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We prove an analogue of Chebyshev's alternation theorem for linearly independent discrete functions $\Phi_n=\{\varphi_k\}_{k=1}^n$ on the interval $[0,q]_{\mathbb{Z}}=[0,q]\cap \mathbb{Z}$. In particular, we establish that the polynomial of best uniform approximation of a discrete function $f$ admits a Chebyshev alternance set of length $n+1$ if and only if $\Phi_n$ is a Chebyshev $T_{\mathbb{Z}}$-system. Also, we obtain a discrete version of Sturm's oscillation theorem, according to which the number of discrete zeros of the polynomial $\sum_{k=m}^{n}a_k\varphi_k$ is no less than $m-1$ and no more than $n-1$. This implies that $\Phi_n$ is a $T_{\mathbb{Z}}$-system and a discrete Sturm-Hurwitz spectral gap theorem is valid. As applications, we study the orthogonal polynomials with removed largest zeros. We establish the monotonicity property of coefficients in the Fourier expansions of such polynomials, thereby strengthening the results of H. Cohn and A. Kumar. We apply this to solve a Yudin-type extremal problem for polynomials with spectral gap., Comment: 31 pages

Wireless radio frequency coils provide a promising solution for clinical MR applications due to several benefits, such as cable-free connection and compatibility with MR platforms of different vendors. Namely, for the purpose of clinical high-field human breast imaging several wireless transceiver coils are known to the date, those operational principle is based on inductive coupling with a body coil. These coils are commonly consist of a several volume resonators to perform bilateral breast imaging. Due to the electrically close location of volume resonators, strong inductive coupling is observed, resulting in the occurrence of hybrid modes. In principle, MR imaging using one of the hybrid modes is possible provided by the homogeneity of a B+ distribution. However, the question of influence of volume resonators coupling on wireless coil transmit efficiency and receive sensitivity was not previously studied. By this work, we performed study to understand this issue. The first wireless coil with decoupled resonators is developed, evaluated numerically and experimentally including in vivo study on healthy volunteers. According to the obtained results, transmit efficiency and receive sensitivity of a pair of decoupled Helmholtz resonators is at least 24% higher than for a pair of coupled resonators., Comment: 12 pages, 10 figures, 2 tables

In this paper, we construct the leash-metric that transforms the set of (partially) mixing actions of a Hausdorff locally compact group with a countable neighborhood base into a complete separable metric space., Comment: in Russian language

We characterize the parameters $(\alpha,\beta,p,q)$ for which the condition $f|x|^\alpha\in L^p$ and $\widehat{f}|\xi|^\beta\in L^q$ implies the validity of the Poisson summation formula, thus completing the study of Kahane and Lemari\'e-Rieusset., Comment: 16 pages

Superpositions of handed molecular states give rise to achiral eigenstates, delocalized across a double-well potential via tunneling. A coherent superposition of these energy eigenstates could dynamically relocalize the molecules into chiral states, which has only been addressed theoretically. Here, we present a microwave six-wave mixing pump-probe study to create and probe coherent chiral tunneling dynamics in a rotational state. Through a time-resolved scheme, we uncover the periodic time evolution of the induced chiral wavepacket under field-free conditions. Moreover, we demonstrate precise phase control of this coherence via phase modulation during pump excitation., Comment: 14 pages, 4 figures in the main text and 27 pages, 12 figures, and 4 tables in the Supplementary Material

We obtain Marcinkiewicz--ygmund (MZ) inequalities in various Banach and quasi-Banach spaces under minimal assumptions on the structural properties of these spaces. Our main results show that the Bernstein inequality in a general quasi-Banach function lattice $X$ implies Marcinkiewicz-Zygmund type estimates in $X$. We present a general approach to obtain MZ inequalities not only for polynomials but for other function classes including entire functions of exponential type, splines, exponential sums, etc.

We present an analytical calculation of the local density of states correlation function $ \beta(\omega) $ in the L\'evy-Rosenzweig-Porter random matrix ensemble at energy scales larger than the level spacing but smaller than the bandwidth. The only relevant energy scale in this limit is the typical level width $\Gamma_0$. We show that $\beta(\omega \ll \Gamma_0) \sim W/\Gamma_0$ (here $W$ is width of the band) whereas $\beta(\omega \gg \Gamma_0) \sim (W/\Gamma_0) (\omega/\Gamma_0)^{-\mu} $ where $\mu$ is an index characterising the distribution of the matrix elements. We also provide an expression for the average return probability at long times: $\ln [R(t\gg\Gamma_0^{-1})] \sim -(\Gamma_0 t)^{\mu/2}$. Numerical results based on the pool method and exact diagonalization are also provided and are in agreement with the analytical theory., Comment: 19 pages, 3 figures

We prove the finiteness of the genus of finite-dimensional division algebras over many infinitely generated fields. More precisely, let $K$ be a finite field extension of a field which is a purely transcendental extension of infinite transcendence degree of some subfield. We show that if $D$ is a central division $K$-algebra, then ${\bf gen}(D)$ consists of Brauer classes $[D']$ such that $[D]$ and $[D']$ generate the same subgroup of $Br(K)$. In particular, the genus of any division $K$-algebra of exponent 2 is trivial. Note that the family of such fields is closed under finitely generated extensions. Moreover, if $char(K) \ne 2$, we prove that the genus of a simple algebraic group of type $\mathrm{G}_2$ over such a field $K$ is trivial.

We show differences between a language-and-vision model CLIP and two text-only models - FastText and SBERT - when it comes to the encoding of individuation information. We study latent representations that CLIP provides for substrates, granular aggregates, and various numbers of objects. We demonstrate that CLIP embeddings capture quantitative differences in individuation better than models trained on text-only data. Moreover, the individuation hierarchy we deduce from the CLIP embeddings agrees with the hierarchies proposed in linguistics and cognitive science.

We present PLUGH (https://www.urbandictionary.com/define.php?term=plugh), a modern benchmark that currently consists of 5 tasks, each with 125 input texts extracted from 48 different games and representing 61 different (non-isomorphic) spatial graphs to assess the abilities of Large Language Models (LLMs) for spatial understanding and reasoning. Our evaluation of API-based and open-sourced LLMs shows that while some commercial LLMs exhibit strong reasoning abilities, open-sourced competitors can demonstrate almost the same level of quality; however, all models still have significant room for improvement. We identify typical reasons for LLM failures and discuss possible ways to deal with them. Datasets and evaluation code are released (https://github.com/altsoph/PLUGH)., Comment: Wordplay Workshop @ ACL 2024

Parametric down-conversion in a nonlinear crystal is a widely employed technique for generating quadrature squeezed light with multiple modes, which finds applications in quantum metrology, quantum information and communication. Here we study the generation of temporally multimode pulsed squeezed light in a synchronously pumped optical parametric oscillator (SPOPO) operating below the oscillation threshold, while considering the presence of non-compensated intracavity group-velocity dispersion. Based on the developed timedomain model of the system, we show that the dispersion results in mode-dependent detuning of the broadband supermodes of the pulsed parametric process from the cavity resonance, as well as linear coupling between these supermodes. With the perturbation theory up to the second order in the coupling coefficients between modes, we obtained a solution for the supermode amplitudes given an arbitrary number of modes and pump level. The dispersion affects the quantum state of the supermodes by influencing their squeezing level and the rotation of the squeezing ellipse. It also affects the entanglement among the supermodes, leading to reduced suppression of shot noise level as measured in the balanced homodyne detection scheme. Furthermore, our study highlights the potential of SPOPO with group-velocity dispersion as a testbench for experimental investigations of multimode effects in linearly evanescent coupled parametric oscillators., Comment: 13 pages, 8 figures

This paper discusses the charge-exchange strength functions $S(E)$ of the isotopes $^{128,130}$Te. The experimental data of the $S(E)$ strength functions obtained from $(^{3}\mathrm{He}, t)$ reactions, as well as the $S(E)$ strength functions calculated in the microscopic theory of finite fermi-systems, are analyzed. The resonance structure of the strength function $S(E)$ is examined, and the Gamow-Teller and Pygmy resonances are identified. The resonance structure of the strength function $S(E)$ is vital for the calculation and analysis of the process of neutrino capture by atomic nuclei.

This study investigates the application of generative artificial intelligence in architectural design. We present a novel methodology that combines multiple neural networks to create an unsupervised and unmoderated stream of unique architectural images. Our approach is grounded in the conceptual framework called machine apophenia. We hypothesize that neural networks, trained on diverse human-generated data, internalize aesthetic preferences and tend to produce coherent designs even from random inputs. The methodology involves an iterative process of image generation, description, and refinement, resulting in captioned architectural postcards automatically shared on several social media platforms. Evaluation and ablation studies show the improvement both in technical and aesthetic metrics of resulting images on each step.

We perform transport and noise measurements for device consisting of a thin NbSe$_2$ flake laid onto the predefined gold electrodes and covered with a thin hBN flake. In the shot noise of a NbSe$_2$/Au tunnel junction (TJ), we identify Andreev reflection regime by demonstrating the effective charge doubling. Further, by creating temperature gradient across the TJ and measuring its delta-$T$ noise in the normal state, we extract electron-phonon scattering length in NbSe$_2$ and its $T$-dependence. The results of delta-$T$ noise measurements in the absence of a magnetic field when the flake is superconducting are in qualitative agreement with expectations. The introduced approach is promising for the study of nonequilibrium configurations in superconductors., Comment: 7 pages + Supplemental Material 4 pages

We prove that the Hausdorff--Young inequality $\|{\widehat{f}}\|_{q(\cdot)} \leq C \|{f}\|_{p(\cdot)}$ with $q(x)=p'(1/x)$ and $p(\cdot)$ even and non-decreasing holds in variable Lebesgue spaces if and only if $p$ is a constant. However, under the additional condition on monotonicity of $f$, we obtain a full characterization of Pitt-type weighted Fourier inequalities in the classical and variable Lebesgue setting.

Chirality, an inherent property of most objects of the universe, is a dynamic research topic in material science, physics, chemistry, and biology. The fundamental appeal of this extensive study is supported by the technological quest to manufacture materials with configurable chiralities for emerging applications ranging from optoelectronics and photonics to pharmaceutics and medicine. Recent advances put forth ferroelectrics as a host of chiral topological states in the form of Bloch domain walls, skyrmions, merons, and Hopfions, offering thus a unique ground for making chirality switchable and tunable. Here we review current developments, milestones achieved, and future routes of chiral ferroelectric materials. We focus on insights into the topological origin of the chirality in the nanostructured ferroelectrics, bringing new controllable functionalities. We pay special attention to novel developments enabling tunability and manipulating the chiroptical response and enantioselectivity, leading to new applications in nano-optoelectronics, plasmonics, pharmaceutics, and bio-medical industries.

We have selected candidate massive stars in the galaxy IC 342 based on archival images from the Hubble Space Telescope and images from the 2 m telescope at the Natioal Astronomical Observatory Rozhen, Bulgaria. Spectral observations of 24 out of 27 selected stars are carried out with the 6 m BTA telescope at the SAO RAS and with the 3.5 m Apache Point Observatory telescope (USA) as part of the program for searching bright massive stars in galaxies outside the Local Group. Our analysis reveals that 12 objects have spectra lacking prominent features, except for the emission lines of the surrounding nebulae and are identified as single supergiants of classes O9 to F5 or spatially unresolved young compact clusters. One source with an absorption spectrum probably belongs to our Galaxy. The spectra of seven other objects show features typical of Wolf-Rayet stars or compact clusters containing Wolf-Rayet stars. Another source is a compact supernova remnant. Two other objects are tentatively classified as cold LBV candidates, and one object is classified as a B[e]-supergiant candidate.

Extractive summarization is a task of highlighting the most important parts of the text. We introduce a new approach to extractive summarization task using hidden clustering structure of the text. Experimental results on CNN/DailyMail demonstrate that our approach generates more accurate summaries than both extractive and abstractive methods, achieving state-of-the-art results in terms of ROUGE-2 metric exceeding the previous approaches by 10%. Additionally, we show that hidden structure of the text could be interpreted as aspects.

We obtain new sampling discretization results in Orlicz norms on finite dimensional spaces. As applications, we study sampling recovery problems, where the error of the recovery process is calculated with respect to different Orlicz norms. In particular, we are interested in the recovery by linear methods in the norms close to $L^2$.

We extend the affine inequalities on $\mathbb{R}^n$ for Sobolev functions in $W^{s,p}$ with $1 \leq p < n/s$ obtained recently by Haddad-Ludwig [16, 17] to the remaining range $p \geq n/s$. For each value of $s$, our results are stronger than affine Moser-Trudinger and Morrey inequalities. As a byproduct, we establish the analog of the classical $L^p$ Bourgain-Brezis-Mironescu inequalities related to the Moser-Trudinger case $p=n$. Our main tool is the affine invariant provided by Besov polar projection bodies.

This paper presents the Character Decision Points Detection (CHADPOD) task, a task of identification of points within narratives where characters make decisions that may significantly influence the story's direction. We propose a novel dataset based on CYOA-like games graphs to be used as a benchmark for such a task. We provide a comparative analysis of different models' performance on this task, including a couple of LLMs and several MLMs as baselines, achieving up to 89% accuracy. This underscores the complexity of narrative analysis, showing the challenges associated with understanding character-driven story dynamics. Additionally, we show how such a model can be applied to the existing text to produce linear segments divided by potential branching points, demonstrating the practical application of our findings in narrative analysis., Comment: GamesAndNLP @ LREC COLING 2024

In this paper, we explore the generation of one-liner jokes through multi-step reasoning. Our work involved reconstructing the process behind creating humorous one-liners and developing a working prototype for humor generation. We conducted comprehensive experiments with human participants to evaluate our approach, comparing it with human-created jokes, zero-shot GPT-4 generated humor, and other baselines. The evaluation focused on the quality of humor produced, using human labeling as a benchmark. Our findings demonstrate that the multi-step reasoning approach consistently improves the quality of generated humor. We present the results and share the datasets used in our experiments, offering insights into enhancing humor generation with artificial intelligence., Comment: ICCC 2024

It is well known that if a function $f$ satisfies $$\|f(x) e^{\pi \alpha |x|^2}\|_p + \| \widehat{f}(\xi) e^{\pi \alpha |\xi|^2} \|_q<\infty \qquad\qquad\qquad(*)$$ with $\alpha=1$ and $1\le p,q<\infty$, then $f\equiv 0.$ We prove that if $f$ satisfies $(*)$ with some $0<\alpha<1$ and $1\le p,q\leq \infty$, then $$ |f(y)|\le C (1+|y|)^{\frac{d}{p}} e^{- \pi \alpha |y|^2}, \quad y\in \mathbb{R}^d, $$ with $ C=C(\alpha,d,p,q)$ and this bound is sharp for $p\neq 1$. We also study a related uncertainty principle for functions satisfying $\;\;\displaystyle\|f(x)|x|^m\|_p+ \|\widehat{f}(\xi)|\xi|^n\|_q <\infty.$, Comment: 30 pages; Remark 1.4 (vii), Acknowledgements, and Proposition 5.5 added

With the rise of computational social science, many scholars utilize data analysis and natural language processing tools to analyze social media, news articles, and other accessible data sources for examining political and social discourse. Particularly, the study of the emergence of echo-chambers due to the dissemination of specific information has become a topic of interest in mixed methods research areas. In this paper, we analyze data collected from two news portals, Breitbart News (BN) and New York Times (NYT) to prove the hypothesis that the formation of echo-chambers can be partially explained on the level of an individual information consumption rather than a collective topology of individuals' social networks. Our research findings are presented through knowledge graphs, utilizing a dataset spanning 11.5 years gathered from BN and NYT media portals. We demonstrate that the application of knowledge representation techniques to the aforementioned news streams highlights, contrary to common assumptions, shows relative "internal" neutrality of both sources and polarizing attitude towards a small fraction of entities. Additionally, we argue that such characteristics in information sources lead to fundamental disparities in audience worldviews, potentially acting as a catalyst for the formation of echo-chambers.

Microbial ecosystems carry out essential functions for global climate, human health, and industry. These complex communities exhibit a surprising amount of functionally relevant diversity at all levels of taxonomic resolution, presenting a significant challenge for most modeling frameworks. A long-standing hope of theoretical ecology is that some patterns might persist despite community complexity -- or perhaps even emerge because of it. A deeper understanding of such "emergent simplicity" could enable new approaches for predicting the behaviors of the complex ecosystems in nature. However, most examples described so far afford limited predictive power, as they focused on reproducibility rather than prediction. Here, we propose an information-theoretic framework for defining, nuancing and quantifying emergent simplicity in empirical data based on the ability of simple models to predict community-level functional properties. Applying this framework to two published datasets, we demonstrate that the majority of properties measured across both experiments exhibit robust evidence of emergent predictability: surprisingly, as community richness increases, simple compositional descriptions become more predictive. We show that this behavior is not typical within the standard modeling frameworks of theoretical ecology, and argue that improving our ability to predict and control natural microbial communities will require a shift of focus: away from complexity of _ecosystems_, and towards prediction complexity of _properties_ of ecosystems., Comment: Revised for clarity. 9 pages, 5 figures + SI

The search for extraterrestrial life hinges on identifying biosignatures, often focusing on gaseous metabolic byproducts as indicators. However, most such biosignatures require assuming specific metabolic processes. It is widely recognized that life on other planets may not resemble that of Earth, but identifying biosignatures ``agnostic'' to such assumptions has remained a challenge. Here, we propose a novel approach by considering the generic outcome of life: the formation of competing ecosystems. We use a minimal model to argue that the presence of ecosystem-level dynamics, characterized by ecological interactions and resource competition, may yield biosignatures independent of specific metabolic activities. Specifically, we propose the emergent stratification of chemical resources in order of decreasing energy content as a candidate new biosignature. While likely inaccessible to remote sensing, this signature could be relevant for sample return missions, or for detection of ancient signatures of life on Earth itself., Comment: 6 pages, 3 figures

In this paper, we study the form of the constant $C$ in the Bernstein--Nikolskii inequalities $\|f^{(s)}\|_q \lesssim C(s, p, q)\left\|f\right\|_p,\,0

In this paper, we study properties of polynomials over division rings. Moreover, we present formulas for finding roots of some polynomials, Comment: 6 pages

We critically address the recent experiment [Science 382, 907 (2023)] on nonequilibrium transport and noise in a strange metal YbRh2Si2 patterned into the nanowire shape. In the long device, resistivity, differential resistance and current noise data seem to be consistent allowing us to extract electron-phonon coupling and the temperature dependence of electron-phonon scattering length. The obtained values can be reconciled with the experimental data for the short device only assuming the significant contact resistance. We discuss its possible origin as due to the current redistribution between YbRh2Si2 and its gold covering, and reveal that this redistribution contact resistance should be proportional to the YbRh2Si2 resistivity. We also discuss some subtleties of the noise measurements. Overall, neglecting electron-phonon energy relaxation even in the shortest devices is arguable so that the observed shot noise suppression can hardly be attributed to the failure of quasiparticle concept., Comment: 6 pages + 3 pages Supplemental Material