Random Exchanges Research Articles

Unraveling the dynamics of wealth inequality and the impact on social mobility and health disparities

Inequalities in wealth, income, access to food and healthcare have been rising worldwide in the past decades, approaching levels seen in the early 20th century. Here we study the relationships between wealth inequality and mobility for different segments of the population, comparing longitudinal surveys conducted in the USA and in Italy. The larger wealth inequality observed in the USA is reflected by poorer health conditions than in Italy. We also find that in both countries wealth mobility becomes slower at the two extremes of the wealth distribution. Households trapped in a state of persistent lack of wealth are generally experiencing greater food insecurity and poorer health than the general population. We interpret the observed association between inequality and immobility using a simple agent based model of wealth condensation driven by random returns and exchanges. The model describes well survey data on a qualitative level, but the mobility is generally overestimated by the model. We trace back this discrepancy to the way income is generated for low-wealth households which is not correctly accounted by the model. On the other hand, the model is excellent in describing the wealth dynamics within a restricted class of ultra-wealthy, as we demonstrate by analyzing billionaires lists. Our results suggest that different forms of inequality are intertwined and should therefore be addressed together.

Kinetic Models of Wealth Distribution with Extreme Inequality: Numerical Study of Their Stability against Random Exchanges.

In view of some recent reports on global wealth inequality, where a small number (often a handful) of people own more wealth than 50% of the world's population, we explored if kinetic exchange models of markets could ever capture features where a significant fraction of wealth can concentrate in the hands of a few as the market size N approaches infinity. One existing example of such a kinetic exchange model is the Chakraborti or Yard-Sale model; in the absence of tax redistribution, etc., all wealth ultimately condenses into the hands of a single individual (for any value of N), and the market dynamics stop. With tax redistribution, etc., steady-state dynamics are shown to have remarkable applicability in many cases in our extremely unequal world. We show that another kinetic exchange model (called the Banerjee model) has intriguing intrinsic dynamics, where only ten rich traders or agents possess about 99.98% of the total wealth in the steady state (without any tax, etc., like external manipulation) for any large N value. We will discuss the statistical features of this model using Monte Carlo simulations. We will also demonstrate that if each trader has a non-zero probability f of engaging in random exchanges, then these condensations of wealth (e.g., 100% in the hand of one agent in the Chakraborti model, or about 99.98% in the hands of ten agents in the Banerjee model) disappear in the large N limit. Moreover, due to the built-in possibility of random exchange dynamics in the earlier proposed Goswami-Sen model, where the exchange probability decreases with the inverse power of the wealth difference between trading pairs, one does not see any wealth condensation phenomena. In this paper, we explore these aspects of statistics of these intriguing models.

Maximum Entropy Design by a Markov Chain Process

Abstract In this article, we study an implementation of maximum entropy (ME) design utilizing a Markov chain. This design, which is also called the conditional Poisson sampling design, is difficult to implement. We first present a new method for calculating the weights associated with conditional Poisson sampling. Then, we study a very simple method of random exchanges of units, which allows switching from one sample to another. This exchange system defines an irreducible and aperiodic Markov chain whose ME design is the stationary distribution. The design can be implemented without enumerating all possible samples. By repeating the exchange process a large number of times, it is possible to select a sample that respects the design. The process is simple to implement, and its convergence rate has been investigated theoretically and by simulation, which led to promising results.

Measuring semantic gap between user-generated content and product descriptions through compression comparison in e-commerce

The significance of user-generated content as a source for business intelligence and analytics has been on the rise since the inception of electronic commerce platforms and has been solidified in the wake of the pandemic due to the prominence of electronic commerce as a sales channel. The prevailing approach to harnessing unstructured data involves the utilization of Artificial Intelligence; however, there exist simpler alternatives capable of yielding valuable information. This article introduces a methodology grounded in information theory to quantify the semantic disparity between the consumer community and product descriptions.This disparity can result in potential misunderstandings in the dialogue among consumers, and incidental costs in the dialogue between consumers and vendors. One plausible explanation for this disparity is that the terminology employed by consumers may possess different meanings compared to that utilized by product description writers. Our methodology employs large corpora of consumer reviews and product descriptions to quantify this semantic disparity across multiple electronic commerce domains through the implementation of random word exchanges and compression. Furthermore, we utilize neural word embeddings to identify specific words exhibiting the greatest semantic drift between reviews and descriptions, thereby providing lexical examples of these gaps. Our findings indicate that lower levels of lexical-semantic gap are associated with better consumer satisfaction.

Superballistic and superdiffusive scaling limits of stochastic harmonic chains with long-range interactions

We consider one-dimensional infinite chains of harmonic oscillators with random exchanges of momenta and long-range interaction potentials which have polynomial decay rate |x|−θ , x → ∞, θ > 1 where is the interaction range. The dynamics conserve total momentum, total length and total energy. We prove that the systems evolve macroscopically on superballistic space-time scale when 1 < θ < 3, when θ = 3, and hyperbolic space-time scale (yɛ −1, tɛ −1) when θ > 3. Combining our results and the results in (Suda 2021 Ann. Inst. Henri Poincare B 57 2268–2314), we show the existence of two different space-time scales on which the systems evolve. In addition, we prove the fluctuations of the normal modes of the superballistic wave equation, which are analogues of the Riemann invariants and capture fluctuations along the characteristics. For the normal modes, the space-time scale is superdiffusive when 2 < θ ⩽ 4 and diffusive when θ > 4.

Transnacionalismo Desmantelando o Cânon: Uma leitura próxima e distante de várias redes literárias transatlânticas na tradução

This essay argues that random acts of poetry translation in transnational context play a significant role in turning any apparently homogenous literary system into a network with many access points. In doing so, they overtly or covertly undermine the idea of a literary canon, since they position, more or less explicitly, such canon against their own literary taste and network of acquaintances. In addition, the lack of financial conditioning makes this kind of translation barters reach literary audiences more easily. Since these exchanges are more commonly initiated by translators working in lesser-known languages, it follows that transnational translation barters level out cultural imbalances by having the translator-poets’ work translated into languages of wider circulation. This contribution presents four kinds of transnational exchanges in Romanian context and argues that more complex translation mechanisms result into a more open, more diverse, and a more dynamic literary scene, in which translators play a prominent role. From a methodological point of view, this essay combines the traditional close reading of the texts and paratexts with quantitative analysis and network visualization to lay out the blueprint of Romanian translations of US and Canadian poetry in periodicals between 2007 and 2017 and quantify the number of random exchanges against a transnational backdrop.

Market Behavior and Evolution of Wealth Distribution: A Simulation Model Based on Artificial Agents

The aim of this work is to simulate a market behavior in order to study the evolution of wealth distribution. The numerical simulations are carried out on a simple economical model with a finite number of economic agents, which are able to exchange goods/services and money; the various agents interact each other by means of random exchanges. The model is micro founded, self-consistent, and predictive. Despite the simplicity of the model, the simulations show a complex and non-trivial behavior. First of all, we are able to recognize two solution classes, namely two phases, separated by a threshold region. The analysis of the wealth distribution of the model agents, in the threshold region, shows functional forms resembling empirical quantitative studies of the probability distributions of wealth and income in the United Kingdom and the United States. Furthermore, the decile distribution of the population wealth of the simulated model, in the threshold region, overlaps in a suggestive way with the real data of the Italian population wealth in the last few years. Finally, the results of the simulated model allow us to draw important considerations for designing effective policies for economic and human development.

Analysis of Solidarity Effect for Entropy, Pareto, and Gini Indices on Two-Class Society Using Kinetic Wealth Exchange Model.

It is well known that two different underlying dynamics lead to different patterns of income/wealth distribution such as the Boltzmann–Gibbs form for the lower end and the Pareto-like power-law form for the higher-end. The Boltzmann–Gibbs distribution is naturally derived from maximizing the entropy of random interactions among agents, whereas the Pareto distribution requires a rational approach of economics dependent on the wealth level. More interestingly, the Pareto regime is very dynamic, whereas the Boltzmann–Gibbs regime is stable over time. Also, there are some cases in which the distributions of income/wealth are bimodal or polymodal. In order to incorporate the dynamic aspects of the Pareto regime and the polymodal forms of income/wealth distribution into one stochastic model, we present a modified agent-based model based on classical kinetic wealth exchange models. First, we adopt a simple two-class society consisting of the rich and the poor where the agents in the same class engage in random exchanges while the agents in the different classes perform a wealth-dependent winner-takes-all trading. This modification leads the system to an extreme polarized society with preserving the Pareto exponent. Second, we incorporate a solidarity formation among agents belonging to the lower class in our model, in order to confront a super-rich agent. This modification leads the system to a drastic bimodal distribution of wealth with a varying Pareto exponent over varying the solidarity parameter, that is, the Pareto-regime becomes narrower and the Pareto exponent gets larger as the solidarity parameter increases. We argue that the solidarity formation is the key ingredient in the varying Pareto exponent and the polymodal distribution. Lastly, we take two approaches to evaluate the level of inequality of wealth such as Gini coefficients and the entropy measure. According to the numerical results, the increasing solidarity parameter leads to a decreasing Gini coefficient not linearly but nonlinearly, whereas the entropy measure is robust over varying solidarity parameters, implying that there is a trade-off between the intermediate party and the high end.

Hybrid-driven finite-time H∞ sampling synchronization control for coupling memory complex networks with stochastic cyber attacks

This paper proposes a new hybrid-driven (HD) sampling control strategy to investigate the finite-time (FT) H∞ synchronization issue for complex networks with stochastic cyber attacks (SCAs) and random memory information exchanges (RMIEs). The HD control scheme with random switching memory storage which is described by independent Bernoulli variables, is employed to alleviate the burden of the network. Different from the existing work, a novel memory interconnection Lyapunov–Krasovskii functional (LKF) is structured by taking full advantage of more information of sampling interval and state, and developing some new terms. Moreover, by utilizing the integral inequality treatment techniques together with stochastic analysis methods, several optimized control algorithms (OCAs) with a larger sampling period (LSP) are established for analyzing the FT synchronization issue of homologous error system with the optimal performance index. Then, the desired controllers can be synthesized by resorting to some matrix inequalities. Finally, the chua’s circuit model is presented to demonstrate the feasibility and validity of the proposed strategies.

Nanoscale Dynamics and Transport in Highly Ordered Low-Dimensional Water.

Highly ordered and highly cooperative water with properties of both solid and liquid states has been observed by means of neutron scattering in hydrophobic one-dimensional channels with van der Waals diameter of 0.78 nm. We have found that in the initial stages of adsorption water molecules occupy niches close to pore walls, followed later by the filling of the central pore area. Intensified by confinement, intermolecular water interactions lead to the formation of well-ordered hydrogen-bonded water chains and to the onset of cooperative vibrations. On the other hand, the same intermolecular interactions lead to two relaxation processes, the faster of which is the spontaneous position exchange between two water molecules placed 3.2-4 Å from each other. Self-diffusion in an axial pore direction is the result of those spontaneous random exchanges and is substantially slower than the self-diffusion in bulk water.

An open microscopic model of heat conduction: evolution and non-equilibrium stationary states

We consider a one-dimensional chain of coupled oscillators in contact at both ends with heat baths at different temperatures, and subject to an external force at one end. The Hamiltonian dynamics in the bulk is perturbed by random exchanges of the neighbouring momenta such that the energy is locally conserved. We prove that in the stationary state the energy and the volume stretch profiles, in large scale limit, converge to the solutions of a diffusive system with Dirichlet boundary conditions. As a consequence the macroscopic temperature stationary profile presents a maximum inside the chain higher than the thermostats temperatures, as well as the possibility of uphill diffusion (energy current against the temperature gradient).

Multiferroic Magnetic Spirals Induced by Random Magnetic Exchanges

Multiferroism can originate from the breaking of inversion symmetry caused by magnetic-spiral order. The usual mechanism for stabilizing a magnetic spiral is competition between magnetic exchange interactions differing by their range and sign, such as nearest-neighbor and next-nearest- neighbor interactions. Since the latter are usually weak the onset temperatures for multiferroism via this mechanism are typically low. By considering a realistic model for YBaCuFeO$_5$ we propose an alternative mechanism for magnetic-spiral order, and hence for multiferroism, that occurs at much higher temperatures. We show using Monte-Carlo simulations and electronic structure calculations based on density functional theory that the Heisenberg model on a geometrically non-frustrated lattice with only nearest-neighbor interactions can have a spiral phase up to high temperature when frustrating bonds are introduced randomly along a single crystallographic direction as caused, e.g., by a particular type of chemical disorder. This long-range correlated pattern of frustration avoids ferroelectrically inactive spin glass order. Finally, we provide an intuitive explanation for this mechanism and discuss its generalization to other materials.

From the Collapse of Signifiers to the Reconstruction of Language: A Psychoanalytic Reading of Robert Antelme’s The Human Race

From the Collapse of Signifiers to the Reconstruction of Language: A Psychoanalytic Reading of Robert Antelme’s The Human Race Dana Amir (bio) Robert Antelme, a member of a French Resistance group headed by Francois Mitterrand, was arrested by the Gestapo in June 1944, sent to Buchenwald, then to a work camp in Germany where he almost died. His moving memoir The Human Race (1957), his only book, is dedicated to the task of tracing the outline of the “human” from the perspective of both victim and witness. Its close observation of language’s most subtle nuances, in an uncompromising effort to represent the event in terms of the experience of the event rather than in the terms of the retrospective observer, makes its reading uncommonly demanding. This demand constitutes itself the gravest and most exposed self-testimony, one in which Antelme constantly warns against slipping into “comfortable” categories and against a possible escape into the saturated state of the “gratified” consciousness and conscience. Whether they concern the executioners or their victims, his descriptions are marked by the same gentle restlessness which turns its penetrating gaze upon the observer no less than upon the object of observation. Survivors’ experience can sometimes be condensed in a single word. Primo Levi (1979), describing a recurrent dream he has about Auschwitz, narrows it thus: “[A] single word, not imperious, but brief and subdued. It is the dawn command of Auschwitz, a foreign word, feared and expected: get up, ‘Wstawach’” (p. 380). Antelme’s nightmare also points at a word that became etched in his memory: “Fertig!”—”that’s it!” (Antelme, 1992/1957, p. 18) It is not just a word that holds the difference between the before and the after, the human and the inhuman, the pre-traumatic and the traumatic. Somehow this word is so powerful exactly because it is quoted (uttered as a direct speech) rather than told about: it is directed straight at the reader, a call one [End Page 685] cannot ignore, a rupture in the continuous language. Unlike the other words, it is uttered in its original language, with its original sound, thus becoming signifier and signified at one and the same time, something that by pointing at the rupture reconstitutes the very rupture itself. Antelme notices that in the seemingly random exchanges between the prisoners while they do their forced labor, they often mention things they owned in the past, especially the food they so badly lack now: Each of us will already be with somebody else in a little while. He’ll explain how his mother makes custard, because he needs to talk about custard and milk and bread [...] We’ll invite each other over to dinner, because by inviting each other we can picture still more meat, more bread. And then, if tonight there are seconds of soup, this guy who’s invited his buddy to come to dinner along with his wife may elbow him out of the way. (p. 44) Not only does speech turn from a mode of communication into a mode of survival—placing the other, the random listener, as a means through which speech can go on rather than as the subject of this speech—but it also turns words that are signifiers into signifieds: talk about bread takes the place of the bread; the invitation to a meal stretches the limits of the concrete stomach by increasing the number of imaginary guests. In the traumatized domain of language, the symbolic gradually collapses into the excess of real suffering. One of the major aspects of this suffering concerns the break in the continuity of identity: That particular Sunday I looked at length at my face in the mirror. It was neither beautiful nor ugly; it was dazzling. It had accompanied me here, here it was on the loose. It was without employment now, but it was still itself, the machine for expression. Next to it an SS mug was nothing. And the face of the guy who when his turn came was going to look at himself in it remained reduced to the state determined by the SS. Only the one in the mirror was distinct. It alone signified something...

Nonlinear Fluctuating Hydrodynamics in One Dimension: The Case of Two Conserved Fields

We study the BS model, which is a one-dimensional lattice field theory taking real values. Its dynamics is governed by coupled differential equations plus random nearest neighbor exchanges. The BS model has exactly two locally conserved fields. Through numerical simulations the peak structure of the steady state space-time correlations is determined and compared with nonlinear fluctuating hydrodynamics, which predicts a traveling peak with KPZ scaling function and a standing peak with a scaling function given by the completely asymmetric Levy distribution with parameter $\alpha = 5/3$. As a by-product, we completely classify the universality classes for two coupled stochastic Burgers equations with arbitrary coupling coefficients.

Clausius inequality and [formula omitted]-theorems for some models of random wealth exchange

We discuss a possibility of deriving an H-theorem for nonlinear discrete time evolution equation that describes random wealth exchanges. In such kinetic models economical agents exchange wealth in pairwise collisions just as particles in a gas exchange their energy. It appears useful to reformulate the problem and represent the dynamics as a combination of two processes. The first is a linear transformation of a two-particle distribution function during the act of exchange while the second one corresponds to new random pairing of agents and plays a role of some kind of feedback control. This representation leads to a Clausius-type inequality which suggests a new interpretation of the exchange process as an irreversible relaxation due to a contact with a reservoir of a special type. Only in some special cases when equilibrium distribution is exactly a gamma distribution, this inequality results in the H-theorem with monotonically growing ‘entropy’ functional which differs from the Boltzmann entropy by an additional term. But for arbitrary exchange rule the evolution has some features of relaxation to a non-equilibrium steady state and it is still unclear if any general H-theorem could exist.

Hydrodynamic Limit for a Hamiltonian System with Boundary Conditions and Conservative Noise

We study the hyperbolic scaling limit for a chain of N coupled anharmonic oscillators. The chain is attached to a point on the left and there is a force (tension) τ acting on the right. In order to provide good ergodic properties to the system, we perturb the Hamiltonian dynamics with random local exchanges of velocities between the particles, so that momentum and energy are locally conserved. We prove that in the macroscopic limit the distributions of the elongation, momentum and energy converge to the solution of the Euler system of equations in the smooth regime.

Impact of Bloom Filter on Infection Rate in Epidemic Forwarding for ICNs

Mobile ad hoc routing protocols fails in intermittently connected networks (ICN) (i.e. characterized by short-range communication and absence of connected path from source to destination). However, Epidemic routing techniques ensures eventual message delivery from source to destination even where there is never a connected path or when a network partition exists at the origin of message. Epidemic Routing uses random pair-wise messages exchanges between nodes with goals to maximize message delivery rate, minimize message latency, and the total resources consumed in message delivery. Epidemic routing uses summary vector to avoid useless transmission and redundancy. Further,to make summery vector efficient, epidemic routing can use bloom filter to significantly reduce the useless transmissions associated with the summary vector. However, the challenge for epidemic routing remains opens is to optimal design of summary vector size for finite buffer while keeping the benefits of infinite buffer space. This paper proposes an improved scheme of Bloom filter (named it modified bloom filter MBLF), which is tailored according to epidemic routing. We performed simulation to support our clam and observed that delivery ratio of MBLF with epidemic routing is 19 % higher then the traditional bloom filter. In this paper, we have proposed a bloom filter based epidemic forwarding for ICNs.

Convergence to an exponential wealth distribution in a random market model

We study the discrete-time model of López-Ruiz, López and Calbet, describing the evolution of a wealth distribution under random pairwise exchanges of wealth among agents. This requires the analysis of the behaviour of iterations of a non-linear operator defined on a space of probability distributions. We prove that, as conjectured by López-Ruiz, López and Calbet, starting from a general wealth distribution, the wealth distribution converges to the exponential equilibrium distribution. The proof employs a special metric defined on spaces of probability distributions through their Laplace transforms.

Modelling and Simulation of a Batch Poly(Vinyl Chloride) Reactor

A population balance model for batch suspension polymerization of vinyl chloride is presented. Break up into two equal volumes of droplets, binary aggregation and random mass exchanges between the colliding droplets are assumed, while the kinetic data of vinyl chloride polymerization are taken from the literature. The model and the process are analyzed by simulation applying a novel Monte Carlo method taking into account breakage and aggregation of droplets as well as micromixing induced by droplet binary collisions as stochastic discrete event processes. The results revealed that this method of modelling describes phenomena in suspension polymerization of vinyl chloride properly.

Monotonic entropy growth for a nonlinear model of random exchanges

We present a proof of the monotonic entropy growth for a nonlinear discrete-time model of a random market. This model, based on binary collisions, also may be viewed as a particular case of Ulam's redistribution of energy problem. We represent each step of this dynamics as a combination of two processes. The first one is a linear energy-conserving evolution of the two-particle distribution, for which the entropy growth can be easily verified. The original nonlinear process is actually a result of a specific "coarse graining" of this linear evolution, when after the collision one variable is integrated away. This coarse graining is of the same type as the real space renormalization group transformation and leads to an additional entropy growth. The combination of these two factors produces the required result which is obtained only by means of information theory inequalities.