Miracle-dz/UniFAR-FTUs huggingface dataset:
Computation of Hopf Galois structures on low degree separable extensions and classification of those for degrees $p^2$ and $2p$

A Hopf Galois structure on a finite field extension $L/K$ is a pair $(H,\mu)$, where $H$ is a finite cocommutative $K$-Hopf algebra and $\mu$ a Hopf action. In this paper we present a program written in the computational algebra system Magma which gives all Hopf Galois structures on separable field extensions of degree up to eleven and several properties of those. Besides, we exhibit several results on Hopf Galois structures inspired by the program output. We prove that if $(H,\mu)$ is an almost classically Hopf Galois structure, then it is the unique Hopf Galois structure with underlying Hopf algebra $H$, up to isomorphism. For $p$ an odd prime, we prove that a separable extension of degree $p^2$ may have only one type of Hopf Galois structure and determine those of cyclic type; we determine as well the Hopf Galois structures on separable extensions of degree $2p$. We highlight the richness of the results obtained for extensions of degree 8 by computing an explicit example and presenting some tables which summarizes these results.
Closed range of $\bar\partial$ in $L^2$-Sobolev spaces on unbounded domains in $\mathbb{C}^n$

Let $\Omega\subset\mathbb{C}^n$ be a domain and $1 \leq q \leq n-1$ fixed. Our purpose in this article is to establish a general sufficient condition for the closed range of the Cauchy-Riemann operator $\bar\partial$ in appropriately weighted $L^2$-Sobolev spaces on $(0,q)$-forms. The domains we consider may be neither bounded nor pseudoconvex, and our condition is a generalization of the classical $Z(q)$ condition that we call weak $Z(q)$. We provide examples that explain the necessity of working in weighted spaces both for closed range in $L^2$ and, even more critically, in $L^2$-Sobolev spaces.
Generation of finite quasisimple groups with an application to groups acting on Beauville surfaces

We develop theorems which produce a multitude of hyperbolic triples for the finite classical groups. We apply these theorems to prove that every quasisimple group except Alt (5) and SL 2(5) is a Beauville group. In particular, we settle a conjecture of Bauer, Catanese and Grunewald which asserts that all non‐abelian finite quasisimple groups except for the alternating group Alt (5) are Beauville groups.
Parabolic and near-parabolic renormalization for local degree three

The invariant class under parabolic and near-parabolic renormalization constructed by Inou and Shishikura has proved extremely useful in recent years. It leads to several important progresses on the dynamics of certain holomorphic maps with a local degree two. In this paper, we give an invariant class under the parabolic renormalization which consists of unicritical holomorphic maps with local degree three. As potential applications, some results of the cubic unicritical polynomials, for example, the existence of unicritical cubic Julia sets with positive measure, the regularity and the self-similarity of the boundaries of the cubic Siegel disks, and the local connectivity of the cubic Multibrot set at some infinitely satellite renormalizable points etc, can be obtained similarly as in the quadratic case.
Emergent Dynamics of Asynchronous Multiagent Systems Under Signed Networks and Limited Communication Resources

Signed networks, usually used to describe cooperative and competitive coordination between agents, have potential applications in fields such as multi-robot formation and opinion dynamics, et al. Existing work on multi-agent dynamics on signed networks assumes that all agents communicate with their neighbors synchronously, which usually requires sufficient communication resources. However, due to the shortage of communication resources in practical applications, the synchronous communication manner is often not easy to achieve, especially on large scale networks. With that in mind, this paper proposes an asynchronous communication manner to investigate the dynamic behavior of multiagent systems on signed networks without structural restrictions, where only part of the communication links are allowed to transmit information each time instant. By designing a distributed feedback control law, the related properties of sub-stochastic matrices can be used to analyze the dynamic behavior of the agents. It turns out that the whole multi-agent system will evolve a variety of dynamic behaviors, including consensus, bipartite consensus and bipartite containment, which is influenced by the locations and roles of agents in the network. At last, computer simulations are provided to demonstrate the theoretical discovery.
Motion-Guided Global–Local Aggregation Transformer Network for Precipitation Nowcasting

Nowadays deep learning-based weather radar echo extrapolation methods have competently improved nowcasting quality. Current pure convolutional or convolutional recurrent neural network-based extrapolation pipelines inherently struggle in capturing both global and local spatiotemporal interactions simultaneously, thereby limiting nowcasting performances, e.g., they not only tend to underestimate heavy rainfalls’ spatial coverage and intensity but also fail to precisely predict nonlinear motion patterns. Furthermore, the usually adopted pixel-wise objective functions lead to blurry predictions. To this end, we propose a novel motion-guided global–local aggregation Transformer network for effectively combining spatiotemporal cues at different time scales, thereby strengthening global–local spatiotemporal aggregation urgently required by the extrapolation task. First, we divide existing observations into both short- and long-term sequences to represent echo dynamics at different time scales. Then, to introduce reasonable motion guidance to Transformer, we customize an end-to-end module for jointly extracting motion representation of short- and long-term echo sequences (MRS, MRL), while estimating optical flow. Subsequently, based on Transformer architecture, MRS is used as queries to retrospect the most useful information from MRL for an effective aggregation of global long-term and local short-term cues. Finally, the fused feature is employed for future echo prediction. Additionally, for the blurry prediction problem, predictions from our model trained with an adversarial regularization achieve superior performances not only in nowcasting skill scores but also in precipitation details and image clarity over existing methods. Extensive experiments on two challenging radar echo datasets demonstrate the effectiveness of our proposed method.
N=2
 supersymmetric higher spin gauge theories and current multiplets in three dimensions

We describe several families of primary linear supermultiplets coupled to three-dimensional ${\cal N}=2$ conformal supergravity and use them to construct topological $BF$-type terms. We introduce conformal higher-spin gauge superfields and associate with them Chern-Simons-type actions that are constructed as an extension of the linearised action for ${\cal N}=2$ conformal supergravity. These actions possess gauge and super-Weyl invariance in any conformally flat superspace and involve a higher-spin generalisation of the linearised ${\cal N}=2$ super-Cotton tensor. For massless higher-spin supermultiplets in (1,1) anti-de Sitter (AdS) superspace, we propose two off-shell Lagrangian gauge formulations, which are related to each other by a dually transformation. Making use of these massless theories allows us to formulate consistent higher-spin supercurrent multiplets in (1,1) AdS superspace. Explicit examples of such supercurrent multiplets are provided for models of massive chiral supermultiplets. Off-shell formulations for massive higher-spin supermultiplets in (1,1) AdS superspace are proposed.
Rigidity results for non local phase transitions in the Heisenberg group $H$

In the Heisenberg group framework, we study rigidity properties for stable solutions of $(-\Delta_H)^s v = f(v)$ in $H$, $s \in (0,1)$. We obtain a Poincar\'e type inequality in connection with a degenerate elliptic equation in $\R^4_+$; through an extension (or "lifting") procedure, this inequality will be then used for giving a criterion under which the level sets of the above solutions are minimal surfaces in $H$, i.e. they have vanishing mean curvature.
Integrable Systems of Double Ramification Type

In this paper we study various aspects of the double ramification (DR) hierarchy, introduced by the 1st author, and its quantization. We extend the notion of tau-symmetry to quantum integrable hierarchies and prove that the quantum DR hierarchy enjoys this property. We determine explicitly the genus $1$ quantum correction and, as an application, compute completely the quantization of the $3$- and $4$-KdV hierarchies (the DR hierarchies for Witten’s $3$- and $4$-spin theories). We then focus on the recursion relation satisfied by the DR Hamiltonian densities and, abstracting from its geometric origin, we use it to characterize and construct a new family of quantum and classical integrable systems that we call of DR type, as they satisfy all of the main properties of the DR hierarchy. In the 2nd part, we obtain new insight towards the Miura equivalence conjecture between the DR and Dubrovin-Zhang (DZ) hierarchies, via a geometric interpretation of the correlators forming the DR tau-function. We then show that the candidate Miura transformation between the DR and DZ hierarchies (which we uniquely identified in our previous paper) indeed turns the DZ Poisson structure into the standard form. Eventually, we focus on integrable hierarchies associated with rank-$1$ cohomological field theories and their deformations, and we prove the DR/DZ equivalence conjecture up to genus $5$ in this context.
The reduction of G-ordinary crystalline representations with G-structure

Fontaine’s D_cris functor allows us to associate an isocrystal to any crystalline representation. For a reductive group G, we study the reduction of lattices inside a germ of crystalline representations with G-structure V, to lattices (which are crystals) with G-structure inside D_cris(V). Using Kisin modules theory, we give a description of this reduction in terms of G, in the case when the representation V is (G-)ordinary. In order to do that, first we need to generalize Fargues’ construction of the Harder-Narasimhan filtration for p-divisible groups to Kisin modules.
Genealogical distance under selection.

We study the genealogical distance of two randomly chosen individuals in a population that evolves according to a two type Moran model with mutation and selection. We prove that this distance is stochastically smaller than the corresponding distance in the neutral model, when the population size is large. Moreover, we prove convergence of the genealogical distance under selection to the distance in the neutral case, when the system is in equilibrium and the selection parameter tends to infinity.
Integration of Differential Graded Manifolds

We consider the problem of integration of $L_\infty $-algebroids (differential non-negatively graded manifolds) to $L_\infty $-groupoids. We first construct a “big” Kan simplicial manifold (Fréchet or Banach) whose points are solutions of a (generalized) Maurer–Cartan equation. The main analytic trick in our work is an integral transformation sending the solutions of the Maurer–Cartan equation to closed differential forms. Following the ideas of Ezra Getzler, we then impose a gauge condition that cuts out a finite-dimensional simplicial submanifold. This “smaller” simplicial manifold is (the nerve of) a local Lie $\ell $-groupoid. The gauge condition can be imposed only locally in the base of the $L_\infty $-algebroid; the resulting local $\ell $-groupoids glue up to a coherent homotopy, that is, we get a homotopy coherent diagram from the nerve of a good cover of the base to the (simplicial) category of local $\ell $-groupoids. Finally, we show that a $k$-symplectic differential non-negatively graded manifold integrates to a local $k$-symplectic Lie $\ell$-groupoid; globally, these assemble to form an $A_\infty$-functor. As a particular case for $k=2$, we obtain integration of Courant algebroids.
Keeping nurses engaged during COVID-19: An i-deal perspective

Orientation The coronavirus disease 2019 (COVID-19) pandemic has impacted all job sectors. Arguably, the hardest hit were healthcare institutions. Nurses are at the front line, and it is known that the pandemic added pressure to the way nurses performed their duties. Their working schedules became more complex, including longer hours, as nurses dealt with high rates of COVID-19 cases while still dealing with other healthcare issues. Research purpose The study aimed to establish the relationship between idiosyncratic deals (i-deals) and work engagement of nurses. The study focused on these three types of i-deals - task, flexibility and career. It investigated which i-deals best predict work engagement among nurses. Motivation for the study There is a need to understand the work arrangements of nurses during the pandemic through i-deals. Although research on idiosyncratic deals has become popular in international research, there is scant research within the South African context. Research approach/design and method The sample consisted of 220 nurses working in three private hospitals in Gauteng, South Africa. Inferential statistics and regression analysis were used to achieve the research objectives. Main findings The study’s findings revealed a correlation between the three types of i-deals and work engagement. However, only task and flexibility i-deals predicted work engagement. The COVID-19 pandemic added pressure to the healthcare industry and to nurses’ challenges. The pandemic highlighted the importance of having an engaged nursing workforce. Thus, recommendations and suggestions for nurses, nursing managers and human resource managers are provided. Practical/managerial implications The concept of i-deals is a reasonably new phenomenon within HR practices, and there is no empirical research within the South African context. Contribution/value-add The study adds value by providing insight into customised work arrangements, from an i-deal perspective, during a much appropriate time and urgently needed for nurses.
Global Regularity for 1D Eulerian Dynamics with Singular Interaction Forces

The Euler-Poisson-Alignment (EPA) system appears in mathematical biology and is used to model, in a hydrodynamic limit, a set agents interacting through mutual attraction/repulsion as well as alignment forces. We consider one-dimensional EPA system with a class of singular alignment terms as well as natural attraction/repulsion terms. The singularity of the alignment kernel produces an interesting effect regularizing the solutions of the equation and leading to global regularity for wide range of initial data. This was recently observed in the paper by Do, Kiselev, Ryzhik and Tan. Our goal in this paper is to generalize the result and to incorporate the attractive/repulsive potential. We prove that global regularity persists for these more general models.
Identifying License Plates in Distorted Vehicle Images: Detecting Distorted Vehicle Licence Plates Using a Novel Preprocessing Methods With Hybrid Feature Descriptors

Intelligent transportation systems (ITSs) play a key role in many people’s lives with different aspects. Most of the ITS applications include a system for detecting license plates (LPs) in transportation vehicles. A new framework for such detection systems is introduced in this article. It includes a novel technique for preprocessing, extraction, and detection stages to identify LPs from distorted vehicle images. An efficient preprocessing method is developed in this study. An enhanced, contrast-limited adaptive histogram equalization method for filtering the unwanted LP features is proposed. At the features-extraction stage, strong hybrid features from extended local binary patterns with a median robust pattern descriptor and speeded-up robust feature descriptor are applied to extract complicated features from LP areas. Those hybrid features can enhance the useful information, and the detection system performed well under difficult scenarios. In the detection stage, the trained model by an extreme learning machine (ELM) classifier, with mean-shift algorithm, is used as a detector to decide output results. Performances of the proposed framework were compared with other classifiers using true- and false-positive rates. The system’s performance improvements by the proposed method were also compared with our previous methods and the existing detection methods in the literature. The experiments on an English car LP’s database and other language vehicle images showed that the proposed method made significant improvements to the accuracy and runtime speed for the detection system under difficult image conditions.
Variability in Specific Absorption Rate From Variation in Tissue Properties

This study evaluates the variance of specific absorption rate (SAR) due to expected variance in the dielectric properties of tissues in a 3D anatomical human head model exposed to a half-wave dipole antenna at 835 and 1900 MHz. Stochastic finite difference time domain (S-FDTD) is applied to calculate variations in the local SAR, and the 1- and 10-gram averaged SAR values. These are also compared at 835 MHz to variations found from Monte Carlo FDTD. It is found that for both frequencies dielectric property variance results in a variance of peak 1- or 10-gram SAR of approximately 30% to 55% of the mean SAR, depending on the frequency. These results show that to reach 95% confidence with the calculated SAR values for evaluating exposure guidelines, statistical variations in tissue electrical properties must be taken into account.
Dynamics for the focusing, energy-critical nonlinear Hartree equation

In (41, 51), the dynamics of the solutions for the focusing energy-critical Hartree equation have been classified when E(u0) < E(W), where W is the ground state. In this paper, we continue the study on the dynamics of the radial solutions with the threshold energy. Our arguments closely follow those in (16, 17, 18, 43, 44). The new ingredient is that we show that the positive solution of the nonlocal elliptic equation in L 2d d 2(R d ) is regular and unique by the moving plane method in its global form, which plays an important role in the spectral theory of the linearized operator and the dynamics behavior of the threshold solution.
On certain type of difference polynomials of meromorphic functions

In this paper, we investigate zeros of difference polynomials of the form $f(z)^nH(z, f)-s(z)$, where $f(z)$ is a meromorphic function, $H(z, f)$ is a difference polynomial of $f(z)$ and $s(z)$ is a small function. We first obtain some inequalities for the relationship of the zero counting function of $f(z)^nH(z, f)-s(z)$ and the characteristic function and pole counting function of $f(z)$. Based on these inequalities, we establish some difference analogues of a classical result of Hayman for meromorphic functions. Some special cases are also investigated. These results improve previous findings.
Monte Carlo Investigation of High-Field Electron Transport Properties in AlGaN/GaN HFETs

This letter analyzes the velocity-field relationship of AlGaN/GaN HFETs via Monte Carlo simulation. This method is based on complete scattering mechanisms such as polarized coulomb field scattering (PCF scattering), polar optical phonon scattering, acoustic deformation potential scattering, inter-valley phonon scattering, and piezoelectric scattering. It is found that the gate bias voltage affects the PCF scattering intensity and the PCF scattering intensity influences the drift velocity under a high electric field. A decrease in peak steady-state drift velocity is observed for our fabricated AlGaN/GaN HFETs from <inline-formula> <tex-math notation="LaTeX">${1.335}\times {10}^{{5}}$ </tex-math></inline-formula> m/s at <inline-formula> <tex-math notation="LaTeX">$\text{V}_{\text {gs}} =$ </tex-math></inline-formula> 0 V to <inline-formula> <tex-math notation="LaTeX">${1.23}\times {10}^{{5}}$ </tex-math></inline-formula> m/s at <inline-formula> <tex-math notation="LaTeX">$\text{V}_{\text {gs}} =-3$ </tex-math></inline-formula> V as the gate voltage becomes more negative. When combined with the velocity-field relationship obtained from Monte Carlo simulations, the calculated current-voltage characteristics of AlGaN/GaN HFET devices are in good agreement with our experiment results. The electron saturation drift velocity deviation of AlGaN/GaN HFETs from the Monte Carlo simulation of the GaN material is attributed to the presence of PCF scattering in AlGaN/GaN HFETs. In the study, we provide strong support for the accurate modeling of AlGaN/GaN HFETs.
A vector field method for radiating black hole spacetimes

We develop a commuting vector field method for a general class of radiating spacetimes. The metrics considered are certain long range perturbations of Minkowski space including those constructed from global stability problems in general relativity. Our method provides sharp peeling estimates for solutions to both linear and nonlinear (null form) scalar fields.
Sign-changing tower of bubbles for a sinh-Poisson equation with asymmetric exponents

Motivated by the statistical mechanics description of stationary 2D-turbulence, for a sinh-Poisson type equation with asymmetric nonlinearity, we construct a concentrating solution sequence in the form of a tower of singular Liouville bubbles, each of which has a different degeneracy exponent. The asymmetry parameter $\gamma\in(0,1]$ corresponds to the ratio between the intensity of the negatively rotating vortices and the intensity of the positively rotating vortices. Our solutions correspond to a superposition of highly concentrated vortex configurations of alternating orientation; they extend in a nontrivial way some known results for $\gamma=1$. Thus, by analyzing the case $\gamma\neq1$ we emphasize specific properties of the physically relevant parameter $\gamma$ in the vortex concentration phenomena.
Equivariant min-max theory

We develop an equivariant min-max theory as proposed by Pitts-Rubinstein in 1988 and then show that it can produce many of the known minimal surfaces in $\mathbb{S}^3$ up to genus and symmetry group. We also produce several new infinite families of minimal surfaces in $\mathbb{S}^3$ proposed by Pitts-Rubinstein. These examples are doublings and desingularizations of stationary integral varifolds in $\mathbb{S}^3$.
Lp‐theory of type 1, 1‐operators

This is a continuation of recent work on the general definition of pseudo‐differential operators of type 1, 1, in Hörmander's sense. Continuity in Lp‐Sobolev spaces and Hölder–Zygmund spaces, and more generally in Besov and Lizorkin–Triebel spaces, is proved for positive smoothness; with extension to arbitrary smoothness for operators in the self‐adjoint subclass. As a main tool the paradifferential decomposition is used for type 1, 1‐operators in combination with the Spectral Support Rule for pseudo‐differential operators and pointwise estimates in terms of maximal functions of Peetre–Fefferman–Stein type.