Miracle-dz/UniFAR-FTUs huggingface dataset:
On the Computation of Gaussian Quadrature Rules for Chebyshev Sets of Linearly Independent Functions

We consider the computation of quadrature rules that are exact for a Chebyshev set of linearly independent functions on an interval $[a,b]$. A general theory of Chebyshev sets guarantees the existence of rules with a Gaussian property, in the sense that $2l$ basis functions can be integrated exactly with just $l$ points and weights. Moreover, all weights are positive and the points lie inside the interval $[a,b]$. However, the points are not the roots of an orthogonal polynomial or any other known special function as in the case of regular Gaussian quadrature. The rules are characterized by a nonlinear system of equations, and earlier numerical methods have mostly focused on finding suitable starting values for a Newton iteration to solve this system. In this paper we describe an alternative scheme that is robust and generally applicable for so-called complete Chebyshev sets. These are ordered Chebyshev sets where the first $k$ elements also form a Chebyshev set for each $k$. The points of the quadrature rule are computed one by one, increasing exactness of the rule in each step. Each step reduces to finding the unique root of a univariate and monotonic function. As such, the scheme of this paper is guaranteed to succeed. The quadrature rules are of interest for integrals with non-smooth integrands that are not well approximated by polynomials.
Lensless coded-aperture imaging with separable Doubly-Toeplitz masks

Abstract. In certain imaging applications, conventional lens technology is constrained by the lack of materials which can effectively focus the radiation within a reasonable weight and volume. One solution is to use coded apertures—opaque plates perforated with multiple pinhole-like openings. If the openings are arranged in an appropriate pattern, then the images can be decoded and a clear image computed. Recently, computational imaging and the search for a means of producing programmable software-defined optics have revived interest in coded apertures. The former state-of-the-art masks, modified uniformly redundant arrays (MURAs), are effective for compact objects against uniform backgrounds, but have substantial drawbacks for extended scenes: (1) MURAs present an inherently ill-posed inversion problem that is unmanageable for large images, and (2) they are susceptible to diffraction: a diffracted MURA is no longer a MURA. We present a new class of coded apertures, separable Doubly-Toeplitz masks, which are efficiently decodable even for very large images—orders of magnitude faster than MURAs, and which remain decodable when diffracted. We implemented the masks using programmable spatial-light-modulators. Imaging experiments confirmed the effectiveness of separable Doubly-Toeplitz masks—images collected in natural light of extended outdoor scenes are rendered clearly.
Elimination of amplitude-phase crosstalk in frequency domain near-infrared spectroscopy

Changes in phase that occur with changes in amplitude impose severe limitations on the accuracy of frequency domain near-infrared spectrometers. Phase is related to the photon pathlength in tissue and phase errors introduced by the instrument can be interpreted as changes in tissue oxygenation. The instrument described in this article employs a reference radio frequency modulated laser diode to eliminate the effects of amplitude-phase crosstalk and requires no feedback. Light from the reference laser diode does not pass through the medium under investigation but passes directly onto the detector. The reference and medium signals follow a common path through the detector and so the same phase error is imposed on both. Summing the reference and medium phase eliminates the crosstalk and enables the resultant to be attributed only to the photon pathlength within the medium. It is also demonstrated that elimination of amplitude-phase crosstalk is a natural consequence of a phased array configuration.
Dimers and amoebae

We study random surfaces which arise as height functions of random perfect matchings (a.k.a. dimer configurations) on a weighted, bipartite, doubly periodic graph G embedded in the plane. We derive explicit formulas for the surface tension and local Gibbs measure probabilities of these models. The answers involve a certain plane algebraic curve, which is the spectral curve of the Kasteleyn operator of the graph. For example, the surface tension is the Legendre dual of the Ronkin function of the spectral curve. The amoeba of the spectral curve represents the phase diagram of the dimer model. Further, we prove that the spectral curve of a dimer model is always a real curve of special type, namely it is a Harnack curve. This implies many qualitative and quantitative statement about the behavior of the dimer model, such as existence of smooth phases, decay rate of correlations, growth rate of height function fluctuations, etc.
Differences between the Tonks regimes in the continuum and on the lattice

Motivated by recent experiments, we compare the Tonks (i.e., hard-core boson gas) regime achieved in an optical lattice with the Tonks regime of a one-dimensional Bose gas in the continuum. For the lattice gas, we compute the local (i.e., on-site) two-body correlations as a function of temperature and the filling of the lattice. It is found that this function saturates to a constant value with increasing temperature. Furthermore, the parameter that characterizes the long-distance correlations in the lattice Tonks regime is also obtained, showing that on the lattice the long-distance correlations enter the Tonks regime more rapidly than in the continuum.
Nonlinear time-fractional dispersive equations

In this paper we study some cases of time-fractional nonlinear dispersive equations (NDEs) involving Caputo derivatives, by means of the invariant subspace method. This method allows to find exact solutions to nonlinear time-fractional partial differential equations by separating variables. We first consider a third order time-fractional NDE that admits a four-dimensional invariant subspace and we find a similarity solution. We also study a fifth order NDE. In this last case we find a solution involving Mittag-Leffler functions. We finally observe that the invariant subspace method permits to find explicit solutions for a wide class of nonlinear dispersive time-fractional equations.
Paths, Crystals and Fermionic Formulae

We introduce a fermionic formula associated with any quantum affine algebra Uq(X (r) N ). Guided by the interplay between corner transfer matrix and Bethe ansatz in solvable lattice models, we study several aspects related to representation theory, most crucially, the crystal basis theory. They include one dimensional sums over both finite and semi-infinite paths, spinon character formulae, Lepowski-Primc type conjectural formula for vacuum string functions, dilogarithm identities, Q-systems and their solution by characters of various classical subalgebras and so forth. The results expand [HKOTY1] including the twisted cases and more details on inhomogeneous paths consisting of non-perfect crystals. As a most intriguing example, certain inhomogeneous one dimensional sums conjecturally give rise to branching functions of an integrable G (1) 2 -module related to the embedding G (1) 2 →֒ B (1) 3 →֒ D (1) 4 .
Synthetic aperture acoustic imaging of canonical targets with a 2-15 kHz linear FM chirp

Synthetic aperture image reconstruction applied to outdoor acoustic recordings is presented. Acoustic imaging is an alternate method having several military relevant advantages such as being immune to RF jamming, superior spatial resolution, capable of standoff side and forward-looking scanning, and relatively low cost, weight and size when compared to 0.5 - 3 GHz ground penetrating radar technologies. Synthetic aperture acoustic imaging is similar to synthetic aperture radar, but more akin to synthetic aperture sonar technologies owing to the nature of longitudinal or compressive wave propagation in the surrounding acoustic medium. The system's transceiver is a quasi mono-static microphone and audio speaker pair mounted on a rail 5meters in length. Received data sampling rate is 80 kHz with a 2- 15 kHz Linear Frequency Modulated (LFM) chirp, with a pulse repetition frequency (PRF) of 10 Hz and an inter-pulse period (IPP) of 50 milliseconds. Targets are positioned within the acoustic scene at slant range of two to ten meters on grass, dirt or gravel surfaces, and with and without intervening metallic chain link fencing. Acoustic image reconstruction results in means for literal interpretation and quantifiable analyses. A rudimentary technique characterizes acoustic scatter at the ground surfaces. Targets within the acoustic scene are first digitally spotlighted and further processed, providing frequency and aspect angle dependent signature information.
Narrow-Linewidth Semiconductor Laser With High-Order Sidewall Gratings

We demonstrate a kind of ridge waveguide semiconductor laser with high-order sidewall gratings around 1550 nm. The ridge waveguide with 11th-order sidewall gratings is fabricated by the standard contact-types <inline-formula> <tex-math notation="LaTeX">$i$ </tex-math></inline-formula>-line lithography. The fabricated device shows an output power of 44 mW at a bias current of 500 mA and a stable single-mode operation over wide ranges of current and temperature conditions. A high side-mode suppression ratio (<inline-formula> <tex-math notation="LaTeX">$\sim 59$ </tex-math></inline-formula> dB), a narrow linewidth of 63 kHz and a low relative intensity noise (<inline-formula> <tex-math notation="LaTeX">$ < -150$ </tex-math></inline-formula> dB/Hz under the frequency range from 0.03 to 20 GHz) have been demonstrated at <inline-formula> <tex-math notation="LaTeX">$25^{\circ }\text{C}$ </tex-math></inline-formula>.
Molecular mechanisms of amyloid-β peptide fibril and oligomer formation: NMR-based challenges

To completely treat and ultimately prevent dementia, it is essential to elucidate its pathogenic mechanisms in detail. There are two major hypotheses for the pathogenesis of Alzheimer’s dementia: the β-amyloid (Aβ) hypothesis and the tau hypothesis. The modified amyloid hypothesis, which proposes that toxic oligomers rather than amyloid fibrils are the essential cause, has recently emerged. Aβ peptides [Aβ(1–40) and Aβ(1–42)] form highly insoluble aggregates in vivo and in vitro. These Aβ aggregates contain many polymorphisms, whereas Aβ peptides are intrinsically disordered in physiological aqueous solutions without any compact conformers. Over the last three decades, solid-state nuclear magnetic resonance (NMR) has greatly contributed to elucidating the structure of each polymorph, while solution NMR has revealed the dynamic nature of the transient conformations of the monomer. Moreover, several methods to investigate the aggregation process based on the observation of magnetization saturation transfer have also been developed. The complementary use of NMR methods with cryo-electron microscopy, which has rapidly matured, is expected to clarify the relationship between the amyloid and molecular pathology of Alzheimer’s dementia in the near future. This review article is an extended version of the Japanese article, Insights into the Mechanisms of Oligomerization/Fibrilization of Amyloid β Peptide from Nuclear Magnetic Resonance, published in SEIBUTSU BUTSURI Vol. 62, p. 39–42 (2022).
On proximal mappings with Young functions in uniformly convex Banach spaces

It is well known in convex analysis that proximal mappings on Hilbert spaces are $1$-Lipschitz. In the present paper we show that proximal mappings on uniformly convex Banach spaces are uniformly continuous on bounded sets. Moreover, we introduce a new general proximal mapping whose regularization term is given as a composition of a Young function and the norm, and formulate our results at this level of generality. It is our aim to obtain the corresponding modulus of uniform continuity explicitly in terms of a modulus of uniform convexity of the norm and of moduli witnessing properties of the Young function. We also derive several quantitative results on uniform convexity, which may be of interest on their own.
Dynamic programming solution of incentive constrained problems

Abstract Several problems in economic theory can be formulated as a dynamic programming problem, plus an additional incentive compatibility constraint. This constraint requires the continuation value along the chosen sequence, at any point in time, to be larger than some prescribed function of the state, the control, or perhaps both. This constraint changes the nature of the problem in a substantial way: for instance, even if the problem is discounted, standard arguments based on contraction principles do not apply. In this paper we show how to reduce this class of problems to a simple variation of standard dynamic programming techniques. In particular the value function for the problem is shown to be the fixed point of an appropriately defined operator. Journal of Economic Literature Classification Numbers: C61, C72, C73, D92.
Testing the (Parametric) Null Model Hypothesis in (Semiparametric) Partial and Generalized Spline Models

On etend les resultats de Cox et Koh (1986) aux modeles generalises de Wahba (1985) et a divers autres modeles splines partiels. On montre que la statistique de test a une relation etroite avec le comportement de la fonction de validation croisee generalisee
The measure of a measurement

We identify a fractal scale s in a family of Borel probability measures μ on the unit interval which arises independently in quantum information theory and in wavelet analysis. The scales s we find satisfy s∊R+ and s≠1, some s 1. We identify these scales s by considering the asymptotic properties of u(J)∕∣J∣s where J are dyadic subintervals, and ∣J∣→0.
Light-Front Dynamics and AdS/QCD Correspondence: The Pion Form Factor in the Space- and Time-Like Regions

at large distances. The AdS/CFT correspondence also provides insights into the inherently non-perturbative aspects of QCD such as the orbital and radial spectra of hadrons and the form of hadronic wavefunctions. In particular, we show that there is an exact correspondence between the fth-dimensional coordinate of anti{de Sitter (AdS) space z and a specic light-front impact variable which measures the separation of the quark and gluonic constituents within the hadron in ordinary space-time. This connection allows one to compute the analytic form of the frame-independent light-front wavefunctions of mesons and baryons, the fundamental entities which encode hadron properties and which allow the computation of decay constants, form factors and other exclusive scattering amplitudes. Relativistic light-front equations in ordinary space-time are found which reproduce the results obtained using the fth-dimensional theory. As specic examples we compute the pion coupling constant f , the pion charge radius r 2 and examine the propagation of the electromagnetic current in AdS space, which determines the space and time-like behavior of the pion form factor and the pole of the meson.
Crystal planes and reciprocal space in Clifford geometric algebra

This paper discusses the geometry of kD crystal cells given by (k+ 1) points in a projective space ℝn+ 1. We show how the concepts of barycentric and fractional (crystallographic) coordinates, reciprocal vectors and dual representation are related (and geometrically interpreted) in the projective geometric algebra Cl(ℝn+ 1) (see (Die Ausdehnungslehre von 1844 und die Geom. Anal. Teubner: Leipzig, 1894)) and in the conformal algebra Cl(ℝn+ 1, 1). The crystallographic notions of d‐spacing, phase angle, structure factors, conditions for Bragg reflections, and the interfacial angles of crystal planes are obtained in the same context. Copyright © 2011 John Wiley & Sons, Ltd.
Anomalous eddy current loss and amorphous magnetic materials with low core loss (invited)

Heat‐treatment methods for obtaining low core loss in Fe rich amorphous alloys with high magnetic induction and the physical mechanism concerned will be discussed. Field annealing is necessary to avoid inducing local magnetic anisotropies or magnetic domain wall fixing, and then to make stress relieving effective. Consequently, field annealing can reduce hysteresis energy loss. However, core loss at high frequencies involves a fairly large anomalous eddy current loss. This is due to a large size of 180° magnetic domains resulting from field annealing. Oblique field annealing is, on the other hand, effective to reduce anomalous eddy current loss, because of increase in the number of 180° domain walls. The experimental relation between core loss and domain structure obtained on Fe(72)Co(8)Si(5)B(15) has satisfactorily been explained by the simple model on the basis of bar‐like 180° wall motion. Magnetic properties of Fe(81)‐(B, C, Si) (19) amorphous alloys suitable for transformer materials will also be rep.
Non-catastrophic resonant states in one dimensional scattering from a rising exponential potential

Investigation of scattering from rising potentials has just begun, these unorthodox potentials have earlier gone unexplored. Here, we obtain reflection amplitude ($r(E)$) for scattering from a two-piece rising exponential potential: $V(x\le 0)=V_1[1-e^{-2x/a}], V(x > 0)=V_2[e^{2x/b}-1]$, where $V_{1,2}>0$. This potential is repulsive and rising for $x>0$; it is attractive and diverging (to $-\infty$) for $x 0$) of $r(E)$ manifest as resonances. Wigner's reflection time-delay displays peaks at energies $E(\approx E_n$) but the eigenstates do not show spatial catastrophe for $E={\cal E}_n$.
Weierstrass-type representation for harmonic maps into general symmetric spaces via loop groups

In (19) a method was presented, which constructs via loop group splittings all harmonic maps into a compact symmetric space. The present paper generalizes this method to all spaces G=K, where G is an arbitrary Lie group (semisimple or not) and K is the fixpoint group of some involution of G. The method is illustrated by a number of examples.
Finite Sample Efficiency of Ordinary Least Squares in the Linear Regression Model With Autocorrelated Errors

Abstract In the standard linear regression model y = X β + u, with errors following a first-order stationary autoregressive process, it is shown that the relative efficiency of the ordinary least squares (OLS) as compared with the Gauss-Markov estimator depends to a great extent on the X matrix observed. In particular, it is seen that the relative efficiency of OLS increases with increasing correlation for certain cases important in practice. Since this seems to run contrary to what one should expect on the basis of previous Monte Carlo studies, some additional sampling experiments are also briefly discussed that keep the X matrix fixed in repeated runs.
SEM—past, present and future

The development of the technology of the scanning electron microscope (SEM) is traced from the early pioneering work in the 1930s to the present day. Recent trends are described and, based on these, some speculative forecasts are made of possible future developments. It is suggested that these will include better vacuum conditions in conventional SEM to permit more accurate surface characterization, and improved electron optics for higher resolution, particularly with low‐voltage operation.
Cyclone Tracking in Different Spatial and Temporal Resolutions

Abstract The quality of cyclone tracks associated with model output of various resolutions is determined using a high-resolution dataset (1.125° × 1.125°, 2 h) mapped to different spatial (triangular truncations, T21, T42, T63, T84) and temporal resolutions (4 h, 6 h, 12 h, 18 h, 24 h). Three sets of comparisons are performed to study the impact of increasing (i) temporal, (ii) spatial, and (iii) spatiotemporal resolutions (T21/24 h, T42/12 h, T63/6 h, T84/4 h). The different “test” resolutions are compared with a “perfect” reference dataset of optimal resolution. A general method to quantitatively compare two sets of tracks is developed. For a given test dataset, this method yields the ratio of perfect tracks (which are also identified in the reference set) and the ratio of missing tracks (present in the reference set, but missing in the test set). In 24-h data (T42) only about 45% of the cyclones can be identified with cyclones in 2-h data (73% in 12 h, 85% in 6 h).
The LED lightbulb: are we there yet? progress and challenges for solid state illumination

Rapid improvement in light emitting diode (LED) performance and an annual multibillion dollar lighting market is motivating worldwide development of LED based illumination systems. In addition to the traditional figures of merit of efficiency and high flux density, the white LED lamps must also have appropriate color characteristics. Current commercial white LED lamps have undesirable color temperatures and uniformity, and inferior color rendering. As discussed below, color uniformity in single phosphor lamps has been improved by deposition of thin uniform phosphor layers conformal to the LED die. Also, 2-phosphor LED lamps with white color characteristics typical of conventional incandescent and halogen sources are described. Furthermore, LED illumination offers additional features not practically achievable with conventional sources.
Continuity of the maximum-entropy inference: Convex geometry and numerical ranges approach

We study the continuity of an abstract generalization of the maximum-entropy inference - a maximizer. It is defined as a right-inverse of a linear map restricted to a convex body which uniquely maximizes on each fiber of the linear map a continuous function on the convex body. Using convex geometry we prove, amongst others, the existence of discontinuities of the maximizer at limits of extremal points not being extremal points themselves and apply the result to quantum correlations. Further, we use numerical range methods in the case of quantum inference which refers to two observables. One result is a complete characterization of points of discontinuity for $3\times 3$ matrices.
Speeding up the elliptic curve scalar multiplication using the window- w non adjacent form

Nowadays, elliptic curve based cryptosystem is an efficient public key cryptosystem, The very expensive operation in this cryptographic protocol is the elliptic curve scalar multiplication (elliptic curve point multiplication). Efforts have been mainly focused on developing efficient algorithms for representing the scalar which is involved of elliptic curve scalar multiplication. One of these is using the window- w non adjacent form method. In the present work, the accelerating elliptic curve scalar multiplication using the window- w non adjacent form method is proposed, where the number of operations in the elliptic curve scalar multiplication has been reduced. The expected gain is about 20%, 14% and 7.6% comparing with using the anther methods to compute the elliptic curve scalar multiplication. 20%.