Miracle-dz/UniFAR-FTUs huggingface dataset:
Monotonicity Analysis over Chains and Curves

Chains are vector-valued signals sampling a curve. They are important to motion signal processing and to many scientific applications including location sensors. We propose a novel measure of smoothness for chains curves by generalizing the scalar-valued concept of monotonicity. Monotonicity can be defined by the connectedness of the inverse image of balls. This definition is coordinate-invariant and can be computed efficiently over chains. Monotone curves can be discontinuous, but continuous monotone curves are differentiable a.e. Over chains, a simple sphere-preserving filter shown to never decrease the degree of monotonicity. It outperforms moving average filters over a synthetic data set. Applications include Time Series Segmentation, chain reconstruction from unordered data points, Optical Character Recognition, and Pattern Matching.
Separating dipolar broadening from the intrinsic switching field distribution in perpendicular patterned media

A critical requirement for bit patterned media applications is the control and minimization of the switching field distribution (SFD). Here, we use the ΔH(M,ΔM) method to separate dipolar interactions due to neighbor islands from the intrinsic SFD by measuring a series of partial reversal curves of perpendicular anisotropy Co∕Pd based multilayer films deposited onto prepatterned Si substrates. For a 100-nm-period island array the dipolar broadening contributes 22% to the observed SFD. For a 45-nm-period array this value increases to 31%. These results highlight the importance of quantifying long-range dipolar interactions for determining the intrinsic SFD of patterned media.
Twisted-Torus Equilibrium Structures of Magnetic Fields in Magnetized Stars

We have investigated the "universality" of the twisted-torus equilibrium structures of the magnetic fields in deformed stars. The Tomimura-Eriguchi scheme for equilibrium structures of uniformly rotating magnetized stars is extended to treat equilibrium configurations of differentially rotating and meridional circulation-free magnetized polytropes with infinite conductivity. Characteristics of the magnetic fields obtained are summarized as follows: The exterior magnetic fields of the stars behave like dipolar poloidal fields, which decrease as r-3 when r → ∞. The interior magnetic fields are a mixture of poloidal and toroidal fields. Their geometric structures are tori of twisted field lines around the symmetry axis and of untwisted poloidal fields that penetrate the surface of the stars to continue to the exterior fields. It has been found that these structures of magnetic fields in stationary magnetic stars are robust and universal in the sense that they are nearly independent of the compressibility of the matter, rotation laws, and degrees of differential rotation. This universality is a consequence of the natural assumption that the electric current should be confined inside the star and of the integrability condition of the basic equation, i.e., that the electric current in the meridional plane is a function of the flux function, whose behavior is governed by a partial differential equation of the elliptic type.
A GENERALIZATION OF THE GABOR-HELSTROM TRANSFORM.

Abstract : A new class of integral transforms which generalizes Helstrom's integral expansion of a signal is developed. The forward transform of the signal, obtained by a one dimensional integration, is a representation of the signal in both time and frequency. All transforms of this class are what is defined as a generalized cross-ambiguity function. Necessary and sufficient conditions for a function of two variables to be a generalized cross-ambiguity function are given. The inverse transform is a two dimensional integral over time and frequency. A new method of synthesizing an ambiguity function is demonstrated. The cross-ambiguity function of the unknown signal and a chosen known signal is first obtained, and from this, the unknown signal is obtained by the factorization theorem for cross-ambiguity functions. (Author)
Asymptotic gradient flow structures of a nonlinear Fokker-Planck equation.

In this paper we consider a nonlinear Fokker-Planck equation with asymptotically small parameters. It describes the diffusion of finite-size particles in the presence of a fixed distribution of obstacles in the limit of low-volume fraction. The equation does not have a gradient flow structure, but can be interpreted as an asymptotic gradient flow, that is, as a gradient flow up to a certain asymptotic order. We use this scalar equation as a simple testbed model for more complicated systems of this kind. We discuss several possible entropy-mobility pairs, illustrate their dynamics with numerical simulations, present global in time existence results and study the long time behavior of solutions.
Drinfeld-type presentations of loop algebras

Let $\mathfrak{g}$ be the derived subalgebra of a Kac-Moody Lie algebra of finite type or affine type, $\mu$ a diagram automorphism of $\mathfrak{g}$ and $L(\mathfrak{g},\mu)$ the loop algebra of $\mathfrak{g}$ associated to $\mu$. In this paper, by using the vertex algebra technique, we provide a general construction of current type presentations for the universal central extension $\widehat{\mathfrak{g}}[\mu]$ of $L(\mathfrak{g},\mu)$. The construction contains the classical limit of Drinfeld's new realization for (twisted and untwisted) quantum affine algebras ([Dr]) and the Moody-Rao-Yokonuma presentation for toroidal Lie algebras ([MRY]) as special examples. As an application, when $\mathfrak{g}$ is of simply-laced type, we prove that the classical limit of the $\mu$-twisted quantum affinization of the quantum Kac-Moody algebra associated to $\mathfrak{g}$ introduced in [CJKT1] is the universal enveloping algebra of $\widehat{\mathfrak{g}}[\mu]$.
Super Ricci flow for disjoint unions

In this paper we consider compact, Riemannian manifolds $M_1, M_2$ each equipped with a one-parameter family of metrics $g_1(t), g_2(t)$ satisfying the Ricci flow equation. Motivated by a characterization of the super Ricci flow developed by McCann-Topping, we introduce the notion of a super Ricci flow for a family of distance metrics defined on the disjoint union $\MM$. In particular, we show such a super Ricci flow property holds provided the distance function between points in $M_1$ and $M_2$ evolves by the heat equation. We also discuss possible applications and examples.
A study of short-time periodic variation of the B8 solar neutrino flux at Super-Kamiokande

Super-Kamiokande(SK) is a real-time detector capable of measuring the exact time of solar neutrino events. This, combined with a relatively high yield of these events of roughly 15 per day, allows a search for short-time variations in the observed flux. Using all 1496 days of SK-I's solar data, we looked for periodic variations of the observed solar neutrino flux, and found no significant periodicity.
Broadband circular and linear polarization conversions realized by thin birefringent reflective metasurfaces

Broadband circular and linear polarization conversions have been proposed in the paper by using thin birefringent reflective metasurfaces, which are composed of two orthogonal I-shaped structures placed on the top of a printed circuit broad with grounded plane on the bottom. We show that the metasurface manipulates the reflective phases of two orthogonal linearly-polarized waves independently by changing the dimensions of I-shaped structure. Hence, the polarization states of a linearly-polarized incident wave with normal incidence can be manipulated as desired after reflected by the anisotropic metasurface. Two polarization conversions have been presented by using such thin birefringent reflective metasurfaces: from linearly-polarized wave to circularly-polarized wave, and from linearly-polarized wave to cross-polarized wave. The metasurfaces work at microwave frequency, and the axial ratio better than 1dB is achieved within fractional bandwidth of 15% for circular polarization. Numerical and experiment results demonstrate good polarization conversions in a broad frequency band, which have excellent agreements with the theoretical calculations.
Gender Differences in First Jobs for New US PhDs in the Mathematical Sciences

We take a long term look at initial employment trends for new doctorates with an eye towards gender, citizenship, and gender and citizenship differences by analyzing data from 1991-2015 AMS-ASA-IMS-MAA- SIAM Annual Surveys. The data show that the unemployment rate for women has been equal to or lower than the rate for men during most of the last quarter century. The one exception is that between 2001 and 2015 the unemployment rate for women who are not U.S. citizens was higher than the rate for non-citizen men. The unemployment rates are higher for males who are U.S. citizens than for non-citizen males in the last fifteen years, a puzzling trend. The data show that men from all pure math programs are considerably more likely than women to take jobs at the top-ranking and top-producing math departments. The data show women take jobs at departments in which the highest degree is a bachelor's degree at much higher rates and men take jobs in business and industry at considerably higher rates. We also find that men from the top-ranking or top-producing doctoral programs tend to be more likely to take jobs at academic institutions or research institutes at least on a par with their degreegranting institutions.
Inclined Magnetic Field Effects on Chaotic Convection for Moderate Prandtl Number

Using the theory of dynamical systems, this study investigated the effects of the inclined magnetic field on chaotic behaviour in a fluid layer heated from below for moderate Prandtl number. A low-dimensional, Lorenz-like model was obtained using the Galerkin truncated approximation. The fourth-order Runge-Kutta method was employed to solve the nonlinear system. The solution shows that it is possible to delay the chaotic convection depending on the Hartmann number.
Intermodal recoding of a video game: Learning to process signals for motion perception in a pure auditory environment

The aim of the study reported here was to investigate people's ability to learn a new auditory environment. A specific coding was developed in order to design an auditory version of a vision‐based simple video game involving moving objects. We investigated the learning process of participants in this purely auditory game and the influence of the following factors on performance: gender, level of practice in video games and three cognitive abilities, namely, mental rotation, visual attention and spatial perception. The results revealed that occasional and regular players' level of performance significantly improved with practice, whereas those of nonplayers did not. They also revealed a significant influence of gender. Scores in the mental rotation test was found to be correlated only with the final level of performance. This study provides insights into people's ability to learn new ways to perceive and interact with auditory objects in motion and highlights the cognitive abilities that influence this learning. Copyright © 2015 John Wiley & Sons, Ltd.
Global decentralised static output feedback slidingmode control for interconnected time-delay systems

Global decentralised stabilisation of a class of interconnected time-varying delay systems is considered, where both known and uncertain interconnections involve time delay. Matched and mismatched interconnections are considered separately to reduce the conservatism. A composite sliding surface is designed and the stability of the associated sliding motion, which is governed by a time delayed interconnected system, is analysed based on the Razumikhin-Lyapunov approach. A decentralised static output feedback variable structure control which is dependent on time delay is synthesised to drive the interconnected system to the sliding surface globally. Simulation results show the effectiveness of the proposed approach.
Journal of Quantitative Analysis in Sports An Improved LRMC Method for NCAA Basketball Prediction

The LRMC method for predicting NCAA Tournament results from regular-season game outcomes is a two-part process consisting of a logistic regression model to estimate head-to-head differences in team strength, followed by a Markov chain model to combine those differences into an overall ranking. We consider replacing each of the two parts of LRMC with alternative models, empirical Bayes and ordinary least squares, that attempt to accomplish the same goal. Computational results show that replacing the logistic regression with either of two empirical Bayes models yields a statistically-significant improvement when the probabilities are jointly conditioned.
Q-graded Hopf quasigroups

Firstly, we introduce a class of new algebraic systems which generalize Hopf quasigroups and Hopf $\pi-$algebras called $Q$-graded Hopf quasigroups, and research some properties of them. Secondly, we define the representations of $Q$-graded Hopf quasigroups, i.e $Q$-graded Hopf quasimodules, research the construction method and fundamental theorem of them. Thirdly, we research the smash products of $Q$-graded Hopf quasigroups.
Yangian doubles of classical types and their vertex representations

The Yangian double $DY(g_N)$ is introduced for the classical types of $g_N=so_{2n+1}$, $sp_{2n}$, $so_{2n}$. Via Gauss decomposition of the generator matrix, the Yangian double is given the Drinfeld presentation. In addition, bosonization of level $1$ realizations for the Yangian double $DY(g_N)$ of non-simply-laced types are explicitly constructed.
Estimating the Expected Total Number of Events in a Process

We consider estimation of the cumulative mean function of a process recurring in time, such as the numbers of arrests or migrations accrued by an individual, as a function of their age. We call this theage profile of a series of events. In some situations we can expect a finite value for the total number of events experienced by an individual, for example, when the distribution of the interevent times is improper, so that the process may cease at a finite time with positive probability. We propose and analyze a new estimator, constructed from Kaplan–Meier (KM) estimators of the interevent time distributions, for such an age profile, and compare it with the Nelson–Aalen (NA) estimator of the cumulative mean function of a process. The KM estimator is proved to be uniformly consistent for the age profile if and only if follow-up in the sample is sufficient in a sense that is manifested in practice by the leveling off of the profiles at their right-side ends, and is asymptotically normally distributed around its true value under mild conditions. Simulation results suggest that it is generally a better estimator than the NA estimator for the total number of events. It also appears to be more stable when applied to real data examples. For accurate estimation, it seems to be important to select a cohort of individuals whose ages at the first event are as similar as possible. The estimators are illustrated on some time-to-arrest data.
Dynamics of the quiescent solar corona

A model for the quiescent, inhomogeneous solar corona is developed, based upon the concept of loop structures as the basic structural element of the corona. The results, which are compared with observations obtained by the S-054 Skylab X-ray telescope, show that (a) hydrostatic solutions are stable only if the temperature maximum is located at the top of loop structures, and the deposition scale length of the coronal heating mechanism is comparable with (or larger than) the loop scale size; (b) the loop temperature (approx.T/sub max/), pressure p, and size L are related by the expression T/sub max/approx.1. 4 x 10/sup 3/(pL)/sup 1/3/, a relation which contains no free parameters; (c) coronal heating models based upon the coronal magnetic field (e.g., Alfven mode dissipation and coronal current heating) are consistent with the loop model, while acoustic mode damping is not.In accordance with these results, we propose a new model of the corona in which the quiescent X-ray corona represents a metastable equilibrium state. Thus, fluctuations in the local heating rate are shown to lead to dynamically unstable states within loops. These may be identified with transient loop brightenings seen in X-rays; with relatively cool coronal loop structures seen in EUV emission lines,more » which have been reported to extend to heights larger than the imputed pressure scale height and may be associated with downflows of plasma; and with the formation of quiescent prominences within loop structures. « less
Clear‐sky stable boundary layers with low winds over snow‐covered surfaces. Part 2: Process sensitivity

This study evaluates the relative impact of snow‐surface coupling, long‐wave radiation, and turbulent mixing on the development of the stable boundary layer over snow. Observations at three sites are compared to WRF single‐column model (SCM) simulations. All three sites have snow‐covered surfaces but are otherwise contrasting: Cabauw (Netherlands, grass), Sodankylä (Finland, needle‐leaf forest) and Halley (Antarctica, ice shelf). All cases are characterized by stable, clear‐sky, and calm conditions. Part 1 of this study determined the optimal SCM forcing strategy. In this study, the process intensities from that reference are perturbed to study their relative significance and to assess which process could be responsible for the most optimal agreement between model and observation.
Experimental validation of a diffraction correction model for high frequency measurement of ultrasound backscatter coefficients

Diffraction correction functions are assessed using a tissue equivalent calibrated phantom and compared to the theoretical model of Chen et al. (UFFC: 44; 515-525, 1997). Two transducers were evaluated: (1) 50 MHz, focal distance at 5.7 mm and f/number of 1.7 and (2) 29 MHz, 10.0 mm and f/2, respectively. The RF backscattered signals from a well calibrated tissue equivalent phantom were compensated for attenuation, squared and filtered, providing the backscattered power as a function of the penetration depth. A polynomial function was fitted and normalized to its peak, resulting in the experimental diffraction correction function. Over a region centered at the focus and corresponding to 25% of the focal distance, the RMS error between Chen's theoretical computation and experimental diffraction correction functions was 3.4% (50 MHz) and 4.3% (29 MHz). Between theoretical and the plane reflector cases the RMS error was; 17.6% (50 MHz) and 10.1% (29 MHz). Chen's theory is an accurate and useful means to correct ultrasound backscatter measurements in the high frequency range.
Robust M-estimators on spheres

We introduce M-estimators for location and concentration parameters of von Mises-Fisher distributions on unit spheres. These include the directional mean, normalized spatial median, spherical median, and the mle of the concentration parameter. We find the influence functions and asymptotic distributions of such estimators and give necessary and sufficient conditions under which the M-estimators become SB-robust. SB-robust M-estimators, which are optimal in a sense similar to Hampel, are proposed. We discuss both simultaneous estimation of location and concentration and estimation of one parameter when the other is known. The behavior of the optimal estimators, together with several alternatives, under extreme contamination and moderate sample sizes is studied using simulation. An example, previously studied by Fisher, Lewis, and Embleton (1987, Analysis of Spherical Data, Cambridge Univ. Press, Cambridge, UK), dealing with remanent magnetization is reanalyzed using these techniques.
A New Interpretation of EXAFS Spectra in Real Space. I. General Formalism

It is shown that the problem of determining the function of radial atomic distribution around an absorbing atom by oscillations of the X-ray absorption coefficient belongs to a family of incorrect problems. A regularization algorithm is proposed for the problem concerned. Computational schemes realized involving the use of computers are described. Some results of model calculations are given. Es wird gezeigt, das das Problem der Bestimmung der radialen atomaren Verteilungsfunktion um ein absorbierendes Atom durch Oszillationen des Rontgenabsorptionskoeffizienten zur Familie der inkorrekten Probleme gehort. Ein Regulierungsalgorithmus wird fur das betrachtete Problem vorgeschlagen. Realisierte Berechnungsschemata, die die Benutzung von Computern einschliesen, werden beschrieben. Einige Ergebnisse von Modellberechnungen werden mitgeteilt.
Rogue wave occurrence and dynamics by direct simulations of nonlinear wave-field evolution

Abstract We study the occurrence and dynamics of rogue waves in three-dimensional deep water using phase-resolved numerical simulations based on a high-order spectral (HOS) method. We obtain a large ensemble of nonlinear wave-field simulations ( $M= 3$ in HOS method), initialized by spectral parameters over a broad range, from which nonlinear wave statistics and rogue wave occurrence are investigated. The HOS results are compared to those from the broad-band modified nonlinear Schrödinger (BMNLS) equations. Our results show that for (initially) narrow-band and narrow directional spreading wave fields, modulational instability develops, resulting in non-Gaussian statistics and a probability of rogue wave occurrence that is an order of magnitude higher than linear theory prediction. For longer times, the evolution becomes quasi-stationary with non-Gaussian statistics, a result not predicted by the BMNLS equations (without consideration of dissipation). When waves spread broadly in frequency and direction, the modulational instability effect is reduced, and the statistics and rogue wave probability are qualitatively similar to those from linear theory. To account for the effects of directional spreading on modulational instability, we propose a new modified Benjamin–Feir index for effectively predicting rogue wave occurrence in directional seas. For short-crested seas, the probability of rogue waves based on number frequency is imprecise and problematic. We introduce an area-based probability, which is well defined and convergent for all directional spreading. Based on a large catalogue of simulated rogue wave events, we analyse their geometry using proper orthogonal decomposition (POD). We find that rogue wave profiles containing a single wave can generally be described by a small number of POD modes.