Miracle-dz/UniFAR-FTUs huggingface dataset:
An Approach to to Cluster Structures on Moduli of Local Systems for General Groups

Let $S$ be a surface, $G$ a simply-connected classical group, and $G'$ the associated adjoint form of the group. In \cite{FG1}, it was shown that the moduli spaces of framed local systems $\X_{G',S}$ and $\A_{G,S}$ have the structure of cluster varieties, and thus together form a cluster ensemble, when $G$ had type $A$. This was extended to classical groups in \cite{Le}. In this paper we give an algorithm for constructing the cluster structure for general reductive groups $G$. The algorithm can be carried out under some mild hypotheses, which we explain, and which we believe hold in general. We show that these hypotheses hold when $G$ has type $G_2$, and therefore we are able to construct the cluster structure in this case. We also illustrate our approach by rederiving the cluster structure for $G$ of type $A$. Our goals are to give some heuristics for the approach taken in \cite{Le}, point out the difficulties that arise for more general groups, and to record some useful calculations. Forthcoming work by Goncharov and Shen gives a different approach to constructing the cluster structure on $\X_{G',S}$ and $\A_{G,S}$. We hope that some of the ideas here complement their more comprehensive work.
HOMOTOPY TYPES OF GAUGE GROUPS OVER NON-SIMPLYCONNECTED CLOSED 4-MANIFOLDS

Abstract Let G be a simple, simply connected, compact Lie group, and let M be an orientable, smooth, connected, closed 4-manifold. In this paper, we calculate the homotopy type of the suspension of M and the homotopy types of the gauge groups of principal G-bundles over M when π1(M) is (1) ℤ*m, (2) ℤ/prℤ, or (3) ℤ*m*(*nj=1ℤ/prjjℤ), where p and the pj's are odd primes.
Reflection positivity and invertible topological phases

We implement an extended version of reflection positivity (Wick-rotated unitarity) for invertible topological quantum field theories and compute the abelian group of deformation classes using stable homotopy theory. We apply these field theory considerations to lattice systems, assuming the existence and validity of low energy effective field theory approximations, and thereby produce a general formula for the group of Symmetry Protected Topological (SPT) phases in terms of Thom's bordism spectra; the only input is the dimension and symmetry group. We provide computations for fermionic systems in physically relevant dimensions. Other topics include symmetry in quantum field theories, a relativistic 10-fold way, the homotopy theory of relativistic free fermions, and a topological spin-statistics theorem.
Network Pharmacology and Molecular Docking Analysis to Explore the Mechanism of Huaiqihuang-Mediated Alleviation of Henoch–Schönlein Purpura Nephritis

Objective Henoch–Schönlein purpura nephritis (HSPN) is considered a major cause of chronic renal failure and is the most common secondary glomerular disease in children. Huaiqihuang (HQH), a traditional Chinese herbal formula, exhibits therapeutic effects against HSPN in clinical practice. However, the potential molecular targets and mechanisms underlying HSPN treatment remain unclear. Methods By constructing a protein-protein interaction (PPI) network, core targets related to HQH and HSPN were identified. Gene Ontology enrichment and Kyoto Encyclopedia of Genes and Genomes pathways were analyzed to identify the main pathways related to HSPN based on the core targets. To screen the main active ingredients of HQH against HSPN, an ingredient-target-pathway network was constructed using the top 10 main pathways associated with HSPN. Then, molecular docking was performed to explore the interactions and binding patterns between molecules and proteins. Results Clinical data showed that HQH combined with conventional medicine significantly reduced 24-hour urine protein excretion, urine microalbumin levels, and erythrocyte counts in the urine sediment of HSPN patients. By constructing PPI models, 15 potential core targets were identified. The top 10 main pathways showed higher enrichment ratios, including the cytokine–cytokine receptor interaction and signaling pathways related to NOD-like receptor, IL-17, etc. Through the ingredient-target-pathway network and molecular docking, we revealed that five active ingredients of HQH had good affinities with three core targets, AKT1, MMP9, and SERPINE1, which may be vital in treating HSPN. Conclusions The study preliminarily explored the active ingredients, targets, and pathways involved in HQH therapy for HSPN. The mechanism of HQH therapy may be attributed to the modulation of inflammatory response, immune response, and oxidative stress. Combined with clinical data, our results indicate that HQH is highly effective in treating HSPN.
Analogs of Cuntz algebras on Lp spaces

For $d = 2, 3, \ldots$ and $p \in [1, \infty),$ we define a class of representations $\rho$ of the Leavitt algebra $L_d$ on spaces of the form $L^p (X, \mu),$ which we call the spatial representations. We prove that for fixed $d$ and $p,$ the Banach algebra ${{\mathcal{O}}_{d}^{p}}$ obtained as the closure of the image of $L_d$ under the representation $\rho$ is the same for all spatial representations $\rho. $ When $p = 2,$ we recover the usual Cuntz algebra ${\mathcal{O}}_{d}. $ We give a number of equivalent conditions for a representation to be spatial. We show that for distinct $p_1$ and $p_2$ in $[1, \infty)$ and arbitrary $d_1$ and $d_2$ in $\{ 2, 3, \ldots \},$ there is no nonzero continuous homomorphism from ${\mathcal{O}}_{d_1}^{p_1}$ to ${\mathcal{O}}_{d_2}^{p_2}. $
Transport of Peripartum Patients for Medical Management: Predictors of Any Intervention During Transport

Background When obstetric patients present to a hospital without obstetric consultants for medical care, they are often transferred for a higher level of care. Factors associated with patient care during transport between hospitals are unknown. Our study investigated factors associated with care intensity. Methods We retrospectively reviewed charts from peripartum adult patients who were transported to our academic quaternary center between January 1, 2012, and April 19, 2020. We excluded patients transported for gynecologic or fetus-related complications. We defined any transport interventions as any ventilator management, any titration of continuous infusions, and any continuation or initiation of medication during transport. Results We included 126 patients, and the mean age (SD) was 29 (7) years. There were 87 (695) antepartum patients, with nine (7%) requiring mechanical ventilation. Of the patients, 98 (78%) received at least one intervention during transport. Transport time (OR: 1.03, 95% CI: 1.001-1.06, P = 0.040), preeclampsia (OR: 3.8, 95% CI: 1.1-12.7, P = 0.030), and any obstetric hemorrhage (OR: 8.3, 95% CI: 1.03-68, P = 0.047), either antepartum or postpartum, were associated with higher likelihood of receiving any intervention. Conclusions Peripartum patients often received interventions during transport. Preeclampsia and hemorrhage were associated with the likelihood of interventions. Transport clinicians should be prepared when transporting these patients. Further studies are needed to confirm our observations.
On the Zero Temperature Coefficient in Cryogenic FD-SOI MOSFETs

In this article, we propose an explanation of the origin of the zero-temperature coefficient (ZTC) in fully depleted-silicon on insulator (FD-SOI) MOSFETs capacitance curves from room to cryogenic temperature. It is demonstrated that the ZTC is a natural consequence of the Fermi–Dirac function controlling the carrier population. Moreover, based on transport analysis in linear region, it is proven that the ZTC point is preserved in the drain current transfer characteristics only if the mobility varies as the reciprocal temperature, i.e., if it is purely phonon scattering-limited. The inclusion of other defective scattering mechanisms dispels the ZTC point. Finally, the model developed is validated by some TCAD simulations down to deep cryogenic temperatures.
Exposure to mercury and thyroid function: Is there a connection?

Mercury (Hg) is one of the most important environmental pollutants with endocrinedisrupting properties. There is little data from epidemiological studies describing the doseresponse relationship between toxic metal levels and hormone levels. The aim of this study was to use the nearest neighbor matching analysis to determine the difference in Hg concentration in healthy/sick subjects with thyroid disease and to use Benchmark modeling to determine the doseresponse relationship between Hg levels in the blood and thyroid-stimulating hormone (TSH) and thyroid hormones in serum. Blood samples were collected and used for Hg measurement using the ICP-MS method, and separated serum was used for hormone analysis. The study showed the existence of a statistically significant difference in Hg levels measured in healthy and sick subjects and the existence of a dose-response relationship between Hg and all measured hormones, with a narrow interval obtained for the Hg-TSH pair. The results of this research support the use of the Benchmark dose approach for the purpose of analyzing data from human studies, and our further research will be focused on examining the impact of low doses on animal models in order to determine more precise effects of low doses on the organism.
DNA origami and unknotted A-trails in torus graphs

Motivated by problem of determining the unknotted routes for the scaffolding strand in DNA origami self-assembly, we examine the existence and knottedness of A-trails in graphs embedded on the torus. We show that any A-trail in a checkerboard-colorable torus graph is unknotted and characterizes the existence of A-trails in checkerboard-colorable torus graphs in terms of pairs of quasitrees in associated embeddings. Surface meshes are frequent targets for DNA nanostructure self-assembly, and so we study both triangular and rectangular torus grids. We show that aside from one exceptional family, a triangular torus grid contains an A-trail if and only if it has an odd number of vertices, and that such an A-trail is necessarily unknotted. On the other hand, while every rectangular torus grid contains an unknotted A-trail, we also show that any torus knot can be realized as an A-trail in some rectangular grid. Lastly, we use a gluing operation to construct infinite families of triangular and rectangular grids containing unknotted A-trails on surfaces of arbitrary genus. We also give infinite families of triangular grids containing no unknotted A-trail on surfaces of arbitrary nonzero genus.
On distance spectral radius of uniform hypergraphs

The distance spectral radius of a connected hypergraph is the largest eigenvalue of its distance matrix. We determine the unique connected k-uniform hypergraphs with minimum distance spectral radius when the number of pendant edges is given, the unique k-uniform non-hyperstar-like hypertrees (non-hyper-caterpillars, respectively) with minimum distance spectral radius, and the unique k-uniform non-hyper-caterpillars with maximum distance spectral radius for .
A Low-Cost System for Quick Measurements on Noise Barriers in Situ

This article describes the development of a low-cost device for measuring the acoustic intrinsic characteristics of noise barriers. The system is based on the Teensy 4.1 microcontroller combined with a few other components. The measurements are carried out using a vertical linear microphone antenna housing six microphones and a lightweight loudspeaker, with a wireless connection to the main unit. Both the main system unit and the amplified loudspeaker are powered by normal 5 V universal serial bus (USB) battery packs, which are easily rechargeable and interchangeable. The system measures six impulse responses using a maximum length sequence (MLS) signal and performs a series of calculations and frequency analyses to characterize the device under test, following a simplified version of the European standards EN 1793-5 and EN 1793-6 (commonly referred to as the “Adrienne method”). One measurement takes a few minutes, obtaining results comparable to those obtained with the Adrienne method, which requires more complicated and heavy measuring equipment and is much more expensive and time-consuming.
The geometry of flip graphs and mapping class groups

The space of topological decompositions into triangulations of a surface has a natural graph structure where two triangulations share an edge if they are related by a so-called flip. This space is a sort of combinatorial Teichmüller space and is quasi-isometric to the underlying mapping class group. We study this space in two main directions. We first show that strata corresponding to triangulations containing a same multiarc are strongly convex within the whole space and use this result to deduce properties about the mapping class group. We then focus on the quotient of this space by the mapping class group to obtain a type of combinatorial moduli space. In particular, we are able to identity how the diameters of the resulting spaces grow in terms of the complexity of the underlying surfaces.
Fundamental gerbes

For a class of affine algebraic groups C over a field, we define the notions of C -fundamental gerbe of a fibered category, generalizing what we had done in [5] for finite group schemes. We give a necessary and sufficient conditions on C implying that a fibered category X over κ satisfying mild hypotheses admits a Nori C -fundamental gerbe. We also give a tannakian interpretation of the gerbe that results by taking as C the class of virtually unipotent group schemes, under a properness condition on X.
Uremic Myopathy and Mitochondrial Dysfunction in Kidney Disease

Alterations in muscle structure and function in chronic kidney disease (CKD) patients are associated with poor outcomes. As key organelles in muscle cell homeostasis, mitochondrial metabolism has been studied in the context of muscle dysfunction in CKD. We conducted a study to determine the contribution of oxidative metabolism, glycolysis and fatty acid oxidation to the muscle metabolism in CKD. Mice developed CKD by exposure to adenine in the diet. Muscle of CKD mice showed significant weight loss compared to non-CKD mice, but only extensor digitorum longus (EDL) muscle showed a decreased number of fibers. There was no difference in the proportion of the various muscle fibers in CKD and non-CKD mice. Muscle of CKD mice had decreased expression of proteins associated with oxidative phosphorylation but increased expression of enzymes and transporters associated with glycolysis. In cell culture, myotubes exposed to uremic serum demonstrated decreased oxygen consumption rates (OCR) when glucose was used as substrate, conserved OCR when fatty acids were used and increased lactate production. In conclusion, mice with adenine-induced CKD developed sarcopenia and with increased glycolytic metabolism but without gross changes in fiber structure. In vitro models of uremic myopathy suggest fatty acid utilization is preserved compared to decreased glucose utilization.
Impacts of Extension Contact on the Adoption of Formulated Fertilizers and Farm Performance among Large-Scale Farms in Rural China

Growing concerns about the environmental costs of agricultural production have given new impetus to the promotion of sustainable agricultural production technologies that can reduce soil erosion and the excessive use of agricultural chemicals. Although numerous policies have been implemented to popularize soil testing and formulated fertilization technologies in China, the diffusion of the technology among large-scale farmers (LSFs) has been addressed only rarely. We used a two-stage controlled function model to control for endogeneity and selection bias in contacting extension staff to assess the effect of an extension contact on technology adoption behavior by LSFs, Propensity Score Matching techniques are also utilized to analyze the effects of extension contact on the rice yields and nutrient use amount. Empirical results from Jiangsu and Jiangxi provinces show that extension contact plays a crucial role in promoting soil testing and the adoption of formulated fertilization technologies; LSFs’ adoption raises rice yields, however, the impact of extension contact on reducing nutrient use amount does not pass the significance test. The findings add to the theoretical literature on technology extension, and we used them to suggest policies to encourage tailored agricultural extension systems by constructing rural technological extension networks.
Cohomologie 𝑝-adique de la tour de Drinfeld: le cas de la dimension 1

<p>We compute the <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3. org/1998/Math/MathML" alttext="p"> <mml:semantics> <mml:mi>p</mml:mi> <mml:annotation encoding="application/x-tex">p</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-adic geometric étale cohomology of the coverings of the Drinfeld half-plane, and we show that, if the base field is <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3. org/1998/Math/MathML" alttext="bold upper Q Subscript p"> <mml:semantics> <mml:msub> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="bold">Q</mml:mi> </mml:mrow> <mml:mi>p</mml:mi> </mml:msub> <mml:annotation encoding="application/x-tex">\mathbf {Q}_p</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, this cohomology encodes the <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3. org/1998/Math/MathML" alttext="p"> <mml:semantics> <mml:mi>p</mml:mi> <mml:annotation encoding="application/x-tex">p</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-adic local Langlands correspondence for <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3. org/1998/Math/MathML" alttext="2"> <mml:semantics> <mml:mn>2</mml:mn> <mml:annotation encoding="application/x-tex">2</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-dimensional de Rham representations (of weight <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="0"> <mml:semantics> <mml:mn>0</mml:mn> <mml:annotation encoding="application/x-tex">0</mml:annotation> </mml:semantics> </mml:math> </inline-formula> and <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="1"> <mml:semantics> <mml:mn>1</mml:mn> <mml:annotation encoding="application/x-tex">1</mml:annotation> </mml:semantics> </mml:math> </inline-formula>). </p>
Topology of two-row Springer fibers for the even orthogonal and symplectic group

We construct an explicit topological model (similar to the topological Springer fibers appearing in work of Khovanov and Russell) for every two-row Springer fiber associated with the even orthogonal group and prove that the respective topological model is homeomorphic to its corresponding Springer fiber. This confirms a conjecture by Ehrig and Stroppel concerning the topology of the equal-row Springer fiber for the even orthogonal group. Moreover, we show that every two-row Springer fiber for the symplectic group is homeomorphic (even isomorphic as an algebraic variety) to a connected component of a certain two-row Springer fiber for the even orthogonal group.
Global existence and steady states of a two competing species Keller-Segel chemotaxis model

We study an one{dimensional quasilinear system proposed by J. Tello and M. Winkler [19] which models the population dynamics of two competing species attracted by the same chemical. The kinetics terms of the interacting species are chosen to be the Lotka{Volterra type. We prove the existence of global bounded and classical solutions for all chemoattraction rates. Under homogeneous Neumann boundary conditions, we establish the existence of nonconstant steady states by local bifurcation theory. The stability of the bifurcating solutions is also obtained when the diff? usivity of both species is large. Finally, we perform extensive numerical studies to demonstrate the formation of stable positive steady states with various interesting spatial structures.
Progress on homogeneous Einstein manifolds and some open probrems

We give an overview of progress on homogeneous Einstein metrics on large classes of homogeneous manifolds, such as generalized flag manifolds and Stiefel manifolds. The main difference between these two classes of homogeneous spaces is that their isotropy representation does not contain/contain equivalent summands. We also discuss a third class of homogeneous spaces that falls into the intersection of such dichotomy, namely the generalized Wallach spaces. We give new invariant Einstein metrics on the Stiefel manifold $V_5\mathbb{R}^n$ ($n\ge 7$) and through this example we show how to prove existence of invariant Einstein metrics by manipulating parametric systems of polynomial equations. This is done by using Gr\"obner bases techniques. Finally, we discuss some open problems.
Higher genus Gromov-Witten theory of the Hilbert scheme of points of the plane and CohFTs associated to local curves

We study the higher genus equivariant Gromov-Witten theory of the Hilbert scheme of n points of the plane. Since the equivariant quantum cohomology is semisimple, the higher genus theory is determined by an R-matrix via the Givental-Teleman classification of Cohomological Field Theories (CohFTs). We uniquely specify the required R-matrix by explicit data in degree 0. As a consequence, we lift the basic triangle of equivalences relating the equivariant quantum cohomology of the Hilbert scheme and the Gromov-Witten/Donaldson-Thomas correspondence for 3-fold theories of local curves to a triangle of equivalences in all higher genera. The proof uses the previously determined analytic continuation of the fundamental solution of the QDE of the Hilbert scheme. The GW/DT edge of the triangle in higher genus concerns new CohFTs defined by varying the 3-fold local curve in the moduli space of stable curves. The equivariant orbifold Gromov-Witten theory of the symmetric product of the plane is also shown to be equivalent to the theories of the triangle in all genera. The result establishes a complete case of the crepant resolution conjecture.
Liouville quantum gravity and the Brownian map II: Geodesics and continuity of the embedding

We endow the √ 8/3-Liouville quantum gravity sphere with a metric space structure and show that the resulting metric measure space agrees in law with the Brownian map. Recall that a Liouville quantum gravity sphere is a priori naturally parameterized by the Euclidean sphere S2. Previous work in this series used quantum Loewner evolution (QLE) to construct a metric dQ on a countable dense subset of S2. Here we show that dQ a.s. extends uniquely and continuously to a metric dQ on all of S2. Letting d denote the Euclidean metric on S2, we show that the identity map between (S2, d) and (S2, dQ) is a.s. Holder continuous in both directions. We establish several other properties of (S2, dQ), culminating in the fact that (as a random metric measure space) it agrees in law with the Brownian map. We establish analogous results for the Brownian disk and plane. Our proofs involve new estimates on the size and shape of QLE balls and related quantum surfaces, as well as a careful analysis of (S2, dQ) geodesics. 1 ar X iv :1 60 5. 03 56 3v 1 [ m at h. PR ] 1 1 M ay 2 01 6
Two-microlocal regularity of quasimodes on the torus

We study the regularity of stationary and time-dependent solutions to strong perturbations of the free Schrodinger equation on two-dimensional flat tori. This is achieved by performing a second microlocalization related to the size of the perturbation and by analysing concentration and nonconcentration properties at this new scale. In particular, we show that sufficiently accurate quasimodes can only concentrate on the set of critical points of the average of the potential along geodesics.