Bouncing ball trajectories are intricately linked to the configuration space of their respective classical billiard systems. In the momentum space, a second pattern of scar-like states is generated by the plane-wave states of the unperturbed flat billiard system. Regarding billiards with a single, uneven surface, the numerical evidence underscores the repulsion of eigenstates from this surface. For the case of two horizontal, uneven surfaces, the repulsion effect is either amplified or canceled out depending on the symmetric or asymmetric pattern of their surface profiles. A substantial repulsive effect pervasively modifies every eigenstate's configuration, showcasing the importance of the symmetric properties in the rough profiles in the context of scattering electromagnetic (or electron) waves through quasi-one-dimensional waveguides. By effectively interacting two artificial flat-surface particles, our approach mirrors the behaviour of a single particle within a corrugated billiard. Following this, the analysis utilizes a two-particle framework, with the irregular shape of the billiard table's boundaries absorbed by a fairly sophisticated potential.

The application of contextual bandits extends to numerous practical challenges encountered in the real world. However, popular algorithms for tackling these issues frequently rely on linear models or exhibit unreliable uncertainty estimations in non-linear models, elements needed to handle the exploration-exploitation trade-off. Motivated by human cognitive theories, we introduce innovative techniques incorporating maximum entropy exploration, utilizing neural networks to discover optimal policies in scenarios encompassing continuous and discrete action spaces. Our work presents two models. The first uses neural networks to estimate rewards, while the second uses energy-based models to calculate the probability of achieving the ideal reward based on the action taken. The models' performance is investigated in both static and dynamic contextual bandit simulation environments. Compared to conventional baseline algorithms, including NN HMC, NN Discrete, Upper Confidence Bound, and Thompson Sampling, both methods showcase superior performance. Energy-based models lead the way in overall effectiveness. Well-performing techniques in static and dynamic situations are provided to practitioners, particularly advantageous for non-linear scenarios with continuous action spaces.

A model resembling a spin-boson model, involving two interacting qubits, is examined. The model's exact solvability is a consequence of the exchange symmetry displayed by the two spins. Analytical determination of first-order quantum phase transitions is facilitated by the explicit representation of eigenstates and eigenenergies. Due to their sudden shifts in two-spin subsystem concurrence, net spin magnetization, and mean photon number, the subsequent phenomena are of physical consequence.

Sets of input and output observations from a stochastic model, when analyzed via Shannon's entropy maximization principle, yield an analytical summary of the variable small data evaluation. This conceptual framework is rigorously defined by a sequential, analytical description, tracing the progression from the likelihood function to the likelihood functional and the Shannon entropy functional. The uncertainty inherent in stochastic data evaluations, stemming from both probabilistic parameters and interfering measurements, is captured by Shannon's entropy. Shannon entropy allows us to pinpoint the most accurate estimations for these parameters, considering the measurement variability to maximize uncertainty (per entropy unit). Stochastic model parameter density estimates, determined via Shannon entropy maximization of small data, inherit the variability inherent in the process of their measurements, as organically dictated by the postulate. Information technology is used in this article to further this principle through the application of Shannon entropy to parametric and non-parametric evaluation of small datasets impacted by interference. click here This article formally introduces three fundamental components: representative examples of parameterized stochastic models to analyze datasets of variable small sizes; procedures for estimating the probability density function of their parameters, using either normalized or interval probabilities; and strategies for generating an ensemble of random vectors representing initial parameter values.

A persistent difficulty in the field of stochastic systems control lies in the accurate tracking of output probability density functions (PDFs), requiring considerable effort in both theoretical development and practical application. Addressing this challenge, this work crafts a novel stochastic control methodology, designed to allow the output probability density function to precisely mirror a given time-varying probability density function. click here The output PDF's weight dynamics conform to a B-spline model approximation. Consequently, the PDF tracking issue is transformed into a state tracking problem for the dynamics of weight. Moreover, the weight dynamics model error is amplified by multiplicative noise terms to more effectively delineate its stochastic behavior. Furthermore, to provide a more practical representation of real-world circumstances, the target being tracked is set to fluctuate over time rather than stay fixed. Accordingly, an augmented probabilistic design (APD), derived from the existing FPD framework, is constructed to tackle multiplicative noise issues and enhance the tracking accuracy of time-varying references. The proposed control framework is substantiated by a numerical example and compared against the linear-quadratic regulator (LQR) in a simulation, thereby illustrating its superior performance.

The discrete Biswas-Chatterjee-Sen (BChS) opinion dynamics model has been studied on Barabasi-Albert networks (BANs). In this model, mutual affinities, contingent upon a pre-established noise parameter, can assume either positive or negative values. Second-order phase transitions were observed using computer simulations augmented by Monte Carlo algorithms and the finite-size scaling hypothesis. The critical exponents' standard ratios, along with the critical noise, have been calculated, contingent on average connectivity, in the thermodynamic limit. A hyper-scaling relation establishes that the system's effective dimension is nearly one, irrespective of its connectivity characteristics. The results indicate a comparable performance for the discrete BChS model when applied to directed Barabasi-Albert networks (DBANs), Erdos-Renyi random graphs (ERRGs), and directed Erdos-Renyi random graphs (DERRGs). click here Despite the ERRGs and DERRGs model exhibiting identical critical behavior at infinite average connectivity, the BAN model's universality class differs substantially from its DBAN counterpart for all studied connectivity values.

Although progress has been made in qubit performance lately, the intricacies of microscopic atomic structure within Josephson junctions, the foundational devices crafted under different preparation procedures, persist as an area needing more research. Using classical molecular dynamics simulations, this paper explores how oxygen temperature and upper aluminum deposition rate impact the topology of the barrier layer in aluminum-based Josephson junctions. To investigate the topological structure of the interface and central regions of the barrier layers, we utilize a Voronoi tessellation process. Maintaining an oxygen temperature of 573 Kelvin and an upper aluminum deposition rate of 4 Angstroms per picosecond yielded a barrier with a minimum of atomic voids and a maximal degree of atomic arrangement. If one analyzes only the atomic arrangement of the central zone, the optimal rate of aluminum deposition stands at 8 A/ps. This work offers microscopic guidelines for the experimental construction of Josephson junctions, thereby leading to improved qubit performance and quicker application of quantum computers.

Estimating Renyi entropy is essential for many applications spanning cryptography, statistical inference, and machine learning. This paper proposes to improve existing estimators by tackling (a) the size of the sample, (b) the ability of the estimators to adapt to different situations, and (c) the simplicity of the analyses. This novel analysis of the generalized birthday paradox collision estimator forms the contribution. The analysis, characterized by its simplicity compared to previous works, offers clear formulas and strengthens existing bounds. Employing the improved bounds, an adaptive estimation technique is designed to outperform prior methods, especially in scenarios involving low or moderate entropy levels. To demonstrate the wider relevance of the developed methodologies, a selection of applications examining the theoretical and practical implications of birthday estimators is provided.

China's water resource management policy currently emphasizes a spatial equilibrium strategy for water resources; a substantial challenge is elucidating the structural relationships in the complex water-society-economy-ecology (WSEE) system. Employing a coupling analysis of information entropy, ordered degree, and connection number, we first investigated the membership characteristics present between different evaluation indicators and the grade criterion. Subsequently, a system dynamics approach was applied to illustrate the interconnectivity patterns among disparate equilibrium subsystems. Employing an integrated model incorporating ordered degree, connection number, information entropy, and system dynamics, the relationship structure and evolutionary path of the WSEE system were simulated and evaluated. Results from the Hefei, Anhui Province, China, application showed that the variation in the WSEE system's overall equilibrium conditions from 2020 to 2029 was higher than the 2010-2019 period, although the rate of increase in the ordered degree and connection number entropy (ODCNE) slowed after 2019.