arXiv subjects

Esteban Guevara Hidalgo

Publications and source records attributed to Esteban Guevara Hidalgo.

15 recordsLinked to original sources

arXiv2018

Breakdown of the Finite-Time and -Population Scalings of the Large Deviation Function in the Large-Size Limit of a Contact Process

In a recent study, the finite-time ($t$) and -population size ($N_c$) scalings in the evaluation of a large deviation function (LDF) estimator were analyzed by means of the cloning algorithm. These scalings provide valuable information about the convergence of the LDF estimator in the infinite-$t$ and infinite-$N_c$ limits. For the cases analyzed in that study, the scalings of the systematic errors of the estimator were found to behave as $t^{-1}$ and $N_c^{-1}$ in the large-$t$ and large-$N_c$ asymptotics. Moreover, it was shown how this convergence speed can be used in order to extract an asymptotic limit which resulted to render a better LDF estimation in comparison to the standard estimator. However, the validity of these scaling laws and thus, the convergence of the estimator was proved only in systems for which the number of sites $L$ (where the dynamics occurs) was small. In this paper, the analysis is extended to a wider range of system sizes $L$. We show how the introduction of the exponents $γ_{t}$ and $γ_{N_c}$ allows to characterize the behavior of the LDF estimator for any system size. From these generalized $t^{-γ_{t}}$- and $N_{c}^{-γ_{N_c}}$- scalings, we verify that in the large-$L$ limit the $t^{-1}$- and $N_c^{-1}$-scalings are no longer valid. Moreover, as the convergence of the estimator relies on the positivity of these exponents, we show how for some cases $γ_{N_c}$ can be negative implying that the estimation provided by the cloning algorithm is no longer reliable.

cond-mat.stat-mech↗

arXiv2018

Cloning Algorithms: from Large Deviations to Population Dynamics

Population dynamics provides a numerical tool allowing for the study of rare events by means of simulating a large number of copies of the system, supplemented with a selection rule that favours the rare trajectories of interest. The cloning algorithm allows the estimation of a large deviation function (LDF) of additive observables in Markov processes. However, such algorithms are plagued by finite simulation time $t$ and finite population size $N_c$ effects that can render their use delicate. First, using a non-constant population approach, we analyze the small-$N_c$ effects in the initial transient regime. These effects play an important role in the numerical determination of LDF. We show how to overcome these effects by introducing a time delay in the evolution of populations, additional to the discarding of the initial regime of the population growth where these discreteness effects are strong. Then, the study of the finite-$t$ and finite-$N_c$ scalings in the LDF evaluation is done using two different versions of the algorithm, in discrete and continuous-time. We show that these scalings behave as $1/N_c$ and $1/t$ in the large-$N_c$ and large-$t$ asymptotics respectively. Moreover, we show that one can make use of this convergence speed in order to extract the asymptotic behavior in the infinite-$t$ and infinite-$N_c$ limits resulting in a better LDF estimation. These scalings are later generalized and evidence of a breakdown for large-size systems is presented.

cond-mat.stat-mech↗

arXiv2017

Discreteness Effects in Population Dynamics

We analyse numerically the effects of small population size in the initial transient regime of a simple example population dynamics. These effects play an important role for the numerical determination of large deviation functions of additive observables for stochastic processes. A method commonly used in order to determine such functions is the so-called cloning algorithm which in its non-constant population version essentially reduces to the determination of the growth rate of a population, averaged over many realizations of the dynamics. However, the averaging of populations is highly dependent not only on the number of realizations of the population dynamics, and on the initial population size but also on the cut-off time (or population) considered to stop their numerical evolution. This may result in an over-influence of discreteness effects at initial times, caused by small population size. We overcome these effects by introducing a (realization-dependent) time delay in the evolution of populations, additional to the discarding of the initial transient regime of the population growth where these discreteness effects are strong. We show that the improvement in the estimation of the large deviation function comes precisely from these two main contributions.

cond-mat.stat-mech↗

arXiv2017

Finite-time and finite-size scalings in the evaluation of large-deviation functions: Analytical study using a birth-death process

The Giardinà-Kurchan-Peliti algorithm is a numerical procedure that uses population dynamics in order to calculate large deviation functions associated to the distribution of time-averaged observables. To study the numerical errors of this algorithm, we explicitly devise a stochastic birth-death process that describes the time evolution of the population probability. From this formulation, we derive that systematic errors of the algorithm decrease proportionally to the inverse of the population size. Based on this observation, we propose a simple interpolation technique for the better estimation of large deviation functions. The approach we present is detailed explicitly in a two-state model.

cond-mat.stat-mech↗

arXiv2017

Finite-Time and -Size Scalings in the Evaluation of Large Deviation Functions: Numerical Approach in Continuous Time

Rare trajectories of stochastic systems are important to understand -- because of their potential impact. However, their properties are by definition difficult to sample directly. Population dynamics provides a numerical tool allowing their study, by means of simulating a large number of copies of the system, which are subjected to selection rules that favor the rare trajectories of interest. Such algorithms are plagued by finite simulation time- and finite population size- effects that can render their use delicate. In this paper, we present a numerical approach which uses the finite-time and finite-size scalings of estimators of the large deviation functions associated to the distribution of rare trajectories. The method we propose allows one to extract the infinite-time and infinite-size limit of these estimators which -- as shown on the contact process -- provides a significant improvement of the large deviation functions estimators compared to the the standard one.

cond-mat.stat-mech↗

arXiv2016

Maximum Entropy, the Collective Welfare Principle and the Globalization Process

Although both systems analyzed are described through two theories apparently different (quantum mechanics and game theory) it is shown that both are analogous and thus exactly equivalents. The quantum analogue of the replicator dynamics is the von Neumann equation. Quantum mechanics could be used to explain more correctly biological and economical processes. It could even encloses theories like games and evolutionary dynamics. We can take some concepts and definitions from quantum mechanics and physics for the best understanding of the behavior of economics and biology. Also, we could maybe understand nature like a game in where its players compete for a common welfare and the equilibrium of the system that they are members. All the members of our system will play a game in which its maximum payoff is the equilibrium of the system. They act as a whole besides individuals like they obey a rule in where they prefer to work for the welfare of the collective besides the individual welfare. A system where its members are in Nash Equilibrium (or ESS) is exactly equivalent to a system in a maximum entropy state. A system is stable only if it maximizes the welfare of the collective above the welfare of the individual. If it is maximized the welfare of the individual above the welfare of the collective the system gets unstable an eventually collapses. The results of this work shows that the "globalization" process has a behavior exactly equivalent to a system that is tending to a maximum entropy state and predicts the apparition of big common markets and strong common currencies that will find its "equilibrium" by decreasing its number until they get a state characterized by only one common currency and only one common market around the world.

q-fin.GN↗

arXiv2016

Common Markets, Strong Currencies & the Collective Welfare

The so called "globalization" process (i.e. the inexorable integration of markets, currencies, nation-states, technologies and the intensification of consciousness of the world as a whole) has a behavior exactly equivalent to a system that is tending to a maximum entropy state. This globalization process obeys a collective welfare principle in where the maximum payoff is given by the equilibrium of the system and its stability by the maximization of the welfare of the collective besides the individual welfare. This let us predict the apparition of big common markets and strong common currencies. They will reach the "equilibrium" by decreasing its number until they reach a state characterized by only one common currency and only one big common community around the world.

q-fin.GN↗

arXiv2016

Quantum Games and the Relationships between Quantum Mechanics and Game Theory

Quantum games have proposed a new point of view for the solution of the classical problems and dilemmas in game theory. Certain quantization relationships can be proposed with the objective that a game can be generalized into a quantum domain where the linear superposition of actions is allowed. This quantization let us describe and solution problems originated by conflicting or cooperative behaviors among the members of a system from the point of view of quantum mechanical interactions. This leads us to interesting aspects which only can be observed through the quantization of a game like the possibility of the entanglement between players, the definition of a socioeconomical temperature in a system, the collective welfare principle,the analysis of a game through elements of quantum information theory and the globalization process. The relationships between quantum mechanics and game theory are also studied and its shown how although both systems analyzed are described through two theories apparently different (quantum mechanics and game theory) both are analogous and thus exactly equivalents.

quant-ph↗

arXiv2016

The Why of the Applicability of Statistical Physics to Economics

We analyze the relationships between game theory and quantum mechanics and the extensions to statistical physics and information theory. We use certain quantization relationships to assign quantum states to the strategies of a player. These quantum states are contained in a density operator which describes the new quantum system. The system is also described through an entropy over its states, its evolution equation which is the quantum replicator dynamics and a criterion of equilibrium based on the Collective Welfare Principle. We show how the density operator and entropy are the bonds between game theories, quantum information theory and statistical physics. We propose the results of the study of these relationships like a reason of the applicability of physics in economics and the born of econophysics.

physics.soc-ph↗

arXiv2016

Quantum Econophysics

The relationships between game theory and quantum mechanics let us propose certain quantization relationships through which we could describe and understand not only quantum but also classical, evolutionary and the biological systems that were described before through the replicator dynamics. Quantum mechanics could be used to explain more correctly biological and economical processes and even it could encloses theories like games and evolutionary dynamics. This could make quantum mechanics a more general theory that we had thought. Although both systems analyzed are described through two apparently different theories (quantum mechanics and game theory) it is shown that both systems are analogous and thus exactly equivalents. So, we can take some concepts and definitions from quantum mechanics and physics for the best understanding of the behavior of economics and biology. Also, we could maybe understand nature like a game in where its players compete for a common welfare and the equilibrium of the system that they are members.

physics.soc-ph↗

arXiv2016

Introduction to the study of entropy in Quantum Games

The present work is an introductory study about entropy its properties and its role in quantum information theory. In a next work, we will use these results to the analysis of a quantum game described by a density operator and with its entropy equal to von Neumann's.

quant-ph↗

arXiv2016

Quantum Replicator Dynamics

We propose quantization relationships which would let us describe and solution problems originated by conflicting or cooperative behaviors among the members of a system from the point of view of quantum mechanical interactions. The quantum analogue of the replicator dynamics is the equation of evolution of mixed states from quantum statistical mechanics. A system and all its members will cooperate and rearrange its states to improve their present condition. They strive to reach the best possible state for each of them which is also the best possible state for the whole system. This led us to propose a quantum equilibrium in which a system is stable only if it maximizes the welfare of the collective above the welfare of the individual. If it is maximized the welfare of the individual above the welfare of the collective the system gets unstable and eventually it collapses.

quant-ph↗

arXiv2016

Quantum Games Entropy

We propose the study of quantum games from the point of view of quantum information theory and statistical mechanics. Every game can be described by a density operator, the von Neumann entropy and the quantum replicator dynamics. There exists a strong relationship between game theories, information theories and statistical physics. The density operator and entropy are the bonds between these theories. The analysis we propose is based on the properties of entropy, the amount of information that a player can obtain about his opponent and a maximum or minimum entropy criterion. The natural trend of a physical system is to its maximum entropy state. The minimum entropy state is a characteristic of a manipulated system i.e. externally controlled or imposed. There exist tacit rules inside a system that do not need to be specified or clarified and search the system equilibrium under the collective welfare principle. The other rules are imposed over the system when one or many of its members violate this principle and maximize its individual welfare at the expense of the group.

quant-ph↗

arXiv2016

Bin Size Independence in Intra-day Seasonalities for Relative Prices

In this paper we perform a statistical analysis over the returns and relative prices of the CAC $40$ and the S\&P $500$ with the purpose of analyzing the intra-day seasonalities of single and cross-sectional stock dynamics. In order to do that, we characterized the dynamics of a stock (or a set of stocks) by the evolution of the moments of its returns (and relative prices) during a typical day. We show that these intra-day seasonalities are independent of the size of the bin, and the index we consider, (but characteristic for each index) for the case of the relative prices but not for the case of the returns. Finally, we suggest how this bin size independence could be used to characterize "atypical days" for indexes and "anomalous behaviours" in stocks.

q-fin.ST↗

arXiv2012

New classes of spin chains from $(S\hat{O}_{(q)}(N)$, $S\hat{p}_{(q)}(N))$ Temperley-Lieb algebras: Data transmission and (q, N) parametrized entanglement entropies

A Temperley-Lieb algebra is extracted from the operator structure of a new class of $N^{2}\times N^{2}$ braid matrices presented and studied in previous papers and designated as $S\hat{O}_{(q)}(N)$, $S\hat{p}%_{(q)}(N)$ for the q-deformed orthogonal and symplectic cases respectively. Spin chain Hamiltonians are derived from such braid matrices and the corresponding chains are studied. Time evolutions of the chains and the possibility of transition of data encoded in the parameters of mixed states from one end to the other are analyzed. The entanglement entropies $% S(q,N)$ of eigenstates of the crucial operator, namely the q-dependent $% N^{2}\times N^{2}$ projector $P_{0}$ appearing in the corresponding Hamiltonian are obtained. Study of entanglements generated under the actions of \ $S\hat{O}(N)$, $S\hat{p}(N)$ braid operators, unitarized with imaginary rapidities is presented as a perspective.

math-ph↗