slow rate. The current around the ring and its free energy are evaluated. We partially explain some of the ... More

The Sun. A typical star in the solar neighborhood?Jul 19 2013The Sun is used as the fundamental standard in chemical abundance studies, thus it is important to know whether the solar abundance pattern is representative of the solar neighborhood. Albeit at low precision (0.05 - 0.10 dex) the Sun seems to be a typical ... More

Elastic and Transition Form Factors in DSEsJan 05 2016A symmetry preserving framework for the study of continuum Quantum Chromodynamics (QCD) is obtained from a truncated solution of the QCD equations of motion or QCD's Dyson-Schwinger equations (DSEs). A nonperturbative solution of the DSEs enables the ... More

$\mathbf{γ_{v} NN^{\ast}}$ Electrocouplings in Dyson-Schwinger EquationsFeb 08 2016A symmetry preserving framework for the study of continuum Quantum Chromodynamics (QCD) is obtained from a truncated solution of the QCD equations of motion or QCD's Dyson-Schwinger equations (DSEs). A nonperturbative solution of the DSEs enables the ... More

Lecture notes on Chern-Simons (super-)gravities. Second edition (February 2008)Feb 22 2005Mar 21 2008This is intended as a broad introduction to Chern-Simons gravity and supergravity. The motivation for these theories lies in the desire to have a gauge invariant system --with a fiber bundle formulation-- in more than three dimensions, which could provide ... More

Laplacian flow of homogeneous G2-structures and its solitonsFeb 26 2016We use the bracket flow/algebraic soliton approach to study the Laplacian flow of $G_2$-structures and its solitons in the homogeneous case. We prove that any homogeneous Laplacian soliton is equivalent to a semi-algebraic soliton (i.e.\ a $G$-invariant ... More

Observational evidence for stellar-mass black holesDec 12 2006Radial velocity studies of X-ray binaries provide the most solid evidence for the existence of stellar-mass black holes. We currently have 20 confirmed cases, with dynamical masses in excess of 3 Msun. Accurate masses have been obtained for a subset of ... More

Symmetries and the Antibracket: The Batalin-Vilkovisky MethodMar 06 1997Apr 07 1997These lectures on the Batalin-Vilkovisky method of quantization were delivered at "VII Mexican School of Particles and Fields", M\'erida, M\'exico, October 30-November 6, 1996. In section II, we study the derivation of BV from Schwinger-Dyson-BRST symmetry; ... More

Quantum Gravity and Lorentz invariance violation in the Standard ModelDec 24 2004Apr 29 2005The most important problem of fundamental Physics is the quantization of the gravitational field. A main difficulty is the lack of available experimental tests that discriminate among the theories proposed to quantize gravity. Recently, Lorentz invariance ... More

Fubini-Tonelli type theorem for non product measures in a product spaceJun 11 2018I prove a theorem about iterated integrals for non-product measures in a product space. The first task is to show the existence of a family of measures on the second space, indexed by the points on of the first space (outside a negligible set), such that ... More

Elastic potentials as yield surfaces for homogeneous materialsMay 31 2018This paper proposes that elastic potentials, which may be rigorously formulated using the negative Gibbs free energy or the complementary strain energy density, should be used as the basis for the plastic part of elasto-plastic constitutive models. Thus, ... More

Poisson Statistics in the Non-Homogeneous Hierarchical Anderson ModelNov 14 2017In this article we study the problem of localization of eigenvalues for the non-homogeneous hierarchical Anderson model. More specifically, given the hierarchical Anderson model with spectral dimension $0<d<1$ with a random potential acting on the diagonal ... More

The norm residue symbol for higher local fieldsFeb 14 2017Aug 25 2018Since the development of higher local class field theory, several explicit reciprocity laws have been constructed. In particular, there are formulas describing the higher-dimensional Hilbert symbol given, among others, by M. Kurihara, A. Zinoviev and ... More

Mutations Vs. Seiberg dualitySep 25 2007Nov 25 2007For a quiver with potential, Derksen, Weyman and Zelevinsky defined a combinatorial transformation - mutations. Mukhopadhyay and Ray, on the other hand, tell us how to compute Seiberg dual quivers for some quivers with potentials through a tilting procedure, ... More

Quantum bound to chaos and the semiclassical limitDec 05 2016Jan 20 2017We discuss the quantum bound on chaos in the context of the free propagation of a particle in an arbitrarily curved surface at low temperatures. The semiclassical calculation of the Lyapunov exponent can be performed in much the same way as the corresponding ... More

Is the third coefficient of the Jones knot polynomial a quantum state of gravity?Oct 25 1995Some time ago it was conjectured that the coefficients of an expansion of the Jones polynomial in terms of the cosmological constant could provide an infinite string of knot invariants that are solutions of the vacuum Hamiltonian constraint of quantum ... More

Extended knots and the space of states of quantum gravityJan 07 1996In the loop representation the quantum constraints of gravity can be solved. This fact allowed significant progress in the understanding of the space of states of the theory. The analysis of the constraints over loop dependent wavefunctions has been traditionally ... More

The Kauffman bracket and the Jones polynomial in quantum gravityOct 25 1995An analysis of the action of the Hamiltonian constraint of quantum gravity on the Kauffman bracket and Jones knot polynomials is proposed. It is explicitely shown that the Kauffman bracket is a formal solution of the Hamiltonian constraint with cosmological ... More

Expansive homeomorphisms of the planeJun 25 2009This article tackles the problem of the classification of expansive homeomorphisms of the plane. Necessary and sufficient conditions for a homeomorphism to be conjugate to a linear hyperbolic automorphism will be presented. The techniques involve topological ... More

Examples of noncommutative manifolds: complex tori and spherical manifoldsMar 28 2007We survey some aspects of the theory of noncommutative manifolds focusing on the noncommutative analogs of two-dimensional tori and low-dimensional spheres. We are particularly interested in those aspects of the theory that link the differential geometry ... More

Heisenberg modules over real multiplication noncommutative tori and related algebraic structuresDec 03 2007Dec 07 2007We review some aspects of the theory of noncommutative two-tori with real multiplication focusing on the role played by Heisenberg groups in the definition of algebraic structures associated to these noncommutative spaces.

Regularity of the vanishing ideal over a bipartite nested ear decompositionMay 28 2018We study the Castelnuovo-Mumford regularity of the vanishing ideal over a bipartite graph endowed with a decomposition of its edge set. We prove that, under certain conditions, the regularity of the vanishing ideal over a bipartite graph obtained from ... More

Quantum statistical mechanics and class field TheoryFeb 13 2007We survey some results relating noncommutative geometry to the class field theory of number fields. These results appear within the context of quantum statistical mechanics where some arithmetic properties of a given number field can be realized in terms ... More

A Quantum Fluctuation TheoremJul 24 2000Aug 16 2001We consider a quantum system strongly driven by forces that are periodic in time. The theorem concerns the probability $P(e)$ of observing a given energy change $e$ after a number of cycles. If the system is thermostated by a (quantum) thermal bath, $e$ ... More

Rheology, and how to stop agingDec 21 1998Recent analytical developments in glass theory are equally relevant to the understanding of anomalous rheology, with characteristic features such as the Reynolds dilatancy and the driving-power dependence of the viscosity arising naturally. A notion of ... More

Einstein solvmanifolds are standardMar 15 2007Feb 02 2010We study Einstein manifolds admitting a transitive solvable Lie group of isometries (solvmanifolds). It is conjectured that these exhaust the class of noncompact homogeneous Einstein manifolds. J. Heber has showed that under certain simple algebraic condition ... More

Characterization of the spontaneous symmetry breaking due to quenching of a one-dimensional superconducting loopJan 05 2013Apr 25 2013We study the final distribution of the winding numbers in a 1D superconducting ring that is quenched through its critical temperature in the absence of magnetic flux. The study is conducted using the stochastic time-dependent Ginzburg--Landau model, and ... More

The Fight Against the Second Law of ThermodynamicsFeb 05 1995Jan 15 1997After presenting possible motives for fighting against the second law of thermodynamics, several attempts to beat this law are analyzed. The second law wins, but an interesting interpretation of it emerges. This interpretation uses the notion of ``encoded ... More