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In this paper we consider dynamics of non-stationary processes that follow the MaxEnt principle. We derive a set of equations describing dynamics of a system for Shannon and Tsallis entropies. Systems with discrete probability distribution are considered under mass conservation and energy conservation constraints. The existence and uniqueness of solution are established and asymptotic stability of the equilibrium is proved. Equations are derived based on the speed-gradient principle originated in control theory.

The determination of the probability distribution function (PDF) of uncertain input and model parameters in engineering application codes is an issue of importance for uncertainty quantification methods. One of the approaches that can be used for the PDF determination of input and model parameters is the application of methods based on the maximum entropy principle (MEP) and the maximum relative entropy (MREP). These methods determine the PDF that maximizes the information entropy when only partial information about the parameter distribution is known, such as some moments of the distribution and its support. In addition, this paper shows the application of the MREP to update the PDF when the parameter must fulfill some technical specifications (TS) imposed by the regulations. Three computer programs have been developed: GEDIPA, which provides the parameter PDF using empirical distribution function (EDF) methods; UNTHERCO, which performs the Monte Carlo sampling on the parameter distribution; and DCP, which updates the PDF considering the TS and the MREP. Finally, the paper displays several applications and examples for the determination of the PDF applying the MEP and the MREP, and the influence of several factors on the PDF.

Spatial and temporal quantum correlations can be unified in the framework of the pseudo-density operators (PDOs), and quantum causality between the involved events in an experiment is encoded in the corresponding PDO. We study the relationship between local causal information and global causal structure. A space-time marginal problem is proposed to infer global causal structures from given marginal causal structures where causal structures are represented by the reduced PDOs; we show that there almost always exists a solution in this case. By imposing the corresponding constraints on this solution set, we could obtain the required solutions for special classes of marginal problems, like a positive semidefinite marginal problem, separable marginal problem, etc. We introduce a space-time entropy and propose a method to determine the global causal structure based on the maximum entropy principle. The notion of quantum pseudo-channel (QPC) is also introduced and we demonstrate that the QPC marginal problem can be solved by transforming it into a PDO marginal problem via the channel-state duality.

In this paper, a new method for constructing the probability box (p-box) model is developed based on maximum entropy principle. The distribution characteristics of probability box variable can be described by the nature of moments. The moment conditions are used to ensure the consistency of the cumulative distribution function (CDF), and the shape conditions are adopted to guarantee the validity of the cumulative distribution function. To ensure the uniqueness of the cumulative distribution function, simultaneously, the cumulative distribution function of the probability box variable is reconstructed based on maximum entropy principle. Then, considering that both aleatory and epistemic uncertainty exist in many engineering problems, a reliability analysis approach based on probability and probability box hybrid model is also developed for uncertain structures. Finally, four numerical examples and two engineering examples are investigated to demonstrate the effectiveness of the present method.

Molecular dynamics (MD) simulations allow the investigation of the structural dynamics of biomolecular systems with unrivaled time and space resolution. However, in order to compensate for the inaccuracies of the utilized empirical force fields, it is becoming common to integrate MD simulations with experimental data obtained from ensemble measurements. We review here the approaches that can be used to combine MD and experiment under the guidance of the maximum entropy principle. We mostly focus on methods based on Lagrangian multipliers, either implemented as reweighting of existing simulations or through an on-the-fly optimization. We discuss how errors in the experimental data can be modeled and accounted for. Finally, we use simple model systems to illustrate the typical difficulties arising when applying these methods.

Aiming at the difficulty of extracting vibration data under actual working conditions of rolling bearings, this paper proposes a bearing reliability evaluation method based on generative adversarial network sample enhancement and maximum entropy method under the condition of few samples. Based on generative adversarial network, data sample enhancement under few samples is carried out, and the reliability analysis model is established by using the maximum entropy principle and Poisson process. The reliability is evaluated according to the reliability variation frequency, variation speed and variation acceleration. The analysis results show that with the gradual increase of running time, the reliability variation frequency shows a nonlinear growth trend, which can be roughly divided into the initial running-in stage, the stable running-in stage and the intense running-in stage. The reliability variation speed is then used to distinguish the specific starting time of the three stages, and finally the preliminary relationship between the reliability variation acceleration and the remaining life is obtained. The experimental results of the XJTU-SY dataset show that compared with the existing reliability evaluation model, the proposed model has the advantages of less samples, no need for preprocessing and higher accuracy. The proposed model has made a beneficial supplement to the existing reliability analysis methods.

Network topology plays a key role in many phenomena, from the spreading of diseases to that of financial crises. Whenever the whole structure of a network is unknown, one must resort to reconstruction methods that identify the least biased ensemble of networks consistent with the partial information available. A challenging case, frequently encountered due to privacy issues in the analysis of interbank flows and Big Data, is when there is only local (node-specific) aggregate information available. For binary networks, the relevant ensemble is one where the degree (number of links) of each node is constrained to its observed value. However, for weighted networks the problem is much more complicated. While the naïve approach prescribes to constrain the strengths (total link weights) of all nodes, recent counter-intuitive results suggest that in weighted networks the degrees are often more informative than the strengths. This implies that the reconstruction of weighted networks would be significantly enhanced by the specification of both strengths and degrees, a computationally hard and bias-prone procedure. Here we solve this problem by introducing an analytical and unbiased maximum-entropy method that works in the shortest possible time and does not require the explicit generation of reconstructed samples. We consider several real-world examples and show that, while the strengths alone give poor results, the additional knowledge of the degrees yields accurately reconstructed networks. Information-theoretic criteria rigorously confirm that the degree sequence, as soon as it is non-trivial, is irreducible to the strength sequence. Our results have strong implications for the analysis of motifs and communities and whenever the reconstructed ensemble is required as a null model to detect higher-order patterns.

The Odd Weibull‐G (OWG) family of distributions has been discussed earlier in the literature. This family of distributions provides a “better fit” in certain practical situations. In a similar fashion, the OWG family of distributions is defined in this article. A method of moments estimator based on the maximum entropy principle is proposed for the discrimination of two members of the OWG family of distributions.

In this paper we present a hydrodynamical model for the description of the charge transport in graphene, including heating effects on the crystal lattice, and conversely the influence of crystal heating on charge transport. The state variables used for the physical system are moments of the electron, hole, and phonon occupation numbers, and their evolution equations are derived by integration from the respective Boltzmann equations. The closure of the system is obtained by means of the maximum entropy principle and all the main scattering mechanisms between charges and phonons and among phonons themselves are taken into account. Numerical simulations are presented in the case of a graphene monolayer, evaluating the influence of the optical and acoustical phonons dynamics on the current-voltage characteristics and the raise rate of the lattice temperature.

Urban dynamics in large metropolitan areas result from complex interactions across social, economic and political factors, including population distribution, flows of wealth and infrastructure requirements. We develop a Census-calibrated model of urban dynamics for the Greater Sydney and Melbourne areas for 2011 and 2016, highlighting the evolution of population distributions and the housing market structure in these two cities in terms of their mortgage and rent distributions. We show that there is a tendency to homophily between renters and mortgage holders: renters tend to cluster nearer commercial centres, whereas mortgagors tend to populate the outskirts of these centres. We also identify a critical threshold at which the long-term evolution of these two cities will bifurcate between a ‘sprawling’ and a ‘polycentric’ configuration, showing that both cities lie on the polycentric side of the critical point in the long-run. Importantly, there is a divergence of these centric tendencies between the renters and mortgage holders. The polycentric patterns characterizing the mortgagors are focused around commercial centres, and we show that the emergent housing patterns follow the major transport routes through the cities.