Miracle-dz/UniFAR-FTUs huggingface dataset:
On Positive Definiteness Over Locally Compact Quantum Groups

Abstract The notion of positive-definite functions over locally compact quantum groups was recently introduced and studied by Daws and Salmi. Based on this work, we generalize various well-known results about positive-definite functions over groups to the quantum framework. Among these are theorems on “square roots” of positive-definite functions, comparison of various topologies, positive-definite measures and characterizations of amenability, and the separation property with respect to compact quantum subgroups.
Comparison and maximum principles for a class of flux-limited diffusions with external force fields

Abstract In this paper, we are interested in a general equation that has finite speed of propagation compatible with Einstein's theory of special relativity. This equation without external force fields has been derived recently by means of optimal transportation theory. We first provide an argument to incorporate the external force fields. Then, we are concerned with comparison and maximum principles for this equation. We consider both stationary and evolutionary problems. We show that the former satisfies a comparison principle and a strong maximum principle while the latter fulfils weaker ones. The key technique is a transformation that matches well with the gradient flow structure of the equation.
Link invariant and $G_2$ web space

In this paper, we reconstruct Kuperberg's $G_2$ web space. We introduce a new web (a trivalent diagram) and new relations between Kuperberg's web diagrams and the new diagram. Using the $G_2$ webs, we define crossing formulas corresponding to R-matrices associated to some $G_2$ irreducible representations and calculate $G_2$ quantum link invariant for some torus links.
Centering Community Voices: Establishment of a Community Advisory Board at a Student-Run Free Clinic

Summary:Student-run free clinics (SRFCs) are common throughout the U.S. and have potential to meet the needs of both health professions trainees and patients in underserved communities. Here, we describe our SRFC's initial process for recruiting, implementing, and evaluating a Community Advisory Board to better align clinic offerings with community needs.
Maximum of a log-correlated Gaussian field

We study the maximum of a Gaussian field on $[0,1]^\d$ ($\d \geq 1$) whose correlations decay logarithmically with the distance. Kahane \cite{Kah85} introduced this model to construct mathematically the Gaussian multiplicative chaos in the subcritical case. Duplantier, Rhodes, Sheffield and Vargas \cite{DRSV12a} \cite{DRSV12b} extended Kahane's construction to the critical case and established the KPZ formula at criticality. Moreover, they made in \cite{DRSV12a} several conjectures on the supercritical case and on the maximum of this Gaussian field. In this paper we resolve Conjecture 12 in \cite{DRSV12a}: we establish the convergence in law of the maximum and show that the limit law is the Gumbel distribution convoluted by the limit of the derivative martingale.
Asymptotics of random Betti tables

The purpose of this paper is twofold. First, we present a conjecture to the effect that the ranks of the syzygy modules of a smooth projective variety become normally distributed as the positivity of the embedding line bundle grows. Then, in an attempt to render the conjecture plausible, we prove a result suggesting that this is in any event the typical behavior from a probabilistic point of view. Specifically, we consider a "random" Betti table with a fixed number of rows, sampled according to a uniform choice of Boij-Soderberg coefficients. We compute the asymptotics of the entries as the length of the table goes to infinity, and show that they become normally distributed with high probability.
The First Survey of X-Ray Flares from Gamma-Ray Bursts Observed by Swift: Spectral Properties and Energetics

GRB observations with Swift produced the initially surprising result that many bursts have large, late-time X-ray flares. The flares were sometimes intense, had rapid rise and decay phases, and occurred late relative to the prompt phase. Many GRBs have had several flares, which were sometimes overlapping. The origin of the flares can be investigated by comparing the spectra during the flares to those of the afterglow and the initial prompt emission. In this work we have analyzed all significant X-ray flares from the first 110 GRBs observed by Swift. Significant X-ray flares (>3 σ ) were found in 33 of these GRBs, with 77 flares detected. A variety of spectral models have been fit to each flare. We find that the spectral fits sometimes favor a Band function model, which is more akin to the prompt emission than to that of the afterglow. While some flares are approximately as energetic as the prompt GRB emission, we find that the average fluence of the flares is approximately 10 times below the average prompt GRB fluence. We also find that the peak energy of the observed flares is typically in the soft X-ray band, as one might expect due to the X-ray selection of the sample. These results, when combined with those presented in the companion paper on temporal properties of flares, support the hypothesis that many X-ray flares are from late-time activity of the internal engine that spawned the initial GRB, not from an afterglow-related effect.
On the geodesic incompleteness of spacetimes containing marginally (outer) trapped surfaces

In a recent paper, Eichmair et al (2012 arXiv:1204.0278v1) have proved a Gannon–Lee-type singularity theorem based on the existence of marginally outer trapped surfaces (MOTS) on noncompact initial data sets for globally hyperbolic spacetimes. A natural question is whether the corresponding incomplete geodesics could still be complete in a possible non-globally hyperbolic extension of spacetime. In this paper, some variants of their result are given with weaker causality assumptions, thus suggesting that the answer is generically negative, at least if the putative extension has no closed timelike curves. We consider first marginally trapped surfaces (MTS) in chronological spacetimes, introducing the natural notion of a generic MTS, a notion also applicable to MOTS. In particular, a Hawking–Penrose-type singularity theorem is proven in chronological spacetimes with dimension n ⩾ 3 containing a generic MTS. Such surfaces naturally arise as cross-sections of quasi-local generalizations of black hole horizons, such as dynamical and trapping horizons, and we discuss some natural conditions which ensure the existence of MTS in initial data sets. Nevertheless, much of the more recent literature has focused on MOTS rather than MTS as quasi-local substitutes for the description of black holes, as they are arguably more natural and easier to handle in a number of situations. It is therefore pertinent to ask to what extent one can deduce the existence of singularities in the presence of MOTS alone. We address this issue and show that singularities indeed arise in the presence of generic MOTS, but under slightly stronger causal conditions than those in the case of MTS (specifically, for causally simple spacetimes). On the other hand, we show that with additional conditions on the MOTS itself, namely that it is either the boundary of a compact spatial region, or strictly stable in a suitable sense, a Penrose–Hawking-type singularity theorem can still be established for chronological spacetimes containing generic MOTS.
Experimental probing of exchange interactions between localized spins in the dilute magnetic insulator (Ga,Mn)N

The sign, magnitude, and range of the exchange couplings between pairs of Mn ions is determined for (Ga,Mn)N and (Ga,Mn)N:Si with x . 3%. The samples have been grown by metalorganic vapor phase epitaxy and characterized by secondary-ion mass spectroscopy; high-resolution transmission electron microscopy with capabilities allowing for chemical analysis, including the annular dark-field mode and electron energy loss spectroscopy; high-resolution and synchrotron x-ray diffraction; synchrotron extended x-ray absorption fine-structure; synchrotron x-ray absorption near-edge structure; infra-red optics and electron spin resonance. The results of high resolution magnetic measurements and their quantitative interpretation have allowed to verify a series of ab initio predictions on the possibility of ferromagnetism in dilute magnetic insulators and to demonstrate that the interaction changes from ferromagnetic to antiferromagnetic when the charge state of the Mn ions is reduced from 3+ to 2+.
Regular and non-regular solutions of the Riemann problem in ideal magnetohydrodynamics

Abstract We have built a code to numerically solve the Riemann problem in ideal magnetohydrodynamics (MHD) for an arbitrary initial condition to investigate a variety of solutions more thoroughly. The code can handle not only regular solutions, in which no intermediate shocks are involved, but also all types of non-regular solutions if any. As a first application, we explored the neighborhood of the initial condition that was first picked up by Brio and Wu (1988) (Brio, M. and Wu, C. C. 1988 An upwind differencing scheme for the equation of ideal magnetohydrodynamics. J. Comput. Phys. 75, 400–422) and has been frequently employed in the literature as a standard problem to validate numerical codes. Contrary to the conventional wisdom that there will always be a regular solution, we found an initial condition for which there is no regular solution but a non-regular one. The latter solution has only regular solutions in its neighborhood and actually sits on the boundary of regular solutions. This implies that the regular solutions are not sufficient to solve the ideal MHD Riemann problem and suggests that at least some types of non-regular solutions are physical. We also demonstrate that the non-regular solutions are not unique. In fact, we found for the Brio and Wu initial condition that there are uncountably many non-regular solutions. This poses an intriguing question: Why a particular non-regular solution is always obtained in numerical simulations? This has important ramifications to the discussion of which intermediate shocks are really admissible.
The mapping class group of connect sums of S 2 × S 1

Let M n be the connect sum of n copies of S 2 × S 1 . A classical theorem of Laudenbach says that the mapping class group Mod( M n ) is an extension of Out( F n ) by a group ( Z / 2) n generated by sphere twists. We prove that this extension splits, so Mod( M n ) is the semidirect product of Out( F n ) by ( Z / 2) n , which Out( F n ) acts on via the dual of the natural surjection Out( F n ) → GL n ( Z / 2). Our splitting takes Out( F n ) to the subgroup of Mod( M n ) consisting of mapping classes that ﬁx the homotopy class of a trivialization of the tangent bundle of M n . Our techniques also simplify various aspects of Laudenbach’s original proof, including the identiﬁcation of the twist subgroup with ( Z / 2) n .
Molecular determinants of the interaction between HSV-1 glycoprotein D and heparan sulfate

Literature has well-established the importance of 3-O-sulfation of neuronal cell surface glycan heparan sulfate (HS) to its interaction with herpes simplex virus type 1 glycoprotein D (gD). Previous investigations of gD to its viral receptors HVEM and nectin-1 also highlighted the conformational dynamics of gD’s N- and C-termini, necessary for viral membrane fusion. However, little is known on the structural interactions of gD with HS. Here, we present our findings on this interface from both the glycan and the protein perspective. We used C-terminal and N-terminal gD variants to probe the role of their respective regions in gD/HS binding. The N-terminal truncation mutants (with Δ1-22) demonstrate equivalent or stronger binding to heparin than their intact glycoproteins, indicating that the first 22 amino acids are disposable for heparin binding. Characterization of the conformational differences between C-terminal truncated mutants by sedimentation velocity analytical ultracentrifugation distinguished between the “open” and “closed” conformations of the glycoprotein D, highlighting the region’s modulation of receptor binding. From the glycan perspective, we investigated gD interacting with heparin, heparan sulfate, and other de-sulfated and chemically defined oligosaccharides using surface plasmon resonance and glycan microarray. The results show a strong preference of gD for 6-O-sulfate, with 2-O-sulfation becoming more important in the presence of 6-O-S. Additionally, 3-O-sulfation shifted the chain length preference of gD from longer chain to mid-chain length, reaffirming the sulfation site’s importance to the gD/HS interface. Our results shed new light on the molecular details of one of seven known protein-glycan interactions with 3-O-sulfated heparan sulfate.
Incremental Constraint Projection Methods for Monotone Stochastic Variational Inequalities

We consider stochastic variational inequalities with monotone operators defined as the expected value of a random operator. We assume the feasible set is the intersection of a large family of convex sets. We propose a method that combines stochastic approximation with incremental constraint projections meaning that at each iteration, a step similar to some variant of a deterministic projection method is taken after the random operator is sampled and a component of the intersection defining the feasible set is chosen at random. Such sequential scheme is well suited for applications involving large data sets, online optimization and distributed learning. First, we assume that the variational inequality is weak-sharp. We provide asymptotic convergence, feasibility rate of $O(1/k)$ in terms of the mean squared distance to the feasible set and solvability rate of $O(1/\sqrt{k})$ (up to first order logarithmic terms) in terms of the mean distance to the solution set for a bounded or unbounded feasible set. Then, we assume just monotonicity of the operator and introduce an explicit iterative Tykhonov regularization to the method. We consider Cartesian variational inequalities so as to encompass the distributed solution of stochastic Nash games or multi-agent optimization problems under a limited coordination. We provide asymptotic convergence, feasibility rate of $O(1/k)$ in terms of the mean squared distance to the feasible set and, in the case of a compact set, we provide a near-optimal solvability convergence rate of $O\left(\frac{k^\delta\ln k}{\sqrt{k}}\right)$ in terms of the mean dual gap-function of the SVI for arbitrarily small $\delta>0$.
Effects of litter chemical traits and species richness on soil carbon cycling changed over time

Litter decomposition is the main driver of nutrient cycling process in terrestrial ecosystems. Afforestation completely altered vegetation composition and litter species, disrupting the long-term carbon balance in grassland ecosystem. However, there is a lack of understanding of how litter mixing effect (LME) affects soil carbon cycling in afforested ecosystem. Here, we investigated the effects of litter richness and quality of tree, shrub, and grass species and their litter mixture on soil CO2 fluxes. The results showed that cumulative soil CO2 flux in the early stage (1–28 days) was 1.75 times higher than that in the late stage (29–113 days), indicating litter decomposition was intensive at first and then decreased with time. Soil carbon flux changed with decomposition stages. In the early-stage of decomposition, soil CO2 flux increased with the concentrations of litter carbon, nitrogen and condense tannin. In the late phase of decomposition, all litter chemical traits were negatively related to the soil carbon flux. Additionally, plant litter richness was negatively correlated to early-stage soil CO2 flux, whereas it was positively related to late-stage soil carbon flux. Our results provide evidence that long-term carbon balance in grassland ecosystems was interrupted by afforestation, and the dominant litter chemical traits that controlling soil carbon cycling changed over time.
Ribosomal control in RNA virus-infected cells

Viruses are strictly intracellular parasites requiring host cellular functions to complete their reproduction cycle involving virus infection of host cell, viral genome replication, viral protein translation, and virion release. Ribosomes are protein synthesis factories in cells, and viruses need to manipulate ribosomes to complete their protein synthesis. Viruses use translation initiation factors through their own RNA structures or cap structures, thereby inducing ribosomes to synthesize viral proteins. Viruses also affect ribosome production and the assembly of mature ribosomes, and regulate the recognition of mRNA by ribosomes, thereby promoting viral protein synthesis and inhibiting the synthesis of host antiviral immune proteins. Here, we review the remarkable mechanisms used by RNA viruses to regulate ribosomes, in particular, the mechanisms by which RNA viruses induce the formation of specific heterogeneous ribosomes required for viral protein translation. This review provides valuable insights into the control of viral infection and diseases from the perspective of viral protein synthesis.
A brief introduction to equi-chordal and equi-isoclinic tight fusion frames

Equi-chordal and equi-isoclinic tight fusion frames (ECTFFs and EITFFs) are both types of optimal packings of subspaces in Euclidean spaces. In the special case where these subspaces are one-dimensional, ECTFFs and EITFFs both correspond to types of optimal packings of lines known as equiangular tight frames. In this brief note, we review some of the fundamental ideas and results concerning ECTFFs and EITFFs.
Phylogeny and mycotoxin profiles of pathogenic Alternaria and Curvularia species isolated from date palm in southern Tunisia

Date palm (Phoenix dactylifera L.), is a widely cultivated crop across North Africa, with about 300 thousand tons of fruits produced per year, in Tunisia. A wide range of fungal pathogens has been associated with leaf spots of date palm, Alternaria species being the most frequently reported. Symptomatic leaves of Deglet Nour variety were randomly collected in six localities in Tunisia. We used a polyphasic approach to identify 45 Alternaria and five Curvularia strains isolated from date palm, confirming their pathogenicity. Sequencing of allergen Alt-a1, glyceraldehyde-3-phosphate dehydrogenase (gpd) and calmodulin genes allowed us to group 35 strains in Alternaria Section, and 10 strains in Ulocladioides section. Based on sequencing analyses of Internal Transcribed Spacer, gpd and elongation factor genomic regions, all Curvularia strains were identified as Curvularia spicifera. All Alternaria and Curvularia species tested on date palm plantlets proved to be pathogenic, fulfilling Koch’s postulates. Although no significant differences were observed among the species, the highest mean disease severity index was observed in A. arborescens, while the lowest corresponded to C. spicifera. The capability of these strains to produce mycotoxins in vitro was evaluated. None of the A. consortialis strains produced any known Alternaria mycotoxin, whereas more than 80% of the strains included in Alternaria section Alternaria produced variable amounts of multiple mycotoxins such as alternariol, alternariol monomethyl ether, altenuene, tenuazonic acid and tentoxin. Curvularia spicifera strains produced detectable traces of fumonisins B. This work reports a first comprehensive multidisciplinary study of mycotoxigenic Alternaria species and C. spicifera associated with leaf spot disease on date palm.
Mitochondrial genomic integrity and the nuclear epigenome in health and disease

Bidirectional crosstalk between the nuclear and mitochondrial genomes is essential for proper cell functioning. Mitochondrial DNA copy number (mtDNA-CN) and heteroplasmy influence mitochondrial function, which can influence the nuclear genome and contribute to health and disease. Evidence shows that mtDNA-CN and heteroplasmic variation are associated with aging, complex disease, and all-cause mortality. Further, the nuclear epigenome may mediate the effects of mtDNA variation on disease. In this way, mitochondria act as an environmental biosensor translating vital information about the state of the cell to the nuclear genome. Cellular communication between mtDNA variation and the nuclear epigenome can be achieved by modification of metabolites and intermediates of the citric acid cycle and oxidative phosphorylation. These essential molecules (e.g. ATP, acetyl-CoA, ɑ-ketoglutarate and S-adenosylmethionine) act as substrates and cofactors for enzymes involved in epigenetic modifications. The role of mitochondria as an environmental biosensor is emerging as a critical modifier of disease states. Uncovering the mechanisms of these dynamics in disease processes is expected to lead to earlier and improved treatment for a variety of diseases. However, the influence of mtDNA-CN and heteroplasmy variation on mitochondrially-derived epigenome-modifying metabolites and intermediates is poorly understood. This perspective will focus on the relationship between mtDNA-CN, heteroplasmy, and epigenome modifying cofactors and substrates, and the influence of their dynamics on the nuclear epigenome in health and disease.
Antibiotic removal does not affect cecal microbiota balance and productive parameters in LP robust rabbit line

Antimicrobial resistance is an important threat to public health worldwide, being one of the main death causes in 2050. Moreover, global health is currently underpinned by the “One Health” concept, whereby livestock is strictly related to human and environmental health. However, in the case of the meat rabbit industry, antibiotic additives are still added to prevent gastrointestinal diseases. Current food and consumer awareness require the implementation of sustainable production systems, where robustness and resilience are increasingly important. Hence, the aim of this study was to evaluate the effect of antibiotic feed supplementation on microbiota, and productive performance during the rabbit growing period in a robust genetic line. For this purpose, a total of 432 weaned rabbits were randomly housed, cecum samples were taken on the weaning day and at the end of the growing period (28 and 61 days of age, respectively), and 16S rRNA sequencing analysis was performed. Results showed a higher microbiota complexity at the end of growing in both experimental groups. Firmicutes represented the dominant phylum of the cecal community, followed by Bacteroidota in both groups. Moreover, Victivallis and Escherichia-Shigella genera were only identified in the experimental group without antibiotic supplementation at the end of the growing period. In conclusion, antibiotic feed supplementation had no effect on microbiota composition and productive performance in the robust genetic line reared. These results evidence the importance of the development of rabbit robust genetic lines as an alternative tool to antibiotic administration in epizootic enteropathy control.