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Electrically induced $p-n$ junctions in graphene bilayer (GBL) have shown superior performance for detection of sub-THz radiation at cryogenic temperatures, especially upon electrical induction of the band gap $E_g$. Still, the upper limits of responsivity and noise equivalent power (NEP) at very large $E_g$ remained unknown. Here, we study the cryogenic performance of GBL detectors at $f=0.13$ THz by inducing gaps up to $E_g \approx 90$ meV, a value close to the limits observed in recent transport experiments. High value of the gap is achieved by using high-$\kappa$ bottom hafnium dioxide gate dielectric. The voltage responsivity, current responsivity and NEP optimized with respect to doping do not demonstrate saturation with gap induction up to its maximum values. The NEP demonstrates an order-of-magnitude drop from $\sim450$ fW/Hz$^{1/2}$ in the gapless state to $\sim30$ fW/Hz$^{1/2}$ at the largest gap. At largest induced band gaps, plasmonic oscillations of responsivity become visible and important for optimization of sub-THz response.

The recently suggested bipartite analysis extends the Kauffman planar decomposition to arbitrary $N$, i.e. extends it from the Jones polynomial to the HOMFLY polynomial. This provides a generic and straightforward non-perturbative calculus in an arbitrary Chern--Simons theory. Technically, this approach is restricted to knots and links which possess bipartite realizations, i.e. can be entirely glued from antiparallel lock (two-vertex) tangles rather than single-vertex $R$-matrices. However, we demonstrate that the resulting positive decomposition (PD), i.e. the representation of the fundamental HOMFLY polynomials as positive integer polynomials of the three parameters $\phi$, $\bar\phi$ and $D$, exists for arbitrary knots, not only bipartite ones. This poses new questions about the true significance of bipartite expansion, which appears to make sense far beyond its original scope, and its generalizations to higher representations. We have provided two explanations for the existence of the PD for non-bipartite knots. An interesting option is to resolve a particular bipartite vertex in a not-fully-bipartite diagram and reduce the HOMFLY polynomial to a linear combination of those for smaller diagrams. If the resulting diagrams correspond to bipartite links, this option provides a PD even to an initially non-bipartite knot. Another possibility for a non-bipartite knot is to have a bipartite clone with the same HOMFLY polynomial providing this PD. We also suggest a promising criterium for the existence of a bipartite realization behind a given PD, which is based on the study of the precursor Jones polynomials., Comment: 37 pages

The Macdonald finite-difference Hamiltonian is lifted to a super-generalization. In addition to canonical bosonic time variables $p_k$ new Grassmann time variables $\theta_k$ are introduced, and the Hamiltonian is represented as a differential operator acting on a space of functions of both types of variables $p_k$ and $\theta_k$. Eigenfunctions for this Hamiltonian are a suitable generalization of Macdonald polynomials to super-Macdonald polynomials discussed earlier in the literature. Peculiarities of the construction in comparison to the canonical bosonic case are discussed.

We construct local and nonlocal Hamiltonian structures and variational symplectic structures for the $(2+1)$-dimensional Euler equation in the vorticity form and study the action of the local Hamiltonian and symplectic structures on the cosymmetries of second order and the contact symmetries.

Carrier transition is one of the major factors hindering the high-speed implementation of M{\o}lmer-S{\o}rensen gates in trapped-ion quantum processors. We present an approach to design laser pulse shapes for M{\o}lmer-S{\o}rensen gate in ion chains which accounts for the effect of carrier transition on qubit-phonon dynamics. We show that the fast-oscillating carrier term effectively modifies the spin-dependent forces acting on ions, and this can be compensated by a simple nonlinear transformation of a laser pulse. Using numerical simulations for short ion chains and perturbation theory for longer chains, we demonstrate that our approach allows to reach the infidelity below $10^{-4}$ while keeping the gate duration below 100 $\mu$s.

While there is a general consensus about the structure of one qubit operations in topological quantum computer, two qubits are as usual a more difficult and complex story of different attempts with varying approaches, problems and effectiveness. In this paper we discuss how to construct an efficient realization of a two qubit gate in topological quantum computer, by using principle of cabling from the knot theory. This allows to construct a braiding of cables dependent on the parameters of the theory where there is a low probability of moving out of computational space (high fidelity of operation) while there is a non-trivial entangling two-qubit operation. We also present some examples of these operations for different parameters of the theory.

The triad refers to embedding the Macdonald polynomials into the Noumi-Shiraishi functions and their reduction to solutions of simple linear equations at particular values of $t$. It provides an alternative definition of Macdonald theory. We discuss lifting the triad to an elliptic generalization of the Noumi-Shiraishi functions. The central unknown ingredient is linear equations, for which we discuss various possible approaches, including immediate elliptic deformation of periodicity conditions, (elliptic) Ding-Iohara-Miki algebra operators, and elliptic Kostka coefficients., Comment: 13 pages

To effectively apply passive speckle reduction methods, it is essential to use an illumination system that maximally exploits the non-ideal temporal coherence and angular diversity (spatial coherence reduction) of laser light. This study examines the necessary conditions for these factors to act independently to achieve maximum speckle reduction. A novel design for decoherent focusing of laser illumination into a rectangular, uniformly lit spot is proposed. The design is based on an array of rectangular prisms of varying heights and a Fresnel lens comprising crossed 1D cylindrical Fresnel lenses with flat facets. Mathematical modelling demonstrates that such a lens can effectively focus a Gaussian beam into a rectangular uniform illuminated spot, even for lenses with a high numerical aperture (NA = 0.2). A planar implementation of this lens is also proposed. The comb-like spectrum of a laser diode is shown to limit the capabilities of passive methods, as it is challenging to generate a significant number of decorrelated laser sub-beams beyond the available spectral modes. Experimental results confirm that applying a slight modulation (~15%) to the laser diode current during intensity integration transforms the comb spectrum into a continuous one. This enables the generation of an unlimited number of decorrelated laser beams, independent of the laser's spectral modes, to achieve the desired number for a specific optical device., Comment: 13 pages, 13 figures, 3 tables, 10 equations

Symplectic mappings of the plane serve as key models for exploring the fundamental nature of complex behavior in nonlinear systems. Central to this exploration is the effective visualization of stability regimes, which enables the interpretation of how systems evolve under varying conditions. While the area-preserving quadratic H\'enon map has received significant theoretical attention, a comprehensive description of its mixed parameter-space dynamics remain lacking. This limitation arises from early attempts to reduce the full two-dimensional phase space to a one-dimensional projection, a simplification that resulted in the loss of important dynamical features. Consequently, there is a clear need for a more thorough understanding of the underlying qualitative aspects. This paper aims to address this gap by revisiting the foundational concepts of reversibility and associated symmetries, first explored in the early works of G.D. Birkhoff. We extend the original framework proposed by H\'enon by adding a period-doubling diagram to his isochronous diagram, which allows to represents the system's bifurcations and the groups of symmetric periodic orbits that emerge in typical bifurcations of the fixed point. A qualitative and quantitative explanation of the main features of the region of parameters with bounded motion is provided, along with the application of this technique to other symplectic mappings, including cases of multiple reversibility. Modern chaos indicators, such as the Reversibility Error Method and the Generalized Alignment Index, are employed to distinguish between various dynamical regimes in the mixed space of variables and parameters. These tools prove effective in differentiating regular and chaotic dynamics, as well as in identifying twistless orbits and their associated bifurcations.

Most algorithms for computing persistent homology do so by tracking cycles that represent homology classes. There are many choices of such cycles, and specific choices have found different uses in applications. Although it is known that persistence diagrams can be computed in matrix multiplication time [8] for the more general case of zigzag persistent homology, it is not clear how to extract cycle representatives, especially if specific representatives are desired. In this paper, we provide the same matrix multiplication bound for computing representatives for the two choices common in applications in the case of ordinary persistent (co)homology. We first provide a fast version of the reduction algorithm, which is simpler than the algorithm in [8], but returns a different set of representatives than the standard algorithm [6] We then give a fast version of a different variant called the row algorithm [4], which returns the same representatives as the standard algorithm.

A new Highly-Granular time-of-flight Neutron Detector (HGND) is being developed and constructed to measure azimuthal neutron flow and neutron yields in nucleus-nucleus interactions in heavy-ion collisions with energies up to 4A GeV in the fixed target experiment BM@N at JINR. Details of the detector design and results of performance studies for neutron identification and reconstruction are shown. Comparison of simulations for different options of the HGND layout at the BM@N is presented. Several proposed methods of neutron reconstruction including machine learning and cluster methods are discussed.

Layered van der Waals tellurides reveal topologically non-trivial properties that give rise to unconventional magneto-transport phenomena. Additionally, their semimetallic character with high mobility makes them promising candidates for large magneto-thermoelectric effects. Remarkable studies on the very large and unconventional Nernst effect in WTe$_2$ have been reported, raising questions about whether this property is shared across the entire family of van der Waals tellurides. In this study, systematic measurements of the Nernst effect in telluride van der Waals Weyl semimetals are presented. Large linear Nernst coefficients in WTe$_2$ and MoTe$_2$ are identified, and moderate Nernst coefficients with non-linear behavior in magnetic fields are observed in W$_{0.65}$Mo$_{0.35}$Te$_2$, TaIrTe$_4$, and TaRhTe$_4$. Within this sample set, a correlation between the dominant linear-in-magnetic-field component of the Nernst coefficient and mobility is established, aligning with the established Nernst scaling framework, though with a different scaling factor compared to existing literature. This enhancement might be caused by the shared favorable electronic band structure of this family of materials. Conversely, the non-linear component of the Nernst effect in a magnetic field could not be correlated with mobility. This non-linear term is almost absent in the binary compounds, suggesting a multiband origin and strong compensation between electron-like and hole-like carriers. This comprehensive study highlights the potential of van der Waals tellurides for thermoelectric conversion.

Within the context of wavefunctions of integrable many-body systems, rational multivariable Baker-Akhiezer (BA) functions were introduced by O. Chalykh, M. Feigin and A. Veselov and, in the case of the trigonometric Ruijsenaars-Schneider system, can be associated with a reduction of the Macdonald symmetric polynomials at $t=q^{-m}$ with integer partition labels substituted by arbitrary complex numbers. A parallel attempt to describe wavefunctions of the bispectral trigonometric Ruijsenaars-Schneider problem was made by M. Noumi and J. Shiraishi who proposed a power series that reduces to the Macdonald polynomials at particular values of parameters. It turns out that this power series also reduces to the BA functions at $t=q^{-m}$, as we demonstrate in this letter. This makes the Macdonald polynomials, the BA functions and the Noumi-Shiraishi (NS) series a closely tied {\it triad} of objects, which have very different definitions, but are straightforwardly related with each other. In particular, theory of the BA functions provides a nice system of simple linear equations, while the NS functions provide a nice way to represent the multivariable BA function explicitly with arbitrary number of variables., Comment: 9 pages

Vanadium dioxide with metal-to-insulator transition (MIT) that is triggered by heat, current or light is a promising material for modern active THz/mid-IR metasurfaces and all-optical big data processing systems. Multilayer VO$_2$-based active metasurfaces are urgently needed however several important issues related to VO$_2$ properties in VO$_2$/TiO$_2$/Al$_2$O$_3$ films should be thoroughly examined first. We study electrical, optical and structural properties of VO$_2$ films as well as their composition and switching characteristics as function of the VO$_2$ layer thickness in VO$_2$/TiO$_2$ composites. XRD analysis revealed an epitaxial growth of films with deformation of the monoclinic VO$_2$ lattice to hexagonal symmetry. Reduced VO$_2$ layer thickness from 170 nm to 20 nm results in increased phase transition temperature while the width of the resistance versus temperature hysteresis loop R(T) remains constant at ~6C for all VO$_2$ thicknesses in the range of 20-170 nm. The resistance alteration ratio is reduced from 4.2e3 to 2.7e2 in thinner films. Raman spectra reveal a significant shift of VO$_2$ lattice vibration modes for films thinner than 30 nm claiming a great structural strain whereas modes position for thicker VO$_2$ layers are similar to those in bulk structure. Composition of VO$_2$ films has revealed only a minor alteration of VO$_2$/V$_2$O$_5$ phases ratio from 1.6 to 1.8 when the film thickness has been increased from 20 nm to 50 nm. Investigation of surface elemental composition and valence states of VO$_2$ films revealed that VO$_2$/V$_2$O$_5$ ratio remains practically unchanged with thickness reduction. The study of electrical MIT dynamics revealed the switching time of a 50 nm VO$_2$ film to be as low as 800 ns.

Macdonald symmetric polynomial at $t=q^{-m}$ reduces to a sum of much simpler complementary non-symmetric polynomials, which satisfy a simple system of the first order linear difference equations with constant coefficients, much simpler than those induced by the usual Ruijsenaars Hamiltonians of the cut-and-join type. We provide examples of explicit expressions for these polynomials nicknamed Baker-Akhiezer functions (BAF), and demonstrate that they further decompose into sums of nicely factorized quantities, perhaps, non-uniquely. Equations and solutions can be easily continued to non-integer parameters $\lambda$, which, in Macdonald polynomial case, are associated with integer partitions. Moreover, there is a straightforward generalization to "twisted" BAF's, which, however, are not so easy to decompose, and factorization of the coefficients is lost, at least naively. Still, these twisted BAF's provide eigenfunctions for Hamiltonians associated with commutative integer ray subalgebras of the Ding-Iohara-Miki algebra., Comment: 19 pages

The performance of the scintillation wall (ScWall) has been studied in the first physics run at the Baryonic Matter at Nuclotron (BM@N) in Xe+CsI reaction at a xenon beam energy of 3.8 and 3.0 AGeV. The design and functionality of the ScWall emphasizing its ability to detect charged spectator fragments produced in nucleus-nucleus interactions are shown. The simulation results regarding ScWall's capability to determine collision geometry and the comparison between measured and simulated charged spectators fragments spectra are discussed.

In machine learning, a loss function measures the difference between model predictions and ground-truth (or target) values. For neural network models, visualizing how this loss changes as model parameters are varied can provide insights into the local structure of the so-called loss landscape (e.g., smoothness) as well as global properties of the underlying model (e.g., generalization performance). While various methods for visualizing the loss landscape have been proposed, many approaches limit sampling to just one or two directions, ignoring potentially relevant information in this extremely high-dimensional space. This paper introduces a new representation based on topological data analysis that enables the visualization of higher-dimensional loss landscapes. After describing this new topological landscape profile representation, we show how the shape of loss landscapes can reveal new details about model performance and learning dynamics, highlighting several use cases, including image segmentation (e.g., UNet) and scientific machine learning (e.g., physics-informed neural networks). Through these examples, we provide new insights into how loss landscapes vary across distinct hyperparameter spaces: we find that the topology of the loss landscape is simpler for better-performing models; and we observe greater variation in the shape of loss landscapes near transitions from low to high model performance.

Characterizing the loss of a neural network with respect to model parameters, i.e., the loss landscape, can provide valuable insights into properties of that model. Various methods for visualizing loss landscapes have been proposed, but less emphasis has been placed on quantifying and extracting actionable and reproducible insights from these complex representations. Inspired by powerful tools from topological data analysis (TDA) for summarizing the structure of high-dimensional data, here we characterize the underlying shape (or topology) of loss landscapes, quantifying the topology to reveal new insights about neural networks. To relate our findings to the machine learning (ML) literature, we compute simple performance metrics (e.g., accuracy, error), and we characterize the local structure of loss landscapes using Hessian-based metrics (e.g., largest eigenvalue, trace, eigenvalue spectral density). Following this approach, we study established models from image pattern recognition (e.g., ResNets) and scientific ML (e.g., physics-informed neural networks), and we show how quantifying the shape of loss landscapes can provide new insights into model performance and learning dynamics.

Cathodoluminescence (CL) microscopy has emerged as a powerful tool for investigating the optical properties of materials at the nanoscale, offering unique insights into the behavior of photonic and plasmonic materials under electron excitation. We introduce an atlas of bulk CL spectra for a range of materials widely used in photonics and plasmonics. Through a combination of experimental CL spectroscopy and Monte Carlo simulations, we characterize electron penetration depth and energy deposition, offering a foundational reference for interpreting CL spectra and understanding material behavior under electron excitation. By capturing CL signal from a diverse range of materials, this atlas provides insights into the intrinsic emission properties essential for material selection and design in photonic and plasmonic device engineering.

The Re5+(5d2) compounds possess large spin-orbital interaction which urges for large anisotropy, non-collinear structures and other phenomena. Here we present ReCl5 composed by separate Re2Cl10 units formed by edge-shared chlorine octahedra. It demonstrates the formation of antiferromagnetically ordered state in two steps at TN1 = 35.5 K and TN2 = 13.2 K seen in dc-, ac-magnetic susceptibility and in specific heat. At 4K it can be transformed to the state with spontaneous magnetic moment by relatively weak magnetic field m0H = 0.5 T via metamagnetic phase transition. Ab initio calculations give anisotropic ferromagnetic exchange interactions J1 and J2 within and between rhenium pairs forming the zig-zag chains along the a-axis. Pairs of zig-zag chains are coupled by ferromagnetic interaction J3 along the c-axis into magnetic honeycomb ladders. The ladders are coupled by significantly weaker interaction J4., Comment: 11 pages, 8 figures

This paper presents the multiplicity of neutral and charged hadrons produced in 90 GeV$/c$ proton-carbon interactions from a dataset taken by the NA61/SHINE experiment in 2017. Particle identification via dE/dx was performed for the charged hadrons $\pi^\pm$, $K^\pm$, and $p / \bar{p}$; the neutral hadrons $K^0_S$, $\Lambda$, and $\bar{\Lambda}$ were identified via an invariant mass analysis of their decays to charged hadrons. Double-differential multiplicity results as a function of laboratory momentum and polar angle are presented for each particle species; these results provide vital constraints on the predicted neutrino beam flux for current and future long-baseline neutrino oscillation experiments.

The Betti tables of a multigraded module encode the grades at which there is an algebraic change in the module. Multigraded modules show up in many areas of pure and applied mathematics, and in particular in topological data analysis, where they are known as persistence modules, and where their Betti tables describe the places at which the homology of filtered simplicial complexes change. Although Betti tables of singly and bigraded modules are already being used in applications of topological data analysis, their computation in the bigraded case (which relies on an algorithm that is cubic in the size of the filtered simplicial complex) is a bottleneck when working with large datasets. We show that, in the special case of $0$-dimensional homology (which is relevant for clustering and graph classification) the Betti tables of a bigraded module can be computed in log-linear time. We also consider the problem of computing minimal presentations, and show that a minimal presentation of $0$-dimensional persistent homology can be computed in quadratic time, regardless of the grading poset., Comment: 19 pages, 1 figure

Zigzag filtrations of simplicial complexes generalize the usual filtrations by allowing simplex deletions in addition to simplex insertions. The barcodes computed from zigzag filtrations encode the evolution of homological features. Although one can locate a particular feature at any index in the filtration using existing algorithms, the resulting representatives may not be compatible with the zigzag: a representative cycle at one index may not map into a representative cycle at its neighbor. For this, one needs to compute compatible representative cycles along each bar in the barcode. Even though it is known that the barcode for a zigzag filtration with $m$ insertions and deletions can be computed in $O(m^\omega)$ time, it is not known how to compute the compatible representatives so efficiently. For a non-zigzag filtration, the classical matrix-based algorithm provides representatives in $O(m^3)$ time, which can be improved to $O(m^\omega)$. However, no known algorithm for zigzag filtrations computes the representatives with the $O(m^3)$ time bound. We present an $O(m^2n)$ time algorithm for this problem, where $n\leq m$ is the size of the largest complex in the filtration.

We generalize the recently discovered planar decomposition (Kauffman bracket) for the HOMFLY polynomials of bipartite knot/link diagrams to (anti)symmetrically colored HOMFLY polynomials. Cabling destroys planarity, but it is restored after projection to (anti)symmetric representations. This allows to go beyond arborescent calculus, which so far produced the majority of results for colored polynomials. Technicalities include combinations of projectors, and these can be handled rigorously, without any guess-work -- what can be also useful for other considerations, where reliable quantization was so far unavailable. We explicitly provide simple examples of calculation of the HOMFLY polynomials in symmetric representations with the use of our planar technique. These examples reveal what we call the bipartite evolution and the bipartite decomposition of squares of $\mathcal{R}$-matrices eigenvalues in the antiparallel channel., Comment: 26 pages

Keyphrase selection is a challenging task in natural language processing that has a wide range of applications. Adapting existing supervised and unsupervised solutions for the Russian language faces several limitations due to the rich morphology of Russian and the limited number of training datasets available. Recent studies conducted on English texts show that large language models (LLMs) successfully address the task of generating keyphrases. LLMs allow achieving impressive results without task-specific fine-tuning, using text prompts instead. In this work, we access the performance of prompt-based methods for generating keyphrases for Russian scientific abstracts. First, we compare the performance of zero-shot and few-shot prompt-based methods, fine-tuned models, and unsupervised methods. Then we assess strategies for selecting keyphrase examples in a few-shot setting. We present the outcomes of human evaluation of the generated keyphrases and analyze the strengths and weaknesses of the models through expert assessment. Our results suggest that prompt-based methods can outperform common baselines even using simple text prompts., Comment: The 12th International Conference on Analysis of Images, Social Networks and Texts (AIST'2024)

Persistent (co)homology is a central construction in topological data analysis, where it is used to quantify prominence of features in data to produce stable descriptors suitable for downstream analysis. Persistence is challenging to compute in parallel because it relies on global connectivity of the data. We propose a new algorithm to compute persistent cohomology in the distributed setting. It combines domain and range partitioning. The former is used to reduce and sparsify the coboundary matrix locally. After this initial local reduction, we redistribute the matrix across processors for the global reduction. We experimentally compare our cohomology algorithm with DIPHA, the only publicly available code for distributed computation of persistent (co)homology; our algorithm demonstrates a significant improvement in strong scaling., Comment: 11 pages, 16 figures

Generative Flow Networks (GFlowNets) are a family of generative models that learn to sample objects with probabilities proportional to a given reward function. The key concept behind GFlowNets is the use of two stochastic policies: a forward policy, which incrementally constructs compositional objects, and a backward policy, which sequentially deconstructs them. Recent results show a close relationship between GFlowNet training and entropy-regularized reinforcement learning (RL) problems with a particular reward design. However, this connection applies only in the setting of a fixed backward policy, which might be a significant limitation. As a remedy to this problem, we introduce a simple backward policy optimization algorithm that involves direct maximization of the value function in an entropy-regularized Markov Decision Process (MDP) over intermediate rewards. We provide an extensive experimental evaluation of the proposed approach across various benchmarks in combination with both RL and GFlowNet algorithms and demonstrate its faster convergence and mode discovery in complex environments.

We prove that normalized colored Alexander polynomial (the $A \rightarrow 1$ limit of colored HOMFLY-PT polynomial) evaluated for one-hook (L-shape) representation R possesses scaling property: it is equal to the fundamental Alexander polynomial with the substitution $q \rightarrow q^{|R|}$. The proof is simple and direct use of Reshetikhin-Turaev formalism to get all required R-matrices., Comment: 20 pages

This article extends the study of dynamical properties of the symmetric McMillan map, emphasizing its utility in understanding and modeling complex nonlinear systems. Although the map features six parameters, we demonstrate that only two are irreducible: the linearized rotation number at the fixed point and a nonlinear parameter representing the ratio of terms in the biquadratic invariant. Through a detailed analysis, we classify regimes of stable motion, provide exact solutions to the mapping equations, and derive a canonical set of action-angle variables, offering analytical expressions for the rotation number and nonlinear tune shift. We further establish connections between general standard-form mappings and the symmetric McMillan map, using the area-preserving H\'enon map and accelerator lattices with thin sextupole magnet as representative case studies. Our results show that, despite being a second-order approximation, the symmetric McMillan map provides a highly accurate depiction of dynamics across a wide range of system parameters, demonstrating its practical relevance in both theoretical and applied contexts.

Quite some years ago, Oleg Chalykh has built a nice theory from the observation that the Macdonald polynomial reduces at $t=q^{-m}$ to a sum over permutations of simpler polynomials called Baker-Akhiezer functions, which can be unambiguously constructed from a system of linear difference equations. Moreover, he also proposed a generalization of these polynomials to the twisted Baker-Akhiezer functions. Recently, in a private communication Oleg suggested that these twisted Baker-Akhiezer functions could provide eigenfunctions of the commuting Hamiltonians associated with the $(-1,a)$ rays of the Ding-Iohara-Miki algebra. In the paper, we discuss this suggestion and some evidence in its support., Comment: 14 pages, LaTeX

Nowadays, low-rank approximations of matrices are an important component of many methods in science and engineering. Traditionally, low-rank approximations are considered in unitary invariant norms, however, recently element-wise approximations have also received significant attention in the literature. In this paper, we propose an accelerated alternating minimization algorithm for solving the problem of low-rank approximation of matrices in the Chebyshev norm. Through the numerical evaluation we demonstrate the effectiveness of the proposed procedure for large-scale problems. We also theoretically investigate the alternating minimization method and introduce the notion of a $2$-way alternance of rank $r$. We show that the presence of a $2$-way alternance of rank $r$ is the necessary condition of the optimal low-rank approximation in the Chebyshev norm and that all limit points of the alternating minimization method satisfy this condition.

A typical example of superintegrability is provided by expression of the Hopf link hyperpolynomial in an arbitrary representation through a pair of the Macdonald polynomials at special points. In the simpler case of the Hopf link HOMFLY-PT polynomial and a pair of the Schur functions, it is a relation in the unitary matrix model. We explain that the Cherednik-Mehta-Macdonald (CMM) identity for bilinear Macdonald residues with an elliptic weight function is nothing but a reformulation of these same formulas. Their lifting to arbitrary knots and links, even torus ones remains obscure., Comment: 12 pages

Novel CaV1-xWxO3 (0.1 < x < 0.33) oxides with an orthorhombically distorted perovskite structure of GdFeO3 type have been synthesized. These compounds contain in B-position W+6 and V cations in an oxidation state between +4 (CaVO3) and +3 (x=0.33). CaV0.9W0.1O3 compound possesses metallic type of conductivity and Pauli paramagnetism. The intermediate compositions are between bad metal and semiconducting type of behavior with paramagnetic response. CaV0.67W0.33O3 is a Mott insulator with localized V+3 moments coupled by strong antiferromagnetic interactions. It demonstrates the reduction of effective magnetic moment at high temperatures and canonical spin glass state formation with the freezing temperature Tg = 27.5 K seen in dc - and ac - magnetic susceptibility. Disorder in the magnetic subsystem induces a broad peak in magnetic contribution of the heat capacity at Tmax = 46 K., Comment: 13 pages, 6 figures

The Shortest-Path Problem in Graph of Convex Sets (SPP in GCS) is a recently developed optimization framework that blends discrete and continuous decision making. Many relevant problems in robotics, such as collision-free motion planning, can be cast and solved as an SPP in GCS, yielding lower-cost solutions and faster runtimes than state-of-the-art algorithms. In this paper, we are motivated by motion planning of robot arms that must operate swiftly in static environments. We consider a multi-query extension of the SPP in GCS, where the goal is to efficiently precompute optimal paths between given sets of initial and target conditions. Our solution consists of two stages. Offline, we use semidefinite programming to compute a coarse lower bound on the problem's cost-to-go function. Then, online, this lower bound is used to incrementally generate feasible paths by solving short-horizon convex programs. For a robot arm with seven joints, our method designs higher quality trajectories up to two orders of magnitude faster than existing motion planners., Comment: To appear in: The International Workshop on the Algorithmic Foundations of Robotics, WAFR 2024

Keyphrase selection plays a pivotal role within the domain of scholarly texts, facilitating efficient information retrieval, summarization, and indexing. In this work, we explored how to apply fine-tuned generative transformer-based models to the specific task of keyphrase selection within Russian scientific texts. We experimented with four distinct generative models, such as ruT5, ruGPT, mT5, and mBART, and evaluated their performance in both in-domain and cross-domain settings. The experiments were conducted on the texts of Russian scientific abstracts from four domains: mathematics & computer science, history, medicine, and linguistics. The use of generative models, namely mBART, led to gains in in-domain performance (up to 4.9% in BERTScore, 9.0% in ROUGE-1, and 12.2% in F1-score) over three keyphrase extraction baselines for the Russian language. Although the results for cross-domain usage were significantly lower, they still demonstrated the capability to surpass baseline performances in several cases, underscoring the promising potential for further exploration and refinement in this research field., Comment: DAMDID-2024

The paper is concerned with Lax representations for the three-dimensional Euler--Helmholtz equation. We show that the parameter in the Lax representation from Theorem 3 in [15] is non-removable. Then we present two new Lax representations with non-removable parameters.

Robustness is critical for machine learning (ML) classifiers to ensure consistent performance in real-world applications where models may encounter corrupted or adversarial inputs. In particular, assessing the robustness of classifiers to adversarial inputs is essential to protect systems from vulnerabilities and thus ensure safety in use. However, methods to accurately compute adversarial robustness have been challenging for complex ML models and high-dimensional data. Furthermore, evaluations typically measure adversarial accuracy on specific attack budgets, limiting the informative value of the resulting metrics. This paper investigates the estimation of the more informative adversarial distance using iterative adversarial attacks and a certification approach. Combined, the methods provide a comprehensive evaluation of adversarial robustness by computing estimates for the upper and lower bounds of the adversarial distance. We present visualisations and ablation studies that provide insights into how this evaluation method should be applied and parameterised. We find that our adversarial attack approach is effective compared to related implementations, while the certification method falls short of expectations. The approach in this paper should encourage a more informative way of evaluating the adversarial robustness of ML classifiers., Comment: Accepted manuscript at International Mechanical Engineering Congress and Exposition IMECE2024

This review paper describes the energy-upgraded CEBAF accelerator. This superconducting linac has achieved 12 GeV beam energy by adding 11 new high-performance cryomodules containing eighty-eight superconducting cavities that have operated CW at an average accelerating gradient of 20 MV/m. After reviewing the attributes and performance of the previous 6 GeV CEBAF accelerator, we discuss the upgraded CEBAF accelerator system in detail with particular attention paid to the new beam acceleration systems. In addition to doubling the acceleration in each linac, the upgrade included improving the beam recirculation magnets, adding more helium cooling capacity to allow the newly installed modules to run cold, adding a new experimental hall, and improving numerous other accelerator components. We review several of the techniques deployed to operate and analyze the accelerator performance, and document system operating experience and performance. In the final portion of the document, we present much of the current planning regarding projects to improve accelerator performance and enhance operating margins, and our plans for ensuring CEBAF operates reliably into the future. For the benefit of potential users of CEBAF, the performance and quality measures for beam delivered to each of the experimental halls is summarized in the appendix., Comment: 66 pages, 73 figures, 21 tables

Superconducting nanowire single-photon detectors are widely used for detecting individual photons across various wavelengths from ultraviolet to near-infrared range. Recently, there has been increasing interest in enhancing their sensitivity to single photons in the mid-infrared spectrum, driven by applications in quantum communication, spectroscopy and astrophysics. Here, we present our efforts to expand the spectral detection capabilities of U-shaped NbTiN-based superconducting nanowire single-photon detectors, fabricated in a 2-wire configuration on a silicon-on-insulator substrate, into the mid-infrared range. We demonstrate saturated internal detection efficiency extending up to a wavelength of 3.5 {\mu}m for a 5 nm thick and 50 nm wide NbTiN nanowire with a dark count rate less than 10 counts per second at 0.9 K and a rapid recovery time of 4.3 ns. The detectors are engineered for integration on waveguides in a silicon-on-insulator platform for compact, multi-channel device applications., Comment: 5 figures, 7 pages

We extend the study of banana diagrams in coordinate representation to the case of curved space-times. If the space is harmonic, the Green functions continue to depend on a single variable -- the geodesic distance. But now this dependence can be somewhat non-trivial. We demonstrate that, like in the flat case, the coordinate differential equations for powers of Green functions can still be expressed as determinants of certain operators. Therefore, not-surprisingly, the coordinate equations remain straightforward -- while their reformulation in terms of momentum integrals and Picard-Fuchs equations can seem problematic. However we show that the Feynman parameter representation can also be generalized, at least for banana diagrams in simple harmonic spaces, so that the Picard-Fuchs equations retain their Euclidean form with just a minor modification. A separate story is the transfer to the case when the Green function essentially depends on several rather than a single argument. In this case, we provide just one example, that the equations are still there, but conceptual issues in the more general case will be discussed elsewhere.

Chern-Simons theory in application to the quantum computing is actively developing at the present. However, most discussed are the questions of using materials with known parameters and building corresponding quantum gates and algorithms. In this paper we discuss opposite problem of finding Chern-Simons level $k$ in the unknown material. For this purpose, we use the previously derived braiding rules for Chern-Simons $SU(2)_k$ anyons. Using certain operations (turnarounds) on three anyons, one can measure probabilities of annihilation of pairs of anyons, which depend on the parameter of the theory. Therefore, Chern-Simons level $k$ can be found from such an experiment. It is implied that anyons additionally possess certain properties which are required for topological quantum computations., Comment: 12 pages, 13 figures

A simple geometric way is suggested to derive the Ward identities in the Chern-Simons theory, also known as quantum $A$- and $C$-polynomials for knots. In quasi-classical limit it is closely related to the well publicized augmentation theory and contact geometry. Quantization allows to present it in much simpler terms, what could make these techniques available to a broader audience. To avoid overloading of the presentation, only the case of the colored Jones polynomial for the trefoil knot is considered, though various generalizations are straightforward. Restriction to solely Jones polynomials (rather than full HOMFLY-PT) is related to a serious simplification, provided by the use of Kauffman calculus. Going beyond looks realistic, however it remains a problem, both challenging and promising., Comment: 16 pages, v2: minor updates

We propose the extension of the position space approach to Feynman integrals from the banana family to generic Feynman diagrams. Our approach is based on getting rid of integration in position space and then writing differential equations for the products of propagators defined for any graph. We employ the so-called ''bananization'' to start with simple Feynman graphs and further substituting each edge with a multiple one. We explain how the previously developed theory of banana diagrams can be used to describe what happens to the differential equations (Ward identities) on Feynman diagrams after this transformation. Our approach works for generic enough (large enough) dimension and masses. We expect that after Fourier transform our equations should be related to the Picard-Fuchs equations. Therefore, we describe the challenges of Fourier transform that arise in our approach.

Traps and structural defects at the hole and electron transport interfaces of the microcrystalline absorber limits the efficiency and long-term stability of perovskite solar cells (PSCs) due to accumulation of the ionic clusters, non-radiative recombination and electrochemical corrosion. Surface engineering using self-assembled monolayers (SAM) was considered as an effective strategy for modification of charge-collection junctions. In this work, we demonstrate the first report about complex integration of a SAM for double-side passivation in p-i-n PSCs. Integrating the novel 5-(4-[bis(4-fluorophenyl)amino]phenyl)thiophene-2-carboxylic acid (FTPATC) as a fluorinated SAM at the hole-transport interface reduced potential barriers and lattice stresses in the absorber. At the electron-transport side, FTPATC interacted with the A-site cations of the perovskite molecule (Cs, formamidinium), inducing a dipole for defect compensation. Using the passivation approach with fluorinated SAM demonstrated benefits in the gain of the output performance up to 22.2%. The key-advantage of double-side passivation was confirmed by the enhanced stability under continuous light-soaking (1-sun equivalent, 65 C, ISOS-L-2), maintaining 88% of the initial performance over 1680 hours and thermal stabilization under harsh heating at 90 C.

Predicting high-fidelity ground motions for future earthquakes is crucial for seismic hazard assessment and infrastructure resilience. Conventional empirical simulations suffer from sparse sensor distribution and geographically localized earthquake locations, while physics-based methods are computationally intensive and require accurate representations of Earth structures and earthquake sources. We propose a novel artificial intelligence (AI) simulator, Conditional Generative Modeling for Ground Motion (CGM-GM), to synthesize high-frequency and spatially continuous earthquake ground motion waveforms. CGM-GM leverages earthquake magnitudes and geographic coordinates of earthquakes and sensors as inputs, learning complex wave physics and Earth heterogeneities, without explicit physics constraints. This is achieved through a probabilistic autoencoder that captures latent distributions in the time-frequency domain and variational sequential models for prior and posterior distributions. We evaluate the performance of CGM-GM using small-magnitude earthquake records from the San Francisco Bay Area, a region with high seismic risks. CGM-GM demonstrates a strong potential for outperforming a state-of-the-art non-ergodic empirical ground motion model and shows great promise in seismology and beyond.

The theory of the Kauffman bracket, which describes the Jones polynomial as a sum over closed circles formed by the planar resolution of vertices in a knot diagram, can be straightforwardly lifted from sl(2) to sl(N) at arbitrary N -- but for a special class of bipartite diagrams made entirely from the anitparallel lock tangle. Many amusing and important knots and links can be described in this way, from twist and double braid knots to the celebrated Kanenobu knots for even parameters -- and for all of them the entire HOMFLY polynomials possess planar decomposition. This provides an approach to evaluation of HOMFLY polynomials, which is complementary to the arborescent calculus, and this opens a new direction to homological techniques, parallel to Khovanov-Rozansky generalisations of the Kauffman calculus. Moreover, this planar calculus is also applicable to other symmetric representations beyond the fundamental one, and to links which are not fully bipartite what is illustrated by examples of Kanenobu-like links., Comment: 33 pages, published version