Giampaolo Cristadoro - Academia.edu (original) (raw)
Papers by Giampaolo Cristadoro
Philosophical transactions. Series A, Mathematical, physical, and engineering sciences, Jan 13, 2016
We perform a statistical study of the distances between successive occurrences of a given dinucle... more We perform a statistical study of the distances between successive occurrences of a given dinucleotide in the DNA sequence for a number of organisms of different complexity. Our analysis highlights peculiar features of the CG dinucleotide distribution in mammalian DNA, pointing towards a connection with the role of such dinucleotide in DNA methylation. While the CG distributions of mammals exhibit exponential tails with comparable parameters, the picture for the other organisms studied (e.g. fish, insects, bacteria and viruses) is more heterogeneous, possibly because in these organisms DNA methylation has different functional roles. Our analysis suggests that the distribution of the distances between CG dinucleotides provides useful insights into characterizing and classifying organisms in terms of methylation functionalities.
Journal of Statistical Physics, 2016
We consider a generalization of a one-dimensional stochastic process known in the physical litera... more We consider a generalization of a one-dimensional stochastic process known in the physical literature as Lévy-Lorentz gas. The process describes the motion of a particle on the real line in the presence of a random array of marked points, whose nearest-neighbor distances are i.i.d. and long-tailed (with finite mean but possibly infinite variance). The motion is a continuous-time, constant-speed interpolation of a symmetric random walk on the marked points. We first study the quenched random walk on the point process, proving the CLT and the convergence of all the accordingly rescaled moments. Then we derive the quenched and annealed CLTs for the continuous-time process.
Hamiltonian systems with a mixed phase space typically exhibit an algebraic decay of correlations... more Hamiltonian systems with a mixed phase space typically exhibit an algebraic decay of correlations and of Poincare' recurrences, with numerical experiments over finite times showing system-dependent power-law exponents. We conjecture the existence of a universal asymptotic decay based on results for a Markov tree model with random scaling factors for the transition probabilities. Numerical simulations for different Hamiltonian systems support this conjecture and permit the determination of the universal exponent.
Journal of Statistical Mechanics: Theory and Experiment, 2015
Continuous-time random walks combining diffusive scattering and ballistic propagation on lattices... more Continuous-time random walks combining diffusive scattering and ballistic propagation on lattices model a class of Lévy walks. The assumption that transitions in the scattering phase occur with exponentially-distributed waiting times leads to a description of the process in terms of multiple states, whose distributions evolve according to a set of delay differential equations, amenable to analytic treatment. We obtain an exact expression of the mean squared displacement associated with such processes and discuss the emergence of asymptotic scaling laws in regimes of diffusive and superdiffusive (subballistic) transport, emphasizing, in the latter case, the effect of initial conditions on the transport coefficients. Of particular interest is the case of rare ballistic propagation, in which case a regime of superdiffusion may lurk underneath one of normal diffusion.
Chaos, Complexity and Transport - Theory and Applications - Proceedings of the CCT '07, 2008
EPL (Europhysics Letters), 2014
Continuous time random walks combining diffusive and ballistic regimes are introduced to describe... more Continuous time random walks combining diffusive and ballistic regimes are introduced to describe a class of Lévy walks on lattices. By including exponentially-distributed waiting times separating the successive jump events of a walker, we are led to a description of such Lévy walks in terms of multistate processes whose time-evolution is shown to obey a set of coupled delay differential equations. Using simple arguments, we obtain asymptotic solutions to these equations and rederive the scaling laws for the mean squared displacement of such processes. Our calculation includes the computation of all relevant transport coefficients in terms of the parameters of the models.
Physical review. E, Statistical, nonlinear, and soft matter physics, 2014
We study diffusion on a periodic billiard table with an infinite horizon in the limit of narrow c... more We study diffusion on a periodic billiard table with an infinite horizon in the limit of narrow corridors. An effective trapping mechanism emerges according to which the process can be modeled by a Lévy walk combining exponentially distributed trapping times with free propagation along paths whose precise probabilities we compute. This description yields an approximation of the mean squared displacement of infinite-horizon billiards in terms of two transport coefficients, which generalizes to this anomalous regime the Machta-Zwanzig approximation of normal diffusion in finite-horizon billiards [J. Machta and R. Zwanzig, Phys. Rev. Lett. 50, 1959 (1983)PRLTAO0031-900710.1103/PhysRevLett.50.1959].
We perform numerical measurements of the moments of the position of a tracer particle in a two-di... more We perform numerical measurements of the moments of the position of a tracer particle in a two-dimensional periodic billiard model (Lorentz gas) with infinite corridors. This model is known to exhibit a weak form of super-diffusion, in the sense that there is a logarithmic correction to the linear growth in time of the meansquared displacement. We show numerically that this expected asymptotic behavior is easily overwhelmed by the subleading linear growth throughout the time-range accessible to numerical simulations. We compare our simulations to the known analytical results for the variance of the anomalously-rescaled limiting normal distributions.
Physics Letters B, 2002
In an extension of the Standard Model with one extra dimension and N=1 supersymmetry compactified... more In an extension of the Standard Model with one extra dimension and N=1 supersymmetry compactified on R 1 /Z 2 × Z ′ 2 , we compute the Higgs boson decay width into two gluons, relevant to Higgs production in hadronic collisions. At one loop, the decay width is significantly suppressed with respect to the SM. For a compactification radius R = (370 ± 70 GeV ) −1 and a Higgs mass m H = 127 ± 8 GeV , as expected in the case of a radiatively generated Fayet-Iliopoulos term, we find it to be less than 15% of the SM result.
Physical Review Letters, 2008
Hamiltonian systems with a mixed phase space typically exhibit an algebraic decay of correlations... more Hamiltonian systems with a mixed phase space typically exhibit an algebraic decay of correlations and of Poincaré recurrences, with numerical experiments over finite times showing system-dependent power-law exponents. We conjecture the existence of a universal asymptotic decay based on results for a Markov tree model with random scaling factors for the transition probabilities. Numerical simulations for different Hamiltonian systems support this conjecture and permit the determination of the universal exponent. PACS numbers: 05.45-a
Physical Review Letters, 2003
We introduce a cycle-expansion (fully deterministic) technique to compute the asymptotic behavior... more We introduce a cycle-expansion (fully deterministic) technique to compute the asymptotic behavior of arbitrary order transport moments. The theory is applied to different kinds of one-dimensional intermittent maps, and Lorentz gas with infinite horizon, confirming the typical appearance of phase transitions in the transport spectrum.
Physical Review E, 2008
We introduce a family of area-preserving maps representing a (non-trivial) two-dimensional extens... more We introduce a family of area-preserving maps representing a (non-trivial) two-dimensional extension of the Pomeau-Manneville family in one dimension. We analyze the long-time behavior of recurrence time distributions and correlations, providing analytical and numerical estimates. We study the transport properties of a suitable lift and use a probabilistic argument to derive the full spectrum of transport moments. Finally the dynamical effects of a stochastic perturbation are considered.
Physical Review E, 2006
We show that the nontwist phenomena previously observed in Hamiltonian systems exist also in time... more We show that the nontwist phenomena previously observed in Hamiltonian systems exist also in time-reversible non-Hamiltonian systems. In particular, we study the two standard collision/reconnection scenarios and we compute the parameter space breakup diagram of the shearless torus. Besides the Hamiltonian routes, the breakup may occur due to the onset of attractors. We study these phenomena in coupled phase oscillators and in non-area-preserving maps.
Physical Review E, 2005
An ensemble of particles in thermal equilibrium at temperature T, modeled by Nosè-Hoover dynamics... more An ensemble of particles in thermal equilibrium at temperature T, modeled by Nosè-Hoover dynamics, moves on a triangular lattice of oriented semidisk elastic scatterers. Despite the scatterer asymmetry, a directed transport is clearly ruled out by the second law of thermodynamics. Introduction of a polarized zero mean monochromatic field creates a directed stationary flow with nontrivial dependence on temperature and field parameters. We give a theoretical estimate of directed current induced by a microwave field in an antidot superlattice in semiconductor heterostructures.
Nuclear Physics B, 2002
In the framework of a recently proposed extension of the Standard Model, with N = 1 Super-Symmetr... more In the framework of a recently proposed extension of the Standard Model, with N = 1 Super-Symmetry in 5 dimensions, compactified on R 1 /Z 2 × Z ′ 2 , we compute the muon anomalous magnetic moment at one loop to order (M W R) 2 , where R is the compactification radius. We find the corrections to be small with respect to the SM pure weak contribution and not capable of explaining the present discrepancy between theory and experiment for any sensible value of R.
Journal of Statistical Physics, 2011
We consider the billiard dynamics in a non-compact set of R d that is constructed as a bi-infinit... more We consider the billiard dynamics in a non-compact set of R d that is constructed as a bi-infinite chain of translated copies of the same d-dimensional polytope. A random configuration of semi-dispersing scatterers is placed in each copy. The ensemble of dynamical systems thus defined, one for each global realization of the scatterers, is called quenched random Lorentz tube. Under some fairly general conditions, we prove that every system in the ensemble is hyperbolic and almost every system is recurrent, ergodic, and enjoys some higher chaotic properties.
Journal of Physics A: Mathematical and Theoretical, 2013
Borrowing and extending the method of images we introduce a theoretical framework that greatly si... more Borrowing and extending the method of images we introduce a theoretical framework that greatly simplifies analytical and numerical investigations of the escape rate in open systems. As an example, we explicitly derive the exact size-and position-dependent escape rate in a Markov case for holes of finite size. Moreover, a general relation between the transfer operators of the closed and corresponding open systems, together with the generating function of the probability of return to the hole is derived. This relation is then used to compute the small hole asymptotic behavior, in terms of readily calculable quantities. As an example we derive logarithmic corrections in the second order term. Being valid for Markov systems, our framework can find application in many areas of the physical sciences such as information theory, network theory, quantum Weyl law and via Ulam's method can be used as an approximation method in general dynamical systems.
Journal of Physics A: Mathematical and General, 2004
We establish a deterministic technique to investigate transport moments of arbitrary order. The t... more We establish a deterministic technique to investigate transport moments of arbitrary order. The theory is applied to the analysis of different kinds of intermittent one-dimensional maps and the Lorentz gas with infinite horizon: the typical appearance of phase transitions in the spectrum of transport exponents is explained.
Journal of Physics A: Mathematical and General, 2006
Dynamical zeta functions provide a powerful method to analyze low dimensional dynamical systems w... more Dynamical zeta functions provide a powerful method to analyze low dimensional dynamical systems when the underlying symbolic dynamics is under control. On the other hand even simple one dimensional maps can show an intricate structure of the grammar rules that may lead to a non smooth dependence of global observable on parameters changes. A paradigmatic example is the fractal diffusion coefficient arising in a simple piecewise linear one dimensional map of the real line. Using the Baladi-Ruelle generalization of the Milnor-Thurnston kneading determinant we provide the exact dynamical zeta function for such a map and compute the diffusion coefficient from its smallest zero.
Philosophical transactions. Series A, Mathematical, physical, and engineering sciences, Jan 13, 2016
We perform a statistical study of the distances between successive occurrences of a given dinucle... more We perform a statistical study of the distances between successive occurrences of a given dinucleotide in the DNA sequence for a number of organisms of different complexity. Our analysis highlights peculiar features of the CG dinucleotide distribution in mammalian DNA, pointing towards a connection with the role of such dinucleotide in DNA methylation. While the CG distributions of mammals exhibit exponential tails with comparable parameters, the picture for the other organisms studied (e.g. fish, insects, bacteria and viruses) is more heterogeneous, possibly because in these organisms DNA methylation has different functional roles. Our analysis suggests that the distribution of the distances between CG dinucleotides provides useful insights into characterizing and classifying organisms in terms of methylation functionalities.
Journal of Statistical Physics, 2016
We consider a generalization of a one-dimensional stochastic process known in the physical litera... more We consider a generalization of a one-dimensional stochastic process known in the physical literature as Lévy-Lorentz gas. The process describes the motion of a particle on the real line in the presence of a random array of marked points, whose nearest-neighbor distances are i.i.d. and long-tailed (with finite mean but possibly infinite variance). The motion is a continuous-time, constant-speed interpolation of a symmetric random walk on the marked points. We first study the quenched random walk on the point process, proving the CLT and the convergence of all the accordingly rescaled moments. Then we derive the quenched and annealed CLTs for the continuous-time process.
Hamiltonian systems with a mixed phase space typically exhibit an algebraic decay of correlations... more Hamiltonian systems with a mixed phase space typically exhibit an algebraic decay of correlations and of Poincare' recurrences, with numerical experiments over finite times showing system-dependent power-law exponents. We conjecture the existence of a universal asymptotic decay based on results for a Markov tree model with random scaling factors for the transition probabilities. Numerical simulations for different Hamiltonian systems support this conjecture and permit the determination of the universal exponent.
Journal of Statistical Mechanics: Theory and Experiment, 2015
Continuous-time random walks combining diffusive scattering and ballistic propagation on lattices... more Continuous-time random walks combining diffusive scattering and ballistic propagation on lattices model a class of Lévy walks. The assumption that transitions in the scattering phase occur with exponentially-distributed waiting times leads to a description of the process in terms of multiple states, whose distributions evolve according to a set of delay differential equations, amenable to analytic treatment. We obtain an exact expression of the mean squared displacement associated with such processes and discuss the emergence of asymptotic scaling laws in regimes of diffusive and superdiffusive (subballistic) transport, emphasizing, in the latter case, the effect of initial conditions on the transport coefficients. Of particular interest is the case of rare ballistic propagation, in which case a regime of superdiffusion may lurk underneath one of normal diffusion.
Chaos, Complexity and Transport - Theory and Applications - Proceedings of the CCT '07, 2008
EPL (Europhysics Letters), 2014
Continuous time random walks combining diffusive and ballistic regimes are introduced to describe... more Continuous time random walks combining diffusive and ballistic regimes are introduced to describe a class of Lévy walks on lattices. By including exponentially-distributed waiting times separating the successive jump events of a walker, we are led to a description of such Lévy walks in terms of multistate processes whose time-evolution is shown to obey a set of coupled delay differential equations. Using simple arguments, we obtain asymptotic solutions to these equations and rederive the scaling laws for the mean squared displacement of such processes. Our calculation includes the computation of all relevant transport coefficients in terms of the parameters of the models.
Physical review. E, Statistical, nonlinear, and soft matter physics, 2014
We study diffusion on a periodic billiard table with an infinite horizon in the limit of narrow c... more We study diffusion on a periodic billiard table with an infinite horizon in the limit of narrow corridors. An effective trapping mechanism emerges according to which the process can be modeled by a Lévy walk combining exponentially distributed trapping times with free propagation along paths whose precise probabilities we compute. This description yields an approximation of the mean squared displacement of infinite-horizon billiards in terms of two transport coefficients, which generalizes to this anomalous regime the Machta-Zwanzig approximation of normal diffusion in finite-horizon billiards [J. Machta and R. Zwanzig, Phys. Rev. Lett. 50, 1959 (1983)PRLTAO0031-900710.1103/PhysRevLett.50.1959].
We perform numerical measurements of the moments of the position of a tracer particle in a two-di... more We perform numerical measurements of the moments of the position of a tracer particle in a two-dimensional periodic billiard model (Lorentz gas) with infinite corridors. This model is known to exhibit a weak form of super-diffusion, in the sense that there is a logarithmic correction to the linear growth in time of the meansquared displacement. We show numerically that this expected asymptotic behavior is easily overwhelmed by the subleading linear growth throughout the time-range accessible to numerical simulations. We compare our simulations to the known analytical results for the variance of the anomalously-rescaled limiting normal distributions.
Physics Letters B, 2002
In an extension of the Standard Model with one extra dimension and N=1 supersymmetry compactified... more In an extension of the Standard Model with one extra dimension and N=1 supersymmetry compactified on R 1 /Z 2 × Z ′ 2 , we compute the Higgs boson decay width into two gluons, relevant to Higgs production in hadronic collisions. At one loop, the decay width is significantly suppressed with respect to the SM. For a compactification radius R = (370 ± 70 GeV ) −1 and a Higgs mass m H = 127 ± 8 GeV , as expected in the case of a radiatively generated Fayet-Iliopoulos term, we find it to be less than 15% of the SM result.
Physical Review Letters, 2008
Hamiltonian systems with a mixed phase space typically exhibit an algebraic decay of correlations... more Hamiltonian systems with a mixed phase space typically exhibit an algebraic decay of correlations and of Poincaré recurrences, with numerical experiments over finite times showing system-dependent power-law exponents. We conjecture the existence of a universal asymptotic decay based on results for a Markov tree model with random scaling factors for the transition probabilities. Numerical simulations for different Hamiltonian systems support this conjecture and permit the determination of the universal exponent. PACS numbers: 05.45-a
Physical Review Letters, 2003
We introduce a cycle-expansion (fully deterministic) technique to compute the asymptotic behavior... more We introduce a cycle-expansion (fully deterministic) technique to compute the asymptotic behavior of arbitrary order transport moments. The theory is applied to different kinds of one-dimensional intermittent maps, and Lorentz gas with infinite horizon, confirming the typical appearance of phase transitions in the transport spectrum.
Physical Review E, 2008
We introduce a family of area-preserving maps representing a (non-trivial) two-dimensional extens... more We introduce a family of area-preserving maps representing a (non-trivial) two-dimensional extension of the Pomeau-Manneville family in one dimension. We analyze the long-time behavior of recurrence time distributions and correlations, providing analytical and numerical estimates. We study the transport properties of a suitable lift and use a probabilistic argument to derive the full spectrum of transport moments. Finally the dynamical effects of a stochastic perturbation are considered.
Physical Review E, 2006
We show that the nontwist phenomena previously observed in Hamiltonian systems exist also in time... more We show that the nontwist phenomena previously observed in Hamiltonian systems exist also in time-reversible non-Hamiltonian systems. In particular, we study the two standard collision/reconnection scenarios and we compute the parameter space breakup diagram of the shearless torus. Besides the Hamiltonian routes, the breakup may occur due to the onset of attractors. We study these phenomena in coupled phase oscillators and in non-area-preserving maps.
Physical Review E, 2005
An ensemble of particles in thermal equilibrium at temperature T, modeled by Nosè-Hoover dynamics... more An ensemble of particles in thermal equilibrium at temperature T, modeled by Nosè-Hoover dynamics, moves on a triangular lattice of oriented semidisk elastic scatterers. Despite the scatterer asymmetry, a directed transport is clearly ruled out by the second law of thermodynamics. Introduction of a polarized zero mean monochromatic field creates a directed stationary flow with nontrivial dependence on temperature and field parameters. We give a theoretical estimate of directed current induced by a microwave field in an antidot superlattice in semiconductor heterostructures.
Nuclear Physics B, 2002
In the framework of a recently proposed extension of the Standard Model, with N = 1 Super-Symmetr... more In the framework of a recently proposed extension of the Standard Model, with N = 1 Super-Symmetry in 5 dimensions, compactified on R 1 /Z 2 × Z ′ 2 , we compute the muon anomalous magnetic moment at one loop to order (M W R) 2 , where R is the compactification radius. We find the corrections to be small with respect to the SM pure weak contribution and not capable of explaining the present discrepancy between theory and experiment for any sensible value of R.
Journal of Statistical Physics, 2011
We consider the billiard dynamics in a non-compact set of R d that is constructed as a bi-infinit... more We consider the billiard dynamics in a non-compact set of R d that is constructed as a bi-infinite chain of translated copies of the same d-dimensional polytope. A random configuration of semi-dispersing scatterers is placed in each copy. The ensemble of dynamical systems thus defined, one for each global realization of the scatterers, is called quenched random Lorentz tube. Under some fairly general conditions, we prove that every system in the ensemble is hyperbolic and almost every system is recurrent, ergodic, and enjoys some higher chaotic properties.
Journal of Physics A: Mathematical and Theoretical, 2013
Borrowing and extending the method of images we introduce a theoretical framework that greatly si... more Borrowing and extending the method of images we introduce a theoretical framework that greatly simplifies analytical and numerical investigations of the escape rate in open systems. As an example, we explicitly derive the exact size-and position-dependent escape rate in a Markov case for holes of finite size. Moreover, a general relation between the transfer operators of the closed and corresponding open systems, together with the generating function of the probability of return to the hole is derived. This relation is then used to compute the small hole asymptotic behavior, in terms of readily calculable quantities. As an example we derive logarithmic corrections in the second order term. Being valid for Markov systems, our framework can find application in many areas of the physical sciences such as information theory, network theory, quantum Weyl law and via Ulam's method can be used as an approximation method in general dynamical systems.
Journal of Physics A: Mathematical and General, 2004
We establish a deterministic technique to investigate transport moments of arbitrary order. The t... more We establish a deterministic technique to investigate transport moments of arbitrary order. The theory is applied to the analysis of different kinds of intermittent one-dimensional maps and the Lorentz gas with infinite horizon: the typical appearance of phase transitions in the spectrum of transport exponents is explained.
Journal of Physics A: Mathematical and General, 2006
Dynamical zeta functions provide a powerful method to analyze low dimensional dynamical systems w... more Dynamical zeta functions provide a powerful method to analyze low dimensional dynamical systems when the underlying symbolic dynamics is under control. On the other hand even simple one dimensional maps can show an intricate structure of the grammar rules that may lead to a non smooth dependence of global observable on parameters changes. A paradigmatic example is the fractal diffusion coefficient arising in a simple piecewise linear one dimensional map of the real line. Using the Baladi-Ruelle generalization of the Milnor-Thurnston kneading determinant we provide the exact dynamical zeta function for such a map and compute the diffusion coefficient from its smallest zero.