Miracle-dz/UniFAR-FTUs huggingface dataset:
Are there higher-order Betchov homogeneity constraints for incompressible isotropic turbulence?

Incompressible and statistically homogeneous flows obey exact kinematic relations. The Betchov homogeneity constraints (Betchov, J. Fluid Mech., vol. 1, 1956, pp. 497-504) for the average principal invariants of the velocity gradient are among the most well known and extensively employed homogeneity relations. These homogeneity relations have far-reaching implications for the coupled dynamics of strain and vorticity, as well as for the turbulent energy cascade. Whether the Betchov homogeneity constraints are the only possible ones or whether additional homogeneity relations exist has not been proven yet. Here we show that the Betchov homogeneity constraints are the only homogeneity constraints for incompressible and statistically isotropic velocity gradient fields. We also extend our results to derive homogeneity relations involving the velocity gradient and other dynamically relevant quantities, such as the pressure Hessian.
Trajectory attractors for 3D damped Euler equations and their approximation

<p style='text-indent:20px;'>We study the global attractors for the damped 3D Euler–Bardina equations with the regularization parameter <inline-formula><tex-math id="M1">\begin{document}$ \alpha>0 $\end{document}</tex-math></inline-formula> and Ekman damping coefficient <inline-formula><tex-math id="M2">\begin{document}$ \gamma>0 $\end{document}</tex-math></inline-formula> endowed with periodic boundary conditions as well as their damped Euler limit <inline-formula><tex-math id="M3">\begin{document}$ \alpha\to0 $\end{document}</tex-math></inline-formula>. We prove that despite the possible non-uniqueness of solutions of the limit Euler system and even the non-existence of such solutions in the distributional sense, the limit dynamics of the corresponding dissipative solutions introduced by P. Lions can be described in terms of attractors of the properly constructed trajectory dynamical system. Moreover, the convergence of the attractors <inline-formula><tex-math id="M4">\begin{document}$ \mathcal A(\alpha) $\end{document}</tex-math></inline-formula> of the regularized system to the limit trajectory attractor <inline-formula><tex-math id="M5">\begin{document}$ \mathcal A(0) $\end{document}</tex-math></inline-formula> as <inline-formula><tex-math id="M6">\begin{document}$ \alpha\to0 $\end{document}</tex-math></inline-formula> is also established in terms of the upper semicontinuity in the properly defined functional space. </p>
Universal Randomized Guessing Subject to Distortion

In this paper, we consider the problem of guessing a sequence subject to a distortion constraint. Specifically, we assume the following game between Alice and Bob: Alice has a sequence <inline-formula> <tex-math notation="LaTeX">${x}$ </tex-math></inline-formula> of length <inline-formula> <tex-math notation="LaTeX">$n$ </tex-math></inline-formula>. Bob wishes to guess <inline-formula> <tex-math notation="LaTeX">${x}$ </tex-math></inline-formula>, yet he is satisfied with finding any sequence <inline-formula> <tex-math notation="LaTeX">$\hat {x}$ </tex-math></inline-formula> which is within a given distortion <inline-formula> <tex-math notation="LaTeX">$D$ </tex-math></inline-formula> from <inline-formula> <tex-math notation="LaTeX">$x$ </tex-math></inline-formula>. Thus, he successively submits queries to Alice, until receiving an affirmative answer, stating that his guess was within the required distortion. Finding guessing strategies which minimize the number of guesses (the guesswork), and analyzing its properties (e.g., its <inline-formula> <tex-math notation="LaTeX">$\rho $ </tex-math></inline-formula>–th moment) has several applications in information security, source and channel coding. Guessing subject to a distortion constraint is especially useful when considering contemporary biometrically–secured systems, where the “password” which protects the data is not a single, fixed vector but rather a ball of feature vectors centered at some <inline-formula> <tex-math notation="LaTeX">${x}$ </tex-math></inline-formula>, and any feature vector within the ball results in acceptance. We formally define the guessing problem under distortion in four different setups: memoryless sources, guessing through a noisy channel, sources with memory and individual sequences. We suggest a randomized guessing strategy which is asymptotically optimal for all setups and is five–fold universal, as it is independent of the source statistics, the channel, the moment to be optimized, the distortion measure and the distortion level.
Regularity of the coefficients of multilinear forms on sequence spaces

The investigation of regularity/summability properties of the coefficients of bilinear forms in sequence spaces was initiated by Littlewood in 1930. Nowadays, this topic has important connections with other fields of Pure and Applied Mathematics as Complex Analysis, Quantum Information Theory, Theoretical Computer Science and Combinatorial Games. In this paper we explore a regularity technique to obtain optimal parameters for several results in this framework, extending/generalizing theorems of Osikiewicz and Tonge (2001), Albuquerque et al. (2016), Aron et al. (2017), Albuquerque and Rezende (2018), Paulino (2020), among others.
A new SPICE subcircuit model of power p-i-n diode

A new modeling approach for the power p-i-n diode is proposed. The base region is represented with a two-port network, obtained by solving the ambipolar diffusion equation with the Laplace transform method, and by approximating the resulting transcendental functions in the s-domain with rational approximations. Two different networks have been obtained. The first one, based on Taylor-series approximation is shown to be a generalization of a two-port model already proposed in the literature for the nonquasi-static modeling of bipolar transistors. The second network representation is based on Pade' approximation and is shown to be more accurate than the Taylor-series approach, The obtained RLC networks are easily implemented in a PSPICE subcircuit which also takes into account the emitter recombination effects and the dynamic of the space-charge voltage build-up. Good agreement has been obtained by comparing the results of the proposed model with numerical device simulations. >
SoK: A Study of the Security on Voice Processing Systems

As the use of Voice Processing Systems (VPS) continues to become more prevalent in our daily lives through the increased reliance on applications such as commercial voice recognition devices as well as major text-to-speech software, the attacks on these systems are increasingly complex, varied, and constantly evolving. With the use cases for VPS rapidly growing into new spaces and purposes, the potential consequences regarding privacy are increasingly more dangerous. In addition, the growing number and increased practicality of over-the-air attacks have made system failures much more probable. In this paper, we will identify and classify an arrangement of unique attacks on voice processing systems. Over the years research has been moving from specialized, untargeted attacks that result in the malfunction of systems and the denial of services to more general, targeted attacks that can force an outcome controlled by an adversary. The current and most frequently used machine learning systems and deep neural networks, which are at the core of modern voice processing systems, were built with a focus on performance and scalability rather than security. Therefore, it is critical for us to reassess the developing voice processing landscape and to identify the state of current attacks and defenses so that we may suggest future developments and theoretical improvements.
Learn Layer-wise Connections in Graph Neural Networks

In recent years, Graph Neural Networks (GNNs) have shown superior performance on diverse applications on real-world datasets. To improve the model capacity and alleviate the over-smoothing problem, several methods proposed to incorporate the intermediate layers by layer-wise connections. However, due to the highly diverse graph types, the performance of existing methods vary on diverse graphs, leading to a need for data-specific layer-wise connection methods. To address this problem, we propose a novel framework LLC (Learn Layer-wise Connections) based on neural architecture search (NAS) to learn adaptive connections among intermediate layers in GNNs. LLC contains one novel search space which consists of 3 types of blocks and learnable connections, and one differentiable search algorithm to enable the efficient search process. Extensive experiments on five real-world datasets are conducted, and the results show that the searched layer-wise connections can not only improve the performance but also alleviate the over-smoothing problem.
Modularity and edge sampling

Suppose that there is an unknown underlying graph $G$ on a large vertex set, and we can test only a proportion of the possible edges to check whether they are present in $G$. If $G$ has high modularity, is the observed graph $G'$ likely to have high modularity? We see that this is indeed the case under a mild condition, in a natural model where we test edges at random. We find that $q^*(G') \geq q^*(G)-\varepsilon$ with probability at least $1-\varepsilon$, as long as the expected number edges in $G'$ is large enough. Similarly, $q^*(G') \leq q^*(G)+\varepsilon$ with probability at least $1-\varepsilon$, under the stronger condition that the expected average degree in $G'$ is large enough. Further, under this stronger condition, finding a good partition for $G'$ helps us to find a good partition for $G$.
An exact dynamic programming algorithm, lower and upper bounds, applied to the large block sale problem

In this article, we address a class of non convex, integer, non linear mathematical programs using dynamic programming. The mathematical program considered may be used to model the optimal liquidation problem of a single asset portfolio. We show the problem can be solved exactly using Dynamic Programming (DP) in polynomial time. We also introduce dedicated heuristics and provide very thin admissible solutions, for medium sized and large instances (for which exact resolution is not efficient). We also derive an upper bound which however is not tight. Lastly, we benchmark our results against a commercial solver, such as LocalSolver [5].
Chain Bundles and Category of Chains

In [7], we introduced the category of chain buldles with examples and established its significance. Here we shall describe certain categories which we call the category of chains in the chain bundle category and discuss some interesting categorical properties of this chain categories. Category theory, in general is a mathematical theory of structures and system of structures which has come to occupy a central position in present day mathematics. Eilenberg and Mac Lane provide a purely abstract definition of a category in 1945 (cf. [1] and [2]). Accordingly a category C can be described as a set Ob whose members are objects of C and for every pair X, Y of objects of C there is Hom(X, Y ) called morphisms from X to Y both satisfying certain specified conditions. There are many situations where one have to deal with chains (sequences) of objects and hence it is natural to consider categories whose objects are chain of objects in some category C and morphisms are appropriate morphisms between such chains. In order to discuss such situations, in [7] we introduced the category of chain bundles as a category whose objects are sequence of objects in a category C with zero such that for any two objects X and Y any subset of Hom(X, Y ) constitute the morphisms between X and Y . A category whose objects are chain bundles and morphisms appropriate chain bundle maps is termed as a category of chain bundles and will be denoted as CBC . In this paper we consider the category of chain bundles (cf. [7]) and descibe the chain bundle categories from directed graph and augmented simplicial categories. Further we discuss certain categorical properties of the chain bundle categories with examples and then describe the category of chains of chain bundle categories. 1. Preliminaries In the following we briefly recall some basic notions such as categories, category with subobjects, factorization of morphisms and the like which are needed in the sequel. Definition 1. A category C consists of (1) a class νC called the class of vertices or objects (2) a class C of disjoint sets C(a, b), one for each pair (a, b) ∈ νC × νC, an element f ∈ C(a, b) called a morphism (arrow) from a to b, where a = dom f and b = cod f 2020 Mathematics Subject Classification. 20M10.
Evidence for Impact of Galaxy Mergers on Stellar Kinematics of Early-type Galaxies

We provide observational evidence that galaxy mergers significantly affect stellar kinematics of early-type galaxies (ETGs) such as specific stellar angular momentum within the half-light radius ( λRe ) and kinematic misalignment (ψ mis), using MaNGA integral field unit spectroscopic data that are in the Stripe 82 region of the Sloan Digital Sky Survey. In this study, tidal features around ETGs, which are detected in deep coadded images, are used as direct evidence for mergers that occurred recently. In the case of ETGs that do not have dust lanes, λRe is lower in ETGs with tidal features than in those without tidal features (median λRe : 0.21 versus 0.39) in all stellar mass and Sérsic index ranges except the most massive bin, so that the fraction of ETGs with tidal features in slow rotators is more than twice as large as that in fast rotators (42% versus 18%). Moreover, ETGs with tidal features have larger ψ mis than those without tidal features (mean ψ mis: 28° versus 15°). By contrast, ETGs with dust lanes are fast rotators, and ETGs with both dust lanes and tidal features have the highest λRe (median λRe : 0.59) among all ETG categories. In addition, ETGs with dust lanes have small ψ mis regardless of the existence of tidal features (ψ mis < 7.°5). Our results can be explained if mergers with different gas fractions generate merger remnants that have different kinematic properties.
Powerful Graph Convolutioal Networks with Adaptive Propagation Mechanism for Homophily and Heterophily

Graph Convolutional Networks (GCNs) have been widely applied in various fields due to their significant power on processing graph-structured data. Typical GCN and its variants work under a homophily assumption (i.e., nodes with same class are prone to connect to each other), while ignoring the heterophily which exists in many real-world networks (i.e., nodes with different classes tend to form edges). Existing methods deal with heterophily by mainly aggregating higher-order neighborhoods or combing the immediate representations, which leads to noise and irrelevant information in the result. But these methods did not change the propagation mechanism which works under homophily assumption (that is a fundamental part of GCNs). This makes it difficult to distinguish the representation of nodes from different classes. To address this problem, in this paper we design a novel propagation mechanism, which can automatically change the propagation and aggregation process according to homophily or heterophily between node pairs. To adaptively learn the propagation process, we introduce two measurements of homophily degree between node pairs, which is learned based on topological and attribute information, respectively. Then we incorporate the learnable homophily degree into the graph convolution framework, which is trained in an end-to-end schema, enabling it to go beyond the assumption of homophily. More importantly, we theoretically prove that our model can constrain the similarity of representations between nodes according to their homophily degree. Experiments on seven real-world datasets demonstrate that this new approach outperforms the state-of-the-art methods under heterophily or low homophily, and gains competitive performance under homophily.
Identifying Internet Mediated Securities Fraud: Trends and Technology

The world wide web has greatly inuenced the incidence of securities fraud. This poses a signicant challenge to securities regulators who in most cases do not become aware of these frauds until after the damage has been done. Identifying these operations early is dicult using traditional surveillance and investigative methods. Innovative technology driven solutions are required and now achievable, enabling earlier pro-active detection and action. Given the prevalence, increasing impact in our society and multi-disciplinary nature of this issue, it is important that this problem be introduced to the Web Science community. To that end, types of internet mediated securities fraud and some of the current technologies available to detect them are reviewed. Scamalyzr, a simple surveillance tool developed by the author, is discussed and areas of needed improvement and further research identied.
Effect of Velocity on Cycle Rate and Length for Three Roller Skiing Techniques

This investigation examined the adjustments made in cycle rate and length to velocity changes during roller skiing with the double pole (DP), kick double pole (KD), and VI skate (VS) techniques. Eight cross-country ski racers roller skied with each technique on a flat track at submaximal and maximal velocities while being videotaped from a lateral view. Increases in submaximal velocities were associated with increases in cycle rate and cycle length for KD and VS but only with increases in cycle rate for DP. Maximal sprint velocities were approximately 7% lower (p < .01) for KD than for DP and VS and were associated with increases (p < .01) in cycle rate for each technique combined with decreases (p < .01) in cycle length for DP and VS. The findings indicate that there are differences among techniques in the manner in which cycle rate and length are adjusted to change submaximal velocity, but each technique relies upon an increase in cycle rate to achieve maximal velocity.
Secondary homological stability for mapping class groups of nonorientable surfaces

Using the Galatius–Kupers–Randal-Williams framework of cellular E 2 -algebras, we prove a secondary stability theorem for mapping class groups of nonorientable surfaces. As a corollary, we obtain a new best known stability range for the homology of the mapping class groups of nonorientable surfaces with respect to adding torus holes.
Mallows permutation models with $L^1$ and $L^2$ distances I: hit and run algorithms and mixing times

Mallows permutation model, introduced by Mallows in statistical ranking theory, is a class of non-uniform probability measures on the symmetric group Sn. The model depends on a distance metric d(σ, τ) on Sn, which can be chosen from a host of metrics on permutations. In this paper, we focus on Mallows permutation models with L and L distances, respectively known in the statistics literature as Spearman’s footrule and Spearman’s rank correlation. Unlike most of the random permutation models that have been analyzed in the literature, Mallows permutation models with L and L distances do not have an explicit expression for their normalizing constants. This poses challenges to the task of sampling from these Mallows models. In this paper, we consider hit and run algorithms for sampling from both models. Hit and run algorithms are a unifying class of Markov chain Monte Carlo (MCMC) algorithms including the celebrated Swendsen-Wang and data augmentation algorithms. For both models, we show order lognmixing time upper bounds for the hit and run algorithms. This demonstrates much faster mixing of the hit and run algorithms compared to local MCMC algorithms such as the Metropolis algorithm. The proof of the results on mixing times is based on the path coupling technique, for which a novel coupling for permutations with one-sided restrictions is involved. Extensions of the hit and run algorithms to weighted versions of the above models, a two-parameter permutation model that involves the L distance and Cayley distance, and lattice permutation models in dimensions greater than or equal to 2 are also discussed. The order logn mixing time upper bound pertains to the two-parameter permutation model. ∗Department of Statistics, Stanford University 1 ar X iv :2 11 2. 13 45 6v 1 [ m at h. PR ] 2 6 D ec 2 02 1
Optomechanical Ground-State Cooling in a Continuous and Efficient Electro-Optic Transducer

The demonstration of a quantum link between microwave and optical frequencies would be an important step towards the realization of a quantum network of superconducting processors. A major impediment to quantum electro-optic transduction in all platforms explored to date is noise added by thermal occupation of modes involved in the transduction process, and it has proved difficult to realize low thermal occupancy concurrently with other desirable features like high duty cycle and high efficiency. In this work, we present an efficient and continuously operating electro-optomechanical transducer whose mechanical mode has been optically sideband-cooled to its quantum ground state. The transducer achieves a maximum efficiency of 47% and minimum input-referred added noise of 3.2 photons in upconversion. Moreover, the thermal occupancy of the transducer's microwave mode is minimally affected by continuous laser illumination with power more than two orders of magnitude greater than that required for optomechanical ground-state cooling.
Implementation of self-consistent MGGA functionals in APW based methods

Functionals of the meta-generalized gradient approximation (MGGA) are nowadays widely used in chemistry and solid-state physics for the simulation of electronic systems like molecules, solids, or surfaces. Due to their dependency on the kinetic energy density, they are in principle more accurate than GGA functionals for various properties (geometry, binding energy, electronic structure, etc.), while being nearly as fast since they are still of the semilocal form. Thus, when an accuracy better than GGA is required, one may consider using a MGGA instead of the much more costly hybrid functionals or methods like the random-phase approximation or GW . In this work, the self-consistent implementation of MGGA functionals in APW based methods is presented. Technical aspects of the implementation are discussed, and calculations of band gaps, lattice constants, and magnetic moments are presented in order to validate our implementation. To test the changes of the electron density due to a MGGA, the electric ﬁeld gradient on transition-metal atoms is calculated.
Stress-tailoring magnetic anisotropy of 
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We report on a temperature-driven reversible change of the in-plane magnetic anisotropy of V$_2$O$_3$/Ni bilayers. This is caused by the rhombohedral to monoclinic structural phase transition of V$_2$O$_3$ at $T_C$ = 160 K. The in-plane magnetic anisotropy is uniaxial above $T_C$, but as the bilayer is cooled through the structural phase transition, a secondary magnetic easy axis emerges. Ferromagnetic resonance measurements show that this change in magnetic anisotropy is reversible with temperature. We identify two structural properties of the V$_2$O$_3$/Ni bilayers affecting the in-plane magnetic anisotropy: (1) a growth-induced uniaxial magnetic anisotropy associated with step-like terraces in the bilayer microstructure and (2) a low-temperature strain-induced biaxial anisotropy associated with the V$_2$O$_3$ structural phase transition. Magnetoresistance measurements corroborate the change in magnetic anisotropy across the structural transition and suggest that the negative magnetostriction of Ni leads to the emergence of a strain-induced easy-axis. This shows that a temperature-dependent structural transition in V$_2$O$_3$ may be used to tune the magnetic anisotropy in an adjacent ferromagnetic thin film.