Miracle-dz/UniFAR-FTUs huggingface dataset:
Augmented base loci and restricted volumes on normal varieties

We extend to normal projective varieties defined over an arbitrary algebraically closed field a result of Ein, Lazarsfeld, Mustaţă, Nakamaye and Popa characterizing the augmented base locus (aka non-ample locus) of a line bundle on a smooth projective complex variety as the union of subvarieties on which the restricted volume vanishes. We also give a proof of the folklore fact that the complement of the augmented base locus is the largest open subset on which the Kodaira map defined by large and divisible multiples of the line bundle is an isomorphism.
MilliPCD

3D Point Cloud Data (PCD) has been used in many research and commercial applications widely, such as autonomous driving, robotics, and VR/AR. But existing PCD generation systems based on RGB-D and LiDARs require robust lighting and an unobstructed field of view of the target scenes. So, they may not work properly under challenging environmental conditions. Recently, millimeter-wave (mmWave) based imaging systems have raised considerable interest due to their ability to work in dark environments. But the resolution and quality of the PCD from these mmWave imaging systems are very poor. To improve the quality of PCD, we design and implement MilliPCD, a "beyond traditional vision" PCD generation system for handheld mmWave devices, by integrating traditional signal processing with advanced deep learning based algorithms. We evaluate MilliPCD with real mmWave reflected signals collected from large, diverse indoor environments, and the results show improvements in the quality w.r. t. the existing algorithms, both quantitatively and qualitatively.
On the topology of n-normed spaces with respect to norms of its quotient spaces.

In this paper, we study some topological characteristics of the n-normed spaces. We observe convergence sequences, closed sets, and bounded sets in the n-normed spaces using norms of quotient spaces that will be constructed. These norms will be a new viewpoint in observing the characteristics of the n-normed spaces. By using these norms, we also review the completeness of the n-normed spaces.
Phenomenology of ESR in heavy-fermion systems: Fermi-liquid and non-Fermi-liquid regimes

We extend and apply a recent theory of the dynamical spin response of Anderson lattice systems to interpret electron-spin resonance (ESR) data on ${\text{YbRh}}_{2}{\text{Si}}_{2}$. Starting within a semiphenomenological Fermi-liquid description at low temperatures $Tl{T}_{x}$ (a crossover temperature) and low magnetic fields $B⪡{B}_{x}$, we extend the description to the non-Fermi-liquid regime by adopting a quasiparticle picture with effective mass and spin susceptibility varying logarithmically with energy/temperature as observed in experiment. We find a sharp ESR resonance line slightly shifted from the local $f$-level resonance and broadened by quasiparticle scattering (taking unequal $g$ factors of conduction and $f$ electrons) and by spin-lattice relaxation, both significantly reduced by the effect of ferromagnetic fluctuations. A detailed comparison of our theory with the data shows excellent agreement in the Fermi-liquid regime. In the non-Fermi-liquid regime we find a close relation of the $T$ dependence of the specific-heat/spin susceptibility with the observed $T$ dependence of line shift and linewidth.
On the Rankin–Selberg method for vector-valued Siegel modular forms

In this work, we use the Rankin–Selberg method to obtain results on the analytic properties of the standard [Formula: see text]-function attached to vector-valued Siegel modular forms. In particular we provide a detailed description of its possible poles and obtain a non-vanishing result of the twisted [Formula: see text]-function beyond the usual range of absolute convergence. Our results include also the case of metaplectic Siegel modular forms. We remark that these results were known in this generality only in the case of scalar weight Siegel modular forms. As an interesting by-product of our work we establish the cuspidality of some theta series.
A derivation of masses and total luminosities of galaxy groups and clusters in the maxBCG catalogue

We report the results of a multi-waveband analysis of the masses and luminosities of $\sim$600 galaxy groups and clusters identified in the maxBCG catalogue. These data are intended to form the basis of future work on the formation of the "$m_{12}$ gap" in galaxy groups and clusters. We use SDSS spectroscopy and $g$, $r$ and $i$ band photometry to estimate galaxy group/cluster virial radii, masses and total luminosities. In order to establish the robustness of our results, we compare them with literature studies that utilize a variety of mass determinations techniques (dynamical, X-ray, weak lensing) and total luminosities estimated in the $B$, $r$, $i$, and $K$ wavebands. We also compare our results to predictions derived from the Millennium Simulation. We find that, once selection effects are properly accounted for, excellent agreement exists between our results and the literature with the exception of a single observational study. We also find that the Millennium Simulation does an excellent job of predicting the effects of our selection criteria. Our results show that, over the mass range $\sim10^{13}-10^{15}$ M$_{\odot}$, variations in the slope of the mass-luminosity scaling relation with mass detected in this and many other literature studies is in part the result of selection effects. We show that this can have serious ramifications on attempts to determine how the mass-to-light ratio of galaxy groups and cluster varies with mass.
On the Fine Structure of Quadratical Quasigroups

We prove that quadratical quasigroups form a variety Q of right and left simple groupoids. New examples of quadratical quasigroups of orders 25 and 29 are given. The fine structure of quadratical quasigroups and inter-relationships between their properties are explored. The spectrum of Q is proved to be contained in the set of integers equal to 1 plus a multiple of 4.
Association between Dimensions of Physical Attractiveness and Risk of Rape Victimization among Adolescent Females

ABSTRACT This study addresses the following question: “Does female physical attractiveness predict the risk of rape victimization? ” Data were analyzed from a large sample of females who participated in the National Longitudinal Study of Adolescent to Adult Health (Add Health). Three conceptualizations of physical attractiveness were operationalized: overall attractiveness, curvaceousness, and weight. Bivariate analysis revealed that rape victimization was predicted by greater curvaceousness and weight but was unrelated to interviewer-rated attractiveness. Respondent age, Hispanic ethnicity, race, general health, physical maturation, and number of sexual partners were added to multivariate models in a stepwise fashion, but physical attractiveness and rape victimization were found to be unrelated in all models, and the positive association between weight and victimization fell to statistical non-significance when general health was added to the model. By contrast, curvaceousness consistently predicted greater victimization risk across all models. Among control variables, females who are older, less healthy, and who have more sexual partners face a higher risk of victimization. Add Health data do not present a straightforward picture of the relationship between various dimensions of physical attractiveness and rape victimization. Findings, study limitations, and theoretical implications are discussed.
Compact perturbations and consequent hereditarily polaroid operators

A Banach space operator $A\in B({\cal{X}})$ is polaroid, $A\in {\cal{P}}$, if the isolated points of the spectrum $\sigma(A)$ are poles of the operator; $A$ is hereditarily polaroid, $A\in{\cal{HP}}$, if every restriction of $A$ to a closed invariant subspace is polaroid. Operators $A\in{\cal{HP}}$ have SVEP on $\Phi_{sf}(A)=\{\lambda: A-\lambda$ is semi Fredholm $\}$: This, in answer to a question posed by Li and Zhou (Studia Math. 221(2014), 175-192), proves the necessity of the condition $\Phi_{sf}^+(A)=\emptyset$. A sufficient condition for $A\in B({\cal{X}})$ to have SVEP on $\Phi_{sf}(A)$ is that its component $\Omega_a(A)=\{\lambda\in\Phi_{sf}(A): \rm{ind}(A-\lambda)\leq 0\}$ is connected. We prove: If $A\in B({\cal{H}})$ is a Hilbert space operator, then a necessary and sufficient condition for there to exist a compact operator $K$ such that $A+K\in{\cal{HP}}$ is that $\Omega_a(A)$ is connected.
Comment on “Spin-dependent tunneling through a symmetric semiconductor barrier: The Dresselhaus effect”

In a recent paper [Wang et al., Phys. Rev. B 72, 153314 (2005)], the ${k}^{3}$ Dresselhaus term in the contacts and the full form of the current operator are considered for spin-dependent tunneling through a symmetric barrier. The authors found that the full form of the current operator has a much larger influence on the spin polarization than was initially thought. In this Comment we will show that their treatment of the other problem, the ${k}^{3}$ Dresselhaus term in the contacts, is incorrect. Their proposed solution in the contacts simply does not obey the Schr\"odinger equation. In this context, we also comment on the definition and the suitability of spin polarization in contacts with spin-orbit coupling.
Differentiating Orlicz spaces with rare bases of rectangles

In the current paper, we study how the speed of convergence of a sequence of angles decreasing to zero influences the possibility of constructing a rare differentiation basis of rectangles in the plane, one side of which makes with the horizontal axis an angle belonging to the given sequence, that differentiates precisely a fixed Orlicz space.
Inequalities on the spectral radius and the operator norm of Hadamard products of positive operators on sequence spaces

Relatively recently, K.M. R. Audenaert (2010), R.A. Horn and F. Zhang (2010), Z. Huang (2011), A.R. Schep (2011), A. Peperko (2012), D. Chen and Y. Zhang (2015) have proved inequalities on the spectral radius and the operator norm of Hadamard products and ordinary matrix products of finite and infinite non-negative matrices that define operators on sequence spaces. In the current paper we extend and refine several of these results and also prove some analogues for the numerical radius. Some inequalities seem to be new even in the case of $n\times n$ non-negative matrices.
Transmutations of supersymmetry through soliton scattering, and self-consistent condensates

We consider the two most general families of the (1+1)D Dirac systems with transparent scalar potentials, and two related families of the paired reflectionless Schrodinger operators. The ordinary N=2 supersymmetry for such Schrodinger pairs is enlarged up to an exotic N=4 nonlinear centrally extended supersymmetric structure, which involves two bosonic integrals composed from the Lax-Novikov operators for the stationary Korteweg-de Vries hierarchy. Each associated single Dirac system displays a proper N=2 nonlinear supersymmetry with a non-standard grading operator. One of the two families of the first and second order systems exhibits the unbroken supersymmetry, while another is described by the broken exotic supersymmetry. The two families are shown to be mutually transmuted by applying a certain limit procedure to the soliton scattering data. We relate the topologically trivial and nontrivial transparent potentials with self-consistent inhomogeneous condensates in Bogoliubov-de Gennes and Gross-Neveu models, and indicate the exotic N=4 nonlinear supersymmetry of the paired reflectionless Dirac systems.
Atiyah covering index theorem for Riemannian foliations

We use the symbol calculus for foliations developed in our previous paper to derive a cohomological formula for the Connes-Chern character of the semi-finite spectral triple. The same proof works for the Type I spectral triple of Connes-Moscovici. The cohomology classes of the two Connes-Chern characters induce the same map on the image of the maximal Baum-Connes map in K-theory, thereby proving an Atiyah $L^2$ covering index theorem.
Breaking Up Is Hard to Do: Magmatism During Oceanic Arc Breakup, Subduction Reversal, and Cessation

The formerly continuous Vitiaz Arc broke into its Vanuatu and Fijian portions during a reversal of subduction polarity in the Miocene. Basaltic volcanism in Fiji that accompanied the breakup ranged from shoshonitic to low‐K and boninitic with increasing distance from the broken edge of the arc that, presumably, marks the broken edge of the slab. The Sr‐Pb‐Nd isotope ratios of the slab‐derived component in the breakup basalts most closely match those of the isotopically most depleted part of the Samoan seamount chain on the Pacific Plate that was adjacent to the site of breakup at 4–8 Ma, and differ from those of subsequent basalts in spreading segments of the surrounding backarc North Fiji and Lau Basins. Subduction of the Samoan Chain along the Vitiaz Trench Lineament may have controlled the limit of polarity reversal and, hence, where the double saloon doors (Martin, 2013) opened. Prior to breakup, Fijian volcanics were more similar isotopically to the Louisville Seamount Chain.
Bayesian estimation of Gegenbauer processes

This paper examines via a simulation study the effectiveness of a number of estimation methods for Gegenbauer seasonal persistent processes. The key result shows that an application of Bayesian methodology returns one of the most accurate estimation methods, in terms of recovering the original process parameters, combined with a substantial reduction in evaluation time over an exact likelihood method.
A toolkit for defect computations in Landau-Ginzburg models

We review the results of arXiv:1208.1481 on orientation reversal and duality for defects in topological Landau-Ginzburg models, with the intention of providing an easily accessible toolkit for computations. As an example we include a proof of the main result on adjunctions in a special case, using Pauli matrices. We also explain how to compute arbitrary correlators of defect-decorated planar worldsheets, and briefly discuss the relation to generalised orbifolds.
Five old open clusters more in the outer Galactic disc

New photometric material is presented for 6 outer disk supposedly old, Galact ic star clusters: Berkeley 76, Haffner 4, Ruprecht 10, Haffner 7, Haffner 11, and Haffner 15, that are projected against the rich and complex Canis Major overde nsity at $225^o \leq l \leq 248^o $, $-7^o \leq b \leq -2^o$. This CCD data-set, in the UBVI pass-bands, is used to derive their fundamental parameters, in particular age and distance. Four of the program clusters turn out to be older than 1 Gyr. This fact makes them ideal targets for future spectroscopic campaigns aiming at deriving their metal abundances. This, in turn, contributes to increase the number of well-studied outer disk o ld open clusters. Only Haffner 15, previously considered an old cluster, is found to be a young, significantly reddened cluster, member of the Perseus arm in the third Galactic quadrant. As for Haffner~4, we suggest an age of about half a Gyr. The most interesting result we found is that Berkeley~76 is probably located at more than 17 kpc from the Galactic center, and therefore is among the most peripherical old open clusters so far detected. Besides, for Ruprecht~10 and Haffner~7, which were never studied before, we pr opose ages larger than 1 Gyr. All the old clusters of this sample are scarcely populated and show evidence o f tidal interaction with the Milky Way, and are therefore most probably in advanced st ages of dynamical dissolution.
Algebras with Parastrophically Uncancellable Quasigroup Equations

We consider $48$ parastrophically uncancellable quadratic functional equations with four object variables and two quasigroup operations in two classes: balanced non--Belousov (consists of 16 equations) and non--balanced non--gemini (consists of 32 equations). A linear representation of a group (Abelian group) for a pair of quasigroup operations satisfying one of these parastrophically uncancellable quadratic equations is obtained. As a consequence of these results, a linear representation for every operation of a binary algebra satisfying one of these hyperidentities is presented.
Hereditary triangular matrix comonads

We recognize Harada’s generalized categories of diagrams as a particular case of modules over a monad defined on a finite direct product of additive categories. We work in the dual (albeit formally equivalent) situation, that is, with comodules over comonads. With this conceptual tool at hand, we obtain several of the Harada results with simpler proofs, some of them under more general hypothesis, besides with a characterization of the normal triangular matrix comonads that are hereditary, that is, of homological dimension less than or equal to 1. Our methods rest on a matrix representation of additive functors and natural transformations, which allows us to adapt typical algebraic manipulations from Linear Algebra to the additive categorical setting.
Dynamics of Nonlinear Waves on Bounded Domains

This thesis is concerned with dynamics of conservative nonlinear waves on bounded domains. In general, there are two scenarios of evolution. Either the solution behaves in an oscillatory, quasiperiodic manner or the nonlinear effects cause the energy to concentrate on smaller scales leading to a turbulent behaviour. Which of these two possibilities occurs depends on a model and the initial conditions. In the quasiperiodic scenario there exist very special time-periodic solutions. They result for a delicate balance between dispersion and nonlinear interaction. The main body of this dissertation is concerned with construction (by means of perturbative and numerical methods) of time-periodic solutions for various nonlinear wave equations on bounded domains. While turbulence is mainly associated with hydrodynamics, recent research in General Relativity has also revealed turbulent phenomena. Numerical studies of a self-gravitating massless scalar field in spherical symmetry gave evidence that anti-de Sitter space is unstable against black hole formation. On the other hand there appeared many examples of asymptotically anti-de Sitter solutions which evade turbulent behaviour and appear almost periodic for long times. We discuss here these two contrasting scenarios putting special attention to the construction and properties of strictly time-periodic solutions. We analyze different models where solutions of this type exist. Moreover, we describe similarities and differences among these models concerning properties of time-periodic solutions and methods used for their construction.
DETECTION OF THE COMPRESSED PRIMARY STELLAR WIND IN η CARINAE

A series of three Hubble Space Telescope/Space Telescope Imaging Spectrograph spectroscopic mappings, spaced approximately one year apart, reveal three partial arcs in [Fe ii] and [Ni ii] emissions moving outward from η Carinae. We identify these arcs with the shell-like structures, seen in the three-dimensional hydrodynamical simulations, formed by compression of the primary wind by the secondary wind during periastron passages.
USP14 promotes pyroptosis of human annulus fibrosus cells derived from patients with intervertebral disc degeneration through deubiquitination of NLRP3

Intervertebral disc degeneration (IVDD) is a general disorder that results in low back pain and disability among many affected individuals. However, the current treatments for IVDD are limited to relieving the symptoms but do not solve the fundamental issue. In this study, the role of USP14 in mediating the activation of the NLRP3 inflammasome and the pyroptosis of AF cells from IVDD patients is determined in vitro, and gain- and loss-of-function assays of USP14 and the NLRP3 inflammasome are conducted. Pyroptosis of AF cells is detected by flow cytometry. The inflammatory cytokines (IL-1β and IL-18) and protein levels of NLRP3, active Caspase-1, Aggrecan, MMP3 and ADAMTS-5 are determined by ELISA and western blot analysis, respectively. The correlation between USP14 and NLRP3 is measured by coimmunoprecipitation and ubiquitination analysis. Upregulation of USP14 is accompanied by increased level of the NLRP3 inflammasome in AF cells from IVDD patients; furthermore, a positive correlation between them is observed. USP14 knockdown inhibits pyroptosis in AF cells by inducing ubiquitination of NLRP3, while overexpression of USP14 has the opposite effect, which is inhibited by the NLRP3 inflammasome inhibitor INF39. USP14 exerts its positive regulatory effect on AF cell pyroptosis by modulating the NLRP3/Caspase-1/IL-1β and IL-18 signaling axes.
Sharpness in the k-Nearest-Neighbours Random Geometric Graph Model

Let S n, k denote the random graph obtained by placing points in a square box of area n according to a Poisson process of intensity 1 and joining each point to its k nearest neighbours. Balister, Bollobás, Sarkar and Walters (2005) conjectured that, for every 0 < ε < 1 and all sufficiently large n, there exists C = C(ε) such that, whenever the probability that S n, k is connected is at least ε, then the probability that S n, k+C is connected is at least 1 - ε. In this paper we prove this conjecture. As a corollary, we prove that there exists a constant C' such that, whenever k(n) is a sequence of integers such that the probability S n,k(n) is connected tends to 1 as n → ∞, then, for any integer sequence s(n) with s(n) = o(logn), the probability S n,k(n)+⌊C'slog logn⌋ is s-connected (i.e. remains connected after the deletion of any s − 1 vertices) tends to 1 as n → ∞. This proves another conjecture given in Balister, Bollobás, Sarkar and Walters (2009).
THE CHANDRA X-RAY POINT-SOURCE CATALOG IN THE DEEP2 GALAXY REDSHIFT SURVEY FIELDS

We present the X-ray point-source catalog produced from the Chandra Advanced CCD Imaging Spectrometer (ACIS-I) observations of the combined ∼3.2 deg2 DEEP2 (XDEEP2) survey fields, which consist of four ∼0.7–1.1 deg2 fields. The combined total exposures across all four XDEEP2 fields range from ∼10 ks to 1.1 Ms. We detect X-ray point sources in both the individual ACIS-I observations and the overlapping regions in the merged (stacked) images. We find a total of 2976 unique X-ray sources within the survey area with an expected false-source contamination of ≈30 sources (≲ 1%). We present the combined log N–log S distribution of sources detected across the XDEEP2 survey fields and find good agreement with the Extended Chandra Deep Field and Chandra-COSMOS fields to . Given the large survey area of XDEEP2, we additionally place relatively strong constraints on the log N–log S distribution at high fluxes (), and find a small systematic offset (a factor ∼1.5) toward lower source numbers in this regime, when compared to smaller area surveys. The number counts observed in XDEEP2 are in close agreement with those predicted by X-ray background synthesis models. Additionally, we present a Bayesian-style method for associating the X-ray sources with optical photometric counterparts in the DEEP2 catalog (complete to RAB < 25.2) and find that 2126 (≈71.4% ± 2.8%) of the 2976 X-ray sources presented here have a secure optical counterpart with a ≲ 6% contamination fraction. We provide the DEEP2 optical source properties (e.g., magnitude, redshift) as part of the X-ray–optical counterpart catalog.
On the spectrum of DW Hamiltonian of quantum SU(2) gauge field

The spectrum of masses of the colorless (color neutral) states of the DW (De Donder-Weyl) Hamiltonian operator of quantum SU(2) Yang-Mills field theory on $\mathbb{R}^D$ obtained via the precanonical quantization is shown to be purely discrete and bounded from below. The scale of the mass gap is estimated to be of the order of magnitude of the scale of the ultra-violet parameter $\varkappa$ introduced by precanonical quantization on dimensional grounds.