Miracle-dz/UniFAR-FTUs huggingface dataset:
Generalization of Faddeev--Popov Rules in Yang--Mills Theories: N=3,4 BRST Symmetries

The Faddeev–Popov rules for a local and Poincare-covariant Lagrangian quantization of a gauge theory with gauge group are generalized to the case of an invariance of the respective quantum actions, S(N), with respect to N-parametric Abelian SUSY transformations with odd-valued parameters λp, p = 1,…,N and generators sp: spsq + sqsp = 0, for N = 3, 4, implying the substitution of an N-plet of ghost fields, Cp, instead of the parameter, ξ, of infinitesimal gauge transformations: ξ = Cpλ p. The total configuration spaces of fields for a quantum theory of the same classical model coincide in the N = 3 and N = 4 symmetric cases. The superspace of N = 3 SUSY irreducible representation includes, in addition to Yang–Mills fields 𝒜μ, (3 + 1) ghost odd-valued fields Cp, B and 3 even-valued Bpq for p, q = 1, 2, 3. To construct the quantum action, S(3), by adding to the classical action, S0(𝒜), of an N = 3-exact gauge-fixing term (with gauge fermion), a gauge-fixing procedure requires (1 + 3 + 3 + 1) additional fiel.
Best Summation Formulae and Discrete Splines

The problem of obtaining a best summation formula for a finite sequence of real numbers in terms of a fixed number of terms of the sequence is reduced to a solvable linear or quadratic programming problem. This is done by developing the appropriate discrete Taylor and Peano theorems. The best summation formulae are related to discrete splines studied earlier. Discrete monosplines are introduced here and related to best summation formulae. Some numerical results are given.
Limit theorems for multivariate Brownian semistationary processes and feasible results

Abstract In this paper we introduce the multivariate Brownian semistationary (BSS) process and study the joint asymptotic behaviour of its realised covariation using in-fill asymptotics. First, we present a central limit theorem for general multivariate Gaussian processes with stationary increments, which are not necessarily semimartingales. Then, we show weak laws of large numbers, central limit theorems, and feasible results for BSS processes. An explicit example based on the so-called gamma kernels is also provided.
The Kato square root problem on irregular open sets

Let $O\subseteq \mathbb{R}^d$ be an open set and $L=-\nabla \cdot A\nabla$ be an elliptic differential operator in divergence form subject to mixed boundary conditions. We show that $L$ possesses the Kato square root property, i.e. the domain of $L^\frac{1}{2}$ coincides with $\mathrm{H}^{1,2}_D(O)$, only assuming that the boundary of $O$ is $(d-1)$-regular together with uniform $(d-1)$-regularity for the Dirichlet part $D$ and uniform Lipschitz charts around $\overline{\partial O\setminus D}$. In particular, we allow $O$ to be an unbounded set and we don't rely on any thickness condition for $O$ itself.
Computing Invariant Sets of Random Differential Equations Using Polynomial Chaos

Differential equations with random parameters have gained significant prominence in recent years due to their importance in mathematical modelling and data assimilation. In many cases, random ordinary differential equations (RODEs) are studied by using Monte-Carlo methods or by direct numerical simulation techniques using polynomial chaos (PC), i.e., by a series expansion of the random parameters in combination with forward integration. Here we take a dynamical systems viewpoint and focus on the invariant sets of differential equations such as steady states, stable/unstable manifolds, periodic orbits, and heteroclinic orbits. We employ PC to compute representations of all these different types of invariant sets for RODEs. This allows us to obtain fast sampling, geometric visualization of distributional properties of invariants sets, and uncertainty quantification of dynamical output such as periods or locations of orbits. We apply our techniques to a predator-prey model, where we compute steady states and stable/unstable manifolds. We also include several benchmarks to illustrate the numerical efficiency of adaptively chosen PC depending upon the random input. Then we employ the methods for the Lorenz system, obtaining computational PC representations of periodic orbits, stable/unstable manifolds and heteroclinic orbits.
AN ALGEBRAIC STRUCTURE FOR ONE-DIMENSIONAL QUANTUM WALKS AND A NEW PROOF OF THE WEAK LIMIT THEOREM

An algebraic structure for one-dimensional quantum walks is introduced. This structure characterizes, in some sense, one-dimensional quantum walks. A natural computation using this algebraic structure leads us to obtain an effective formula for the characteristic function of the transition probability. Then, the weak limit theorem for the transition probability of quantum walks is deduced by using simple properties of the Chebyshev polynomials.
Characterization of Resting-State Striatal Differences in First-Episode Depression and Recurrent Depression

The presence of reward deficits in major depressive disorder is associated with abnormal striatal function. However, differences in striatal whole-brain functional between recurrent depressive episode (RDE) and first-episode depression (FDE) have not been elucidated. Thirty-three patients with RDE, 27 with FDE, and 35 healthy controls (HCs) were recruited for this study. A seed-based functional connectivity (FC) method was used to analyze abnormalities in six predefined striatal subregion circuits among the three groups of subjects and to further explore the correlation between abnormal FC and clinical symptoms. The results revealed that compared with the FDE group, the RDE group showed higher FC of the striatal subregion with the left middle occipital gyrus, left orbital area of the middle frontal gyrus, and bilateral posterior cerebellar gyrus, while showing lower FC of the striatal subregion with the right thalamus, left inferior parietal lobule, left middle cingulate gyrus, right angular gyrus, right cerebellum anterior lobe, and right caudate nucleus. In the RDE group, the HAMD-17 scores were positively correlated with the FC between the left dorsal rostral putamen and the left cerebellum posterior lobe. This study provides new insights into understanding the specificity of striatal circuits in the RDE group.
Excited state entanglement in homogeneous fermionic chains

We study the Rényi entanglement entropy of an interval in a periodic fermionic chain for a general eigenstate of a free, translational invariant Hamiltonian. In order to analytically compute the entropy we use two technical tools. The first is used to logarithmically reduce the complexity of the problem and the second to compute the Rényi entropy of the chosen subsystem. We introduce new strategies to perform the computations, derive new expressions for the entropy of these general states and show the perfect agreement of the analytical computations and the numerical outcome. Finally we discuss the physical interpretation of our results and generalize them to compute the entanglement entropy for a fragment of a fermionic ladder.
Postural Control Alterations in Children with Mild Forms of Spastic Cerebral Palsy

Purpose To determine the postural control responses’ differences between children with mild spastic Cerebral Palsy (CP) and children who are typically developing (TD). Patients and Methods Children with spastic CP, Level I–II (n=20, mean age=9.42±4.59 years, 50% girls, 50% boys) and children with TD (N=20, mean age=9.65±3.03, 55% girls, 45% boys) were included in the study. All participants were evaluated with Computerized Dynamic Posturography, Sensory Organization Test (SOT). Results There were differences between children with spastic CP and children with TD in visual and composite balance score of SOT significantly (p<0.05); there were no differences at vestibular and somatosensory scores of SOT. Children with CP had more postural sway than children with TD (p<0.05). Conclusion There were differences between children with mild CP and TD in terms of postural control responses.
Automatic Identification of a Depressive State in Primary Care

The Center for Epidemiologic Studies Depression Scale (CES-D) performs well in screening depression in primary care. However, people are looking for alternatives because it screens for too many items. With the popularity of social media platforms, facial movement can be recorded ecologically. Considering that there are nonverbal behaviors, including facial movement, associated with a depressive state, this study aims to establish an automatic depression recognition model to be easily used in primary healthcare. We integrated facial activities and gaze behaviors to establish a machine learning algorithm (Kernal Ridge Regression, KRR). We compared different algorithms and different features to achieve the best model. The results showed that the prediction effect of facial and gaze features was higher than that of only facial features. In all of the models we tried, the ridge model with a periodic kernel showed the best performance. The model showed a mutual fund R-squared (R2) value of 0.43 and a Pearson correlation coefficient (r) value of 0.69 (p < 0.001). Then, the most relevant variables (e.g., gaze directions and facial action units) were revealed in the present study.
A dynamic light scattering study on mutual diffusion coefficient of BSA in concentrated aqueous solutions

Dynamic light scattering has been used to measure the mutual diffusion coefficient of bovine serum albumin under isothermal condition as a function of protein concentration and in the presence of a viscous cosolvent such as glycerol. The results are discussed in connection with the influence of the solvent envinronment on both direct and hydrodynamic interactions.
The Calder\'on problem for quasilinear elliptic equations

In this paper we show uniqueness of the conductivity for the quasilinear Calder\'on's inverse problem. The nonlinear conductivity depends, in a nonlinear fashion, of the potential itself and its gradient. Under some structural assumptions on the direct problem, a real-valued conductivity allowing a small analytic continuation to the complex plane induces a unique Dirichlet-to-Neumann (DN) map. The method of proof considers some complex-valued, linear test functions based on a point of the boundary of the domain, and a linearization of the DN map placed at these particular set of solutions.
Retrospective studies and failure time models

SUMMARY The proportional hazards failure time model of Cox (1972) is adapted to the retrospective epidemiological study, in which cases and controls are sampled from a population in order to relate disease incidence rates to exposure to suspected risk factors. The method permits simultaneous study of several exposure variables, that may be discrete or continuous or a mixture of both, in the presence of additional explanatory variables and competing risks. The proportional hazards framework provides a fresh look at the concepts of matching, choice of controls, confounding and effect modification. The relative risk is a common and useful measure of association between a chronic disease and suspected risk factors. It is given by the ratio of disease incidence rates for variously exposed individuals. Use of this measure involves the often implicit assumption that the ratios of incident rates are relatively constant with respect to age and other personal char- acteristics. The proportional hazards model introduced by Cox (1972) gives a probabilistic formulation for the constant relative risk concept. It has been discussed both in relation to survival studies (Kalbfleisch & Prentice, 1973; Breslow, 1975) and in relation to prospective epidemiological studies (Breslow, 1977). The prospective epidemiological study involves follow- ing disease-free individuals having various exposure levels forward in time to observe disease incidence. Such studies, unfortunately, are frequently too long term and expensive to be feasible, especially if diseases of low incidence are under study. The retrospective case- control study attempts to circumvent these difficulties by selecting, from a well-defined population, cases with the study disease for comparison with a control sample of persons who are disease-free or have some other diagnosis. Exposure histories and other personal data are determined retrospectively by interview or other means. This paper proposes to adapt the proportional hazards model for use in case-control investigations. This approach enables one to associate multiple qualitative and quantitative exposure variables with one or more diseases in a general regression framework. Interaction terms in the regression equation lead to relaxation and testing of the constant relative risk assumption.
Irregular effects on the transition from regular to Mach reflection of shock waves in wind tunnel flows

Configurations of shock wave reflection in steady supersonic flows have been experimentally investigated using a combination of two wedges. It has been experimentally proved by a symmetric arrangement that both regular and Mach reflections are possible in the dual-solution domain for various aspect ratio models. In the arrangement for the purpose of clarifying the influence of the wedge three-dimensionality, the transition from regular to Mach reflection can happen at any inlet aspect ratio, both when the inlet aspect ratio is increased and when it is reduced. The inlet aspect ratio has no effect on the transition provided it is high enough for the regular reflection point at the spanwise centre to be free from information from wedge edges. Flow visualization data produced using the vapour screen technique indicate that, in a region influenced by information from wedge edges, the three-dimensionality of experimental models promotes regular reflection rather than Mach reflection. To study the criteria for the transition between regular and Mach reflections, an asymmetric arrangement of two wedges has been used, and a hysteresis effect is clearly evident. The transition from regular to Mach reflection, however, occurs significantly below the detachment condition, and moreover, the repeatability of the transition angle is not satisfactorily achieved. These experimental results imply that wind tunnel disturbances may dominate the transition in the dual-solution domain. The stability of regular reflection in the dual-solution domain is discussed, and effects of free-stream disturbances are experimentally examined by producing water vapour in the free stream as an artificial disturbance.
CRISPR/Cas9-Based Knock-Out of the PMR4 Gene Reduces Susceptibility to Late Blight in Two Tomato Cultivars

Phytophthora infestans, the causal agent of late blight (LB) in tomato (Solanum lycopersicum L.), is a devastating disease and a serious concern for plant productivity. The presence of susceptibility (S) genes in plants facilitates pathogen proliferation; thus, disabling these genes may help provide a broad-spectrum and durable type of tolerance/resistance. Previous studies on Arabidopsis and tomato have highlighted that knock-out mutants of the PMR4 susceptibility gene are tolerant to powdery mildew. Moreover, PMR4 knock-down in potato has been shown to confer tolerance to LB. To verify the same effect in tomato in the present study, a CRISPR–Cas9 vector containing four single guide RNAs (sgRNAs: sgRNA1, sgRNA6, sgRNA7, and sgRNA8), targeting as many SlPMR4 regions, was introduced via Agrobacterium-tumefaciens-mediated transformation into two widely grown Italian tomato cultivars: ‘San Marzano’ (SM) and ‘Oxheart’ (OX). Thirty-five plants (twenty-six SM and nine OX) were selected and screened to identify the CRISPR/Cas9-induced mutations. The different sgRNAs caused mutation frequencies ranging from 22.1 to 100% and alternatively precise insertions (sgRNA6) or deletions (sgRNA7, sgRNA1, and sgRNA8). Notably, sgRNA7 induced in seven SM genotypes a −7 bp deletion in the homozygous status, whereas sgRNA8 led to the production of fifteen SM genotypes with a biallelic mutation (−7 bp and −2 bp). Selected edited lines were inoculated with P. infestans, and four of them, fully knocked out at the PMR4 locus, showed reduced disease symptoms (reduction in susceptibility from 55 to 80%) compared to control plants. The four SM lines were sequenced using Illumina whole-genome sequencing for deeper characterization without exhibiting any evidence of mutations in the candidate off-target regions. Our results showed, for the first time, a reduced susceptibility to Phytophtora infestans in pmr4 tomato mutants confirming the role of KO PMR4 in providing broad-spectrum protection against pathogens.
Effects of New Technologies on Work: The Case of Additive Manufacturing

The authors study the effects on work of additive manufacturing (AM), an emerging technology that may replace significant segments of traditional manufacturing (TM). Compared to TM, AM is more integrated and offers greater flexibility in design, materials, and customizability; thus, it should entail more demanding tasks and higher skill levels. The authors analyze vacancies for AM and TM workers, focusing on plants that posted vacancies in both technologies to control for factors that may affect the content of job postings. Findings show that AM jobs are more complex (with more non-routine analytic and less routine cognitive content) in comparison to TM jobs, and AM jobs require more high-level technical skills and more reasoning skills. The relative differences are larger for lower-skill workers (operators) than for high-skill workers (engineers). The authors conclude that AM is an upskilling technology that is skill biased in favor of low-skill workers and therefore reduces the skill gap.
Improving Public Health Policy by Comparing the Public Response during the Start of COVID-19 and Monkeypox on Twitter in Germany: A Mixed Methods Study

Little is known about monkeypox public concerns since its widespread emergence in many countries. Tweets in Germany were examined in the first three months of COVID-19 and monkeypox to examine concerns and issues raised by the public. Understanding views and positions of the public could help to shape future public health campaigns. Few qualitative studies reviewed large datasets, and the results provide the first instance of the public thinking comparing COVID-19 and monkeypox. We retrieved 15,936 tweets from Germany using query words related to both epidemics in the first three months of each one. A sequential explanatory mixed methods research joined a machine learning approach with thematic analysis using a novel rapid tweet analysis protocol. In COVID-19 tweets, there was the selfing construct or feeling part of the emerging narrative of the spread and response. In contrast, during monkeypox, the public considered othering after the fatigue of the COVID-19 response, or an impersonal feeling toward the disease. During monkeypox, coherence and reconceptualization of new and competing information produced a customer rather than a consumer/producer model. Public healthcare policy should reconsider a one-size-fits-all model during information campaigns and produce a strategic approach embedded within a customer model to educate the public about preventative measures and updates. A multidisciplinary approach could prevent and minimize mis/disinformation.
Examining the interdisciplinary approach for treatment of persistent post-concussion symptoms in adults: a systematic review

Abstract Background: The objective of this review is to examine the evidence for the interdisciplinary approach in treatment of persistent post-concussion symptoms in adults. Methods: This systematic literature search was undertaken according to the Preferred Reporting Items for Systematic and Meta-Analysis (PRISMA) guidelines. Five electronic databases were searched: CINAHL, Informit, ProQuest, PubMed and Scopus. After screening and quality assessment, the review included six studies published in English and peer-reviewed journals, between 2011 and 2021 to return contemporary evidence. Results: The results revealed that there was significant variation between measures used and the timing of the pre- and post-treatment assessment. The studies found an interdisciplinary approach to be beneficial, however, the challenges of inherent heterogeneity, lack of clarity for definitions and diagnosis, and mixed results were apparent. The interdisciplinary interventions applied in all identified studies were found to reduce post-concussion symptoms across the symptom subtypes: headache/migraine, vestibular, cognitive, ocular motor and anxiety/mood. Conclusions: The results demonstrated evidence for a reduction in persistent post-concussion symptoms following interdisciplinary intervention. This evidence will inform health services, clinicians, sports administrators and researchers with regard to concussion clinic and rehabilitation team design and service delivery.
The Hamiltonian constraint in 3d Riemannian loop quantum gravity

We discretize the Hamiltonian scalar constraint of three-dimensional Riemannian gravity on a graph of the loop quantum gravity phase space. This Hamiltonian has a clear interpretation in terms of discrete geometries: it computes the extrinsic curvature from dihedral angles. The Wheeler–DeWitt equation takes the form of difference equations, which are actually recursion relations satisfied by Wigner symbols. On the boundary of a tetrahedron, the Hamiltonian generates the exact recursion relation on the 6j-symbol which comes from the Biedenharn–Elliott (pentagon) identity. This fills the gap between the canonical quantization and the symmetries of the Ponzano–Regge state-sum model for 3d gravity.
A multitask recommendation algorithm based on DeepFM and Graph Convolutional Network

For a long time, the problems of cold start and sparse data have always been the key problems to be solved by the recommendation system. Researchers usually use auxiliary information to deal with the aforementioned problems, thereby achieving the purpose of enhancing the recommendation effect. For example, the multitask feature learning framework (MKR) uses knowledge graphs as auxiliary information to enhance recommendations. However, the MKR algorithm has the problem of insufficient semantic information representation which affect the recommendation results. Thus, a multitask recommendation algorithm based on DeepFM and graph convolutional network (DeepFM_GCN) is proposed. The graph convolution network is used to deeply mine auxiliary entity information in the knowledge graph to supplement the sparse item semantics information in the recommendation task. Through the method of cross compression unit combined with Deep Neural Network to achieve feature sharing items and entities which to make up for the impact of insufficient feature representation. Then the DeepFM_GCN model utilizes DeepFM to deeply mine the interaction feature of users and items to avoid inaccurate items recommended to users. From the analysis of the experimental results, the DeepFM_GCN model can more fully explore user and item features, accordingly avoiding semantic ambiguity and improving prediction accuracy.
The numerical range of certain 0,1-matrices †

Let A be a 0, 1-matrix with at most one 1 in each row and column. The authors prove that the numerical range of A is the convex hull of a polygon and a circular disk, both centered at the origin and contained in the unit disk. The proof uses a permutation similarity to reduce A to a direct sum of matrices whose numerical ranges can be determined. A computer program, developed by the authors, which plots the boundary of the numerical range of an arbitrary complex matrix is also discussed.
Limits Under Conjugacy of the Diagonal Subgroup in SL(n,R)

We give a quadratic lower bound on the dimension of the space of conjugacy classes of subgroups of SL(n,R) that are limits under conjugacy of the diagonal subgroup. We give the first explicit examples of abelian n-1 dimensional subgroups of SL(n,R) which are not such a limit, however all such abelian groups are limits of the diagonal group iff n < 5.