Miracle-dz/UniFAR-FTUs huggingface dataset:
A Fourier‐Mukai approach to the enumerative geometry of principally polarized abelian surfaces

We study twisted ideal sheaves of small length on an irreducible principally polarized abelian surface \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}$({\mathbb T},\ell )$\end{document}. Using Fourier‐Mukai techniques we associate certain jumping schemes to such sheaves and completely classify such loci. We give examples of applications to the enumerative geometry of \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}${\mathbb T}$\end{document} and show that no smooth genus 5 curve on such a surface can contain a \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}$g^1_3$\end{document}. We also describe explicitly the singular divisors in the linear system |2ℓ|.
Weighted Singular Value Thresholding and its Application to Background Estimation

Singular value thresholding (SVT) plays an important role in the well-known robust principal component analysis (RPCA) algorithms which have many applications in computer vision and recommendation systems. In this paper, we formulate and study a weighted singular value thresholding (WSVT) problem, which uses a combination of the nuclear norm and a weighted Frobenius norm. We present an algorithm to numerically solve WSVT and establish the convergence of the algorithm. As a proof of concept, we apply WSVT with a simple choice of weight learned from the data to the background estimation problem in computer vision. The numerical experiments show that our method can outperform RPCA algorithms. This indicates that instead of tackling the computationally expensive $\ell_1$ norm employed in RPCA, one may switch to the weighted Frobenius norm and achieve about the same or even better performance.
Genomic Classifier for Patient Enrichment: Misclassification and Type I Error Issues in Pharmacogenomics Noninferiority Trial

Unlike the phenotypic characteristics, a genomic diagnostic assay is needed to assess whether a patient truly has the genomic characteristics of interest for therapeutic investigation. However, in reality, the diagnostic assay is not perfect without misclassification error. We consider a targeted or enrichment pharmacogenomics clinical trial with a noninferiority objective. We assume the probability of response of the misclassified subjects is identical in the treated and control groups because the blinding should yield no preferential misclassification. We show that the maximum Type I error rate associated with falsely concluding noninferiority can be substantially liberal if the accuracy of the diagnostic assay is much less than perfect. When the diagnostic assay has moderate to high sensitivity and specificity, a reasonable range of false nondisease prediction rate among test positives can be identified where the maximum Type I error rate inflation is much less. To achieve a prescribed level of positive predictive value, the feasibility of a genomic biomarker for enrichment in a noninferiority study is a function of disease prevalence. Given the evidential standard of much less inflation of Type I error rate can be shown, a genomic biomarker, if qualified, may be useful as an adjunct tool for patient selection.
The p-Laplace Equation in Domains with Multiple Crack Section via Pencil Operators

Abstract The p-Laplace equation ∇ · (|∇u|p−2∇u) = 0, where p > 2, in a bounded domain Ω ⊂ ℝ2, with inhomogeneous Dirichlet conditions on the smooth boundary ∂Ω is considered. In addition, there is a finite collection of curves Γ = Γ1 ∪ . ∪ Γm ⊂ Ω, on which we assume homogeneous Dirichlet conditions u = 0, modeling a multiple crack formation, focusing at the origin 0 ∈ Ω. This makes the above quasilinear elliptic problem overdetermined. Possible types of the behaviour of solution u(x, y) at the tip 0 of such admissible multiple cracks, being a “singularity” point, are described, on the basis of blow-up scaling techniques and a “nonlinear eigenvalue problem” via spectral theory of pencils of non self-adjoint operators. Specially interesting is the application of those techniques to non-linear problems as the one considered here. To do so we introduce a very novel change of variable compared with the classical one introduced by Kondratiev for the analysis of non-smooth domains, such as domains with corner points, edges, etc, studying the behaviour of the solutions at those problematic points. Typical types of admissible cracks are shown to be governed by nodal sets of a countable family of nonlinear eigenfunctions, which are obtained via branching from harmonic polynomials that occur for p = 2. Using a combination of analytic and numerical methods, saddle-node bifurcations in p are shown to occur for those nonlinear eigenvalues/ eigenfunctions.
Approximating Fixed points of Bregman Generalized $\alpha$-nonexpansive mappings.

In this paper, we introduce a new class of Bregman generalized $\alpha$-nonexpansive mappings in terms of Bregman distances, and investigate the Ishikawa and Noor iterations for these mappings. We establish weak and strong convergence theorems of Ishikawa and Noor iterative schemes for Bregman generalized $\alpha$-nonexpansive mappings in Banach spaces. Furthermore, we propose an example of our generated mapping and some numerical examples which support our main theorem. Our results are new and improve the recent ones in the literature.
Scissor Congruence and Suslin reciprocity law

We prove the strong Suslin reciprocity law conjectured by Alexander Goncharov and describe it's corollaries for the theory of scissor congruence of polyhedra in hyperbolic space. The proof is based on the study of Goncharov conjectural description of certain rational motivic cohomology groups of a field. Our main result is a homotopy invariance theorem for these groups.
Homological algebra in characteristic one

This article develops several main results for a general theory of homological algebra in categories such as the category of sheaves of idempotent modules over a topos. In the analogy with the development of homological algebra for abelian categories the present paper should be viewed as the analogue of the development of homological algebra for abelian groups. Our selected prototype, the category Bmod of modules over the Boolean semifield B is the replacement for the category of abelian groups. We show that the semi-additive category Bmod fulfills analogues of the axioms AB1 and AB2 for abelian categories. By introducing a precise comonad on Bmod we obtain the conceptually related Kleisli and Eilenberg-Moore categories. The latter category Bmod^s is simply Bmod in the topos of sets endowed with an involution and as such it shares with Bmod most of its abstract categorical properties. The three main results of the paper are the following. First, when endowed with the natural ideal of null morphisms, the category Bmod^s is a semi-exact, homological category in the sense of M. Grandis. Second, there is a far reaching analogy between Bmod^s and the category of operators in Hilbert space, and in particular results relating null kernel and injectivity for morphisms. The third fundamental result is that, even for finite objects of Bmod^s the resulting homological algebra is non-trivial and gives rise to a computable Ext functor. We determine explicitly this functor in the case provided by the diagonal morphism of the Boolean semiring into its square.
Jump splicing schemes for elliptic interface problems and the incompressible Navier-Stokes equations

We present a general framework for accurately evaluating finite difference operators in the presence of known discontinuities across an interface. Using these techniques, we develop simple-to-implement, second-order accurate methods for elliptic problems with interfacial discontinuities and for the incompressible Navier-Stokes equations with singular forces. To do this, we first establish an expression relating the derivatives being evaluated, the finite difference stencil, and a compact extrapolation of the jump conditions. By representing the interface with a level set function, we show that this extrapolation can be constructed using dimension- and coordinate-independent normal Taylor expansions with arbitrary order of accuracy. Our method is robust to non-smooth geometry, permits the use of symmetric positive-definite solvers for elliptic equations, and also works in 3D with only a change in finite difference stencil. We rigorously establish the convergence properties of the method and present extensive numerical results. In particular, we show that our method is second-order accurate for the incompressible Navier-Stokes equations with surface tension.
The red‐shift effect and radiation decay on black hole spacetimes

We consider solutions to the linear wave equation □gϕ = 0 on a (maximally extended) Schwarzschild spacetime with parameter M > 0, evolving from sufficiently regular initial data prescribed on a complete Cauchy surface Σ, where the data are assumed only to decay suitably at spatial infinity. (In particular, the support of ϕ may contain the bifurcate event horizon.) It is shown that the energy flux F T̃ϕ (𝒮) of the solution (as measured by a strictly timelike T̃ that asymptotically matches the static Killing field) through arbitrary achronal subsets 𝒮 of the black hole exterior region satisfies the bound F T̃ϕ (𝒮) ≤ C E(v −2+ + u −2+ ), where v and u denote the infimum of the Eddington‐Finkelstein advanced and retarded time of 𝒮, v+ denotes max{1, v}, and u+ denotes max{1, u}, where C is a constant depending only on the parameter M, and E depends on a suitable norm of the solution on the hypersurface t ≐ u + v = 1. (The bound applies in particular to subsets 𝒮 of the event horizon or null infinity.) It is also shown that ϕ satisfies the pointwise decay estimate |ϕ| ≤ C Ev −1+ in the entire exterior region, and the estimates |rϕ| ≤ CR̃E(1 + |u|)−1/2 and |r1/2ϕ| ≤ CR̃Eu −1+ in the region {r ≥ R̃} ∩ J+(Σ) for any R̃ > 2M. The estimates near the event horizon exploit an integral energy identity normalized to local observers. This estimate can be thought to quantify the celebrated red‐shift effect. The results in particular give an independent proof of the classical result |ϕ| ≥ C E of Kay and Wald without recourse to the discrete isometries of spacetime. © 2009 Wiley Periodicals, Inc.
Intersection multiplicity, Milnor number and Bernstein's theorem

We explicitly characterize when the Milnor number at the origin of a polynomial or power series (over an algebraically closed field k of arbitrary characteristic) is the minimum of all polynomials with the same Newton diagram, which completes works of Kushnirenko (Invent. Math., 1976) and Wall (J. Reine Angew. Math., 1999). Given a fixed collection of n convex integral polytopes in R^n, we also give an explicit characterization of systems of n polynomials supported at these polytopes which have the maximum number (counted with multiplicity) of isolated zeroes on k^n, or more generally, on a union of torus orbits on k^n; this completes the program (undertaken by many authors including Khovanskii (Funkcional. Anal. i Prilozen, 1978), Huber and Sturmfels (Discrete Comput. Geom., 1997), Rojas (J. Pure Appl. Algebra, 1999)) of the extension to k^n of Bernstein's theorem (Funkcional. Anal. i Prilozen, 1975) on number of solutions of n polynomials on (k^*)^n. Our solutions to these two problems are connected by the computation of the intersection multiplicity at the origin of n hypersurfaces determined by n generic polynomials.
ASTROPHYSICAL GYROKINETICS: KINETIC AND FLUID TURBULENT CASCADES IN MAGNETIZED WEAKLY COLLISIONAL PLASMAS

This paper presents a theoretical framework for understanding plasma turbulence in astrophysical plasmas. It is motivated by observations of electromagnetic and density fluctuations in the solar wind, interstellar medium and galaxy clusters, as well as by models of particle heating in accretion disks. All of these plasmas and many others have turbulent motions at weakly collisional and collisionless scales. The paper focuses on turbulence in a strong mean magnetic field. The key assumptions are that the turbulent fluctuations are small compared to the mean field, spatially anisotropic with respect to it and that their frequency is low compared to the ion cyclotron frequency. The turbulence is assumed to be forced at some system-specific outer scale. The energy injected at this scale has to be dissipated into heat, which ultimately cannot be accomplished without collisions. A kinetic cascade develops that brings the energy to collisional scales both in space and velocity. The nature of the kinetic cascade in various scale ranges depends on the physics of plasma fluctuations that exist there. There are four special scales that separate physically distinct regimes: the electron and ion gyroscales, the mean free path and the electron diffusion scale. In each of the scale ranges separated by these scales, the fully kinetic problem is systematically reduced to a more physically transparent and computationally tractable system of equations, which are derived in a rigorous way. In the “inertial range” above the ion gyroscale, the kinetic cascade separates into two parts: a cascade of Alfvénic fluctuations and a passive cascade of density and magnetic-field-strength fluctuations. The former are governed by the reduced magnetohydrodynamic (RMHD) equations at both the collisional and collisionless scales; the latter obey a linear kinetic equation along the (moving) field lines associated with the Alfvénic component (in the collisional limit, these compressive fluctuations become the slow and entropy modes of the conventional MHD). In the “dissipation range” below ion gyroscale, there are again two cascades: the kinetic-Alfvén-wave (KAW) cascade governed by two fluid-like electron reduced magnetohydrodynamic (ERMHD) equations and a passive cascade of ion entropy fluctuations both in space and velocity. The latter cascade brings the energy of the inertial-range fluctuations that was Landau-damped at the ion gyroscale to collisional scales in the phase space and leads to ion heating. The KAW energy is similarly damped at the electron gyroscale and converted into electron heat. Kolmogorov-style scaling relations are derived for all of these cascades. The relationship between the theoretical models proposed in this paper and astrophysical applications and observations is discussed in detail.
Magnetische Untersuchungen an Pd‐Mischkristallen mit Übergangselementen

Es wurden Suszeptibilitatsmessungen an Pd-Mischkristallen mit den Ubergangselementen Ti, V, Cr, Mn, Fe, Co, Ni, Zr, Nb, Mo, Ta, W und Re, bei denen die 3d-, 4d-, und 5d-Schale im Aufbau ist, im Temperaturbereich zwischen 90 und 1100° K vorgenommen. Die Ergebnisse werden mit Hilfe der aus der Elektronentheorie der Metalle fur den Spinparamagnetismus von Pauli und Stoner entwickelten Gleichungen diskutiert.
The effects of an external electric field on the dynamics of cold plasma jets—experimental and computational studies

Atmospheric pressure plasma jets provide a convenient and stable means to transport highly reactive plasma species beyond the confines of the plasma generating electrodes and into the ambient air; such characteristics make them an ideal tool for many emerging plasma processing applications. As the guided streamer exits the jet capillary, the application of an external electric field can significantly influence the dynamics of propagation, potentially providing a means to manipulate the transport of plasma species to a downstream substrate. In this paper the influence of positive and negative voltages pulses applied to an external electrode situated along the axis of streamer propagation is examined experimentally and computationally using a simplified 1.5D model. It is shown that application of a positive voltage pulse to the external electrode reduces the velocity of propagation of the cathode-directed streamer and the application of a negative voltage pulse increases the velocity of propagation. Further to this, the application of high positive voltages to the external electrodes effectively inhibits propagation and results in a significant decrease in the emission intensity from excited states populated by energetic electrons. The results obtained experimentally are compared and contrasted with those from the computational model to uncover the underlying physical mechanisms at play.
Reactive collisions of atomic antihydrogen with H, He+ and He

The fermion molecular dynamics (FMD) method is used to determine the rearrangement and destruction cross sections for collisions of antihydrogen with H, He+ and He at collision energies above 0.1 au. The results for the H and He+ targets satisfactorily merge with previous calculations done for lower collision energies. Despite the absence of a critical distance, the destruction cross section for collisions of with He, previously uncalculated, is found to be comparable with the destruction cross sections for collisions with H and He+. All three cross sections are shown to be given quite reasonably by simple classical orbiting formulae at energies that are very low but still high enough for L > 0 partial waves to be dominant. The cross sections for formation of the antiprotonic atoms (Pn or ) and their initial quantum numbers with the projectile are found to be significantly different from the analogous cross sections for projectiles.
Random matrix products: Universality and least singular values

We establish local universality of the $k$-point correlation functions associated with products of independent iid random matrices, as the sizes of the matrices tend to infinity, under a moment matching hypothesis. We also prove Gaussian limits for the centered linear spectral statistics of products of independent GinUE matrices, which we then extend to more general product matrices by way of another moment matching argument. In a similar fashion, we establish Gaussian limits for the centered linear spectral statistics of products of independent truncated random unitary matrices. Moreover, we are able to obtain explicit expressions for the limiting variances in each of these cases. The key technical lemma required for these results is a lower bound on the least singular value of the translated linearization matrix associated with the product of $M$ normalized independent random matrices with independent and identically distributed subgaussian entries.
Multilayered image compression

The main contribution of this work is a new paradigm for image compression. We describe a new multi-layered representation technique for images. An image is encoded as the superposition of one main approximation, and a sequence of residuals. The strength of the multi-layered method comes from the fact that we use different bases to encode the main approximation and the residuals. For instance, we can use: a wavelet basis to encode a coarse main approximation of the image, wavelet packet bases to encode textured patterns, brushlet bases to encode localized oriented textured features, etc.
Control of Group Velocity via Spontaneous Generated Coherence and Kerr Nonlinearity

A four-level N-type atomic medium is considered to study the effect of spontaneous generated coherence (SGC) and Kerr nonlinearity on light pulse propagation. A light pulse is propagating inside the medium where each atom follows four-level N-type atom-field configuration of rubidium (85Rb) atom. The atom-field interaction leads to electromagnetically induced transparency (EIT) process. The atom-field interaction is accompanied by normal dispersion and in the presence of SGC and Kerr nonlinearity the dispersion property of the proposed atomic medium is modified, which leads to enhancement of positive group index of the medium. The enhancement of positive group index then leads to slow group velocity inside the medium. A more slow group velocity is also investigated by incorporated the collective effect of SGC and Kerr nonlinearity. The control of group velocity inside a four-level N-type atomic medium via collective effect of SGC and Kerr nonlinearity is the major part of this work.
Complex multipole pulsed beams and Hermite pulsed beams: a novel expansion scheme for transient radiation from well-collimated apertures

We are concerned with an expansion scheme for radiation from well-collimated pulsed aperture distribution that uses a new set of pulsed-beam (PB) basis functions. Several beam-expansion schemes have been introduced recently. They are based on local matching, within a self-consistent phase space format, of beam propagators to the source distribution. For well-collimated source distributions, greater efficiency may be obtained by matching wide beams to the entire aperture distribution, so that the propagators exhibit the same radiation properties as the entire aperture. This is the underlying strategy of the well-known Hermite–Gaussian-beam expansion of time-harmonic fields. In the present study a type of PB propagator, complex multipole PB’s (CMPB’s), is introduced and utilized in a similar expansion scheme for time-dependent radiation. CMPB’s are exact, highly localized, space–time wave-packet solutions that can be modeled analytically in terms of radiation from time-dependent complex multipoles as a generalization of the recently introduced complex source PB. The CMPB’s have paraxial profiles that involve transverse oscillations expressed in terms of Hermite polynomials and temporal derivatives; hence they form a biorthogonal set of basis functions for the expansion of collimated time-dependent fields. It is shown that the representation is most efficient if both the wave-front curvature and the collimation of the CMPB’s are matched to those of the aperture so that they exhibit the same far-field properties (e.g., diffraction angle and decay rate). We therefore introduce criteria to determine the collimation (Fresnel) length of a given pulsed source distribution and thereby for the optimal expansion parameters. To establish the near- and the far-field convergence properties of the expansion under matched and unmatched conditions, we derive closed-form expressions for the expansion amplitudes for a general class of time-dependent distributions and examine extensive numerical results.
On non-improvability of full-memory strategies in problems of optimization of the guaranteed result

The paper addresses the problem of optimization of a guaranteed (worst case) result for a control system driven by a controlling side in presence of a dynamical disturbance. The disturbances as functions of time are subject to functional constraints belonging to a given family of constraints. The latter family is known to the controlling side that does not observe the disturbance and uses full-memory strategies to form the control actions. The study is focused on the case where disturbance varies in open-loop disturbances chosen in advance and the case where the disturbances are restricted to a $L_2$--compact set fixed in advance but unknown to the controlling side. In these cases it is shown that the optimal guaranteed result is non-improvable in the sense that it coincides with that obtained in the class of quasi-strategies -- nonantisipatory transformations of disturbances into controls. An $\varepsilon$--optimal full-memory strategy is constructed. An illustrative nonlinear example is given.
$K$-theory as an Eilenberg-Maclane spectrum

For an additive Waldhausen category linear over a ring $k$, the corresponding $K$-theory spectrum is a module spectrum over the $K$-theory spectrum of $k$. Thus if $k$ is a finite field of characteristic $p$, then after localization at $p$, we obtain an Eilenberg-Maclane spectrum -- in other words, a chain complex. We propose an elementary and direct construction of this chain complex that behaves well in families and uses only method of homological algebra (in particular, the notions of a ring spectrum and a module spectrum are not used).