Miracle-dz/UniFAR-FTUs huggingface dataset:
On Rational Cuspidal Projective Plane Curves

In 2002, L. Nicolaescu and the fourth author formulated a very general conjecture which relates the geometric genus of a Gorenstein surface singularity with rational homology sphere link with the Seiberg‐‐Witten invariant (or one of its candidates) of the link. Recently, the last three authors found some counterexamples using superisolated singularities. The theory of superisolated hypersurface singularities with rational homology sphere link is equivalent with the theory of rational cuspidal projective plane curves. In the case when the corresponding curve has only one singular point one knows no counterexample. In fact, in this case the above Seiberg‐‐Witten conjecture led us to a very interesting and deep set of ‘compatibility properties’ of these curves (generalising the Seiberg‐‐Witten invariant conjecture, but sitting deeply in algebraic geometry) which seems to generalise some other famous conjectures and properties as well (for example, the Noether‐‐Nagata or the log Bogomolov‐‐Miyaoka‐‐Yau inequalities). Namely, we provide a set of ‘compatibility conditions’ which conjecturally is satisfied by a local embedded topological type of a germ of plane curve singularity and an integer d if and only if the germ can be realized as the unique singular point of a rational unicuspidal projective plane curve of degree d. The conjectured compatibility properties have a weaker version too, valid for any rational cuspidal curve with more than one singular point. The goal of the present article is to formulate these conjectured properties, and to verify them in all the situations when the logarithmic Kodaira dimension of the complement of the corresponding plane curves is strictly less than 2. 2000 Mathematics Subject Classification 14B05, 14J17, 32S25, 57M27, 57R57 (primary), 14E15, 32S45, 57M25 (secondary).
Vimentin epigenetic deregulation in Bladder Cancer associates with acquisition of invasive and metastatic phenotype through epithelial-to-mesenchymal transition

Bladder cancer (BlCa) is the ninth most common cancer worldwide, associated with significant morbidity and mortality. Thus, understand the biological mechanisms underlying tumour progression is of great clinical significance. Vimentin (VIM) is (over)expressed in several carcinomas, putatively in association with EMT. We have previously found that VIM promoter methylation accurately identified BlCa and VIM expression associated with unfavourable prognosis. Herein, we sought to investigate VIM expression regulation and its role in malignant transformation of BlCa. Analysis of tissue samples disclosed higher VIM transcript, protein, and methylation levels in BlCa compared with normal urothelium. VIM protein and transcript levels significantly increased from non-muscle invasive (NMIBC) to muscle-invasive (MIBC) cases and to BlCa metastases. Inverse correlation between epithelial CDH1 and VIM, and a positive correlation between mesenchymal CDH2 and VIM were also observed. In BlCa cell lines, exposure to demethylating agent increased VIM protein, with concomitant decrease in VIM methylation. Moreover, exposure to histone deacetylases pan-inhibitor increased the deposit of active post-translational marks (PTMs) across VIM promoter. In primary normal urothelium cells, lower levels of active PTMs with concomitant higher levels of repressive marks deposit were observed. Finally, VIM knockdown in UMUC3 cell line increased epithelial-like features and decreased migration and invasion in vitro, decreasing tumour size and angiogenesis in vivo. We demonstrated that VIM promoter is epigenetically regulated in normal and neoplastic urothelium, which determine a VIM switch associated with EMT and acquisition of invasive and metastatic properties. These findings might allow for development of new, epigenetic-based, therapeutic strategies for BlCa.
Predictive mapping of wetland soil types in the Canadian Prairie Pothole Region using high-resolution digital elevation model terrain derivatives

Abstract Wetland soil types, which can be distinguished based on calcium carbonate content, vary in their effect on ecosystem functions like phosphorus retention, salinity contributions, and greenhouse gas forcing. These soil types may be predictively mapped with machine learning models that use terrain derivatives calculated from high-resolution digital elevation models. Soil profiles from three Saskatchewan study sites were classified into three functional categories—upland, calcareous wetland, or noncalcareous wetland—and used to train random forest models for predictive soil mapping. Multiple terrain derivatives were included as predictor variables to capture local- and landscape-scale morphometry and hydrology influences, including five derivatives developed for this study. Models were developed at three spatial resolutions: 2, 5, and 10 m, and tested via internal cross-validation and independent validation with datasets from previous studies. Predictive accuracies were highest when mapping at 2 m resolution (independent validation accuracy range = 64%–100%) but also successful when mapping at 5 and 10 m resolutions (independent validation accuracy range = 63%–100%); however, visual inspection determined that the maps generated at 10 m resolution were less detailed and occasionally featured questionable discontinuous soil distributions. Three of the five terrain derivatives developed for this study were among the most important predictor variables (first, second, and 10th most important). Models trained using only data from a specific site had slightly better performance than models trained using data from all sites, except in regions where training data were lacking.
Bowing of biexciton binding in AlxGa1-xN ternary alloys

Biexciton binding in AlxGa1-xN ternary alloys as a function of alloy composition is reviewed on the basis of our recent experimental observations. The biexciton binding energy in GaN and AlN was evaluated to be 5.6 and 19.3 meV, respectively. The biexciton binding energy in Ga-rich AlxGa1-xN ternary alloys (x=0.019~0.092) and Al-rich AlxGa1-xN ternary alloys (x=0.81 and 0.89) was also evaluated on the basis of two-photon absorption of biexcitons. The biexciton binding energy in Ga-rich ternary alloys increased linearly with aluminum composition and reached to 16.6 meV for x=0.092. This value was three times as large as the biexciton binding energy in GaN. Similarly, the biexciton binding energy in Al-rich ternary alloys increased with decreasing aluminum composition and reached to 56 meV for x=0.81. A strong enhancement of the biexciton binding was observed for both Ga-rich and Al-rich ternary alloys. The enhancement was attributed to the effect of localization due to alloy disorder. The results indicated that a linear interpolation between GaN and AlN did not apply to the biexciton binding energy in the ternary alloys. A large bowing existed in the biexciton binding energy in the ternary alloys.
On the resonant reflection of weak, nonlinear sound waves off an entropy wave

We analyze the resonant reflection of very weak, nonlinear sound waves off a weak sawtooth entropy wave for spatially periodic solutions of the one‐dimensional, nonisentropic gas dynamics equations. The case of an entropy wave with a sawtooth profile is of interest because the oscillations of the reflected sound waves are nondispersive with frequency independent of their wavenumber, leading to an unusual type of nonlinear dynamics. On an appropriate long time scale, we show that a complex amplitude function for the spatial profile of the sound waves satisfies a degenerate quasilinear Schrödinger equation. We present some numerical solutions of this equation that illustrate the generation of small spatial scales by a resonant four‐wave cascade and front propagation in compactly supported solutions.
High-Specificity Test Algorithm for Bovine Tuberculosis Diagnosis in African Buffalo (Syncerus caffer) Herds

Ante-mortem bovine tuberculosis (bTB) tests for buffaloes include the single comparative intradermal tuberculin test (SCITT), interferon-gamma (IFN-γ) release assay (IGRA) and IFN-γ-inducible protein 10 release assay (IPRA). Although parallel test interpretation increases the detection of Mycobacterium bovis (M. bovis)-infected buffaloes, these algorithms may not be suitable for screening buffaloes in historically bTB-free herds. In this study, the specificities of three assays were determined using M. bovis-unexposed herds, historically negative, and a high-specificity diagnostic algorithm was developed. Serial test interpretation (positive on both) using the IGRA and IPRA showed significantly greater specificity (98.3%) than individual (90.4% and 80.9%, respectively) tests or parallel testing (73%). When the SCITT was added, the algorithm had 100% specificity. Since the cytokine assays had imperfect specificity, potential cross-reactivity with nontuberculous mycobacteria (NTM) was investigated. No association was found between NTM presence (in oronasal swab cultures) and positive cytokine assay results. As a proof-of-principle, serial testing was applied to buffaloes (n = 153) in a historically bTB-free herd. Buffaloes positive on a single test (n = 28) were regarded as test-negative. Four buffaloes were positive on IGRA and IPRA, and M. bovis infection was confirmed by culture. These results demonstrate the value of using IGRA and IPRA in series to screen buffalo herds with no previous history of M. bovis infection.
Lavrent'ev regularization of ill-posed problems containing nonlinear near-to-monotone operators with application to autoconvolution equation

In this paper the method of Lavrent'ev for regularization of ill-posed problems with near-to-monotone operators is considered. An a priori rule of choice of the parameter of regularization is presented and the corresponding error estimate is derived. The theory is applied to the autoconvolution equation. Numerical examples are provided.
Mesoscopic central limit theorem for general $\beta$-ensembles

We prove that the linear statistics of eigenvalues of $\beta$-log gasses satisfying the one-cut and off-critical assumption with a potential $V \in C^6(\mathbb{R})$ satisfy a central limit theorem at all mesoscopic scales $\alpha \in (0; 1)$. We prove this for compactly supported test functions $f \in C^5(\mathbb{R})$ using loop equations at all orders along with rigidity estimates.
Brownian motion on stationary random manifolds

We introduce the concept of a stationary random manifold with the objective of treating in a unified way results about manifolds with transitive isometry group, manifolds with a compact quotient, and generic leaves of compact foliations. We prove inequalities relating linear drift and entropy of Brownian motion with the volume growth of such manifolds, generalizing previous work by Avez, Kaimanovich, and Ledrappier among others. In the second part we prove that the leaf function of a compact foliation is semicontinuous, obtaining as corollaries Reeb's local stability theorem, part of Epstein's the local structure theorem for foliations by compact leaves, and a continuity theorem of Alvarez and Candel.
The Ihara zeta function for infinite graphs

We put forward the concept of measure graphs. These are (possibly uncountable) graphs equipped with an action of a groupoid and a measure invariant under this action. Examples include finite graphs, periodic graphs, graphings and percolation graphs. Making use of Connes' non-commutative integration theory we construct a Zeta function and present a determinant formula for it. We further introduce a notion of weak convergence of measure graphs and show that our construction is compatible with it. The approximation of the Ihara Zeta function via the normalized version on finite graphs in the sense of Benjamini-Schramm follows as a special case. Our framework not only unifies corresponding earlier results occurring in the literature. It likewise provides extensions to rich new classes of objects such as percolation graphs.
Stabilization for Networked Control Systems with Simultaneous Input Delay and Markovian Packet Losses

The mean square stabilization problem for discrete-time networked control systems (NCSs) is investigated in this article. What the difference from most previous works is that input delay and packet losses occur simultaneously in the communication channel, moreover, the data packet dropout is modeled as a time-homogeneous Markov process which will bring some difficulties in solving the problem due to the temporal correlation. The contributions in this paper can be summarized as two points. Firstly, the equivalence condition for the solvability of linear quadratic optimal problem in finite horizon subject to the discrete-time NCSs is expressed by solving the forward and backward stochastic difference equations (FBSDEs-M) which is derived from the maximum principle involving Markov jump and delay. Secondly, under basic assumption, the necessary and sufficient condition of mean square stabilization is given by the solutions to the coupled algebraic Riccati equations with Markov jump (CAREs-M). To our best knowledge, the problems studied in this paper are new because most previous works mainly discussed the case of only delay or packet dropout in NCSs.
Slow Manifolds and Multiple Equilibria in Stratocumulus‐Capped Boundary Layers

In marine stratocumulus‐capped boundary layers under strong inversions, the timescale for thermodynamic adjustment is roughly a day, much shorter than the multiday timescale for inversion height adjustment. Slow‐manifold analysis is introduced to exploit this timescale separation when boundary layer air columns experience only slow changes in their boundary conditions. Its essence is that the thermodynamic structure of the boundary layer remains approximately slaved to its inversion height and the instantaneous boundary conditions; this slaved structure determines the entrainment rate and hence the slow evolution of the inversion height and can be regarded as a one‐dimensional slow manifold. Slow‐manifold analysis is applied to mixed‐layer model and large‐eddy simulations of an idealized nocturnal stratocumulus‐capped boundary layer. Both models are found to have multiple equilibria; depending on the initial inversion height, the simulations slowly evolve toward a shallow thin‐cloud boundary layer or a deep, well‐mixed thick cloud boundary layer. In the mixed‐layer model, this can be described using a single slow manifold bifurcated by an unstable equilibrium inversion height which separates a branch that evolves toward a deep steady state from a branch which shallows indefinitely. In the large‐eddy simulations, there are two separate slow manifolds (one of which becomes unstable if cloud droplet concentration is reduced). On one, the boundary layer is well‐mixed and deepens to a thick‐cloud steady state. On the other, the boundary layer is decoupled and shallows to a thin‐cloud steady state. If the initial inversion height supports an optically thick but nearly nondrizzling cloud, it evolves onto the well‐mixed manifold; if the initial cloud layer is either too thin to efficiently radiatively cool, or thick enough to heavily drizzle, it evolves onto the decoupled manifold. Applications to analysis of stratocumulus observations and to pockets of open cells and ship tracks are proposed.
Micronutrients in Adverse Pregnancy Outcomes

About 10 to 20% of reported pregnancies have complications like spontaneous abortion (SA), preeclampsia (PE), preterm birth (PTB), and fetal growth restriction (FGR); 60% are attributed to maternal nutritional alterations. Multiple micronutrients (MMN) are supplemented in the antenatal period, but no proper validation/guidelines are available regarding dosing/time, the need for initiation, and the duration of supplementation. Studies have reported adverse pregnancy complications related to the overuse/unwanted use of multiple micronutrient supplementations during pregnancy. Identifying the exact population requiring supplementation is necessary to prevent its abuse. This article attempts to review the impacts of micronutrient deficiency/supplementation in cases of SA, FGR, and gestational diabetes mellitus (GDM), preterm delivery and PE. The study used a literature search using PubMed, Google Scholar, Mendeley, and Scopus Databases using search words pregnancy, spontaneous abortion, gestational diabetes mellitus (GDM), fetal growth restriction (FGR), preterm delivery, preeclampsia (PE) or “adverse pregnancy” associated with minerals, micronutrients, or supplementation. The review also considered in-house literature databases, a single-window search at Kasturba Medical College (KMC) Health sciences library, MAHE (Manipal Academy of Higher Education). The figures included in the study were created by Biorender.com. Micronutrients play multiple roles during pregnancy and fetoplacental growth stimulating growth hormone secretion, Lysyl oxidase (LOX), involved in the crosslinking between collagen and elastin in the amniotic membrane, downregulation of interleukin (IL)-1 alpha, IL-1 beta, IL-4, IL-6, Il-10, IL-12, tumor necrosis factor (TNF)-alpha and several chemokines involved in hypertension, immune-inflammatory pathways, attenuate insulin resistance a structural development of neurons and glia. Over-supplementation has led to complications such as spontaneous abortion and gestational diabetes mellitus. Since there is a lack of standardization concerning micronutrient supplementation during pregnancy, there is a need for systematic study related to the role of micronutrients during each trimester of pregnancy to optimize its supplementation and to prevent hazards associated with its abuse.
A stochastic solution with Gaussian stationary increments of the symmetric space-time fractional diffusion equation

Abstract The stochastic solution with Gaussian stationary increments is established for the symmetric space-time fractional diffusion equation when 0 < β < α ≤ 2, where 0 < β ≤ 1 and 0 < α ≤ 2 are the fractional derivation orders in time and space, respectively. This solution is provided by imposing the identity between two probability density functions resulting (i) from a new integral representation formula of the fundamental solution of the symmetric space-time fractional diffusion equation and (ii) from the product of two independent random variables. This is an alternative method with respect to previous approaches such as the scaling limit of the continuous time random walk, the parametric subordination and the subordinated Langevin equation. A new integral representation formula for the fundamental solution of the space-time fractional diffusion equation is firstly derived. It is then shown that, in the symmetric case, a stochastic solution can be obtained by a Gaussian process with stationary increments and with a random wideness scale variable distributed according to an arrangement of two extremal Lévy stable densities. This stochastic solution is self-similar with stationary increments and uniquely defined in a statistical sense by the mean and the covariance structure. Numerical simulations are carried out by choosing as Gaussian process the fractional Brownian motion. Sample paths and probability densities functions are shown to be in agreement with the fundamental solution of the symmetric space-time fractional diffusion equation.
ON A LINEAR RUNS AND TUMBLES EQUATION

We consider a linear runs and tumbles equation in dimension d ≥ 1 for which we establish the existence of a unique positive and normalized steady state as well as its asymptotic stability, improving similar results obtained by Calvez et al. [5] in dimension d = 1. Our analysis is based on the Krein-Rutman theory revisited in [18] together with some new moment estimates for proving confinement mechanism as well as dispersion, multiplicator and averaging lemma arguments for proving some regularity property of suitable iterated averaging quantities.
Discrete local induction equation

The local induction equation, or the binormal flow on space curves is a well-known model of deformation of space curves as it describes the dynamics of vortex filaments, and the complex curvature is governed by the nonlinear Schr\"odinger equation. In this paper, we present its discrete analogue, namely, a model of deformation of discrete space curves by the discrete nonlinear Schr\"odinger equation. We also present explicit formulas for both smooth and discrete curves in terms of $\tau$ functions of the two-component KP hierarchy.
Analytic solutions for marginal deformations in open superstring field theory

We construct analytic solutions for marginal deformations satisfying the reality condition in open superstring field theory formulated by Berkovits when operator products made of the marginal operator and the associated superconformal primary field are regular. Our strategy is based on the recent observation by Erler that the problem of finding solutions for marginal deformations in open superstring field theory can be reduced to a problem in the bosonic theory of finding a finite gauge parameter for a certain pure-gauge configuration labeled by the parameter of the marginal deformation. We find a gauge transformation generated by a real gauge parameter which infinitesimally changes the deformation parameter and construct a finite gauge parameter by its path-ordered exponential. The resulting solution satisfies the reality condition by construction.
A Riemann–Kempf singularity theorem for higher rank Brill–Noether loci

Given a vector bundle V of rank r over a curve X , we define and study a surjective rational map Hilbd(PV)⤍Quot0,d(V∗) generalising the natural map SymdX→Quot0,d(OX) . We then give a generalisation of the geometric Riemann–Roch theorem to vector bundles of higher rank over X . We use this to give a geometric description of the tangent cone to the higher rank Brill–Noether locus Br,dk at a suitable bundle E . This gives a generalisation of the Riemann–Kempf singularity theorem. As a corollary, if k=r and h0(X,E)=r+n , we show that the n th secant variety of the rank one locus of PEndE is contained in the tangent cone to Br,dr .
Supplementation of an Anthocyanin-Rich Elderberry (Sambucus nigra L.) Extract in FVB/n Mice: A Healthier Alternative to Synthetic Colorants

Sambucus nigra L. , popularly known as elderberry, is renowned for its amazing therapeutic properties, as well as its uses as a food source, in nutraceuticals, and in traditional medicine. This study’s aim was to investigate the effects of an elderberry extract (EE) on mice for 29 days, as well as the safety of the extract when used as a natural colorant. Twenty-four FVB/n female mice (n = 6) were randomly assigned to one of four groups: control, 12 mg/mL EE (EE12), 24 mg/mL EE (EE24), or 48 mg/mL EE (EE48). The predominant anthocyanins detected were cyanidin-3-O-sambubioside and cyanidin-3-O-glucoside. Food and drink intake were similar between groups, with the exception of EE48, who drank significantly less compared with the Control. Biochemical analysis of the liver showed that the changes observed in histological analysis had no pathological significance. The EE, at doses of 24 and 48 mg/mL, significantly reduced the oxidative DNA damage compared with the non-supplemented group. The S. nigra extract showed a favorable toxicological profile, affording it potential to be used in the food industry.