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In this paper, we enhanced change point detection in skew normal distribution models by integrating the EM algorithm's Q-function with the modified information criterion (MIC). The new QMIC framework improves sensitivity and accuracy in detecting changes, outperforming the modified information criterion (MIC) and the traditional Bayesian information criterion (BIC). Due to the complexity of deriving analytic asymptotic distributions, bootstrap simulations were used to determine critical values at various significance levels. Extensive simulations demonstrate that QMIC offers superior detection capabilities. We applied the QMIC method to two stock market datasets, successfully identifying multiple change points, and highlighting its effectiveness for real-world financial data analysis. [ABSTRACT FROM AUTHOR]

In this paper, we enhanced change point detection in skew normal distribution models by integrating the EM algorithm's Q-function with the modified information criterion (MIC). The new QMIC framework improves sensitivity and accuracy in detecting changes, outperforming the modified information criterion (MIC) and the traditional Bayesian information criterion (BIC). Due to the complexity of deriving analytic asymptotic distributions, bootstrap simulations were used to determine critical values at various significance levels. Extensive simulations demonstrate that QMIC offers superior detection capabilities. We applied the QMIC method to two stock market datasets, successfully identifying multiple change points, and highlighting its effectiveness for real-world financial data analysis.

Empirical evidence indicates that asset returns adhere to an extended normal distribution characterized by excessive kurtosis and non-zero skewness. Consequently, option prices derived from this distribution diverge from those predicted by the Black–Scholes model. Despite the significance of option price sensitivities for risk management in investment portfolios, the existing literature lacks a thorough exploration of these sensitivities within the context of the extended normal distribution. This article addresses this research gap by deriving the Greeks for options based on the extended normal distribution. The Greeks under consideration include Vega, Delta, Theta, Gamma, Rho, Vanna, Charm, and Vera, all of which are crucial for informed financial decision-making. Furthermore, this study provides a detailed analysis of how these option price sensitivities vary with different levels of kurtosis, offering valuable insights for various market applications. This contribution not only enhances the theoretical understanding of option pricing under non-standard distributions but also presents practical implications for portfolio risk management. [ABSTRACT FROM AUTHOR]

Devido ao crescente desenvolvimento tecnol´ogico e `as consequentes aplicaç˜oes industriais, novos m´etodos para o projeto de controle e Aprendizado por Reforço tem sido desenvolvidas, n˜ao apenas para resolver novos problemas de controle, mas tamb´em para melhorar o desempenho de controladores j´a implementados em sistemas do mundo real. As abordagens de Aprendizagem por Reforc¸o e Regulador Quadr´atico Linear Discreto s˜ao conectadas por m´etodos de Programaç˜ao Dinˆamica Adaptativa. Esses paradigmas s˜ao orientados para o projeto de controladores ´otimos em sistemas multivari´aveis. Para o caso do Regulador Quadr´atico Linear Discreto, AD-HDP, Aprendizado por Reforc¸o, Pol´ıtica de Iterac¸ ˜ao e Valor de Iterac¸ ˜ao, um m´etodo e um algoritmo s˜ao desenvolvidos e implementados para projeto de controle online. Com base na seleção das matrizes de ponderac¸ ˜ao Q e R, tamb´em ´e apresentado um m´etodo para ajustar controladores reguladores lineares quadr´aticos discretos. Este m´etodo fornece diretrizes para a construção de heur´ısticas para a seleç˜ao de matrizes de ponderaç˜ao, aspectos de convergˆencia relacionados `as variaç˜oes das matrizes de ponderaç˜ao s˜ao investigados. Para um sistema dinˆamico multivari´avel de terceira ordem, o algoritmo proposto e a heur´ıstica de ajuste s˜ao avaliados pela capacidade de estabelecer a pol´ıtica de controle ´otima

The finite-horizon optimal secure tracking control (FHOSTC) problem for cyber–physical systems under actuator denial-of-service (DoS) attacks is addressed in this paper. A model-free method based on the Q-function is designed to achieve FHOSTC without the system model information. First, an augmented time-varying Riccati equation (TVRE) is derived by integrating the system with the reference system into a unified augmented system. Then, a lower bound on malicious DoS attacks probability that guarantees the solutions of the TVRE is provided. Third, a Q-function that changes over time (time-varying Q-function, TVQF) is devised. A TVQF-based method is then proposed to solve the TVRE without the need for the knowledge of the augmented system dynamics. The developed method works backward-in-time and uses the least-squares method. To validate the performance and features of the developed method, simulation studies are conducted in the end. • The augmented time-varying value function (TVRE) can be represented as the time-varying quadratic form is demonstrated. In conjunction with this finding, the time-varying Riccati equation for the finite-horizon optimal secure tracking control problem is derived. • The impact of the DoS attacks on the solution of the TVRE is demonstrated. The convergence of the TVRE is proved under certain assumptions. Furthermore, a lower bound on the probability of DoS attacks that satisfies these assumptions is derived. • A time-varying Q-function (TVQF) is designed. The equivalence between the approximation of the TVQF kernel matrix and the solution of the derived TVRE is proved. Additionally, a TVQF-based model-free optimal secure tracking control algorithm is developed. [ABSTRACT FROM AUTHOR]

Considering overshoot and chatter caused by the unknown interference, this article studies the adaptive robust optimal controls of continuous‐time (CT) multi‐input systems with an approximate dynamic programming (ADP) based Q‐function scheme. An adaptive integral reinforcement learning (IRL) scheme is proposed to study the optimal solutions of Q‐functions. First, multi‐input value functions are presented, and Nash equilibrium is analyzed. A complex Hamilton–Jacobi–Issacs (HJI) equation is constructed with the multi‐input system and the zero‐sum‐game‐based value function. It is a challenging task to solve the HJI equation for nonlinear system. Thus, A transformation of the HJI equation is constructed as a Q‐function. The neural network (NN) is applied to learn the solution of the transformed Q‐functions based on the adaptive IRL scheme. Moreover, an error information is added to the Q‐function for the issue of insufficient initial incentives to relax the persistent excitation (PE) condition. Simultaneously, an IRL signal of the critic networks is introduced to study the saddle‐point intractable solution, such that the system drift and NN derivatives in the HJI equation are relaxed. The convergence of weight parameters is proved, and the closed‐loop stability of the multi‐system with the proposed IRL Q‐function scheme is analyzed. Finally, a two‐engine driven F‐16 aircraft plant and a nonlinear system are presented to verify the effectiveness of the proposed adaptive IRL Q‐function scheme. [ABSTRACT FROM AUTHOR]

In this paper, we present some new results on the existence of fixed points for multivalued mappings endowed with Q-function in the setting of quasi-metric space. Examples are also provided in support of our main results. We conclude that our results in fact either improve or generalize some classical metric fixed point results as well. [ABSTRACT FROM AUTHOR]

AbstractThis paper presents new simple lower and upper bounds for the cumulative normal distribution function, Φ(z). The accuracy and closeness of the proposed bounds to the exact Φ(z) are investigated based on the maximum absolute error and the mean absolute error. It is found that the maximum absolute error of the proposed lower bound is 8.55×10−3 and it is 4.1×10−4 for the upper bound. In addition, based on 5001 values between z=0 and z=5 with step 0.001, we found that the mean absolute error is 3.27×10−3 for the lower bound and it is 1.1×10−4 for the upper bound and these two values decrease with increasing the z value. [ABSTRACT FROM AUTHOR]

In this paper, model‐free finite‐horizon H∞$$ {H}_{\infty } $$ tracking control for discrete‐time linear systems is studied. By formulating an augmented system consisting of the considered linear system and the command generator system, an augmented time‐varying Riccati equation whose solutions can achieve the finite‐horizon H∞$$ {H}_{\infty } $$ tracking control is derived. Then, a time‐varying Q‐function which contains the control input and disturbance input is designed. A time‐varying Q‐function‐based method is developed to learn the solutions of the finite‐horizon H∞$$ {H}_{\infty } $$ tracking control problem without knowing the system model information nor any model identification methods. It is proved that the solutions of the time‐varying Q‐function‐based method converge to the optimal solutions of the augmented time‐varying Riccati equation. At last, simulation examples are provided to show the feasibility and advantages of the time‐varying Q‐function‐based method compared to the infinite‐horizon Q‐learning‐based H∞$$ {H}_{\infty } $$ tracking control method. [ABSTRACT FROM AUTHOR]

Empirical evidence indicates that asset returns adhere to an extended normal distribution characterized by excessive kurtosis and non-zero skewness. Consequently, option prices derived from this distribution diverge from those predicted by the Black–Scholes model. Despite the significance of option price sensitivities for risk management in investment portfolios, the existing literature lacks a thorough exploration of these sensitivities within the context of the extended normal distribution. This article addresses this research gap by deriving the Greeks for options based on the extended normal distribution. The Greeks under consideration include Vega, Delta, Theta, Gamma, Rho, Vanna, Charm, and Vera, all of which are crucial for informed financial decision-making. Furthermore, this study provides a detailed analysis of how these option price sensitivities vary with different levels of kurtosis, offering valuable insights for various market applications. This contribution not only enhances the theoretical understanding of option pricing under non-standard distributions but also presents practical implications for portfolio risk management.

In this paper, we propose a novel method for a tighter approximation of the Q -function using the two-point Gauss quadrature rule. In the proposed method, the integral used for approximation can be divided into any number of sub-intervals and result in an approximated expression, which is a simple summation of exponentials. The proposed approximation provides lesser relative error not only at smaller but also at larger arguments of Q -function. As an application, the proposed approximation of the Q -function can be efficiently used to evaluate the closed-form expressions of symbol error probability (SEP) for various modulation techniques over generalized fading channels. In order to show the applicability and tightness of the proposed approximation, we have derived more accurate approximated expressions for binary phase shift keying (BPSK) and triangular quadrature amplitude modulation (TQAM) schemes over α–κ–μ fading channel. The results indicate a comparison between the proposed approximation and existing approximations while demonstrating improved accuracy in terms of the relative error and hence achieve a tighter bound while calculating the error performance of the digital modulation schemes at both lower and higher values of SNRs. The accuracy of the proposed work is also verified by analytical and Monte-Carlo simulations. [ABSTRACT FROM AUTHOR]

In this paper, we first review some important definitions and notions related to best proximity point theory by considering the lack of symmetry property of quasi metric. Then, we introduce a new notion of BG-multivalued contraction mappings. Then, a best proximity point result is obtained via Q-function on quasi metric. Also, we present a noteworthy illustrative example to show the effect of our results. Finally, we give an existence and uniqueness result for the solution of nonlinear integral equations via our result. [ABSTRACT FROM AUTHOR]

In this paper, we introduce two new properties to the Q-function, called as the 0-property and the small self-distance property, which is frequently used in studies of fixed point theory in quasimetric spaces. Then, with the help of Q-functions having these properties, we present some fixed point theorems for Prešić-type mappings in quasimetric spaces. Finally, we state a theorem for the existence and uniqueness of the solution to a boundary value problem for (p; q)-difference equations to demonstrate the applicability of our theoretical results, which we support with an example. [ABSTRACT FROM AUTHOR]

Most researches interested in finding the bounds of the cumulative standard normal distribution Φx are not tight for all positive values of the argument x. This paper mainly proposes new simple lower and upper bounds for Φx. Over the whole range of the positive argument x, the maximum absolute difference between the proposed lower bound and Φx is less than 3×10−4, while it is less than 4.8×10−4 between the proposed upper bound and Φx. Numerical comparisons have been made between the proposed bounds and some of the other existing bounds, which showed that the proposed bounds are more compact than most alternative bounds found in the literature. [ABSTRACT FROM AUTHOR]

In this paper, we study quantum entanglement and non-classical statistical aspects for a model describing two three-level Λ atoms interacting with a single-mode cavity field. The Hamiltonian describes multi-photon processes and includes the Kerr-like medium in the resonance case. The constants of motion are obtained from the Hamiltonian operators under the rotating wave approximation. The exact solution of the wave function for the whole system is obtained under the special initial conditions when the atom is in the ground state and the field in the coherent states. The results are used to perform some studies on the temporal evolution of collapse revival, normal squeezing function, photon antibunching and Q-function to measure the degree of entanglement between subsystems. Entanglement dynamics using von Neumann entropy and Shannon information is used to quantify the entanglement in the quantum subsystems. The numerical results show that the presence of these parameters plays an essential role in developing these aspects. The above optical schemes have many advantages and can be used in various experiments in quantum optics and information, such as trapped ions and quantum electrodynamics resonators. [ABSTRACT FROM AUTHOR]

We study the continuous-time counterpart of Q-learning for reinforcement learning (RL) under the entropy-regularized, exploratory diffusion process formulation introduced by Wang et al. (2020). As the conventional (big) Q-function collapses in continuous time, we consider its first-order approximation and coin the term "(little) q-function". This function is related to the instantaneous advantage rate function as well as the Hamiltonian. We develop a "q-learning" theory around the q-function that is independent of time discretization. Given a stochastic policy, we jointly characterize the associated q-function and value function by martingale conditions of certain stochastic processes, in both on-policy and off-policy settings. We then apply the theory to devise different actor{critic algorithms for solving underlying RL problems, depending on whether or not the density function of the Gibbs measure generated from the q-function can be computed explicitly. One of our algorithms interprets the well-known Q-learning algorithm SARSA, and another recovers a policy gradient (PG) based continuous-time algorithm proposed in Jia and Zhou (2022b). Finally, we conduct simulation experiments to compare the performance of our algorithms with those of PG-based algorithms in Jia and Zhou (2022b) and time-discretized conventional Q-learning algorithms. [ABSTRACT FROM AUTHOR]

Conventionally, as the system dynamics is known, the finite-horizon optimal control of zero-sum games relies on solving the time-varying Riccati equations. In this paper, with unknown system dynamics being considered, a Q-function-based finite-horizon control method is introduced to approximate the solutions of the time-varying Riccati equations. First, a time-varying Q-function explicitly dependent on the time-varying control and disturbance is defined. Then the defined time-varying Q-function is utilised to represent the time-varying control and disturbance which are equivalent to the solutions of the time-varying Riccati equations by relaxing the system dynamics. Finally, a model-free method is introduced to approximate the defined time-varying Q-function. Simulation studies are conducted to demonstrate the validity of the developed method. [ABSTRACT FROM AUTHOR]

An entangled quantum state is considered by applying a local photon excitation to each mode of an entangled coherent state. The entanglement property is investigated in terms of the entropy of entanglement. It is shown that applying a photon addition can improve the amount of entanglement. It is also examined that in a specific region of parameters, the state | ψ1 (α m; n)i is least entangled when photon excitation is minimum. We study the statistical properties of such states by employing the quasi-probability functions. [ABSTRACT FROM AUTHOR]

We develop a combinatorial approach to the description of lattice random fields with general (Polish) state space. This approach based on so-called P-functions, which can be interpreted as a system of limiting correlation functions. We suggest a method of construction of P-functions, which can be applied in the theory of Gibbs random fields. [ABSTRACT FROM AUTHOR]

The Gaussian Q-function has considerable applications in numerous areas of science and engineering. However, the fact that a closed-form expression for this function does not exist encourages finding approximations or bounds of the Q-function. In this paper, we determine analytically two novel interval upper bound Q-function approximations and show that they could be used efficiently not only for the symbol error probability (SEP) estimation of transmission over Nakagami-m fading channels, but also for the average symbol error probability (ASEP) evaluation for two modulation formats. Specifically, we determine analytically the composition of the upper bound Q-function approximations specified at disjoint intervals of the input argument values so as to provide the highest accuracy within the intervals, by utilizing the selected one of two upper bound Q-function approximations. We show that a further increase of the accuracy, achieved in the case with two upper-bound approximations composing the interval approximation, can be obtained by forming a composite interval approximation of the Q-function that assumes another extra interval and by specifying the third form for the upper-bound Q-function approximation. The proposed analytical approach can be considered universal and widely applicable. The results presented in the paper indicate that the proposed Q-function approximations outperform in terms of accuracy other well-known approximations carefully chosen for comparison purposes. This approximation can be used in numerous theoretical communication problems based on the Q-function calculation. In this paper, we apply it to estimate the average bit error rate (ABER), when the transmission in a Nakagami-m fading channel is observed for the assumed binary phase-shift keying (BPSK) and differentially encoded quadrature phase-shift keying (DE-QPSK) modulation formats, as well as to design scalar quantization with equiprobable cells for variables from a Gaussian source.

We shill analyze quantum statistical properties for a quantum state which describes a charged particle moving in a uniform magnetic field. We will examine some of their non-classical properties, especially the quadrature variance add to the second-order correlation function. Discussion is included of the quasi probability distribution functions (Qfunctions). Finally, we display the phase distribution in the framework of Pegg and Barnett formalism is considered. [ABSTRACT FROM AUTHOR]

Topological measures and quasi-linear functionals generalize measures and li\-near functionals. Deficient topological measures, in turn, generalize topological measures. In this paper we continue the study of topological measures on locally compact spaces. For a compact space the existing ways of obtaining topological measures are (a) a method using super-measures, (b) composition of a q-function with a topological measure, and (c) a method using deficient topological measures and single points. These techniques are applicable when a compact space is connected, locally connected, and has a certain topological characteristic, called ``genus'', equal to 0 (intuitively, such spaces have no holes). We generalize known techniques to the situation where the space is locally compact, connected, and locally connected, and whose Alexandroff one-point compactification has genus 0. We define super-measures and q-functions on locally compact spaces. We then obtain methods for generating new topological measures by using super-measures and also by composing q-functions with deficient topological measures. We also generalize an existing method and provide a new method that utilizes a point and a deficient topological measure on a locally compact space. The methods presented allow one to obtain a large variety of finite and infinite topological measures on spaces such as $ {\mathbb R}^n$, half-spaces in ${\mathbb R}^n$, open balls in ${\mathbb R}^n$, and punctured closed balls in ${\mathbb R}^n$ with the relative topology (where $n \geq 2$).

Dynamic treatment regimes (DTRs) adaptively prescribe treatments based on patients' intermediate responses and evolving health status over multiple treatment stages. Data from sequential multiple assignment randomization trials (SMARTs) are recommended to be used for learning DTRs. However, due to re‐randomization of the same patients over multiple treatment stages and a prolonged follow‐up period, SMARTs are often difficult to implement and costly to manage, and patient adherence is always a concern in practice. To lessen such practical challenges, we propose an alternative approach to learn optimal DTRs by synthesizing independent trials over different stages. Specifically, at each stage, data from a single randomized trial along with patients' natural medical history and health status in previous stages are used. We use a backward learning method to estimate optimal treatment decisions at a particular stage, where patients' future optimal outcome increments are estimated using data observed from independent trials with future stages' information. Under some conditions, we show that the proposed method yields consistent estimation of the optimal DTRs and we obtain the same learning rates as those from SMARTs. We conduct simulation studies to demonstrate the advantage of the proposed method. Finally, we learn optimal DTRs for treating major depressive disorder (MDD) by stagewise synthesis of two randomized trials. We perform a validation study on independent subjects and show that the synthesized DTRs lead to the greatest MDD symptom reduction compared to alternative methods. [ABSTRACT FROM AUTHOR]

Conventionally, as the system’s dynamics is known, the optimal consensus control problem relies on solving the coupled Hamilton–Jacobi–Bellman (HJB) equations. In this paper, with the unknown system dynamics being considered, a local ${Q}$ -function-based adaptive dynamic programming method is put forward to deal with the optimal consensus control problem for unknown discrete-time nonlinear multiagent systems by approximating the solutions of the coupled HJB equations. First, a local ${Q}$ -function is defined, which considers the local consensus error and the actions of the agent and its neighbors. Using the ${Q}$ -function, it is convenient to get the derivatives with regard to the weights of the consensus control policies, even without the model of system dynamics. Then, with the defined local ${Q}$ -function, a distributed policy iteration technique is developed, which is theoretically proved to be convergent to the solutions of the coupled HJB equations. An actor–critic neural network framework for implementing the developed model-free optimal consensus control method is constructed to approximate the local ${Q}$ -functions and the control policies. Finally, the feasibility and effectiveness of the developed method are verified by a series of simulations. [ABSTRACT FROM AUTHOR]

We consider the interaction between two three-level atoms in the Ξ configuration and a quantum system described through SU(1) group algebra operators. To study the quantum phenomena and underlying dynamical behavior, we calculate the wave function of the system. In particular, we investigate collapse and revival phenomena, the correlation function, and the Husimi quasidistribution Q-function. [ABSTRACT FROM AUTHOR]

• The proposed sparse Gaussian processes with Q-function (SGP-Q) is a novel and online method for anomaly detection of time-series data. • The SGP-Q method can address concept drift well by employing the Q-function properly. • The SGP-Q method uses the sparse Gaussian process regression (SGPR) to model time-series data, which speeds up online anomaly detection. • The SGP-Q method makes use of few abnormal data in the training data, thus making the trained SGPR models more accurate and anomaly detection results better. • Experiments on the Numenta Anomaly Benchmark (NAB) dataset validate the effectiveness and rationality. Online anomaly detection of time-series data is an important and challenging task in machine learning. Gaussian processes (GPs) are powerful and flexible models for modeling time-series data. However, the high time complexity of GPs limits their applications in online anomaly detection. Attributed to some internal or external changes, concept drift usually occurs in time-series data, where the characteristics of data and meanings of abnormal behaviors alter over time. Online anomaly detection methods should have the ability to adapt to concept drift. Motivated by the above facts, this paper proposes the method of sparse Gaussian processes with Q-function (SGP-Q). The SGP-Q employs sparse Gaussian processes (SGPs) whose time complexity is lower than that of GPs, thus significantly speeding up online anomaly detection. By using Q-function properly, the SGP-Q can adapt to concept drift well. Moreover, the SGP-Q makes use of few abnormal data in the training data by its strategy of updating training data, resulting in more accurate sparse Gaussian process regression models and better anomaly detection results. We evaluate the SGP-Q on various artificial and real-world datasets. Experimental results validate the effectiveness of the SGP-Q. [ABSTRACT FROM AUTHOR]

A novel identity for the Gaussian Q-function of the sum of two non-negative variables is introduced as an extension of Craig’s Q-function formula. It is shown that this new identity provides a unified framework in the performance analysis of dual-branch equal-gain combining (EGC) diversity, similar to that of Craig’s Q-function formula for maximum ratio combining diversity. Then, the performance of dual correlated branch EGC in Nakagami- $m$ fading is studied using this novel approach. For coherent modulations with error probabilities in terms of the Gaussian Q-function, it is shown that the average error probability of the dual correlated branch EGC in Nakagami- $m$ fading is the same as the average error probability of a modeled single-channel receiver in the same fading environment. Using this fact, simple exact and approximate closed-form expressions for this average error probability are derived. The analytical results are verified and illustrated by numerical results and computer simulations. [ABSTRACT FROM AUTHOR]

A novel framework of model-based fault detection and identification (MFDI) for induction motor (IM)-driven rotating machinery (RM) is proposed in this study. A data-driven subspace identification (SID) algorithm is employed to obtain the IM state-space model from the voltage and current signals in a quasi-steady-state condition. This study aims to improve the frequency–domain fault detection and identification (FDI) by replacing the current signal with a residual signal where a thresholding method is applied to the residual signal. Through the residual spectrum and threshold comparison, a binary decision is made to find fault signatures in the spectrum. The statistical Q-function is used to generate the fault frequency band to distinguish between the fault signature and the noise signature. The experiment in this study is performed on a wastewater pump in an existing industrial facility to verify the proposed FDI. Two faulty conditions with mathematically known and mathematically unknown faulty signatures are experimented with and diagnosed. The study results present that the residual spectrum demonstrated to be more sensitive to fault signatures compare to the current spectrum. The proposed FDI has successfully shown to identify the fault signatures even for the mathematically unknown faulty signatures.

Time reversal processes have been used to improve communication performance in the severe underwater communication environment characterized by significant multipath channels by reducing inter-symbol interference and increasing signal-to-noise ratio. In general, the performance of the time reversal is strongly related to the behavior of the q-function, which is estimated by a sum of the autocorrelation of the channel impulse response for each channel in the receiver array. The q-function depends on the complexity of the communication channel, the number of channel elements and their spacing. A q-function with a high side-lobe level and a main-lobe width wider than the symbol duration creates a residual ISI (inter-symbol interference), which makes communication difficult even after time reversal is applied. In this paper, we propose a new parameter, Eq, to describe the performance of time reversal communication. Eq is an estimate of how much of the q-function lies within one symbol duration. The values of Eq were estimated using communication data acquired at two different sites: one in which the sound speed ratio of sediment to water was less than unity and one where the ratio was higher than unity. Finally, the parameter Eq was compared to the bit error rate and the output signal-to-noise ratio obtained after the time reversal operation. The results show that these parameters are strongly correlated to the parameter Eq. [ABSTRACT FROM AUTHOR]

We communicate three formulas for the permanents of degenerate Schur and circulant matrices. These combinatorial and integral formulas are intended for the analytical and asymptotic evaluation of the permanents as well as for the solution of three-dimensional Ising model. The paper's goal is to draw attention to the open fundamental problem of finding the permanents' asymptotics. A solution to this problem would be tremendously important for physics of many-body systems and critical phenomena, as well as for quantum field theory. [ABSTRACT FROM AUTHOR]

An echo state network (ESN)‐based Q‐learning method is developed for optimal energy management of an office, where the solar energy is introduced as the renewable source, and a battery is installed with a control unit. The energy consumption in the office, also considered as the energy demand, is separated into those from sockets, lights and air‐conditioners. First, ESNs, well known for their excellent modelling performance for time series, are employed to model the time series of the real‐time electricity rate, renewable energy and energy demand as periodic functions. Second, given the periodic models of the electricity rate, renewable energy and energy demand, an ESN‐based Q‐learning method with the Q‐function approximated by an ESN is developed and implemented to determine the optimal charging/discharging/idle strategies for the battery in the office, so that the total cost of electricity from the grid can be reduced. Finally, numerical analysis is conducted to illustrate the performance of the developed method. [ABSTRACT FROM AUTHOR]