Bouncing ball trajectories are intricately linked to the configuration space of their respective classical billiard systems. A second, scar-like set of states appears in momentum space, originating from the plane-wave states of the unperturbed, flat billiard. For billiard tables with a single rough surface, the numbers demonstrate eigenstates' avoidance of this uneven surface. When analyzing two horizontal, uneven surfaces, the repulsion effect exhibits either an increase or a decrease, depending on the symmetrical or asymmetrical nature of their surface configurations. The effect of repulsion is robust, altering the architecture of all eigenstates, thereby emphasizing the significance of symmetric properties of the rough profiles for the problem of scattering electromagnetic (or electron) waves through quasi-one-dimensional waveguides. Our approach is predicated on the simplification of a single, corrugated-surface particle into a model of two interacting artificial particles on a flat surface. In this manner, the analysis employs a two-particle model, and the unevenness of the billiard table's boundaries are absorbed within a considerably involved potential.
Contextual bandits are a powerful tool for tackling a diverse range of real-world issues. Despite this, common algorithms for these problems often employ linear models or experience unreliable uncertainty estimations in non-linear models, which are critical for addressing the exploration-exploitation trade-off. Drawing inspiration from theories of human cognition, we present novel methods that leverage maximum entropy exploration, employing neural networks to identify optimal strategies within environments featuring both continuous and discrete action spaces. Two model architectures are presented. The first uses neural networks for reward estimation, and the second incorporates energy-based models to gauge the probability of obtaining the optimal reward contingent upon the action. These models' performance is evaluated in static and dynamic contextual bandit simulation environments. Both techniques demonstrably outperform standard baseline algorithms, including NN HMC, NN Discrete, Upper Confidence Bound, and Thompson Sampling, with energy-based models achieving the best overall outcome. Techniques for practitioners exhibit robust performance in static and dynamic situations, with special suitability for non-linear scenarios featuring continuous action spaces.
The interacting qubits within a spin-boson-like model are investigated. The exchange symmetry between the two spins leads to the model being exactly solvable. Eigenstates and eigenenergies, when explicitly expressed, permit the analytical exploration of first-order quantum phase transitions. Due to their sudden shifts in two-spin subsystem concurrence, net spin magnetization, and mean photon number, the subsequent phenomena are of physical consequence.
The article provides an analytical summary of applying Shannon's entropy maximization principle to sets of observations from the input and output entities of a stochastic model, for evaluating variable small data. 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. Shannon's entropy measures the uncertainty not only arising from probabilistic elements in a stochastic data evaluation model, but also from disturbances that distort the measurements of parameters. Based on Shannon entropy, the best estimations of these parameter values are obtainable, considering the maximum uncertainty (per unit of entropy) introduced by the measurement variability. The variability in the process of measuring parameters of the small data stochastic model, as determined via Shannon entropy maximization and the postulate's organic transfer, is reflected in the estimates of their probability distribution. The article details the implementation of this principle in information technology, employing Shannon entropy to produce both parametric and non-parametric evaluation methods for small datasets which are measured under conditions of interference. read more The article's formalization clarifies three core components: examples of parameterized stochastic models for assessing datasets of variable small sizes; methods for determining the probability density function of the parameters, represented as either normalized or interval probabilities; and strategies for generating an ensemble of random initial parameter vectors.
The pursuit of output probability density function (PDF) tracking control in stochastic systems has consistently presented a significant challenge across theoretical frameworks and engineering applications. 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. read more An approximation of the output PDF's weight dynamics is dictated by the B-spline model. Ultimately, the PDF tracking problem is reinterpreted as a state tracking issue for the kinetic behavior of weight. Moreover, the weight dynamics model error is amplified by multiplicative noise terms to more effectively delineate its stochastic behavior. Additionally, the tracking subject is made time-dependent, rather than static, to better model real-world applications. Practically speaking, a refined fully probabilistic design (RFD), based on the established FPD, has been crafted to tackle multiplicative noise and improve time-varying reference tracking. In conclusion, the proposed control framework is confirmed by a numerical example, and a comparative simulation with the linear-quadratic regulator (LQR) method is presented to showcase its superiority.
Barabasi-Albert networks (BANs) have been used to examine a discrete form of the Biswas-Chatterjee-Sen (BChS) model in opinion dynamics systems. The pre-defined noise parameter in this model dictates the assignment of either positive or negative values to the mutual affinities. Extensive computer simulations coupled with Monte Carlo algorithms and the finite-size scaling hypothesis demonstrated the occurrence of second-order phase transitions. Critical noise, along with typical ratios of critical exponents, have been determined, dependent on average connectivity, within the thermodynamic limit. The system's effective dimensionality, as determined by a hyper-scaling relationship, is near unity, proving independent of connectivity. In directed Barabasi-Albert networks (DBANs), Erdos-Renyi random graphs (ERRGs), and directed Erdos-Renyi random graphs (DERRGs), the discrete BChS model shows comparable characteristics, as shown in the results. read more Although the ERRGs and DERRGs model displays identical critical behavior with unbounded average connectivity, the BAN model and its DBAN counterpart belong to different universality classes for the full range of connectivity examined.
In spite of the progress in qubit performance seen recently, the subtle variations in the microscopic atomic configurations of Josephson junctions, the essential components produced under differing preparation parameters, need further investigation. The topology of the barrier layer in aluminum-based Josephson junctions, as affected by oxygen temperature and upper aluminum deposition rate, is presented herein using classical molecular dynamics simulations. To map the topological features of the barrier layer's interface and central areas, we implement a Voronoi tessellation strategy. At an oxygen temperature of 573 Kelvin and an upper aluminum deposition rate of 4 Angstroms per picosecond, the barrier exhibits the fewest atomic voids and the most tightly packed atoms. Nevertheless, focusing solely on the atomic configuration of the core region reveals an optimal aluminum deposition rate of 8 A/ps. This work provides microscopic direction for the experimental fabrication of Josephson junctions, thereby boosting qubit efficiency and speeding up the real-world application of quantum computers.
Renyi entropy estimation plays a crucial role in various cryptographic, statistical inference, and machine learning applications. This paper's goal is to develop improved estimators relative to (a) sample size requirements, (b) their ability to adapt to various conditions, and (c) the overall ease of analysis. A novel analysis of the generalized birthday paradox collision estimator is presented as the contribution. This analysis simplifies prior work, featuring clear formulae and augmenting existing limitations. Employing the improved bounds, an adaptive estimation technique is designed to outperform prior methods, especially in scenarios involving low or moderate entropy levels. Finally, to underscore the broader appeal of the developed techniques, a range of applications pertaining to the theoretical and practical aspects of birthday estimators are explored.
China currently utilizes a water resource spatial equilibrium strategy as a foundational element of its integrated water resource management; delineating the relational characteristics within the intricate WSEE system is a considerable obstacle. In the initial phase, we utilized a coupling approach involving information entropy, ordered degree, and connection number to discern the membership relationships between evaluation indicators and grade criteria. Secondarily, the system dynamics method was employed to define the interactions and characteristics among the different equilibrium sub-systems. Using an integrated model combining ordered degree, connection number, information entropy, and system dynamics, the relationship structure and future evolutionary trajectory of the WSEE system were investigated. The application results from Hefei, Anhui Province, China, show a more substantial variation in the WSEE system's overall equilibrium conditions between 2020 and 2029 compared to 2010 and 2019. This is despite the growth rate of ordered degree and connection number entropy (ODCNE) slowing after 2019.