The relevance of this research lies in the growing demand for unmanned aerial vehicles (UAVs) capable of operating reliably in complex environments where conventional navigation becomes unreliable due to interference, poor visibility, or camouflage. Hyperspectral imaging (HSI) provides unique opportunities for UAV-based computer vision by enabling fine-grained material recognition and object differentiation, which are critical for navigation, surveillance, agriculture, and environmental monitoring. The aim of this work is to develop a deep learning architecture integrating HSI into UAV perception for navigation, object detection, and terrain classification. Objectives include: reviewing existing HSI methods, designing a hybrid 2D/3D convolutional architecture with spectral-spatial cross-attention, training, and benchmarking. The methodology is based on the modification of the Mobile 3D Vision Transformer (MDvT) by introducing the proposed SpectralCA block. This block employs bi-directional cross-attention to fuse spectral and spatial features, enhancing accuracy while reducing parameters and inference time. Experimental evaluation was conducted on the WHU-Hi-HongHu dataset, with results assessed using Overall Accuracy, Average Accuracy, and the Kappa coefficient. The findings confirm that the proposed architecture improves UAV perception efficiency, enabling real-time operation for navigation, object recognition, and environmental monitoring tasks. Keywords: SpectralCA, deep learning, computer vision, hyperspectral imaging, unmanned aerial vehicle, object detection, semi-supervised learning.

We present an explicit numerical approximation scheme, denoted by $\{X^n\}$, for the effective simulation of solutions $X$ to a multivariate stochastic differential equation (SDE) with a superlinearly growing $\kappa$-dissipative drift, where $\kappa>1$, driven by a multiplicative heavy-tailed L\'evy process that has a finite $p$-th moment, with $p>0$. We show that for any $q\in (0,p+\kappa-1)$, the strong$L^q$-convergence$\sup_{t\in[0,T]}\mathbf{E} \|X^n_t-X_t\|^q=\mathcal{O} (h_n^{\gamma})$ holds true, in particular, our numerical scheme preserves the $q$-moments of the solution beyond the order $p$. Additionally, for any $q\in (0,p)$ we establish strong uniform convergence: $\mathbf{E}\sup_{t\in[0,T]} \|X^n_t-X_t\|^q=\mathcal{O} ( h_n^{\delta_q^\mathrm{uc}} )$. In both cases we determine the convergence rates $\gamma$ and $\delta_q^\mathrm{uc}$. In the special case of SDEs driven solely by a Brownian motion, our numerical scheme preserves super-exponential moments of the solution. The scheme $\{X^n\}$ is realized as a combination of a well-known Euler method with a Lie--Trotter type splitting technique.

We study linear perturbations against static spherically symmetric background configurations of General Relativity with a real scalar field (SF), which is minimally coupled with gravity; it is non-linear due to the presence of the self-action potential. The background solutions have a naked singularity at the center of the configuration. The focus is on the stability of the background and fundamental frequencies of the quasi-normal modes (QNM) of the axial perturbations in the Regge-Wheeler gauge. The problem is reduced to one hyperbolic master equation with an effective potential $W_{\rm eff}$, which turns out to be positive for a general non-negative SF potential; this ensures the linear stability with respect to this kind of perturbations. For numerical simulations, the SF potential was chosen in the power-law form $V(\phi)\sim\phi^{2n}$ with $2

This article presents the results of research into the causes of the Gibbs paradox in the formulation discussed by J. W. Gibbs himself. In this formulation, we are talking about an inexplicable (paradoxical) jump in the entropy of mixing of two ideal gases during the transition from mixing different to mixing identical gases. It is shown that the entropy of mixing of different ideal gases and the entropy of mixing of identical ideal gases are different (non-identical) functions of the same gas parameters. That, called a paradoxical jump in the entropy of mixing, is not a jump in the value of some function, but is the difference in the values of various functions, on condition that the variables and parameters on which these functions depend remain constant. Those who were looking for an explanation of the original Gibbs paradox did not notice this and tried to solve an unsolvable falsely posed problem: to find a parameter that change during the transition from different to identical gases caused the difference in the values of non-identical functions.

Motivated by the phenomenon of transport barriers in fusion plasma devices, we write a mathematical model of heat dispersion in a turbulent fluid with a transport barrier, properly idealized; in a scaling limit of the turbulence model with separation of scales we get a heat equation with space-dependent diffusion coefficient, poorly diffusing near the barrier; then we investigate the scaling limit when the diffused barrier converges to a sharp separating surface and describe the limit by means of the stochastic process called Brownian motion with hard membrane.

We obtain a complete characterization of planar monotone $\sigma$-continuous valuations taking integer values, without assuming invariance under any group of transformations. We further investigate the consequences of dropping monotonicity or $\sigma$-continuity and give a full classification of line valuations. We also introduce a construction of the product for valuations of this type.

We study effects of the particles coupling with scalar field (SF) on the distribution of stable circular orbits (SCO) around the naked singularity described by the well-known Fisher-Janis-Newman-Winicour solution. The power-law and exponential models of the particle--SF interaction are analyzed. The focus is on the non-connected SCO distributions. We show that coupling between particles and SF can essentially complicate the topology of the SCO distributions. In particular, it can lead to new non-overlapping SCO regions, which are separated by unstable orbits and/or by regions where the circular orbits do not exist.

The idea of value-aware model learning, that models should produce accurate value estimates, has gained prominence in model-based reinforcement learning. The MuZero loss, which penalizes a model's value function prediction compared to the ground-truth value function, has been utilized in several prominent empirical works in the literature. However, theoretical investigation into its strengths and weaknesses is limited. In this paper, we analyze the family of value-aware model learning losses, which includes the popular MuZero loss. We show that these losses, as normally used, are uncalibrated surrogate losses, which means that they do not always recover the correct model and value function. Building on this insight, we propose corrections to solve this issue. Furthermore, we investigate the interplay between the loss calibration, latent model architectures, and auxiliary losses that are commonly employed when training MuZero-style agents. We show that while deterministic models can be sufficient to predict accurate values, learning calibrated stochastic models is still advantageous.

A linear magnetic topological defect (cosmic string) is modeled as a magnetic flux-carrying tube that is impenetrable to external spinor matter. The matter field is quantized in the background of this tube, with the most general set of boundary conditions ensuring both the tube's impenetrability and the self-adjointness of the Dirac Hamiltonian operator. We compute the induced vacuum magnetic flux along the tube in (3+1)-dimensional space-time. It was shown that the requirement for the total induced vacuum magnetic flux to be finite restricts the admissible boundary conditions to only one choice: the MIT quark bag boundary condition. The dependence of the effect on the transverse size of the tube and the flux inside the tube was also analyzed.

In case of a spherically symmetric non-linear scalar field (SF) in flat space, besides singularity at the center, spherical singularities can occur for non-zero values of radial variable $r>0$. We show that in the General Relativity the gravitational field suppresses the occurrence of the spherical singularities under some generic conditions. Our consideration deals with asymptotically flat space-times around static spherically symmetric configurations in presence of $N$ non-linear SFs, which are minimally coupled to gravity. Constraints are imposed on the SF potentials, which guarantee a monotonicity of the fields as functions of radial variable; also the potentials are assumed to be exponentially bounded. We give direct proof that solutions of the joint system of Einstein -- SF equations satisfying the conditions of asymptotic flatness are regular for all values of $r$, except for naked singularities in the center $r=0$ in the Schwarzschild (curvature) coordinates. Asymptotic relations for SF and metric near the center are derived, which appear to be remarkably similar to the case of the Fisher solution for free SF. These relations determine two main types of the corresponding geodesic structure when photons can be captured by the singularity or not depending on the existence of the photon sphere. To illustrate, the case of one SF with monomial potential is analyzed in detail numerically. We show that the image of the accretion disk around the singularity, observed from infinity, can take the form of a bright ring with a dark spot in the center, like the case of an ordinary black hole.

In this paper, we discuss the generation of symbols (and alphabets) based on specific user requirements (medium, priorities, type of information that needs to be conveyed). A framework for the generation of alphabets is proposed, and its use for the generation of a shorthand writing system is explored. We discuss the possible use of machine learning and genetic algorithms to gather inputs for generation of such alphabets and for optimization of already generated ones. The alphabets generated using such methods may be used in very different fields, from the creation of synthetic languages and constructed scripts to the creation of sensible commands for multimodal interaction through Human-Computer Interfaces, such as mouse gestures, touchpads, body gestures, eye-tracking cameras, and brain-computing Interfaces, especially in applications for elderly care and people with disabilities.

In this paper, we discuss the generation of symbols (and alphabets) based on specific user requirements (medium, priorities, type of information that needs to be conveyed). A framework for the generation of alphabets is proposed, and its use for the generation of a shorthand writing system is explored. We discuss the possible use of machine learning and genetic algorithms to gather inputs for generation of such alphabets and for optimization of already generated ones. The alphabets generated using such methods may be used in very different fields, from the creation of synthetic languages and constructed scripts to the creation of sensible commands for multimodal interaction through Human-Computer Interfaces, such as mouse gestures, touchpads, body gestures, eye-tracking cameras, and brain-computing Interfaces, especially in applications for elderly care and people with disabilities.

In this work we established the relationship between the crystalline structure symmetry, point defects and possible appearance of the ferroelectric-like polarization in HfO2-y nanoparticles. Notably, that XRD and EPR analysis revealed the formation of the ferroelectric-like orthorhombic phase in the oxygen-deficient HfO2-y nanoparticles (pure and doped with rare-earth element yttrium). DFT calculations showed that small HfO2 nanoparticles may become polar, especially in the presence of impurity atoms and/or oxygen vacancies. To explain the experimental results, we have modified the effective LGD model through the parameterization approach, focusing on the Landau expansion coefficients associated with the polar (FE) and antipolar (AFE) orderings, which agrees with the performed DFT calculations. The effective LGD model can be useful for the development of the novel generation of silicon-compatible ferroelectric nanomaterials based on the HfxZr1-xO2-y.

This paper targets the problem of encoding information into binary cell assemblies. Spiking neural networks and k-winners-take-all models are two common approaches, but the first is hard to use for information processing and the second is too simple and lacks important features of the first. We present an intermediate model that shares the computational ease of kWTA and has more flexible and richer dynamics. It uses explicit inhibitory neurons to balance and shape excitation through an iterative procedure. This leads to a recurrent interaction between inhibitory and excitatory neurons that better adapts to the input distribution and performs such computations as habituation, decorrelation, and clustering. To show these, we investigate Hebbian-like learning rules and propose a new learning rule for binary weights with multiple stabilization mechanisms. Our source code is publicly available.

This article presents the results of research into the causes of the Gibbs paradox in the formulation discussed by J. W. Gibbs himself. In this formulation, we are talking about an inexplicable (paradoxical) jump in the entropy of mixing of two ideal gases during the transition from mixing different to mixing identical gases. It is shown that the entropy of mixing of different ideal gases and the entropy of mixing of identical ideal gases are different (non-identical) functions of the same gas parameters. That, called a paradoxical jump in the entropy of mixing, is not a jump in the value of some function, but is the difference in the values of various functions, on condition that the variables and parameters on which these functions depend remain constant. Those who were looking for an explanation of the original Gibbs paradox did not notice this and tried to solve an unsolvable falsely posed problem: to find a parameter that change during the transition from different to identical gases caused the difference in the values of non-identical functions.

The article reveals the error that in classical thermodynamics leads to the Gibbs paradox. The essence of the error lies in the fact that the entropy of an ideal gas is attributed to additive quantities, but it is not correct. The value of an additive quantity for a whole object is equal to the sum of its values for the parts of the object in any division of the object into parts. The entropy of an ideal gas in classical thermodynamics is expressed by the equation that contains the term Rnln(V/n), where n is the number of moles of gas, V is the volume of gas, R is the universal gas constant, or by equations equivalent to it. As a result, the entropy of an ideal gas is equal to the sum of the entropies of its parts only if the parts of the gas are in different places (separated by an impermeable partition). If the parts of the gas form a mixture, then the sum of the entropies of the parts is not equal to the entropy of the gas. Despite this, the entropy of an ideal gas is considered to be an additive quantity. This gives rise to a series of inexplicable conclusions known as various formulations of the Gibbs paradox.

To build large language models for Ukrainian we need to expand our corpora with large amounts of new algorithmic tasks expressed in natural language. Examples of task performance expressed in English are abundant, so with a high-quality translation system our community will be enabled to curate datasets faster. To aid this goal, we introduce a recipe to build a translation system using supervised finetuning of a large pretrained language model with a noisy parallel dataset of 3M pairs of Ukrainian and English sentences followed by a second phase of training using 17K examples selected by k-fold perplexity filtering on another dataset of higher quality. Our decoder-only model named Dragoman beats performance of previous state of the art encoder-decoder models on the FLORES devtest set.

This paper studies a nonzero-sum stochastic differential game in the context of shared spatial-domain pollution control. The pollution dynamics are governed by a stochastic partial differential equation (SPDE) driven by a Brownian sheet, capturing the stochastic nature of environmental fluctuations. Two players, representing different regions, aim to minimize their respective cost functionals, which balance pollution penalties with the cost of implementing control strategies. The nonzero-sum framework reflects the interdependent yet conflicting objectives of the players, where both cooperation and competition influence the outcomes. We derive necessary and sufficient conditions for Nash equilibrium strategies, using a maximum principle approach. This approach involves the introduction of a new pair of adjoint variables, (L_1, L_2), which do not appear in a corresponding formulation with the classical (1-parameter) Brownian motion. Finally, we apply our results to two case studies in pollution control, demonstrating how spatial and stochastic dynamics shape the equilibrium strategies.

At present, in the theory of stochastic process modeling a problem of assessment of reliability and accuracy of stochastic process model in $C(T)$ space wasn't studied for the case of implicit decomposition of process in the form of a series with independent terms. The goal is to study reliability and accuracy in $C(T)$ of models of processes from $Sub_\varphi(\Omega)$ that cannot be decomposed in a series with independent elements explicitly. Using previous research in the field of modeling of stochastic processes, assumption is considered about possibility of decomposition of a stochastic process in the series with independent elements that can be found using approximations. Impact of approximation error of process decomposition in series with independent elements on reliability and accuracy of modeling of stochastic process in $C(T)$ is studied. Theorems are proved that allow estimation of reliability and accuracy of a model in $C(T)$ of a stochastic process from $Sub_\varphi(\Omega)$ in the case when decomposition of this process in a series with independent elements can be found only with some error, for example, using numerical approximations.

This review examines the conditions that lead to the formation of flexo-sensitive chiral polar structures in thin films and core-shell ferroelectric nanoparticles. It also analyzes possible mechanisms by which the flexoelectric effect impacts the polarization structure in core-shell ferroelectric nanoparticles. Special attention is given to the role of the anisotropic flexoelectric effect in forming a unique type of polarization states with distinct chiral properties, referred to as "flexons". In the first part of the review, we study the influence of the flexoelectric coupling on the polarity, chirality and branching of metastable labyrinthine domain structures in uniaxial ferroelectric core-shell nanoparticles. We reveal that the transition from sinuous branched domain stripes to spiral-like domains occurs gradually as the flexoelectric coupling strength is increased. Our findings indicate that the joint action of flexoelectric effect and chemical strains, termed as "flexo-chemical" coupling, can significantly influence the effective Curie temperature, polarization distribution, domain morphology, and chirality in multiaxial ferroelectric core-shell nanoparticles. Furthermore, we demonstrate that the combination of flexo-chemical coupling and screening effects leads to the appearance and stabilization of a chiral polarization morphology in nanoflakes of van der Waals ferrielectrics. In the second part of the review, we discuss several advanced applications of flexo-sensitive chiral polar structures in core-shell ferroelectric nanoparticles for nanoelectronics elements and cryptography. We underline the possibilities of the flexoelectric control of multiple-degenerated labyrinthine states, which may correspond to a differential negative capacitance (NC) state stabilized in the uniaxial ferroelectric core by the presence of a screening shell.