Miracle-dz/UniFAR-FTUs huggingface dataset:
Rigidity and Edge Universality of Discrete β‐Ensembles

We study discrete β‐ensembles as introduced in [17]. We obtain rigidity estimates on the particle locations; i.e., with high probability, the particles are close to their classical locations with an optimal error estimate. We prove the edge universality of the discrete β‐ensembles; i.e., for β ≥ 1, the distribution of extreme particles converges to the Tracy‐Widom β‐distribution. As far as we know, this is the first proof of general Tracy‐Widom β‐distributions in the discrete setting. A special case of our main results implies that under the Jack deformation of the Plancherel measure, the distribution of the lengths of the first few rows in Young diagrams converges to the Tracy‐Widom β‐distribution, which answers an open problem in [38]. Our proof relies on Nekrasov's (or loop) equations, a multiscale analysis, and a comparison argument with continuous β‐ensembles. © 2019 Wiley Periodicals, Inc.
A Parametric Interpolation Framework for 1D Scalar Conservation Laws using the Equal Area Principle

In this paper we develop a novel framework for numerically solving scalar conservation laws in one space dimension. Utilizing the method of characteristics in conjunction with the equal area principle we develop an approach where the weak solution is obtained purely as the solution of a parametric interpolation problem. As this framework hinges on the validity of the equal area principle, we provide a rigorous discussion of the equal area principle and show that, indeed, the equal area principle is equivalent to the Rankine-Hugoniot condition, within the specific context studied in this paper. Combining these results with properties of the characteristic equations yields the desired setting to define the equivalent parametric interpolation problem. We conclude by applying this framework to Burgers' equation and show how one obtains machine precision in the shock position when the initial condition can be represented exactly in the chosen space of parametric polynomials.
Polarimetric imaging of the Galactic center at 12.4 microns - The detailed magnetic field structure in the northern arm and the east-west bar

Recent closely sampled imaging polarimetry of the central 0.5 pc of the Galaxy at 12.4 microns with a 58 x 62 array camera system is presented. The results clearly show that the magnetic field is a property of the diffuse material of the large-scale structures in Sgr A (the northern arm and east-west bar) rather than the embedded sources. The magnetic field is independent of the changes of density and temperature in the compact source environments. The magnetic field direction in much of the east-west bar is complex, and its polarization is probably the result of the superposition of differently oriented filaments. The abrupt decrease of polarization southwest of IRS 1 observed previously is confirmed and shown to reverse sign. This is due either to a rapid change of magnetic field direction close to the dynamical center, or to the superposition of nearly orthogonal fields. The field direction changes smoothly across IRS 1, and no discontinuity of motion here is found.
Identification of Several Aspergillus Isolates Candidates for Bio Fertilizer Agents Using Molecular Markers

This research is an activity to characterize and determine several types of soil-borne fungi based on the use of DNA sequences. This study aims to determine the species name and genealogy of four selected fungal isolates from the genus Aspergillus isolated from horticultural fields in Bumiaji, Batu, East Java. The identification of biocontrol agents begins with macroscopic and microscopic morphological observations, followed by DNA isolation, polymerase chain reaction application using ITS 1 and ITS 4 primers. Sequencing is done using Sanger sequencing. The nucleotides generated from the sequencer machine (ABI 3730XL sequencer) were compared with the gene bank using the BLAST-NCBI program, and their relationships were analyzed using MEGA X software. The results showed that based on BLAST analysis of the nucleotide sequences of Aspergilus spp. isolates 6, 7, 17, and 21 were compatible with Aspergillus tamarii with 100% Query Cover and 100% identical rate. These four Aspergillus isolates have the potential as bofertilizer agents and can be used for various industrial purposes.
Local graph cut criterion for supervised dimensionality reduction

Graph cut criterion has been proven to be robust and applicable in clustering problems. In this paper the graph cut criterion is applied to construct a supervised dimensionality reduction. A new graph cut, scaling cut, is proposed based on the classical normalized cut. Scaling cut depicts the relationship between samples, which makes it can handle the heteroscedastic and multimodel data in which LDA fails. Meanwhile, the solution to scaling cut is global optimal for it is a generalized eigenvalue problem. To obtain a more reasonable projection matrix and reduce the computational complexity as well, the localized k-nearest neighbor graph is introduced in, which leads to equivalent or better results compared with scaling cut.
Electron spin resonance centers associated with oxygen precipitates in Czochralski silicon crystals

We have previously concluded that the oxygen-precipitate-associated defects that we identified by the deep levels at Ev+0.30 eV and Ec−0.25 eV were the Pb centers generated in the interface between the oxygen precipitates and the surrounding silicon crystal lattice [M. Koizuka and H. Yamada-Kaneta, J. Appl. Phys. 84, 4255 (1998)]. In order to confirm this conclusion, we have made electron spin resonance (ESR) measurements on the Czochralski-grown silicon crystals containing the oxygen precipitates generated by the two-step anneals of 500 °C, 20 h+700 °C, 60 h. We have found the ESR lines whose g values well coincide with those of the Pb0 and Pb1 centers. Thus it has been clarified that the Pb0 and Pb1 centers are generated by the oxygen precipitation as well as by the thermal oxidation. The present successful application of the ESR method to the annealed silicon crystals suggests that it can be a useful tool to characterize the precipitation state of the oxygen in silicon.
Generalised Brownian Motion and Second Quantisation

A new approach to the generalised Brownian motion introduced by M. Bouzejko and R. Speicher is described, based on symmetry rather than deformation. The symmetrisation principle is provided by Joyal’s notions of tensorial and combinatorial species. Any such species V gives rise to an endofunctor FV of the category of Hilbert spaces with contractions. A generalised Brownian motion is an algebra of creation and annihilation operators acting on FV (H) for arbitrary Hilbert spaces H and having a prescription for the calculation of vacuum expectations in terms of a function t on pair partitions. The positivity is encoded by a � -semigroup of “broken pair partitions” whose representation space with respect to t is V . The existence of the second quantisation as functor t from Hilbert spaces to noncommutative probability spaces is proved to be equivalent to the multiplicative property of the function t . For a certain one parameter interpolation between the fermionic and the free Brownian motion it is shown that the “field algebras” ( K) are type II1 factors when K is infinite dimensional.
The homotopy sequence for regular singular stratified bundles

A separable, proper morphism of varieties with geometrically connected fibers induces a homotopy exact sequence relating the \'etale fundamental groups of source, target and fiber. Extending work of dos Santos, we prove the existence of an analogous homotopy exact sequence for fundamental group schemes classifying regular singular stratified bundles, under the additional assumption that the morphism in question can be (partially) compactified to a log smooth morphism.
A geometric criterion for prescribing residues and some applications

An old theorem of Weil and Kodaira says that for a compact Kahler manifold $X$ there is a closed logarithmic $1$-form with residue divisor $D$ if and only if $D$ is homologous to zero in $H_{2n-2}(X,\mathbb C)$. In the first part of this paper, we generalize the above theorem to general compact complex manifolds by showing that the necessary and sufficient condition in general is described by a holomorphic invariant called the $\mathcal Q$-flat class. Next, we prove that the holomorphic criterion is reduced to the topological one when $X$ has Property $(H)$. Since all Kahler manifolds have Property $(H)$, this gives an alternative proof of Weil and Kodaira's original theorem. Then, we prove some decomposition theorems for closed meromorphic $1$-forms by applying the above general theorem. In the second part of the paper, we turn to the study of pluriharmonic functions on projective manifolds and classify all the pluriharmonic functions with mild singularity.
K-theoretic invariants of Hamiltonian fibrations

We introduce new invariants of Hamiltonian fibrations with values in the suitably twisted K-theory of the base. Inspired by techniques of geometric quantization, our invariants arise from the family analytic index of a family of natural $Spin^c$-Dirac operators. As an application we give new examples of non-trivial Hamiltonian fibrations, that have not been previously detected by other methods. As one crucial ingredient we construct a potentially new homotopy equivalence map, with a certain naturality property, from $BU$ to the space of index $0$ Fredholm operators on a Hilbert space, using elements of modern theory of homotopy colimits.
The E-11 origin of all maximal supergravities

Starting from the eleven dimensional E11 non-linear realisation of M-theory we compute all possible forms, that is objects with totally antisymmetrised indices, that occur in four dimensions and above as well as all the 1-forms and 2-forms in three dimensions. In any dimension D, the D−1-forms lead to maximal supergravity theories with cosmological constants and they are in precise agreement with the patterns of gauging found in any dimension using supersymmetry. The D-forms correspond to the presence of space-filling branes which are crucial for the consistency of orientifold models and have not been derived from an alternative approach, with the exception of the 10-dimensional case. It follows that the gaugings of supergravities and the spacetime-filling branes possess an eleven dimensional origin within the E11 formulation of M-theory. This and previous results very strongly suggest that all the fields in the adjoint representation of E11 have a physical interpretation.
On stochastic differential equations with arbitrary slow convergence rates for strong approximation

In the recent article [Hairer, M. , Hutzenthaler, M. , Jentzen, A. , Loss of regularity for Kolmogorov equations, Ann. Probab. 43 (2015), no. 2, 468--527] it has been shown that there exist stochastic differential equations (SDEs) with infinitely often differentiable and globally bounded coefficients such that the Euler scheme converges to the solution in the strong sense but with no polynomial rate. Hairer et al.'s result naturally leads to the question whether this slow convergence phenomenon can be overcome by using a more sophisticated approximation method than the simple Euler scheme. In this article we answer this question to the negative. We prove that there exist SDEs with infinitely often differentiable and globally bounded coefficients such that no approximation method based on finitely many observations of the driving Brownian motion converges in absolute mean to the solution with a polynomial rate. Even worse, we prove that for every arbitrarily slow convergence speed there exist SDEs with infinitely often differentiable and globally bounded coefficients such that no approximation method based on finitely many observations of the driving Brownian motion can converge in absolute mean to the solution faster than the given speed of convergence.
Nephrologist referrals of older patients with chronic kidney disease in Singapore: a cross-sectional study

Background Chronic kidney disease (CKD) is common in the older population. By 2035, approximately one-quarter of Singapore residents are expected to have CKD. Many of these patients are not referred to nephrologists. Aim To compare the characteristics of older patients (aged ≥65 years) with CKD stage ≥3B in the referral and non-referral groups. Design & settings A cross-sectional study in the primary care organisation National University Polyclinics (NUP), Singapore. Method Retrospective data were extracted from the electronic health records of patients with CKD (aged ≥65 years) with CKD stage ≥3B. Results From 1 January–31 December 2018, a total of 1536 patients aged ≥65 years were diagnosed with CKD stage ≥3B (non-referral group = 1179 versus referral group = 357). The mean patient age in the non-referral group (78.4 years) was older than that in the referral group (75.9 years) (P<0.001). Indian older patients were referred more compared with their Chinese counterparts (P = 0.008). The non-referral group was prescribed significantly less fibrate, statins, insulin, sulfonylureas, dipeptidyl peptidase-4 (DPP4) inhibitors, and antiplatelet than the referral group (P<0.05), but only the difference in fibrates remained significant on subsequent multivariate analysis. Conclusion This study demonstrates that there is a considerable number of older patients with CKD exclusively managed in the primary care setting (n = 1179) and that referrals primarily depend on demographic factors, namely age and ethnic group, rather than medical determinants of CKD severity or case complexity.
Extended and constrained diagonal weighting algorithm with application to inverse problems in image reconstruction

The algebraic reconstruction of images in computerized tomography gives rise to large, sparse and ill-conditioned inverse problems, in which the ‘effect’ (measurement of the attenuation of x-ray intensities after penetration of the analyzed body) is used to compute the ‘cause’ (the values of the attenuation function inside the body, i.e. the image). Algebraic reconstruction techniques (ART), on both their successive or simultaneous formulation, have been developed since the early 1970s as efficient ‘row action methods’ for solving the image reconstruction problem in computerized tomography. In this respect, two important development directions were concerned with their extension to the inconsistent case of the reconstruction problem as well as with their combination with constraining strategies, imposed by the particularities of the reconstructed image. In our paper we analyze, from these two points of view, the diagonal weighting (DW) algorithm proposed by Y Censor, D Gordon and R Gordon in 2001 as an improvement of the classical Cimmino's reflection method. In the first part of the paper we introduce general extended and constraining procedures for ART, based on a minimal set of sufficient assumptions that ensure the convergence of the corresponding algorithms. Starting from this general context we then design an extended form of the DW algorithm together with a constraining procedure for which we prove convergence under appropriate assumptions. Numerical experiments are presented on two phantoms widely used in the literature.
Epidemiology of Traumatic Spinal Cord Injuries in Iran; a Systematic Review and Meta-Analysis

Introduction: Understanding the epidemiology of traumatic spinal cord injuries (TSCIs) can be helpful for policymakers and planners to consider appropriate strategies to control and prevent these injuries. This study aimed to determine the epidemiological characteristics of TSCI in Iran in order to increase knowledge and awareness of these injuries. Methods: A systematic literature search was conducted up to January 2022 in the electronic databases, including PubMed, Scopus, Web of Science, Google Scholar, SID, Iranmedex, and Magiran. The quality of included studies was evaluated using the STORBE checklist. Comprehensive meta-analysis was used to analyze the data. Results: Nineteen studies involving 9416 cases were included in the study. Participants’ pooled mean age was 35.80 ± 1.07 years (95% CI: 33.69 to 37.91), of whom 69% (95% CI: 68% to 70%; P<0.05) were male. The most frequent TSCI occurred in the age group of less than 30 years. Motor vehicle collisions (MVCs) was the most common cause of TSCI (57%; 95% CI: 25% to 63%), followed by falls (32%; 95% CI: 26% to 38%). Most participants had thoracolumbar (27%; 95% CI: 10% to 55%) and cervical injuries (23%; 95% CI: 16% to 31%), respectively. The incidence of TSCI was estimated at 10.5 per million people. The prevalence of TSCI was 3 per 10000 people. The mortality rate due to TSCI was 3.9% (95% CI: 0.02 to 0.06; P<0.05). Conclusion: Based on the findings of this meta-analysis, the pooled incidence and prevalence of TSCI in the Iranian population were 10.5/1000.000 people and 4.4/10.000 people, respectively. TSCIs had occurred more frequently in males following MVCs, and in the age group under 30 years. The pooled mortality rate due to TSCI was 3.9% (95% CI: 0.02 to 0.06; P<0.05).
Prevalence and molecular characterization of extended-spectrum β-lactamase (ESBL) producing Escherichia coli isolated from dogs suffering from diarrhea in and around Kolkata

Background: Dogs are the favorite companion animals among humans. The close interaction between dogs and people increases the risk of antibiotic resistance spreading. Surveillance for antimicrobial resistance and the identification of ESBL-producing Escherichia coli as an indicator bacterium is an important tool for managing antimicrobial drug therapy. Aims: The present study targeted to identify and characterize ESBL-producing E. coli among dogs suffering from diarrhea in and around Kolkata. Methods: Isolation and identification of E. coli from dogs suffering from diarrhea (n=70) along with screening for the production of both ESBL and AmpC. The isolates were further characterized through antimicrobial resistance profiling, resistance genes (blaCTX-M, blaTEM, and blaSHV) screening, and phylogenetic group study. Results: Among the 70 isolates, 21 (30%) were confirmed ESBL producers. An antibiogram typing of ESBL-producing E. coli revealed that the majority of them were resistant to norfloxacin (85.7%) followed by tetracycline (61.90%), doxycycline (57.14%), piperacillin/tazobactam (52.38%), cotrimoxazole (47.62%), gentamicin (42.62%), amikacin (23.81%), and chloramphenicol (19.05%). Major resistance genes included blaCTX-M (100%), blaTEM (28.57%), and blaSHV (9.50%). The predominant phylogenetic groups were phylogroup A (76%) followed by phylogroup D (24%). Conclusion: The current investigation reported a high prevalence of both ESBL and AmpC β-lactamase (AmpC) producing E. coli, co-resistance to a distinct group of antibiotics, and co-existence of different ESBL genes in dogs. Our findings highlight the importance of diagnostic antimicrobial susceptibility testing for proper antimicrobial therapy and to prevent antimicrobial resistance from spreading to humans from dogs in Kolkata and the surrounding area.
Applied Algebra and Geometry: A SIAGA of Seven Pictures

The cover of the SIAM Journal on Applied Algebra and Geometry shows seven pictures. We describe these pictures and discuss the topics they represent. About the Author: Anna Seigal is a graduate student at UC Berkeley working in applied algebra. Her interests lie in tensors and applications to biological systems. She has a particular penchant for writing about mathematics in terms of pictures and also blogs on this subject at this https URL
SOUND TRANSMISSION THROUGH A RIB-STIFFENED PLATE: COMPARISONS OF A LIGHT-FLUID APPROXIMATION WITH EXPERIMENTAL RESULTS

Interest in stiffened plate constructions has been widespread recently in aerospace, marine and engineering structures : their vibratory response can be greatly modified by small weight added to the hull. Semi-analytical and finite element modellings are mostly based on a weak (energetic) formulation of the in vacuo problem. First, the analysis has been simplified by applying the so-called orthotropic equivalent plate theory only valid when the mechanical wavelengths are greater than the stiffeners spacing~; a more accurate and robust method is the discrete model in which the system is divided into subelements~: the stiffeners are therefore considered as beams exerting efforts on the plate. Moreover, the vibro-acoustic response of the system fluid/structure is approximated under the assumption that the fluid-loading is a small perturbation with respect to the in vacuo problem since the surrounding fluid is a gas. This paper applies this approximation to the case of a baffled plate stiffened by ribs.
Theory of the Hilbert Spectrum

This paper is a contribution to the old problem of representing a signal in the coordinates of time and frequency. As the starting point, we abandon Gabor's complex extension and re-evaluate fundamental principles of time-frequency analysis. We provide a multicomponent model of a signal that enables rigorous definition of instantaneous frequency on a per-component basis. Within our framework, we have shifted all uncertainty of the latent signal to its quadrature. In this approach, uncertainty is not a fundamental limitation of analysis, but rather a manifestation of the limited view of the observer. With the appropriate assumptions made on the signal model, the instantaneous amplitude and instantaneous frequency can be obtained exactly, hence exact representation of a signal in the coordinates of time and frequency can be achieved. However, uncertainty now arises in obtaining the correct assumptions, i.e.~how to correctly choose the quadrature of the components.
Ergodic problems for Hamilton-Jacobi equations: yet another but efficient numerical method

We propose a new approach to the numerical solution of ergodic problems arising in the homogenization of Hamilton-Jacobi (HJ) equations. It is based on a Newton-like method for solving inconsistent systems of nonlinear equations, coming from the discretization of the corresponding ergodic HJ equations. We show that our method is able to solve efficiently cell problems in very general contexts, e.g., for first and second order scalar convex and nonconvex Hamiltonians, weakly coupled systems, dislocation dynamics and mean field games, also in the case of more competing populations. A large collection of numerical tests in dimension one and two shows the performance of the proposed method, both in terms of accuracy and computational time.
An algorithm for computing the reduction of 2-dimensional crystalline representations of Gal(ℚ¯p/ℚp)

We describe an algorithm to compute the reduction modulo [Formula: see text] of a crystalline Galois representation of dimension [Formula: see text] of [Formula: see text] with distinct Hodge–Tate weights via the semi-simple modulo [Formula: see text] Langlands correspondence. We give some examples computed with an implementation of this algorithm in SAGE.
Scattered Classes of Graphs

For a class $\mathcal C$ of graphs $G$ equipped with functions $f_G$ defined on subsets of $E(G)$ or $V(G)$, we say that $\mathcal{C}$ is $k$-scattered with respect to $f_G$ if there exists a constant $\ell$ such that for every graph $G\in \mathcal C$, the domain of $f_G$ can be partitioned into subsets of size at most $k$ so that the union of every collection of the subsets has $f_G$ value at most $\ell$. We present structural characterizations of graph classes that are $k$-scattered with respect to several graph connectivity functions. In particular, our theorem for cut-rank functions provides a rough structural characterization of graphs having no $mK_{1,n}$ vertex-minors, which allows us to prove that such graphs have bounded linear rank-width.