arXiv subjects

Filippo Palombi

Publications and source records attributed to Filippo Palombi.

15 recordsLinked to original sources

arXiv2020

Coevolutionary dynamics of a variant of the cyclic Lotka-Volterra model with three-agent interactions

We study a variant of the cyclic Lotka-Volterra model with three-agent interactions. Inspired by a multiplayer variation of the Rock-Paper-Scissors game, the model describes an ideal ecosystem in which cyclic competition among three species develops through cooperative predation. Its rate equations in a well-mixed environment display a degenerate Hopf bifurcation, occurring as reactions involving two predators plus one prey have the same rate as reactions involving two preys plus one predator. We estimate the magnitude of the stochastic noise at the bifurcation point, where finite size effects turn neutrally stable orbits into erratically diverging trajectories. In particular, we compare analytic predictions for the extinction probability, derived in the Fokker-Planck approximation, with numerical simulations based on the Gillespie stochastic algorithm. We then extend the analysis of the phase portrait to heterogeneous rates. In a well-mixed environment, we observe a continuum of degenerate Hopf bifurcations, generalizing the above one. Neutral stability ensues from a complex equilibrium between different reactions. Remarkably, on a two-dimensional lattice, all bifurcations disappear as a consequence of the spatial locality of the interactions. In the second part of the paper, we investigate the effects of mobility in a lattice metapopulation model with patches hosting several agents. We find that strategies propagate along the arms of rotating spirals, as they usually do in models of cyclic dominance. We observe propagation instabilities in the regime of large wavelengths. We also examine three-agent interactions inducing nonlinear diffusion.

q-bio.PE↗

arXiv2019

A perturbative approach to the reconstruction of the eigenvalue spectrum of a normal covariance matrix from a spherically truncated counterpart

In this paper we propose a perturbative method for the reconstruction of the covariance matrix of a multinormal distribution, under the assumption that the only available information amounts to the covariance matrix of a spherically truncated counterpart of the same distribution. We expand the relevant equations up to the fourth perturbative order and discuss the analytic properties of the first few perturbative terms. We finally compare the proposed approach with an exact iterative algorithm (presented in Palombi et al. (2017)) in the hypothesis that the spherically truncated covariance matrix is estimated from samples of various sizes.

math.ST↗

arXiv2017

Influence of periodic external fields in multiagent models with language dynamics

We investigate large-scale effects induced by external fields, phenomenologically interpreted as mass media, in multiagent models evolving with the microscopic dynamics of the binary naming game. In particular, we show that a single external field, broadcasting information at regular time intervals, can reverse the majority opinion of the population, provided the frequency and the effectiveness of the sent messages lie above well-defined thresholds. We study the phase structure of the model in the mean field approximation and in numerical simulations with several network topologies. We also investigate the influence on the agent dynamics of two competing external fields, periodically broadcasting different messages. In finite regions of the parameter space we observe periodic equilibrium states in which the average opinion densities are reversed with respect to naive expectations. Such equilibria occur in two cases: (i) when the frequencies of the competing messages are different but close to each other; (ii) when the frequencies are equal and the relative time shift of the messages does not exceed half a period. We interpret the observed phenomena as a result of the interplay between the external fields and the internal dynamics of the agents and conclude that, depending on the model parameters, the naming game is consistent with scenarios of first- or second-mover advantage (to borrow an expression from the jargon of business strategy).

physics.soc-ph↗

arXiv2017

Topological aspects of the multi-language phases of the Naming Game on community-based networks

The Naming Game is an agent-based model where individuals communicate to name an initially unnamed object. On a large class of networks continual pairwise interactions lead the system to an ultimate consensus state, in which agents converge on a globally shared name. Soon after the introduction of the model, it was observed in literature that on community-based networks the path to consensus passes through metastable multi-language states. Subsequently, it was proposed to use this feature as a mean to discover communities in a given network. In this paper we show that metastable states correspond to genuine multi-language phases, emerging in the thermodynamic limit when the fraction of links connecting communities drops below critical thresholds. In particular, we study the transition to multi-language states in the stochastic block model and on networks with community overlap. We also examine the scaling of critical thresholds under variations of topological properties of the network, such as the number and relative size of communities and the structure of intra-/inter-community links. Our results provide a theoretical justification for the proposed use of the model as a community-detection algorithm.

physics.soc-ph↗

arXiv2016

On the Power-Law Tails of Vote Distributions in Proportional Elections

In proportional elections with open lists the excess of preferences received by candidates with respect to the list average is known to follow a universal lognormal distribution. We show that lognormality is broken provided preferences are conditioned to lists with many candidates. In this limit power-law tails emerge. We study the large-list limit in the framework of a quenched approximation of the word-of-mouth model introduced by Fortunato and Castellano (Phys.Rev.Lett.99(13):138701,2007), where the activism of the agents is mitigated and the noise of the agent-agent interactions is averaged out. Then we argue that our analysis applies mutatis mutandis to the original model as well.

physics.soc-ph↗

arXiv2015

Use of Dirichlet Distributions and Orthogonal Projection Techniques for the Fluctuation Analysis of Steady-State Multivariate Birth-Death Systems

Approximate weak solutions of the Fokker-Planck equation can represent a useful tool to analyze the equilibrium fluctuations of birth-death systems, as they provide a quantitative knowledge lying in between numerical simulations and exact analytic arguments. In the present paper, we adapt the general mathematical formalism known as the Ritz-Galerkin method for partial differential equations to the Fokker-Planck equation with time-independent polynomial drift and diffusion coefficients on the simplex. Then, we show how the method works in two examples, namely the binary and multi-state voter models with zealots.

physics.soc-ph↗

arXiv2014

Stochastic Dynamics of the Multi-State Voter Model over a Network based on Interacting Cliques and Zealot Candidates

The stochastic dynamics of the multi-state voter model is investigated on a class of complex networks made of non-overlapping cliques, each hosting a political candidate and interacting with the others via Erdős-Rényi links. Numerical simulations of the model are interpreted in terms of an ad-hoc mean field theory, specifically tuned to resolve the inter/intra-clique interactions. Under a proper definition of the thermodynamic limit (with the average degree of the agents kept fixed while increasing the network size), the model is found to display the empirical scaling discovered by Fortunato and Castellano (Phys Rev Lett 99(13):138701, 2007), while the vote distribution resembles roughly that observed in Brazilian elections.

physics.soc-ph↗

arXiv2014

Numerical reconstruction of the covariance matrix of a spherically truncated multinormal distribution

In this paper we relate the matrix $S_B$ of the second moments of a spherically truncated normal multivariate to its full covariance matrix $Σ$ and present an algorithm to invert the relation and reconstruct $Σ$ from $S_B$. While the eigenvectors of $Σ$ are left invariant by the truncation, its eigenvalues are non-uniformly damped. We show that the eigenvalues of $Σ$ can be reconstructed from their truncated counterparts via a fixed point iteration, whose convergence we prove analytically. The procedure requires the computation of multidimensional Gaussian integrals over a Euclidean ball, for which we extend a numerical technique, originally proposed by Ruben in 1962, based on a series expansion in chi-square distributions. In order to study the feasibility of our approach, we examine the convergence rate of some iterative schemes on suitably chosen ensembles of Wishart matrices. We finally discuss the practical difficulties arising in sample space and outline a regularization of the problem based on perturbation theory.

math.ST↗

arXiv2013

A note on the variance of the square components of a normal multivariate within a Euclidean ball

We present arguments in favour of the inequalities $var(X_n^2|X \in B_v(ρ)) \le 2λ_n E[X_n^2|X \in B_v(ρ)]$, where $X \sim N_v(0,Λ)$ is a normal vector in $v\ge 1$ dimensions, with zero mean and covariance matrix $Λ= \diag(λ)$, and $B_v(ρ)$ is a centered $v$-dimensional Euclidean ball of square radius $ρ$. Such relations lie at the heart of an iterative algorithm, proposed in ref. [1] to perform a reconstruction of $Λ$ from the covariance matrix of $X$ conditioned to $B_v(ρ)$. In the regime of strong truncation, i.e. for $ρ\lesssim λ_n$, the above inequality is easily proved, whereas it becomes harder for $ρ\gg λ_n$. Here, we expand both sides in a function series controlled by powers of $λ_n/ρ$ and show that the coefficient functions of the series fulfill the inequality order by order if $ρ$ is sufficiently large. The intermediate region remains at present an open challenge.

math.PR↗

arXiv2010

Universality of the topological susceptibility in the SU(3) gauge theory

The definition and computation of the topological susceptibility in non-abelian gauge theories is complicated by the presence of non-integrable short-distance singularities. Recently, alternative representations of the susceptibility were discovered, which are singularity-free and do not require renormalization. Such an expression is here studied quantitatively, using the lattice formulation of the SU(3) gauge theory and numerical simulations. The results confirm the expected scaling of the susceptibility with respect to the lattice spacing and they also agree, within errors, with computations of the susceptibility based on the use of a chiral lattice Dirac operator.

hep-lat↗

arXiv2008

Fluctuations and reweighting of the quark determinant on large lattices

We propose to stabilise HMC simulations of lattice QCD with very light Wilson quarks by splitting the quark determinant into two factors and by treating the factor that includes the contribution of the low modes of the Dirac operator as a reweighting factor. In general, determinant reweighting becomes inefficient on large lattices, because the statistical fluctuations of quark determinants increase exponentially with the lattice volume. Random matrix theory and some numerical studies now suggest that the low-mode contribution to the determinant behaves differently, which allows factorisations to be devised that preserve the efficiency of the simulation on large lattices.

hep-lat↗

arXiv2008

Non-perturbative renormalization of the static vector current and its O(a)-improvement in quenched QCD

We carry out the renormalization and the Symanzik O(a)-improvement programme for the static vector current in quenched lattice QCD. The scale independent ratio of the renormalization constants of the static vector and axial currents is obtained non-perturbatively from an axial Ward identity with Wilson-type light quarks and various lattice discretizations of the static action. The improvement coefficients cVstat and bVstat are obtained up to O(g_0^4)-terms by enforcing improvement conditions respectively on the axial Ward identity and a three-point correlator of the static vector current. A comparison between the non-perturbative estimates and the corresponding one-loop results shows a non-negligible effect of the O(g_0^4)-terms on the improvement coefficients but a good accuracy of the perturbative description of the ratio of the renormalization constants.

hep-lat↗

arXiv2007

Non-perturbative renormalization of static-light four-fermion operators in quenched lattice QCD

We perform a non-perturbative study of the scale-dependent renormalization factors of a multiplicatively renormalizable basis of $Δ{B}=2$ parity-odd four-fermion operators in quenched lattice QCD. Heavy quarks are treated in the static approximation with various lattice discretizations of the static action. Light quarks are described by non-perturbatively ${\rm O}(a)$ improved Wilson-type fermions. The renormalization group running is computed for a family of Schroedinger functional (SF) schemes through finite volume techniques in the continuum limit. We compute non-perturbatively the relation between the renormalization group invariant operators and their counterparts renormalized in the SF at a low energy scale. Furthermore, we provide non-perturbative estimates for the matching between the lattice regularized theory and all the SF schemes considered.

hep-lat↗

arXiv2004

NLO anomalous dimension of multiplicatively renormalizable four-fermion operators in Schroedinger Functional schemes

Renormalization constants for multiplicatively renormalizable parity-odd four-fermion operators are computed in various different Schroedinger Functional (SF) schemes and lattice regularizations with Wilson quarks at one-loop order in perturbation theory. Our results are used in the calculation of their NLO anomalous dimensions, through matching to continuum schemes. They also enable a comparison of the two-loop perturbative RG running to the previously obtained nonperturbative one in the region of small renormalized coupling.

hep-lat↗

arXiv2003

Heavy-light decay constants from the step scaling method

We discuss results for the heavy-light decay constants in the continuum limit of quenched lattice QCD from finite size scaling techniques. We disentangle the simultaneous presence of the different energy scales characterizing heavy-light physics by first performing simulations at the unphysical volume L_0=0.4 fm, and then evolving the results towards the infinite volume. We find f_{Bs}= 192(6)(4) MeV and f_{Ds}=240(5)(5) MeV. The approach has been developed by the APE group at the University of Rome ``Tor Vergata''.

hep-lat↗