The Kirchhoff-Law–Johnson-Noise (KLJN) key exchange protocol offers a classical, physics-based alternative to quantum key distribution for achieving informationtheoretic security. It offers a classical and cost-effective solution to secure communications. In this paper we present a simulation framework that models the entire KLJN loop, enabling detailed exploration of the scheme, and propose workflows to generate KLJN key-exchange probability density functions, and to validate their accuracy against analytically calculated ones. We also use our simulation to empirically verify that voltage and current standard deviations of a KLJN scheme follow chi-distributions, a result that crucially impacts threshold optimization and bit-classification algorithms. We also introduce correction techniques that reconstruct the original statistical behavior after signal-processing operations such as windowing and low-pass filtering, which are essential for reducing transients between bit transfers and enhancing security. This work integrates statistical signal analysis, and simulation-driven validation to strengthen the theoretical and practical foundations of KLJN-based secure communication.
Machine learning is shown not to increase Eve's successful bit-guessing probability in the binary-classifier-based wire-resistance attack on the Kirchhoff Law-Johnson Noise (KLJN) key exchange when the resistor gap is narrow. Using time-domain simulations of a non-ideal KLJN loop with R_L = 9 kΩ, R_H = 10 kΩ and wire resistances from 0 to 3200 Ω, we generate 3000 secure bits per wire resistance and evaluate the mean-square noise voltages at both ends over 100-sample bit exchange periods (BEPs). This probability p is evaluated for the sign rule, the nearest-line rule, logistic regression, support vector machine (SVM), k-nearest neighbors, random forest and gradient boosting. The sign rule gives p = 0.711 at 50 Ω and 0.682 at 3200 Ω. The nearest-line rule, logistic regression and SVM stay close to it and the other classifiers perform worse. For Gaussian noise, the likelihood ratio between the HL and LH cases depends only on the difference of the two mean-square voltages, so the sign rule is Bayes-optimal. The resulting p_max reproduces the measured values and predicts that about 900 to 1200 samples per bit are needed for p = 0.95. This difference carries about 0.19 bit per secure bit, 1.5 times the hard-decision value.
The objective of this work is to explore the impact of physical parameters on the Casson nanofluid flow over a cylinder in the presence of gyrotactic motile microorganisms. Furthermore, the impact of an exponential heat source is considered. Moreover, the heat and mass transfer characteristics are investigated utilizing Brownian motion and thermophoresis impacts. The governing equations of the considered problem are developed in the form of partial differential equations, which are then transformed into ordinary differential equations by using similarity transformations. These transformed equations are numerically tackled by using the shooting scheme via the BVP4C solver in MATLAB. The influences of flow-controlling parameters on the velocity field, temperature distribution and volumetric concentration of nanoparticles and microorganisms’ profiles are analyzed through graphs. The parametric values are taken as [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] for the purpose of generating modified results. In particular, changes in these parameters can significantly influence the momentum, heat and mass transfer and microorganism transport around the cylinder. These findings offer useful insight into the regulation and optimization of coupled transport processes in non-Newtonian nanofluid systems with bioconvection and simultaneous heat and mass transfer. Such findings are relevant to a range of engineering and biofluid applications involving complex thermal and transport phenomena.
Against the backdrop of rising uncertainty in global energy markets, the tail directional connectedness between energy-price fluctuations and macroeconomic conditions has become an important issue for macroprudential monitoring. Drawing on the mixed-frequency information stacking idea of the MF-VAR-DY model, this paper constructs an MF-QVAR-DY model that embeds high-frequency energy prices and low-frequency macroeconomic variables within a unified conditional quantile system, and examines the directional connectedness structure among fossil energy, clean energy and US macroeconomic variables. The results show that: first, total connectedness between energy markets and macroeconomic variables exhibits a pronounced high-at-both-ends, low-in-the-middle pattern; second, from a mixed-frequency perspective, crude oil is a stable outward risk transmitter, whereas clean energy plays a stronger outward spillover role at extreme quantiles; third, during the COVID-19 pandemic, fossil and clean energy jointly transmitted risk, whereas during the Russia–Ukraine conflict, the crude oil market dominated risk spillovers. This paper provides empirical evidence for using high-frequency energy information in macroeconomic tail-risk monitoring.
This paper involves the numerical exploration of both stochastic and deterministic SIRS epidemic models with saturated incidence rates. The implicit Runge-Kutta method, Euler-Maruyama method and stochastic Runge-Kutta methods are employed to analyze the dynamic patterns of the epidemic. The deterministic model is formulated using an ordinary differential system and is deep-seated in the well-established classical SIRS epidemic framework. A stochastic model is formulated by incorporating the elements of white noise in order to explain the effect of random environmental fluctuations. The proposed numerical experiments are efficiently used to assess the impact of environmentally induced changes on the SIRS epidemic model transmission dynamics. The incidence of transmission of each type of population is predicted by varying the rate of recruiting new susceptible populations, the rate of immunity decay, the rate of natural mortality, mortality due to disease and the rate of recovery of infected individuals. The deterministic modelling solutions are approximated using the state-of-the-art implicit Runge-Kutta method, while the probabilistic versions of the model are explored using the Euler-Maruyama and stochastic Runge-Kutta techniques. Both deterministic and stochastic disease models are extensively compared and analyzed in the light of sundry scenarios of environmental changes with the view of obtaining an insight into the trends in disease transmission.
