Miracle-dz/UniFAR-FTUs huggingface dataset:
Atomic Radial Distribution Functions of As-Se Glasses

X-ray-diffraction data from a series of arsenic-selenium glasses with compositions in the range Se---50-at. % As have been used to obtain atomic radial distribution functions for these materials. The first-neighbor correlation peak shifts linearly from 2.34 \AA{} for Se to 2.41 \AA{} for 36-at. % As and remains constant at higher As concentrations. Peak areas increase linearly with arsenic concentration and the magnitude agrees well with a model which assumes twofold coordination of selenium and threefold coordination of arsenic. At 40-at. % As and at 50-at. % As the first-neighbor peak is very similar to that obtained from the crystals ${\mathrm{As}}_{2}$${\mathrm{Se}}_{3}$ and ${\mathrm{As}}_{4}$${\mathrm{Se}}_{4}$. However, beginning with the second-neighbor peak at about 3.70 \AA{}, there are significant differences between the crystalline and amorphous distributions. There is a smaller second peak in the glasses, the third crystalline peak is completely absent, and there are shifts in the positions of higher-order shells. Consequently, structural models based on microcrystalline regions of ${\mathrm{As}}_{2}$${\mathrm{Se}}_{3}$ for 40-at. % As or ${\mathrm{As}}_{4}$${\mathrm{Se}}_{4}$ for 50-at. % As did not give satisfactory agreement with the experimental distributions. In particular, the results do not support the existence of ${\mathrm{As}}_{2}$${\mathrm{Se}}_{3}$ layers in the 40-at. % As structure.
An explicit inversion formula for the $p$-adic Whittaker transform on $\text{GL}_n(\mathbb{Q}_p)$

Whittaker functions on non-archimedean fields were first introduced in the work of Jacquet, and they were characterized explicitly by Shintani. We obtain an explicit inversion formula and a Plancherel formula for the $p$-adic Whittaker transform on $\text{GL}_n(\mathbb{Q}_p)$. As an application, integral representations are obtained for the local factors of certain symmetric power $L$-functions.
lp parameter perturbation and design of robust controllers for linear systems

In this paper, linear systems with characteristic equations that are linearly dependent on some uncertain parameters are considered. A new procedure is proposed for the calculation of D-stability margins in the parameter space in general lp- norms. The procedure is simple and computationally efficient. For several important regions of interest in the complex plane, e.g. left hand plane, sectors and circles centred at the origin, it requires the solution of only one equation. Based on this result, a new method is presented for the design of robust controllers. Robust placement of the closed-loop poles inside the regions of interest is addressed. The method provides a simple and computationally tractable solution to the robust controller design problem. It can be used to synthesize robust controllers with general rational transfer functions for plants modelled as the ratio of two uncertain polynomials subjected to lp parameter perturbation.
Computing Complex Dimension Faster and Deterministically (Extended Abstract)

We give a new complexity bound for calculating the complex dimension of an algebraic set. Our algorithm is completely deterministic and approaches the best recent randomized complexity bounds. We also present some new, significantly sharper quantitative estimates on rational univariate representations of roots of polynomial systems. As a corollary of the latter bounds, we considerably improve a recent algorithm of Koiran for deciding the emptiness of a hypersurface intersection over the complex numbers, given the truth of the Generalized Riemann Hypothesis (GRH).
Branches of Triangulated Origami Near the Unfolded State

Origami structures are characterized by a network of folds and vertices joining unbendable plates. For applications to mechanical design and self-folding structures, it is essential to understand the interplay between the set of folds in the unfolded origami and the possible 3D folded configurations. When deforming a structure that has been folded, one can often linearize the geometric constraints, but the degeneracy of the unfolded state makes a linear approach impossible there. We derive a theory for the second-order infinitesimal rigidity of an initially unfolded triangulated origami structure and use it to study the set of nearly-unfolded configurations of origami with four boundary vertices. We find that locally, this set consists of a number of distinct "branches" which intersect at the unfolded state, and that the number of these branches is exponential in the number of vertices. We find numerical and analytical evidence that suggests that the branches are characterized by choosing each internal vertex to either "pop up" or "pop down". The large number of pathways along which one can fold an initially-unfolded origami structure strongly indicate that a generic structure is likely to become trapped in a "misfolded" state. Thus, new techniques for creating self-folding origami are likely necessary; controlling the popping state of the vertices may be one possibility.
Hodge theory of the Goldman bracket

In this paper we show that, after completion in the I-adic topology, the Goldman bracket on the space spanned by homotopy classes of loops on a smooth, complex algebraic curve is a morphism of mixed Hodge structure. We prove similar statements for the natural action (defined by Kawazumi and Kuno) of the loops in X on paths from one "boundary component" to another. These results are used to construct torsors of isomorphisms of the the completed Goldman Lie algebra with the completion of its associated graded Lie algebra. Such splittings give torsors of partial solutions to the Kashiwara--Vergne problem (arXiv:1611.05581) in all genera. Compatibility of the cobracket with Hodge theory is established in arXiv:1807.09209.
On distance and Laplacian matrices of trees with matrix weights

ABSTRACT The distance matrix of a simple connected graph G is , where is the distance between the vertices i and j in G. We consider a weighted tree T on n vertices with edge weights are square matrices of the same size. The distance between the vertices i and j is the sum of the weight matrices of the edges in the unique path from i to j. In this article, we establish a characterization for the trees in terms of the rank of (matrix) weighted Laplacian matrix associated with it. We present a necessary and sufficient condition for the distance matrix D, with matrix weights, to be invertible and the formula for the inverse of D, if it exists. Then we study some of the properties of the distance matrices of matrix weighted trees in connection with the Laplacian matrices, incidence matrices, and g-inverses. Finally, we derive an interlacing inequality for the eigenvalues of distance and Laplacian matrices for the case of positive definite matrix weights.
On the singular hyperbolicity of star flows

We prove for a generic star vector field $X$ that, if for every chain recurrent class $C$ of $X$ all singularities in $C$ have the same index, then the chain recurrent set of $X$ is singular hyperbolic. We also prove that every Lyapunov stable chain recurrent class of $X$ is singular hyperbolic. As a corollary, we prove that the chain recurrent set of a generic 4-dimensional star flow is singular hyperbolic.
Tunnel near-field optical microscopy (TNOM-2)

Light emitted from the aperture of a near-field optical probe in the close vicinity of a dielectric object propagates in classically `forbidden' as well as `allowed' directions; the two zones are separated by the critical angle for total internal reflection. The new `tunnel' near-field optical microscopy (TNOM) technique makes use of forbidden and allowed radiation, in contrast to standard scanning near-field optical microscopy (SNOM or NSOM), which records only the allowed light. Scan images obtained with allowed and forbidden light are complementary to some extent; the latter, however, provide high contrast and resolution even in situations in which standard SNOM/NSOM shows little or no contrast. The influence of topography on image formation is analyzed and discussed.
A Simple Panel Unit‐Root Test with Smooth Breaks in the Presence of a Multifactor Error Structure

This paper proposes a new simple panel unit-root test by extending the cross-sectionally augmented panel unit-root test (CIPS) developed by Pesaran et al. (2013) to allow for smoothing structural changes in deterministic terms, approximated by a Fourier series. The proposed statistic is the simple average of the individual statistics constructed from the breaks and cross-sectional dependence augmented Dickey-Fuller (BCADF) regression and is called the BCIPS statistic. We initially develop the tests by assuming that the number of factors in the model is known and show that the limiting distribution of the BCADF statistic is free of nuisance parameters. The nonstandard limiting distribution of the (truncated) BCIPS statistic is also shown to exist and its critical values are tabulated. Monte-Carlo experiments point out that the sizes and powers of the BCIPS statistic are generally satisfactory as long as T is greater than or equal to fifty and a hundred, respectively. By using two different methods to determine the number of factors, both the BCIPS and CIPS tests are applied to examine the validity of long-run purchasing power parity. The proposed test complements the panel unit-root tests with breaks using dummy variables.
Characterization of field homomorphisms through Pexiderized functional equations

ABSTRACT The aim of this paper is to prove characterization theorems for field homomorphisms. More precisely, the main result investigates the following problem. Let be arbitrary, a field and additive functions. Suppose further that equation is also satisfied. Then the functions are linear combinations of field homomorphisms from to .
Chordal SLE$_6$ explorations of a quantum disk

We consider a particular type of $\sqrt{8/3}$-Liouville quantum gravity surface called a doubly marked quantum disk (equivalently, a Brownian disk) decorated by an independent chordal SLE$_6$ curve $\eta$ between its marked boundary points. We obtain descriptions of the law of the quantum surfaces parameterized by the complementary connected components of $\eta([0,t])$ for each time $t \geq 0$ as well as the law of the left/right $\sqrt{8/3}$-quantum boundary length process for $\eta$.
Self-pulsing instabilities in backward parametric wave mixing

We investigate temporal stability of stationary solutions for backward degenerate parametric mixing. We show that self-oscillating solutions can be obtained from properly chosen continuous-wave counterpropagating inputs at fundamental and second-harmonic frequencies under general phase-mismatched conditions. The temporal oscillation period near the bifurcation points is predicted by linear stability analysis and verified by numerical simulation of the governing equations.
Statistical mechanics of the periodic Benjamin–Ono equation

The periodic Benjamin-Ono equation is an autonomous Hamiltonian system with a Gibbs measure on $L^2({\mathbb T})$. The paper shows that the Gibbs measures on bounded balls of $L^2$ satisfy some logarithmic Sobolev inequalities. The space of $n$-soliton solutions of the periodic Benjamin-Ono equation, as discovered by Case, is a Hamiltonian system with an invariant Gibbs measure. As $n\rightarrow\infty$, these Gibbs measures exhibit a concentration of measure phenomenon. Case introduced soliton solutions that are parameterised by atomic measures in the complex plane. The limiting distributions of these measures gives the density of a compressible gas that satisfies the isentropic Euler equations.
Head Pose-Based Conditional Regression Forest for Facial Feature Detection

Multi-angles of facial feature detection is still a challenging research. In this paper, the author proposes a precision head pose estimation method as a condition to improve the performance of regression forests, and decreases the missing rate caused by head deflection. The basic idea is used by locality preserving projection, a kind of manifold learning, and nonlinear regression (LPP+NLR) for getting the global information of pose and label it, then utilize trained conditional regression classifier to identify the feature points in global characteristics. The effectiveness of the proposed facial feature detection algorithm is illustrated in the experiments and the comparison with several recent methods.
The He-3/He-4 ratios for solar energetic particle events during the Combined Release and Radiation Effects Satellite Mission

Helium data measured by the University of Chicago instrument, ONR-604, are employed to determine the ratio of He-3 to He-4 for solar energetic particle (SEP) events over an energy range 50-110 MeV/nucleon during the 1990/1991 Combined Release and Radiation Effects Satellite mission. The Sun in this period is extremely active. A total of 29 separate SEP events have been identified; among them 16 major events have been analyzed to obtain He-3/He-4 ratios, with a mass resolution of 0.10 amu. Thirteen events have a He-3/He-4 ratio larger than 0.005, one order of magnitude greater than the solar coronal value. The He-3/He-4 ratio at energies of 50-110 MeV/nucleon is independent of the size of the SEP event, for the moderately large flares analyzed here. The helium energy spectra are represented by power laws. During the 1991 June flare period, different large-particle injections associated with different solar flares, but occurring from the same active region, have a similar average spectral index and a similar He-3/He-4 ratio. The spectral index of He-4 varies from event to event, i.e., from as small as 1.5 to as large as 7.5. A correlation is found between the inferred spectral index from gamma-ray measurements and our measured spectral indices for the 1991 June 11 and June 15 events, suggesting that the high-energy SEPs may come from the same acceleration event as the particles that interact at the Sun and produce the gamma rays. The implications of these results for particle acceleration and propagation at the flare site and in the solar corona are discussed.
Hydrodynamic limit and viscosity solutions for a 2D growth process in the anisotropic KPZ class

We study a $(2+1)$-dimensional stochastic interface growth model, that is believed to belong to the so-called Anisotropic KPZ (AKPZ) universality class [Borodin and Ferrari, 2014]. It can be seen either as a two-dimensional interacting particle process with drift, that generalizes the one-dimensional Hammersley process [Aldous and Diaconis 1995, Seppalainen 1996], or as an irreversible dynamics of lozenge tilings of the plane [Borodin and Ferrari 2014, Toninelli 2015]. Our main result is a hydrodynamic limit: the interface height profile converges, after a hyperbolic scaling of space and time, to the solution of a non-linear first order PDE of Hamilton-Jacobi type with non-convex Hamiltonian (non-convexity of the Hamiltonian is a distinguishing feature of the AKPZ class). We prove the result in two situations: (i) for smooth initial profiles and times smaller than the time $T_{shock}$ when singularities (shocks) appear or (ii) for all times, including $t>T_{shock}$, if the initial profile is convex. In the latter case, the height profile converges to the viscosity solution of the PDE. As an important ingredient, we introduce a Harris-type graphical construction for the process.
Motivic Chern classes and K‐theoretic stable envelopes

We consider a smooth algebraic variety with an action of a linear algebraic group acting with finitely many orbits. We study equivariant characteristic classes of the orbits, namely the equivariant motivic Chern classes, in the K‐theory of the ambient space. We prove that the motivic Chern class satisfies the axiom system inspired by that of ‘K‐theoretic stable envelopes’, recently defined by Okounkov and studied in relation with quantum group actions on the K‐theory algebra of moduli spaces. We also give explicit formulas for the equivariant motivic Chern classes of Schubert cells and matrix Schubert cells. Finally, we calculate the equivariant motivic Chern class of the orbits of the A2 quiver representation, which yields formulas for the motivic Chern classes of determinantal varieties and more general degeneracy loci.
Four-cycle free graphs, height functions, the pivot property and entropy minimality

Fix $d\geq 2$ . Given a finite undirected graph ${\mathcal{H}}$ without self-loops and multiple edges, consider the corresponding ‘vertex’ shift, $\text{Hom}(\mathbb{Z}^{d},{\mathcal{H}})$ , denoted by $X_{{\mathcal{H}}}$ . In this paper, we focus on ${\mathcal{H}}$ which is ‘four-cycle free’. There are two main results of this paper. Firstly, that $X_{{\mathcal{H}}}$ has the pivot property, meaning that, for all distinct configurations $x,y\in X_{{\mathcal{H}}}$ , which differ only at a finite number of sites, there is a sequence of configurations $x=x^{1},x^{2},\ldots ,x^{n}=y\in X_{{\mathcal{H}}}$ for which the successive configurations $x^{i},x^{i+1}$ differ exactly at a single site. Secondly, if ${\mathcal{H}}$ is connected ,then $X_{{\mathcal{H}}}$ is entropy minimal, meaning that every shift space strictly contained in $X_{{\mathcal{H}}}$ has strictly smaller entropy. The proofs of these seemingly disparate statements are related by the use of the ‘lifts’ of the configurations in $X_{{\mathcal{H}}}$ to the universal cover of ${\mathcal{H}}$ and the introduction of ‘height functions’ in this context.
Transmission of high definition imagery using hybrid FSO/RF links for real-time surveillance, event detection, and follow-up

High definition (HD) quality imagery provides clearer and more detailed information for use in advanced video surveillance systems. The deployment of such surveillance systems where no fixed communications infrastructure exists presents an ideal application for high data rate directional FSO/RF links and networks. Next generation surveillance systems using HD imagery will be able to detect and analyze objects in detail and at large distances. Such flexibly deployable surveillance systems will be very valuable for military and homeland security surveillance. Nevertheless, designing these types of systems is not an easy task. First, HD images require large amounts of bandwidth: compressed high definition television (HDTV 1080i) images require bit rates of approximately 20Mb/s, which rise to above 1Gb/s for uncompressed images at 30 frames/s, and an increase in the number of cameras in one single system can saturate the available bandwidth. Second, advanced surveillance requires significant computational power for real-time object detection, tracking, and discrimination. This paper analyzes these issues and proposes a solution with on demand video compression and real-time object detection algorithms. A system architecture of a HD scalable system with the ability to track and discriminate objects and events within the system's deployed area will be described. Practical examples of autonomous event detection in wirelessly transmitted HDTV images will be given.
Convex Design of Structured Controllers using Block-Diagonal Lyapunov Functions

We consider the problem of synthesizing structured controllers for complex systems over directed graphs. In particular, we consider three tasks, i.e., $\mathcal{P}_1$: structured stabilization, $\mathcal{P}_2$: structured optimal control, and $\mathcal{P}_3$: communication topology design. These problems are known to be non-convex, and previous attempts have addressed them separately using different approaches, e.g., by characterizing special systems that allow convex formulations, or by employing certain techniques to obtain convex relaxations. In this paper, we provide a simple and unified convex strategy to deal with these three problems systematically by assuming that the closed-loop system admits a block-diagonal Lyapunov function. Also, two sufficient conditions are introduced to guarantee the block-diagonal stabilization. The block-diagonal assumption naturally guarantees a property of sparsity invariance, indicating that the structured constraint on controllers can be exactly transformed to constraints on Lyapunov variables. Using this assumption, a linear matrix inequality (LMI) approximation is used to solve $\mathcal{P}_1$; an LMI approximation and a gradient projection method are proposed to address $\mathcal{P}_2$; and an iterative algorithm is introduced to solve $\mathcal{P}_3$. Two illustrative examples are used to demonstrate the effectiveness of the proposed solutions.
Multispecies TASEP and the tetrahedron equation

We introduce a family of layer to layer transfer matrices in a three-dimensional (3D) lattice model which can be viewed as partition functions of the q-oscillator valued six-vertex model on an m × n square lattice. By invoking the tetrahedron equation we establish their commutativity and bilinear relations mixing various boundary conditions. At q = 0 and m = n, they ultimately yield a new proof of the steady state formula for the n-species totally asymmetric simple exclusion process obtained recently by the authors, revealing the 3D integrability in the matrix product construction.
A millimeter wave dielectrometer for high loss liquids based on the Zenneck wave

The propagation of an electromagnetic wave in a dielectric rod placed in a high loss liquid was studied theoretically and experimentally. It is shown that the wave has a bulk character in the rod and a surface character in the liquid. The attenuation and phase velocity of this wave have strong dependence upon the dielectric properties of the liquid and the rod, while the phase velocity of this wave exceeds the light velocity in the rod material. It enables one to consider the studied wave to be similar to the Zenneck wave. A characteristic equation for the structure under study was derived and analyzed. The attenuation and phase velocity of this wave in the presence of distilled water and a water–ethanol solution were measured. Owing to these data, the real and imaginary parts of the complex permittivity of high loss liquids under test were determined. We have good agreement between the theoretical and experimental results. A differential dielectrometer based on the usage of the Zenneck wave was designed. Thus, the complex permittivity of high loss liquids with sufficiently high accuracy can be obtained. It is also possible to record a rather small difference between two similar liquids according to their dielectric properties.
Uniform boundedness on extremal subsets in Alexandrov spaces.

In this paper, we study extremal subsets in $n$-dimensional Alexandrov spaces with curvature $\ge\kappa$ and diameter $\le D$. We show that the number of extremal subsets in an Alexandrov space, the Betti number of an extremal subset, and the volume of an extremal subset are uniformly bounded above by some constant depending only on $n$, $\kappa$ and $D$. The proof is an application of essential coverings introduced by T. Yamaguchi.