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The increasing density of space objects in low-Earth orbit highlights the critical need for accurate orbit predictions to minimise operational disruptions. One significant challenge lies in accurately modelling the interaction of gas particles with the surfaces of these objects, as errors in aerodynamic coefficient modelling directly impact orbit prediction accuracy. Current approaches rely on empirical models, such as those by Sentman and Cercignani-Lampis-Lord, incorporating one or two adjustable parameters typically calibrated with orbital acceleration data. However, these models fall short in capturing essential gas-solid interaction processes, including multiple reflections, shadowing, and backscattering caused by surface roughness. We present a novel, physics-based gas-surface interaction model that utilises electromagnetic wave theory to account for macroscopic effects of surface roughness on gas particle scattering distributions. This approach not only offers a more accurate representation of gas-surface interactions but also allows parameter determination through a combination of ground-based surface roughness measurements and molecular dynamics simulations at the atomic scale. The model validity is tested across the entire parameter space using a test-particle Monte Carlo method on a simulated rough surface. Furthermore, it successfully reproduces experimental results from the literature on the scattering of Argon and Helium from smooth and rough Kapton and Aluminium surfaces. Finally, we demonstrate the model's impact on aerodynamic coefficients for simple geometric shapes, comparing the results with those from the Sentman and Cercignani-Lampis-Lord models. This comparison reveals that inconsistencies previously observed between these models and tracking data for spherical satellites can be attributed to surface roughness effects, which our model effectively accounts for.

The mean-field game system is treated as an Euler Lagrange system corresponding to an optimal control problem governed by Fokker-Planck equation.

Quantum Tiq-Taq-Toe is a well-known benchmark and playground for both quantum computing and machine learning. Despite its popularity, no reinforcement learning (RL) methods have been applied to Quantum Tiq-Taq-Toe. Although there has been some research on Quantum Chess this game is significantly more complex in terms of computation and analysis. Therefore, we study the combination of quantum computing and reinforcement learning in Quantum Tiq-Taq-Toe, which may serve as an accessible testbed for the integration of both fields. Quantum games are challenging to represent classically due to their inherent partial observability and the potential for exponential state complexity. In Quantum Tiq-Taq-Toe, states are observed through Measurement (a 3x3 matrix of state probabilities) and Move History (a 9x9 matrix of entanglement relations), making strategy complex as each move can collapse the quantum state.

One proves the well-posedness in the Sobolev space H^{-1} of nonlinear Fokker-Planck equations with singular drifts.Applications to existence of strong solutions to McKean-Vlasov equations are given.

A vortices-bubble system may be depicted by some features which may lead to infer its acoustic charge and its spin angular momentum. We study the dynamics of this system within the framework of fluid physics and with the help of Maxwell's hydrodynamic equations. Since we will adopt an approach of a fluid without viscosity and without gravity, then the fluid is in steady state if also we will neglect the acoustic radiation. When we expressed the energy (the kinetic and potential energy) of the vortex-bubble system we found out that the state of bubble which is captured in the core of the vortex is more stable than it is out of the core. For the above allegations we consider that this system, namely a vortex-bubble system, is a good approach for an acoustic particle with charge and spin angular momentum. This system owns to the Acoustic World., Comment: 15 pages

In this paper we construct a stochastic process, more precisely, a (nonlinear) Markov process, which is related to the parabolic $p$-Laplace equation in the same way as Brownian motion is to the classical heat equation given by the (2-) Laplacian.

The Covariance Matrix Adaptation Evolutionary Strategy (CMA-ES) is one of the most advanced algorithms in numerical black-box optimization. For noisy objective functions, several approaches were proposed to mitigate the noise, e.g., re-evaluations of the same solution or adapting the population size. In this paper, we devise a novel method to adaptively choose the optimal re-evaluation number for function values corrupted by additive Gaussian white noise. We derive a theoretical lower bound of the expected improvement achieved in one iteration of CMA-ES, given an estimation of the noise level and the Lipschitz constant of the function's gradient. Solving for the maximum of the lower bound, we obtain a simple expression of the optimal re-evaluation number. We experimentally compare our method to the state-of-the-art noise-handling methods for CMA-ES on a set of artificial test functions across various noise levels, optimization budgets, and dimensionality. Our method demonstrates significant advantages in terms of the probability of hitting near-optimal function values.

In this paper we study the properties of vortexes, as systems specific to the Acoustic World, using both hydrodynamic theory and the corresponding hydrodynamic Maxwell equations. According to this study, it follows that the vortex behaves like an acoustic dipole that has intrinsic/internal angular momentum. The system of two identical vortices also has orbital angular momentum and behaves, at distances much greater than the distance between the axes of the vortices, as a single vortex. With the help of Maxwell's hydrodynamic equations for the vortex we deduced the force between two vortices and obtained the expression of the equivalent mass of the vortex and the permittivity of the electroacoustic field. We also obtained and interpreted the expression for the energy density of the acoustic field. The density and pressure variations induced by the vortex cause the change in the propagation speed of the acoustic waves and the acoustic lensing property of the vortex., Comment: 12 pages

The present study focuses on the intrinsic properties of the SmFe10Co2-xVx (x = 0-2) alloys, which includes the SmFe10Co2 alloy, one of the most promising permanent magnets with the ThMn12 type of structure due to its large saturation magnetization (1.78 T), high Curie temperature (Tc = 859 K), and anisotropy field (12 T) experimentally obtained. Unfortunately, its low coercivity (<0.4 T) hinders its use in permanent magnet applications. The effect of V-doping on magnetization, magnetocrystalline anisotropy energy, and Curie temperature is investigated by electronic band structure calculations. The spin-polarized fully relativistic Korringa-Kohn-Rostoker (SPR-KKR) band structure method, which employs the coherent potential approximation (CPA) to deal with substitutional disorder, has been used. The Hubbard-U correction to local spin density approximation (LSDA +U) was used to account for the large correlation effects due to the 4f electronic states of Sm. The computed magnetic moments and magnetocrystalline anisotropy energies were compared with existing experimental data to validate the theoretical approach's reliability. The exchange-coupling parameters from the Heisenberg model were used for obtaining the mean-field estimated Curie temperature. The magnetic anisotropy energy was separated into contributions from transition metals and Sm, and its relationships with the local environment, interatomic distances, and valence electron delocalization were analyzed. The suitability of the hypothetical SmFe10CoV alloy for permanent magnet manufacture was assessed using the calculated anisotropy field, magnetic hardness, and intrinsic magnetic properties., Comment: 21 pages, 5 figures

Public availability of Artificial Intelligence generated information can change the markets forever, and its factoring into economical dynamics may take economists by surprise, out-dating models and schools of thought. Real estate hyper-inflation is not a new phenomenon but its consistent and almost monotonous persistence over 12 years, coinciding with prominence of public estimation information from Zillow, a successful Mass Real Estate Estimator (MREE), could not escape unobserved. What we model is a repetitive theoretical game between the MREE and the home owners, where each player has secret information and expertise. If the intention is to keep housing affordable and maintain old American lifestyle with broad home-ownership, new challenges are defined. Simulations show that a simple restriction of MREE-style price estimation availability to opt-in properties may help partially reduce feedback loop by acting on its likely causes, as suggested by experimental simulation models. The conjecture that the MREE pressure on real estate inflation rate is correlated with the absolute MREE estimation errors, which is logically explainable, is then validated in simulations., Comment: On February 15, 2022 we uploaded in overleaf the first draft of this paper under the name "Public AI on house price estimations through Zillow may influence a monotonic house price increase and inflation forever according to simulations", https://www.overleaf.com/read/yttcffkrhvjf\#7120e1

During the SARS-CoV-2 pandemic, wastewater-based genomic surveillance (WWGS) emerged as an efficient viral surveillance tool that takes into account asymptomatic cases and can identify known and novel mutations and offers the opportunity to assign known virus lineages based on the detected mutations profiles. WWGS can also hint towards novel or cryptic lineages, but it is difficult to clearly identify and define novel lineages from wastewater (WW) alone. While WWGS has significant advantages in monitoring SARS-CoV-2 viral spread, technical challenges remain, including poor sequencing coverage and quality due to viral RNA degradation. As a result, the viral RNAs in wastewater have low concentrations and are often fragmented, making sequencing difficult. WWGS analysis requires advanced computational tools that are yet to be developed and benchmarked. The existing bioinformatics tools used to analyze wastewater sequencing data are often based on previously developed methods for quantifying the expression of transcripts or viral diversity. Those methods were not developed for wastewater sequencing data specifically, and are not optimized to address unique challenges associated with wastewater. While specialized tools for analysis of wastewater sequencing data have also been developed recently, it remains to be seen how they will perform given the ongoing evolution of SARS-CoV-2 and the decline in testing and patient-based genomic surveillance. Here, we discuss opportunities and challenges associated with WWGS, including sample preparation, sequencing technology, and bioinformatics methods., Comment: V Munteanu and M Saldana contributed equally to this work. M H\"olzer, A Smith and S Mangul jointly supervised this work. For correspondence: serghei.mangul@gmail.com

The outcome of this paper was a shape of the interaction of two oscillating bubbles. This was done to express the secondary Bjerknes force using the Maxwell equations for a liquid. These subsequent equations were written for the quantities velocity, pressure, and density as deviations from steady state. Also, as it will show in the following rows, we found the expressions of the acoustic charge and of the acoustic intensity. Our results may facilitate the adoption of an approach for the interaction of two vortices and for the entrapment of a bubble by a vortex. This approach leads to a model for an acoustic charged particle which has internal angular momentum., Comment: 12, Fixed typos. Revised argument in section 3, new results

In light of the continuous transmission and evolution of SARS-CoV-2 coupled with a significant decline in clinical testing, there is a pressing need for scalable, cost-effective, long-term, passive surveillance tools to effectively monitor viral variants circulating in the population. Wastewater genomic surveillance of SARS-CoV-2 has arrived as an alternative to clinical genomic surveillance, allowing to continuously monitor the prevalence of viral lineages in communities of various size at a fraction of the time, cost, and logistic effort and serving as an early warning system for emerging variants, critical for developed communities and especially for underserved ones. Importantly, lineage prevalence estimates obtained with this approach aren't distorted by biases related to clinical testing accessibility and participation. However, the relative performance of bioinformatics methods used to measure relative lineage abundances from wastewater sequencing data is unknown, preventing both the research community and public health authorities from making informed decisions regarding computational tool selection. Here, we perform comprehensive benchmarking of 18 bioinformatics methods for estimating the relative abundance of SARS-CoV-2 (sub)lineages in wastewater by using data from 36 in vitro mixtures of synthetic lineage and sublineage genomes. In addition, we use simulated data from 78 mixtures of lineages and sublineages co-occurring in the clinical setting with proportions mirroring their prevalence ratios observed in real data. Importantly, we investigate how the accuracy of the evaluated methods is impacted by the sequencing technology used, the associated error rate, the read length, read depth, but also by the exposure of the synthetic RNA mixtures to wastewater, with the goal of capturing the effects induced by the wastewater matrix, including RNA fragmentation and degradation., Comment: For correspondence: serghei.mangul@gmail.com

In this work we prove uniqueness of distributional solutions to $2D$ Navier-Stokes equations in vorticity form $u_t-\nu\Delta u+ div (K(u)u)=0$ on $(0,\infty)\times\mathbb{R}^2$ with Radon measures as initial data, where $K$ is the Biot-Savart operator in 2-D. As a consequence, one gets the uniqueness of probabilistically weak solutions to the corresponding McKean-Vlasov stochastic differential equations. It is also proved that for initial conditions with density in $L^4$ these solutions are strong, so can be written as a functional of the Wiener process, and that pathwise uniqueness holds in the class of weak solutions, whose time marginal law densities are in $L^{\frac43}$ in space-time. In particular, one derives a stochastic representation of the vorticity $u$ of the fluid flow in terms of a solution to the McKean-Vlasov SDE. Finally, it is proved that the family $\mathbb{P}_{s,\zeta},$ $s \geq 0$, $\zeta=$probability measure on $\mathbb{R}^d$, of path laws of the solutions to the McKean-Vlasov SDE, started with $\zeta$ at $s$, form a nonlinear Markov process in the sense of McKean.

This work is concerned with the existence of mild solutions and the uniqueness of distributional solutions to nonlinear Fokker-Planck equations with nonlocal operators $\Psi(-\Delta)$, where $\Psi$ is a Bernstein function. As applications, the existence and uniqueness of solutions to the corresponding nonlinear martingale problems are proved. Furthermore, it is shown that these solutions form a nonlinear Markov process in the sense of McKean such that their one-dimensional time marginal law densities are the solutions to the nonlocal nonlinear Fokker-Planck equation. Hence, McKean's program envisioned in his PNAS paper from 1966 is realized for these nonlocal PDEs., Comment: arXiv admin note: text overlap with arXiv:2210.05612

Numerically calculating the interaction forces between two free bubbles under the action of a background of random acoustic radiation, we highlight the contributions of radiative coefficient and absorption damping coefficient to the size of these forces.It is quantitatively demonstrated, for different radii of the oscillating bubbles, that the scattering absorption forces and the scattering scattering forces are close in magnitude.For superfluid helium, the forces change direction, oscillatingly, and the ratio of the forces is much less than one., Comment: 15 pages, 12 tables, 11 graphs