Miracle-dz/UniFAR-FTUs huggingface dataset:
On feebly compact topologies on the semilattice $\exp_n\lambda$

We study feebly compact topologies $\tau$ on the semilattice $\left(\exp_n\lambda,\cap\right)$ such that $\left(\exp_n\lambda,\tau\right)$ is a semitopological semilattice. All compact semilattice $T_1$-topologies on $\exp_n\lambda$ are described. Also we prove that for an arbitrary positive integer $n$ and an arbitrary infinite cardinal $\lambda$ for a $T_1$-topology $\tau$ on $\exp_n\lambda$ the following conditions are equivalent: $(i)$ $\left(\exp_n\lambda,\tau\right)$ is a compact topological semilattice; $(ii)$ $\left(\exp_n\lambda,\tau\right)$ is a countably compact topological semilattice; $(iii)$ $\left(\exp_n\lambda,\tau\right)$ is a feebly compact topological semilattice; $(iv)$ $\left(\exp_n\lambda,\tau\right)$ is a compact semitopological semilattice; $(v)$ $\left(\exp_n\lambda,\tau\right)$ is a countably compact semitopological semilattice. We construct a countably pracompact $H$-closed quasiregular non-semiregular topology $\tau_{\operatorname{\textsf{fc}}}^2$ such that $\left(\exp_2\lambda,\tau_{\operatorname{\textsf{fc}}}^2\right)$ is a semitopological semilattice with discontinuous semilattice operation and prove that for an arbitrary positive integer $n$ and an arbitrary infinite cardinal $\lambda$ every $T_1$-semiregular feebly compact semitopological semilattice $\exp_n\lambda$ is a compact topological semilattice.
A fast direct imaging method for the inverse obstacle scattering problem with nonlinear point scatterers

Consider the scattering of a time-harmonic plane wave by heterogeneous media consisting of linear or nonlinear point scatterers and extended obstacles. A generalized Foldy-Lax formulation is developed to take fully into account of the multiple scattering by the complex media. A new imaging function is proposed and an FFT-based direct imaging method is developed for the inverse obstacle scattering problem, which is to reconstruct the shape of the extended obstacles. The novel idea is to utilize the nonlinear point scatterers to excite high harmonic generation so that enhanced imaging resolution can be achieved. Numerical experiments are presented to demonstrate the effectiveness of the proposed method.
Detection Of Insider Attacks In Block Chain Network Using The Trusted Two Way Intrusion Detection System

— For data privacy, system reliability, and security, Blockchain technologies have become more popular in recent years. Despite its usefulness, the blockchain is vulnerable to cyber assaults; for example, in January 2019 a 51% attack on Ethereum Classic successfully exposed flaws in the platform's security. From a statistical point of view, attacks represent a highly unusual occurrence that deviates significantly from the norm. Blockchain attack detection may benefit from Deep Learning, a field of study whose aim is to discover insights, patterns, and anomalies within massive data repositories. In this work, we define an trusted two way intrusion detection system based on a Hierarchical weighed fuzzy algorithm and self-organized stacked network (SOSN) deep learning model, that is trained exploiting aggregate information extracted by monitoring blockchain activities. Here initially the smart contract handles the node authentication. The purpose of authenticating the node is to ensure that only specific nodes can submit and retrieve the information. We implement Hierarchical weighed fuzzy algorithm to evaluate the trustability of the transaction nodes. Then the transaction verification step ensures that all malicious transactions or activities on the submitted transaction by self-organized stacked network deep learning model. The whole experimentation was carried out under matlab environment. Extensive experimental results confirm that our suggested detection method has better performance over important indicators (such as Precision, Recall, F-Score, overhead )
CURVATURE MOTION IN A MINKOWSKI PLANE

In this paper we study the curvature ow of a curve in a plane endowed with a minkowskian norm whose unit ball is smooth. We show that many of the properties known in the euclidean case can be extended (with due adaptations) to this new situation. In particular, we show that simple, closed, strictly convex, smooth curves remain so until the area enclosed by them vanishes. Moreover, their isoperimetric ratios converge to the minimum possible value, only attained by the minkowskian circle { so these curves converge to a minkowskian "circular point" as the enclosed area approaches zero. by @ @t (u;t) = k (u;t)N (u;t) where k and N are the curvature and the inwards unit normal vector to the closed curve ( ;t) at the point (u;t). A series of papers ((3), (4), (5) and (6)) has shown that any embedded curve in the Euclidean plane remains embedded and converges to a "circular point" in nite time. Moreover, if L (t) and A (t) are the length of and the area it encloses, some very simple formulae can be shown about their evolutions: dL dt = Z k 2 ds dA dt = 2
Profinite topologies

Profinite semigroups are a generalization of finite semigroups that come about naturally when one is interested in considering free structures with respect to classes of finite semigroups. They also appear naturally through dualization of Boolean algebras of regular languages. The additional structure is given by a compact zero-dimensional topology. Profinite topologies may also be considered on arbitrary abstract semigroups by taking the initial topology for homomorphisms into finite semigroups. This text is the proposed chapter of the Handdbook of Automata Theory dedicated to these topics. The general theory is formulated in the setting of universal algebra because it is mostly independent of specific properties of semigroups and more general algebras naturally appear in this context. In the case of semigroups, particular attention is devoted to solvability of systems of equations with respect to a pseudovariety, which is relevant for solving membership problems for pseudovarieties. Focus is also given to relatively free profinite semigroups per se, specially "large" ones, stressing connections with symbolic dynamics that bring light to their structure.
Do highly over-parameterized neural networks generalize since bad solutions are rare?

We study over-parameterized classifiers where Empirical Risk Minimization (ERM) for learning leads to zero training error. In these over-parameterized settings there are many global minima with zero training error, some of which generalize better than others. We show that under certain conditions the fraction of"bad"global minima with a true error larger than {\epsilon} decays to zero exponentially fast with the number of training data n. The bound depends on the distribution of the true error over the set of classifier functions used for the given classification problem, and does not necessarily depend on the size or complexity (e.g. the number of parameters) of the classifier function set. This insight may provide a novel perspective on the unexpectedly good generalization even of highly over-parameterized neural networks. We substantiate our theoretical findings through experiments on synthetic data and a subset of MNIST. Additionally, we assess our hypothesis using VGG19 and ResNet18 on a subset of Caltech101.
Spatial and spectral shape of inhomogeneous nonequilibrium exciton-polariton condensates

We develop a mean-field theory of the spatial profile and the spectral properties of polariton condensates in nonresonantly pumped semiconductor microcavities in the strong coupling regime. Specific signatures of the nonequilibrium character of the condensation process are pointed out: a striking sensitivity of the condensate shape on the optical pump spot size is demonstrated by analytical and numerical calculations, in good quantitative agreement with recent experimental observations.
Boost invariant spin hydrodynamics within the first order in derivative expansion

Boost-invariant equations of spin hydrodynamics confined to the first-order terms in gradients are numerically solved. The spin equation of state, relating the spin density tensor to the spin chemical potential, is consistently included in the first order. Depending on its form and the structure of the spin transport coefficients, we find solutions which are both stable and unstable within the considered evolution times of 10 fm/c. These findings are complementary to the recent identification of stable and unstable modes for perturbed uniform spin systems described by similar hydrodynamic frameworks.
Tuning Language Models as Training Data Generators for Augmentation-Enhanced Few-Shot Learning

Recent studies have revealed the intriguing few-shot learning ability of pretrained language models (PLMs): They can quickly adapt to a new task when fine-tuned on a small amount of labeled data formulated as prompts, without requiring abundant task-specific annotations. Despite their promising performance, most existing few-shot approaches that only learn from the small training set still underperform fully supervised training by nontrivial margins. In this work, we study few-shot learning with PLMs from a different perspective: We first tune an autoregressive PLM on the few-shot samples and then use it as a generator to synthesize a large amount of novel training samples which augment the original training set. To encourage the generator to produce label-discriminative samples, we train it via weighted maximum likelihood where the weight of each token is automatically adjusted based on a discriminative meta-learning objective. A classification PLM can then be fine-tuned on both the few-shot and the synthetic samples with regularization for better generalization and stability. Our approach FewGen achieves an overall better result across seven classification tasks of the GLUE benchmark than existing few-shot learning methods, improving no-augmentation methods by 5+ average points, and outperforming augmentation methods by 3+ average points.
Lifting $G$-Valued Galois Representations when $\ell \neq p$

In this paper we study the universal lifting spaces of local Galois representations valued in arbitrary reductive group schemes when $\ell \neq p$. In particular, under certain technical conditions applicable to any root datum we construct a canonical smooth component in such spaces, generalizing the minimally ramified deformation condition previously studied for classical groups. Our methods involve extending the notion of isotypic decomposition for a $\textrm{GL}_n$-valued representation to general reductive group schemes. To deal with certain scheme-theoretic issues coming from this notion, we are led to a detailed study of certain families of disconnected reductive groups, which we call weakly reductive group schemes. Our work can be used to produce geometric lifts for global Galois representations, and we illustrate this for $\mathrm{G}_2$-valued representations.
Projection error-based guaranteed L2 error bounds for finite element approximations of Laplace eigenfunctions

For conforming finite element approximations of the Laplacian eigenfunctions, a fully computable guaranteed error bound in the $L^2$ norm sense is proposed. The bound is based on the a priori error estimate for the Galerkin projection of the conforming finite element method, and has an optimal speed of convergence for the eigenfunctions with the worst regularity. The resulting error estimate bounds the distance of spaces of exact and approximate eigenfunctions and, hence, is robust even in the case of multiple and tightly clustered eigenvalues. The accuracy of the proposed bound is illustrated by numerical examples. The demonstration code is available at https://ganjin.online/xfliu/EigenfunctionEstimation4FEM .
Finite Horizon Time Inhomogeneous Singular Control Problem of One-dimensional Diffusion via Dynkin Game

The Hamilton-Jacobi-Bellman equation (HJB) associated with the time inhomogeneous singular control problem is a parabolic partial differential equation, and the existence of a classical solution is usually difficult to prove. In this paper, a class of finite horizon stochastic singular control problems of one dimensional diffusion is solved via a time inhomogeneous zero-sum game (Dynkin game). The regularity of the value function of the Dynkin game is investigated, and its integrated form coincides with the value function of the singular control problem. We provide conditions under which a classical solution to the associated HJB equation exists, thus the usual viscosity solution approach is avoided. We also show that the optimal control policy is to reflect the diffusion between two time inhomogeneous boundaries. For a more general terminal payoff function, we showed that the optimal control involves a possible impulse at maturity.
Comparative analysis of atmospheric parameters from 
high-resolution spectroscopic sky surveys: APOGEE, GALAH, Gaia-ESO

SDSS-IV APOGEE-2, GALAH and Gaia-ESO are high resolution, ground-based, multi-object spectroscopic surveys providing fundamental stellar atmospheric parameters and multiple elemental abundance ratios for hundreds of thousands of stars of the Milky Way. We undertake a comparison between the most recent data releases of these surveys to investigate the accuracy and precision of derived parameters by placing the abundances on an absolute scale. We discuss the correlations in parameter and abundance differences as a function of main parameters. Uncovering the variants provides a basis to on-going efforts of future sky surveys. Quality samples from the APOGEE-GALAH, APOGEE-GES and GALAH-GES overlapping catalogs are collected. We investigate the mean variants between the surveys, and linear trends are also investigated. We compare the slope of correlations and mean differences with the reported uncertainties. The average and scatter of vrad, Teff, log g, [M/H] and vmicro, along with numerous species of elemental abundances in the combined catalogs show that in general there is a good agreement between the surveys. We find large radial velocity scatters ranging from 1.3 km/s to 4.4 km/s when comparing the three surveys. We observe weak trends: e.g. in $\Delta$Teff vs. $\Delta$log g for the APOGEE-GES stars, and a clear correlation in the vmicro-$\Delta$vmicro planes in the APOGEE-GALAH common sample. For [$\alpha$/H], [Ti/H] (APOGEE-GALAH giants) and [Al/H] (APOGEE-GALAH dwarfs) potential strong correlations are discovered as a function of the differences in the main atmospheric parameters, and we find weak trends for other elements. In general we find good agreement between the three surveys within their respective uncertainties. However, there are certain regimes in which strong variants exist, which we discuss. There are still offsets larger than 0.1 dex in the absolute abundance scales.
On intrinsic and extrinsic rational approximation to Cantor sets

We establish various new results on a problem proposed by Mahler [Some suggestions for further research. Bull. Aust. Math. Soc. 29 (1984), 101–108] concerning rational approximation to fractal sets by rational numbers inside and outside the set in question. Some of them provide a natural continuation and improvement of recent results of Broderick, Fishman and Reich, and Fishman and Simmons. A key feature is that many of our new results apply to more general, multi-dimensional fractal sets and require only mild assumptions on the iterated function system. Moreover, we provide a non-trivial lower bound for the distance of a rational number $p/q$ outside the Cantor middle-third set $C$ to the set $C$ , in terms of the denominator $q$ . We further discuss patterns of rational numbers in fractal sets. We highlight two of them: firstly, an upper bound for the number of rational (algebraic) numbers in a fractal set up to a given height (and degree) for a wide class of fractal sets; and secondly, we find properties of the denominator structure of rational points in ‘missing-digit’ Cantor sets, generalizing claims of Nagy and Bloshchitsyn.
LOCAL ABSORPTION OF HIGH-ENERGY EMISSION FROM GAMMA-RAY BURSTS

High-energy photons emitted from gamma-ray bursts (GRBs) are subject to pair-production interactions with lower energy photons, leading to an effective optical depth. In this paper, we estimate the opacity resulting from photon fields located at various distances from long GRB sites: those of the binary companion to the massive stellar progenitor, the star-forming molecular cloud containing the GRB, and the total photon field of the host galaxy. The first two photon fields are found to be transparent for most reasonable sets of assumptions about these systems. In the case of galactic radiation fields, we have performed several numerical simulations to calculate the expected opacities for two different line-of-sight geometries through the host galaxy and include a full accounting of the infrared radiation produced by the absorption and re-radiation of starlight by dust. The optical depth for GeV gamma rays due to direct starlight is less than unity for all host galaxies. At higher energies, >10 TeV, a spectral cutoff can occur due to the rapidly increasing number of mid- to far-IR intragalactic photons re-radiated by dust. Photons in the extragalactic background light therefore remain the only relevant source of photon–photon opacity for ongoing GRB observations with Fermi-LAT and potential future detections with ground-based gamma-ray telescopes.
Comparison of recent SnIa datasets

We rank the six latest Type Ia supernova (SnIa) datasets (Constitution (C), Union (U), ESSENCE (Davis) (E), Gold06 (G), SNLS 1yr (S) and SDSS-II (D)) in the context of the Chevalier-Polarski-Linder (CPL) parametrization w(a) = w0+w1(1−a), according to their Figure of Merit (FoM), their consistency with the cosmological constant (ΛCDM), their consistency with standard rulers (Cosmic Microwave Background (CMB) and Baryon Acoustic Oscillations (BAO)) and their mutual consistency. We find a significant improvement of the FoM (defined as the inverse area of the 95.4% parameter contour) with the number of SnIa of these datasets ((C) highest FoM, (U), (G), (D), (E), (S) lowest FoM). Standard rulers (CMB+BAO) have a better FoM by about a factor of 3, compared to the highest FoM SnIa dataset (C). We also find that the ranking sequence based on consistency with ΛCDM is identical with the corresponding ranking based on consistency with standard rulers ((S) most consistent, (D), (C), (E), (U), (G) least consistent). The ranking sequence of the datasets however changes when we consider the consistency with an expansion history corresponding to evolving dark energy (w0,w1) = (−1.4,2) crossing the phantom divide line w = −1 (it is practically reversed to (G), (U), (E), (S), (D), (C)). The SALT2 and MLCS2k2 fitters are also compared and some peculiar features of the SDSS-II dataset when standardized with the MLCS2k2 fitter are pointed out. Finally, we construct a statistic to estimate the internal consistency of a collection of SnIa datasets. We find that even though there is good consistency among most samples taken from the above datasets, this consistency decreases significantly when the Gold06 (G) dataset is included in the sample.
Scalar curvature and properness on Sasaki manifolds

We study (transverse) scalar curvature type equation on compact Sasaki manifolds, in view of recent breakthrough of Chen-Cheng \cite{CC1, CC2, CC3} on existence of K\"ahler metrics with constant scalar curvature (csck) on compact K\"ahler manifolds. Following their strategy, we prove that given a Sasaki structure (with Reeb vector field and complex structure on its cone fixed ), there exists a Sasaki structure with transverse constant scalar curvature (cscs) if and only if the $\mathcal{K}$-energy is reduced proper modulo the identity component of the automorphism group which preserves both the Reeb vector field and transverse complex structure. Technically, the proof mainly consists of two parts. The first part is a priori estimates for scalar curvature type equations which are parallel to Chen-Cheng's results in \cite{CC2, CC3} in Sasaki setting. The second part is geometric pluripotential theory on a compact Sasaki manifold, building up on profound results in geometric pluripotential theory on K\"ahler manifolds. There are notable, and indeed subtle differences in Sasaki setting (compared with K\"ahler setting) for both parts (PDE and pluripotential theory). The PDE part is an adaption of deep work of Chen-Cheng \cite{CC1, CC2, CC3} to Sasaki setting with necessary modifications. While the geometric pluripotential theory on a compact Sasaki manifold has new difficulties, compared with geometric pluripotential theory in K\"ahler setting which is very intricate. We shall present the details of geometric pluripotential on Sasaki manifolds in a separate paper \cite{HL} (joint work with Jun Li).
Finite-dimensional representations constructed from random walks

Given a $1$-cocycle $b$ with coefficients in an orthogonal representation, we show that any finite dimensional summand of $b$ is cohomologically trivial if and only if $\| b(X_n) \|^2/n$ tends to a constant in probability, where $X_n$ is the trajectory of the random walk $(G,\mu)$. As a corollary, we obtain sufficient conditions for $G$ to satisfy Shalom's property $H_{\mathrm{FD}}$. Another application is a convergence to a constant in probability of $\mu^{*n}(e) -\mu^{*n}(g)$, $n\gg m$, normalized by its average with respect to $\mu^{*m}$, for any finitely generated amenable group without infinite virtually Abelian quotients. Finally, we show that the harmonic equivariant mapping of $G$ to a Hilbert space obtained as an $U$-ultralimit of normalized $\mu^{*n}- g \mu^{*n}$ can depend on the ultrafilter $U$ for some groups.
PHOTOMETRIC CHARACTERIZATION OF THE GALACTIC STAR CLUSTER TRUMPLER 20

We present deep UBVI photometry for Trumpler 20, a rich, intermediate-age open cluster located at l = 301. °47, b = +2. °22 (α = 12h39m34s, δ = −60°37′00″, J2000.0) in the fourth Galactic quadrant. In spite of its interesting properties, this cluster has received little attention, probably because the line of sight to it crosses the Carina spiral arm twice (and possibly also the Scutum-Crux arm), which causes significant contamination of its color–magnitude diagram (CMD) by field stars, therefore seriously complicating its interpretation. In this paper, we provide more robust estimates of the fundamental parameters of Trumpler 20 and investigate the most prominent features of its CMD: a rich He-burning star clump, and a vertical sequence of stars above the turnoff, which can be either blue stragglers or field stars. Our precise photometry, in combination with previous investigations, has allowed us to derive updated values of the age and heliocentric distance of Trumpler 20, which we estimate to be 1.4 ± 0.2 Gyr and 3.0 ± 0.3 kpc, respectively. As predicted by models, at this age the clump has a tail toward fainter magnitudes and bluer colors, thus providing further confirmation of the evolutionary status of stars in this particular phase. The derived heliocentric distance places the cluster in the inter-arm region between the Carina and Scutum arms, which naturally explains the presence of the vertical sequence of stars (which was originally interpreted as the cluster itself) observed in the upper part of the CMD. Most of these stars would therefore belong to the general galactic field, while only a few of them would be bona fide cluster blue stragglers. Our data suggest that the cluster metallicity is solar and its reddening is E(B − V) = 0.35 ± 0.04. Finally, we believe we have solved a previously reported inconsistency between the spectroscopic temperatures and colors of giant stars in the cluster.