Search

We consider dimer models on growing Aztec diamonds, which are certain domains in the square lattice, with edge weights of the form $\nu(\,\cdot\,)^\beta$, where $\nu(\,\cdot\,)$ is a doubly periodic function on the edges of the lattice and $\beta$ is an inverse temperature parameter. We prove that in the zero-temperature ($\beta\to\infty$) limit, and for generic values of $\nu(\,\cdot\,)$, these dimer models undergo crystallization: The limit shape converges to a piecewise linear function called the tropical limit shape, and the local fluctuations are governed by the Gibbs measures with the slope dictated by the tropical limit shape for high enough values of $\beta$. We also show that the tropical limit shape and the tropical arctic curve (consisting of ridges of the crystal) are described in terms of a tropical curve and a tropical action function on that curve, which are the tropical analogs of the spectral curve and the action function that describe the finite-temperature models. The tropical curve is explicit in terms of the edge weights, and the tropical action function is a solution of Kirchhoff's problem on the tropical curve., Comment: 52 pages, 20 figures

Automatic Speaker Verification (ASV) systems, which identify speakers based on their voice characteristics, have numerous applications, such as user authentication in financial transactions, exclusive access control in smart devices, and forensic fraud detection. However, the advancement of deep learning algorithms has enabled the generation of synthetic audio through Text-to-Speech (TTS) and Voice Conversion (VC) systems, exposing ASV systems to potential vulnerabilities. To counteract this, we propose a novel architecture named AASIST3. By enhancing the existing AASIST framework with Kolmogorov-Arnold networks, additional layers, encoders, and pre-emphasis techniques, AASIST3 achieves a more than twofold improvement in performance. It demonstrates minDCF results of 0.5357 in the closed condition and 0.1414 in the open condition, significantly enhancing the detection of synthetic voices and improving ASV security., Comment: 8 pages, 2 figures, 2 tables. Accepted paper at the ASVspoof 2024 (the 25th Interspeech Conference)

In this paper we study the asymptotic behavior of the Asymmetric Simple Exclusion Process (=ASEP) with finitely many particles. It turns out that a certain randomized initial condition is the most amenable to such an analysis. Our main result is the behavior of such an ASEP in the KPZ limit regime. A key technical tool introduced in the paper -- the coloring of ASEP particles with the use of random Mallows permutations -- may be of independent interest., Comment: 13 pages

In the problem of online unweighted interval selection, the objective is to maximize the number of non-conflicting intervals accepted by the algorithm. In the conventional online model of irrevocable decisions, there is an Omega(n) lower bound on the competitive ratio, even for randomized algorithms [Bachmann et al. 2013]. In a line of work that allows for revocable acceptances, [Faigle and Nawijn 1995] gave a greedy 1-competitive (i.e. optimal) algorithm in the real-time model, where intervals arrive in order of non-decreasing starting times. The natural extension of their algorithm in the adversarial (any-order) model is 2k-competitive [Borodin and Karavasilis 2023], when there are at most k different interval lengths, and that is optimal for all deterministic, and memoryless randomized algorithms. We study this problem in the random-order model, where the adversary chooses the instance, but the online sequence is a uniformly random permutation of the items. We consider the same algorithm that is optimal in the cases of the real-time and any-order models, and give an upper bound of 2.5 on the competitive ratio under random-order arrivals. We also show how to utilize random-order arrivals to extract a random bit with a worst case bias of 2/3, when there are at least two distinct item types. We use this bit to derandomize the barely random algorithm of [Fung et al. 2014] and get a deterministic 3-competitive algorithm for single-length interval selection with arbitrary weights., Comment: 18 pages, 7 figures

Scaling magnets down to where quantum size effects become prominent triggers quantum tunneling of magnetization (QTM), profoundly influencing magnetization dynamics. Measuring magnetization switching in an Fe atomic chain under a carefully tuned transverse magnetic field, we observe a non-monotonic variation of magnetization lifetimes around a level crossing, known as the diabolic point (DP). Near DPs, local environment effects causing QTM are efficiently suppressed, enhancing lifetimes by three orders of magnitude. Adjusting interatomic interactions further facilitates multiple DPs. Our study provides a deeper understanding of quantum dynamics near DPs and enhances our ability to engineer a quantum magnet., Comment: Main text and Supplementary

One of the most crucial components in the field of biometric security is the automatic speaker verification system, which is based on the speaker's voice. It is possible to utilise ASVs in isolation or in conjunction with other AI models. In the contemporary era, the quality and quantity of neural networks are increasing exponentially. Concurrently, there is a growing number of systems that aim to manipulate data through the use of voice conversion and text-to-speech models. The field of voice biometrics forgery is aided by a number of challenges, including SSTC, ASVSpoof, and SingFake. This paper presents a system for automatic speaker verification. The primary objective of our model is the extraction of embeddings from the target speaker's audio in order to obtain information about important characteristics of his voice, such as pitch, energy, and the duration of phonemes. This information is used in our multivoice TTS pipeline, which is currently under development. However, this model was employed within the SSTC challenge to verify users whose voice had undergone voice conversion, where it demonstrated an EER of 20.669.

At ambient conditions, SiC is known to be resistant to irradiation with swift heavy ions (SHI) decelerating in the electronic stopping regime. However, there is no experimental data on the SiC irradiation at elevated temperatures. To investigate this problem, we evaluate the stability of SiC to SHI impacts at high temperatures up to 2200 K. We apply the combination of the Monte-Carlo code TREKIS-3, describing excitation of the electronic and atomic systems using temperature-dependent scattering cross-sections, with molecular-dynamic modeling of the lattice response to the excitation. We demonstrate that increasing irradiation temperature increases the energy transferred to the atomic lattice from the excited electronic system. This material heating leads to formation of a stable nanometric damaged core along the trajectory of 710 MeV Bi ion when the irradiation temperature overcomes the threshold of ~1800 K. In this case, a chain of nanometric voids along the ion trajectory forms due to the mass transport from the track core by edge dislocations. Voids of larger sizes appear at higher irradiation temperatures. At lower irradiation temperatures, the damaged regions recrystallize completely within ~100 ps after the ion passage.

In this paper we assign a family of $n$ coupled line ensembles to any $U_q (\widehat{\mathfrak{sl}}_{n+1})$ colored stochastic fused vertex model, which satisfies two properties. First, the joint law of their top curves coincides with that of the colored height functions for the vertex model. Second, the $n$ line ensembles satisfy an explicit Gibbs property prescribing their laws if all but a few of their curves are conditioned upon. We further describe several examples of such famlies of line ensembles, including the ones for the colored stochastic six-vertex and $q$-boson models. The appendices (which may be of independent interest) include an explanation of how the $U_q (\widehat{\mathfrak{sl}}_{n+1})$ colored stochastic fused vertex model degenerates to the log-gamma polymer, and an effective rate of convergence of the colored stochastic six-vertex model to the colored ASEP., Comment: 90 pages, 23 figures

This paper presents the experimental results on research of growth processes of GaAs layers on silicon substrates by molecular beam epitaxy. The formation of buffer Si layer in a single growth process has been found to significantly improve the crystalline quality of the GaAs layers formed on its surface, as well as to prevent the formation of anti-phase domains both on offcutted towards the [110] direction and on singular Si(100) substrates. It has been demonstrated that the use of cyclic thermal annealing at temperatures 350-660{\deg}C in the flow of arsenic atoms makes it possible to reduce the number of threading dislocations and increase the smoothness of the GaAs layers surface. At the same time, the article considers possible mechanisms that lead to an improvement in the quality of the surface layers of GaAs. It is shown that the thus obtained GaAs layers of submicron thickness on the singular Si(100) substrates have a mean square value of surface roughness 1.9 nm. The principal possibility of using thin GaAs layers on silicon as templates for forming on them light-emitting semiconductor heterostructures with active area based on self-organizing InAs quantum dots and InGaAs quantum well is presented. They are shown to exhibit photoluminescence at 1.2 um at room temperature., Comment: 18 pages, in Russian language, 6 figures

Let $\{C_{\alpha}\}_{\alpha\in \Omega}$ be a family of closed and convex sets in a Hilbert space $H$, having a nonempty intersection $C$. We consider a sequence $\{x_n\}$ of remote projections onto them. This means, $x_0\in H$, and $x_{n+1}$ is the projection of $x_n$ onto such a set $C_{\alpha(n)}$ that the ratio of the distances from $x_n$ to this set and to any other set from the family is at least $t_n\in [0,1]$. We study properties of the weakness parameters $t_n$ and of the sets $C_\alpha$ which ensure the norm or weak convergence of the sequence $\{x_n\}$ to a point in $C$. We show that condition (T) is necessary and sufficient for the norm convergence of $x_n$ to a point in $C$ for any starting element and any family of closed, convex, and symmetric sets $C_\alpha$. This generalizes a result of Temlyakov who introduced (T) in the context of greedy approximation theory. We give examples explaining to what extent the symmetry condition on the sets $C_{\alpha}$ can be dropped. Condition (T) is stronger than $\sum t_n^2=\infty$ and weaker than $\sum t_n/n=\infty$. The condition $\sum t_n^2=\infty$ turns out to be necessary and sufficient for the sequence $\{x_n\}$ to have a partial weak limit in $C$ for any family of closed and convex sets $C_\alpha$ and any starting element.

The cactus group $J_n$ is the $S_n$-equivariant fundamental group of the real locus of the Deligne-Mumford moduli space of stable rational curves with marked points. This group plays the role of the braid group for the monoidal category of Kashiwara crystals attached to a simple Lie algebra. Following Frenkel, Kirillov and Varchenko, one can identify the multiplicity set in a tensor product of $\mathfrak{sl}_2$-crystals with the set of arc diagrams on a disc, thus allowing a much simpler description of the corresponding $J_n$-action. We address the problem of classifying the orbits of this cactus group action. Namely, we describe some invariants of this action and show that in some (fairly general) classes of examples there are no other invariants. Furthermore, we describe some additional relations, including the braid relation, that this action places on the generators of $J_n$., Comment: 22 pages, 10 figures

Some results of a computational experiment for determining the intrinsic dimension of linguistic varieties for the Bengali and Russian languages are presented. At the same time, both sets of words and sets of bigrams in these languages were considered separately. The method used to solve this problem was based on formal concept analysis algorithms. It was found that the intrinsic dimensions of these languages are significantly less than the dimensions used in popular neural network models in natural language processing., Comment: Preprint, 10th International Conference on Pattern Recognition and Machine Intelligence (PReMI 2023)

The present paper introduces a novel object of study - a language fractal structure. We hypothesize that a set of embeddings of all $n$-grams of a natural language constitutes a representative sample of this fractal set. (We use the term Hailonakea to refer to the sum total of all language fractal structures, over all $n$). The paper estimates intrinsic (genuine) dimensions of language fractal structures for the Russian and English languages. To this end, we employ methods based on (1) topological data analysis and (2) a minimum spanning tree of a data graph for a cloud of points considered (Steele theorem). For both languages, for all $n$, the intrinsic dimensions appear to be non-integer values (typical for fractal sets), close to 9 for both of the Russian and English language., Comment: Preprint. Under review

Vanishing polynomials are polynomials over a ring which output $0$ for all elements in the ring. In this paper, we study the ideal of vanishing polynomials over specific types of rings, along with the closely related ring of polynomial functions. In particular, we provide several results on generating vanishing polynomials. We first analyze the ideal of vanishing polynomial over $\mathbb{Z}_n$, the ring of the integers modulo $n$. We then establish an isomorphism between the vanishing polynomials of a ring and the vanishing polynomials of the constituent rings in its decomposition. Lastly, we generalize our results to study the ideal of vanishing polynomials over arbitrary commutative rings., Comment: 12 pages

We consider probability measures arising from the Cauchy summation identity for the LLT (Lascoux--Leclerc--Thibon) symmetric polynomials of rank $n \geq 1$. We study the asymptotic behaviour of these measures as one of the two sets of polynomials in the Cauchy identity stays fixed, while the other one grows to infinity. At $n=1$, this corresponds to an analogous limit of the Schur process, which is known to be given by the Gaussian Unitary Ensemble (GUE) corners process. Our main result states that, for $n>1$, our measures asymptotically split into two parts: a continuous one and a discrete one. The continuous part is a product of $n$ GUE corners processes; the discrete part is an explicit finite distribution on interlacing $n$-colourings of $n$ interlacing triangles, which has weights that are rational functions in the LLT parameter $q$. The latter distribution has a number of interesting (partly conjectural) combinatorial properties, such as $q$-nonnegativity and enumerative phenomena underlying its support. Our main tools are two different representations of the LLT polynomials, one as partition functions of a fermionic lattice model of rank $n$, and the other as finite-dimensional contour integrals, which were recently obtained in arXiv:2012.02376, arXiv:2101.01605., Comment: 55 pages

InSe is a promising material for a next-generation of two-dimensional electronic and optical devices, characteristics of which are largely determined by the type of band structure, direct or indirect. In general, different methods can be sensitive to different peculiarities of the electronic structure leading to different results. In this work, we will focus on the luminescent properties of few-layer $\beta$-InSe with a thickness of 6 to 75 monolayers (ML). Low-temperature micro-photoluminescence ($mu$-PL) studies show a sharp increase in PL intensity in the range of thicknesses from 16 to 20 monolayers, where, in addition, there is a singularity in the dependence of the work function on the thickness. Time-resolved photoluminescence spectroscopy (TRPL) reveals three characteristic PL decay times that differ from each other by about an order of magnitude. We associate the processes underlying the two faster decays with the recombination of electrons and holes between the band extrema, either directly or through the interband relaxation of holes. Their contributions to the total PL intensity increase significantly in the same thickness range, 16-20 MLs. On the contrary, the slowest contribution, which we attribute mainly to the defect-assisted recombination, prevails at a smaller number of monolayers and then noticeably decreases. These results indicate the indirect-to-direct bandgap transition near 16-20 MLs, which determines the range of applicability of a few-layer $\beta$-InSe for efficient light emitters.

The purpose of the present work is to provide a detailed asymptotic analysis of the $k\times\ell$ doubly periodic Aztec diamond dimer model of growing size for any $k$ and $\ell$ and under mild conditions on the edge weights. We explicitly describe the limit shape and the 'arctic' curves that separate different phases, as well as prove the convergence of local fluctuations to the appropriate translation-invariant Gibbs measures away from the arctic curves. We also obtain a homeomorphism between the rough region and the amoeba of an associated Harnack curve, and illustrate, using this homeomorphism, how the geometry of the amoeba offers insight into various aspects of the geometry of the arctic curves. In particular, we determine the number of frozen and smooth regions and the number of cusps on the arctic curves. Our framework essentially relies on three somewhat distinct areas: (1) Wiener-Hopf factorization approach to computing dimer correlations; (2) Algebraic geometric `spectral' parameterization of periodic dimer models; and (3) Finite-gap theory of linearization of (nonlinear) integrable partial differential and difference equations on the Jacobians of the associated algebraic curves. In addition, in order to access desired asymptotic results we develop a novel approach to steepest descent analysis on Riemann surfaces via their amoebas., Comment: 95 pages, 22 figures, corrected typos, appendix added