Qiuping Alexandre Wang

ESIEA Paris France · Campus Ivry; Laval

This work is a formulation of the least action principle for classical mechanical dissipative systems. We consider a whole conservative system composed of a damped moving body and its environment receiving the dissipated energy. This composite system has a conservative Hamiltonian H = K 1 + V 1 + H 2 where K 1 is the kinetic energy of the moving bo...

The objective of this work is to provide a mathematical proof of time irreversibility on the ground of indeterministic motion. The starting point is the formulation of a mathematical definition of time implementing a widely accepted old idea associating time with movement or change, and establishing a univocal link between time and trajectory of mo...

This paper provides a derivation of Zipf-Pareto laws directly from the principle of least effort. A probabilistic functional of efficiency is introduced as the consequence of an extension of the nonadditivity of the efficiency of thermodynamic engine to a large number of living agents assimilated to engines, all randomly distributed over their outp...

The discovery of the second law of thermodynamics is shortly revisited, with a stress on the unbreakable connection between the second law and the law of energy conservation. The aim is to remind that the second law is an inviolable iron rule. Any presumable violation of this law, even a probabilistic one hinted in the probabilistic interpretation...

The aim of this work is to provide a possible philosophical motivation to the variational principles of physics in general and a possible way to unify the axiomatizations of mechanics theories. The leitmotif of this work is a dialectical view of the world: any smooth motion in nature is the consequence of the interplay and dynamical balance between...

The principle of least effort is believed to be a universal rule for living systems. Its application to the derivation of the power law probability distributions of living systems has long been challenging. Recently, a measure of efficiency was proposed as a tool of deriving Zipf's and Pareto's laws directly from the principle of least effort. The...

In this paper we present a formulation of the stochastic least action principle (SAP) to encompass random movements with black swan events (of non dissipative systems) in terms of heavy tailed distributions. The black swan events are rare and drastic events, such as earthquakes and financial crisis. It has been observed that the Tsallis entropy sui...

This work is a derivation of Zipf-Pareto laws directly from the principle of least effort with the help of a system-independent functional of efficiency inspired by the nonadditivity of the efficiency of thermodynamic engine. This probabilistic expression of efficiency is applied to living systems or systems driven by a large number of living agent...

The principle of least effort is believed to be a universal rule for living systems. Its application to the derivation of the power law probability distributions of living systems has long been challenging. Recently, a measure of efficiency was proposed as a tool of deriving Zipf’s and Pareto’s laws directly from the principle of least effort. The...

A numerical experiment of ideal stochastic motion of a particle subject to conservative forces and Gaussian noise reveals that the path probability depends exponentially on action. This distribution implies a fundamental principle generalizing the least action principle of the Hamiltonian-Lagrangian mechanics and yields an extended formalism of mec...

"Each individual will adopt a course of action that will involve the expenditure of the probably least average of his work." This statement was named "the principle of least effort". The principle of least effort is often known as a "deterministic description of human behavior". In this paper, we present a brief introduction of this principle. Appl...

This work is an analytical and numerical study of the composition of several fractals into one and of the relation between the composite dimension and the dimensions of the component fractals. In the case of composition of standard IFS with segments of equal size, the composite dimension can be expressed as a function of the component dimensions. B...

Probabilistic uncertainty analysis is a common means of evaluating mathematical models. In mathematical modeling, the uncertainty in input variables is specified through distribution laws. Its contribution to the uncertainty in model response is usually analyzed by assuming that input variables are independent of each other. However, correlated par...

The formation of continuous opinion dynamics is investigated based on a virtual gambling mechanism where agents fight for a limited resource. We propose a model with agents holding opinions between and 1. Agents are segregated into two cliques according to the sign of their opinions. Local communication happens only when the opinion distance betwee...

In the complexity modeling, variance decomposition technique is widely used for the quantification of the variation in the output variables explained by covariates. In this work, the satisfaction of sampling-based variance decomposition strategy (SVDS) is firstly testified in the implementation of an analytic method for uncertainty and sensitivity...

An analytic formula is proposed to characterize the variance propagation from correlated input variables to the model response, by using multi-variate Taylor series. With the formula, partial variance contributions to the model response are then straightforwardly evaluated in the presence of input correlations. Additionally, an arbitrary variable i...

Sensitivity analysis is concerned with understanding how the model output depends on uncertainties (variances) in inputs and then identifies which inputs are important in contributing to the prediction imprecision. Uncertainty determination in output is the most crucial step in sensitivity analysis. In the present paper, an analytic expression, whi...

In this paper, we investigate the random walks on metro systems in 28 cities from worldwide via the Laplacian spectrum to realize the trapping process on real systems. The average trapping time is a primary description to response the trapping process. Firstly, we calculate the mean trapping time to each target station and to each entire system, re...

It is shown that an oldest form of variational calculus of mechanics, the Maupertuis least action principle, can be used as a simple and powerful approach for the formulation of the variational principle for damped motions, allowing a simple derivation of the Lagrangian mechanics for any dissipative systems and an a connection of the optimization o...

In this paper, we aim at investigating how the energy of a graph depends upon its underlying topological structure for regular and sparse scale free networks. Firstly, the spectra and energies of some simple regular graphs are calculated exactly and an exact expression is derived for the eigenvalues of adjacency matrix of regular graphs with degree...

Complex networks have been extensively studied across many fields, especially in interdisciplinary areas. It has since long been recognized that topological structures and dynamics are important aspects for capturing the essence of complex networks. The recent years have also witnessed the emergence of several new elements which play important role...

In this work, we study the problem of diffusing a product (idea, opinion, disease etc.) among agents on spatial network. The network is constructed by random addition of nodes on the planar. The probability for a previous node to be connected to the new one is inversely proportional to their spatial distance to the power of α. The diffusion rate be...

Inspired by the maxim ”long union divides and long division unites”, a phenomenological model with the simplification of real social networks is proposed to explore the evolutionary features of these networks composed of the entities whose behaviors are dominated by two events: union and division. The nodes are endowed with some attributes such as...

This work is an analytical calculation of the path probability for random dynamics of mechanical system described by Langevin equation with Gaussian noise. The result shows an exponential dependence of the probability on the action. In the case of non dissipative limit, the action is the usual one in mechanics in accordance with the previous result...

This work is an analytical and numerical study of the composition of several fractals into one and of the relation between the composite dimension and the dimensions of the component fractals. In the case of composition of standard IFS with segments of equal size, the composite dimension can be expressed as a function of the component dimensions. B...

A numerical experiment of ideal stochastic motion of a particle subject to conservative forces and Gaussian noise reveals that the path probability depends exponentially on action. This distribution implies a fundamental principle generalizing the least action principle of the Hamiltonian/Lagrangian mechanics and yields an extended formalism of mec...

The Zipf's law is the major regularity of statistical linguistics that served as a prototype for rank-frequency relations and scaling laws in natural sciences. Here we show that the Zipf's law -- together with its applicability for a single text and its generalizations to high and low frequencies including hapax legomena -- can be derived from assu...

We investigate, by numerical simulation, the path probability of non dissipative mechanical systems undergoing stochastic motion. The aim is to search for the relationship between this probability and the usual mechanical action. The model of simulation is a one-dimensional particle subject to conservative force and Gaussian random displace-ment. T...

The Zipf's law states that the ordered frequencies $f_1>f_2> ...$ of different words in a text hold $f_r\propto r^{-\gamma}$ with $\gamma\approx 1$ and rank $r$. The law applies to many languages with alphabetical writing systems, but was so far found to be absent for the rank-frequency relation of the Chinese characters, the main (and oldest) exam...

We study the minimal thermodynamically consistent model for an adaptive machine that transfers particles from a higher chemical potential reservoir to a lower one. This model describes essentials of the inhomogeneous catalysis. It is supposed to function with the maximal current under uncertain chemical potentials: if they change, the machine tunes...

This work is a modeling of evolutionary networks embedded in one or two dimensional configuration space. The evolution is based on two attachments depending on degree and spatial distance. The probability for a new node nn to connect with a previous node ii at distance rnirni follows aki∑jkj+(1−a)rni−α∑jrnj−α, where kiki is the degree of node ii, α...

A least action principle for damping motion has been previously proposed with a Hamiltonian and a Lagrangian containing the energy dissipated by friction. Due to the space-time nonlocality of the Lagrangian, mathematical uncertainties persist about the appropriate variational calculus and the nature (maxima, minima and inflection) of the stationary...

The epidemic spreading on spatial-driven network is studied with the spatial susceptible-infected-susceptible (SIS) model. The network is constructed by random addition of nodes on the plan. The probability for a previous node to be connected to the new one is inversely proportional to their spatial distance to the power α. The spreading rate betwe...

This work is devoted to the modeling of energy fluctuation effect on the behavior of small classical thermodynamic systems. It is known that when an equilibrium system gets smaller and smaller, one of the major quantities that becomes more and more uncertain is its internal energy. These increasing fluctuations can considerably modify the original...

The Casimir effect of an ideal Bose gas trapped in a generic power-law potential and confined between two slabs with Dirichlet, Neumann, and periodic boundary conditions is investigated systematically, based on the grand potential of the ideal Bose gas, the Casimir potential and force are calculated. The scaling function is obtained and discussed....

The mathematical expression of nonadditivity X(1 ∪ 2) = X(1) + X(2) + αX(1)X(2) has been frequently used for the development of statistical physics for nonadditive system, where X is entropy or energy, and α is hoped to be a parameter characterising the nonadditive property of the composite system (1 ∪ 2). Here we show that this relationship cannot...

Ranking is a ubiquitous phenomenon in the human society. By clicking the web pages of Forbes, you may find all kinds of rankings, such as world's most powerful people, world's richest people, top-paid tennis stars, and so on and so forth. Herewith, we study a specific kind, sports ranking systems in which players' scores and prize money are calcula...

A simple model is presented to illustrate the equilibrium thermostatistics of a nonentensive finite system. Interaction between the finite system and the reservoir is taken into account as a nonextensive term λH1H2λH1H2 in the expression of total energy (H1H1 and H2H2 are the energy of the finite system and the reservoir respectively, λλ is nonaddi...

Based on the canonical ensemble, we suggested the simple scheme for taking into account Gaussian fluctuations in a finite system of ideal boson gas. Within framework of scheme we investigated the influence of fluctuations on the particle distribution in Bose -gas for two cases - with taking into account the number of particles in the ground state a...

We present the result of a dual modeling of opinion network. The model complements the agent-based opinion models by attaching to the social agent (voters) network a political opinion (party) network having its own intrinsic mechanisms of evolution. These two sub-networks form a global network which can be either isolated from or dependent on the e...

The path probability of stochastic motion of non dissipative or quasi-Hamiltonian systems is investigated by numerical experiment. The simulation model generates ideal one-dimensional motion of particles subject only to conservative forces in addition to Gaussian distributed random displacements. In the presence of dissipative forces, application o...

The aim of this work is to formulate for dissipative system a least action principle that can keep all the main features of the conventional Hamiltonian/Lagrangian mechanics such as the Hamiltonian, Lagrangian and Hamilton-Jacobi equations, three formulations of the classical mechanics, with a unique single Lagrangian function which has the usual c...

This work reports on numerical simulations of Brownian motion in the non-dissipative limit. The objective was to prove the existence of path probability and to compute probability values for some sample paths. By simulating a large number of particles moving from point to point under Gaussian noise and conservative forces, we numerically determine...

Varentropy is used as a general measure of probabilistic uncertainty for a complex network, inspired by the first and second laws of thermodynamics, but not limited to the equilibrium system. By exploring the relationship between the varentropy of the scale free distribution and the exponent of power laws as well as network size, we get the optimal...

We investigate the energy nonadditivity relationship E(A∪B) = E(A) + E(B) + αE(A)E(B) which is often considered in the development of the statistical physics of nonextensive systems. It was recently found that α in this equation was not constant for a given system in a given situation and could not characterize nonextensivity for that system. In th...

English and Chinese language frequency time series (LFTS) were constructed based on an English and two Chinese novels. Methods of statistical hypothesis testing were adopted to test the nonlinear properties of the LFTS. Results suggest the series exhibited non-normal, auto-correlative, and stationary characteristics. Moreover, we found that LFTS fo...

We construct a weighted network of scientific collaboration in computational geometry and study the statistical properties of the network. In addition, we introduce a parameter called the collaboration relationship parameter to measure the collaboration between scientists. The collaboration relationship parameter of two scientists depends not only...

On the basis of the relative daily logarithmic returns of 88 different funds in the Chinese fund market (CFM) from June 2005 to October 2009, we construct the cross-correlation matrix of the CFM. It is shown that the logarithmic returns follow an exponential distribution, which is commonly shared by some emerging markets. We hereby analyze the stat...

By testing 88 different funds of the Chinese fund market (CFM), we find fractal behavior and long-range correlations in the return series, which are insensitive to the kind of funds. Meanwhile, a power-law relationship between the deviation DD of prices and the Hurst exponent HH has been obtained, which may be useful for predicting the price time s...

We present the result of a dual modeling of opinion networks. The model complements the agent-based opinion models by attaching to the social agent (voters) network a political opinion (party) network having its own intrinsic mechanisms of evolution. These two subnetworks form a global network, which can be either isolated from, or dependent on, th...

The exponential degree distribution has been found in many real world complex networks, based on which, the random growing process has been introduced to analyze the formation principle of such kinds of networks. Inspired from the non-equilibrium network theory, we construct the network according to two mechanisms: growing and adjacent random attac...

This work is a numerical experiment of stochastic motion of conservative Hamiltonian system or weakly damped Brownian particles. The objective is to prove the existence of path probability and to compute its values. By observing a large number of particles moving from one point to another under Gaussian noise and conservative forces, it is determin...

Recent result of the numerical simulation of stochastic motion of conservative mechanical or weakly damped Brownian motion subject to conservative forces reveals that, in the case of Gaussian random forces, the path probability depends exponentially on Lagrangian action. This distribution implies a fundamental principle generalizing the least actio...

Deviation from simple power law is widely observed in complex networks. We introduce a model including possible mechanisms leading to the deviation. In this model, probabilistic addition of nodes and links, as well as rewiring of links are considered. Using master equation, through theoretical calculation and numerical simulation, double power laws...

The double power-law function, p(x) ~ 1/(xb + cxd) where x is the degree of one node, and b, c, d are parameters, is used to fit the degree distribution of urban road network of Le Mans city in France. It is called "double power-law" since it behaves as two power laws respectively, in large and small degree region with a crossing in-between. The po...

Based on the q-exponential distribution which has been observed in more and more physical systems, the varentropy method is used to derive the uncertainty measure of such an abnormal distribution function. The uncertainty measure obtained here can be considered as a new entropic form for the abnormal physical systems with complex interaction. The e...

Based on the grand potentials of ideal quantum gases, the number of particles, internal energy, three diagonal components of the pressure tensor, and other thermodynamic quantities of the ideal quantum gas systems confined in a rectangular box are analytically derived. It is found that the internal energy of the systems is non-extensive and that th...

For a random variable x we can define a variational relationship with practical physical meaning as dI=dbar x-/line{dx}, where I is the uncertainty measure. With the help of a generalized definition of expectation, bar x=∑ ig(\{p_i\})x_i, we can find the concrete forms of the maximizable entropies for any given probability distribution function, wh...

This is a general description of a probabilistic formalism of mechanics, i.e., an extension of the Newtonian mechanics principles to the systems undergoing random motion. From an analysis of the induction procedure from experimental data to the Newtonian laws, it is shown that the experimental verification of Newton law in a random motion implies a...

An urban road network of Le Mans in France is analyzed. Some topological properties of network are investigated, such as degree distribution, clustering coefficient, diameter, and characteristic path length. These results suggest that our network is a "small- world" network with short average shortest path and large clustering coefficient. Furtherm...

We introduce a new universality class of one-dimensional iteration models giving rise to self-similar motion. The curves of the mean square displacement versus time show that the motion is a kind of anomalous diffusion with the diffusion coefficient depending on the self-similar rates. Moreover, it is found that the distribution of the displacement...

This is a note showing that, contrary to our lasting belief, the nonadditivity X(1+2)=X(1)+X(2)+\alpha X(1)X(2) is not a true physical property. \alpha in this expression cannot be unique for a given system. It unavoidably depends on how one mathematically divides the system and cannot be used to characterize nonadditivity. As a matter of fact, its...

By using a functional of probability distributions, several different statistical physics including extensive and nonextensive statistics are unified in a general formalism. It’s shown that the equivalence between the Maxent approach and the relation dU = TdS can be seen from the virtual work principle of mechanics. From dU = TdS, any entropic form...

An abstract mathematical framework is presented in this paper as a unification of several deformed or generalized algebra proposed recently in the context of generalized statistical theories intended to treat certain complex thermodynamic or statistical systems. It is shown that, from a mathematical point of view, any bijective function can in prin...

A stochastic action principle for random dynamics is revisited. Numerical diffusion experiments are carried out to show that the diffusion path probability depends exponentially on the Lagrangian action . This result is then used to derive the Shannon measure for path uncertainty. It is shown that the maximum entropy principle and the least action...

With the help of a general expression of the entropies in extensive and nonextensive systems, some important relations between thermodynamics and statistical mechanics are revealed through the views of thermodynamics and statistical physics. These relations are proved through the MaxEnt approach once again. It is found that for a reversible isother...

Based on the principle of maximum entropy, the q-exponential distribution can be derived from several different nonextensive entropies including the incomplete entropy. It is widely used in nonextensive statistical mechanics. In the present paper, it is shown that the incomplete expectation value and incomplete entropy are stable under small deform...

We investigate the statistical properties of the empirical data taken from the Chinese stock market during the time period from January, 2006 to July, 2007. By using the methods of detrended fluctuation analysis (DFA) and calculating correlation coefficients, we acquire the evidence of strong correlations among different stock types, stock index, s...