Miracle-dz/UniFAR-FTUs huggingface dataset:
Extending Romanovski polynomials in quantum mechanics

Some extensions of the (third-class) Romanovski polynomials (also called Romanovski/pseudo-Jacobi polynomials), which appear in bound-state wavefunctions of rationally-extended Scarf II and Rosen-Morse I potentials, are considered. For the former potentials, the generalized polynomials satisfy a finite orthogonality relation, while for the latter an infinite set of relations among polynomials with degree-dependent parameters is obtained. Both types of relations are counterparts of those known for conventional polynomials. In the absence of any direct information on the zeros of the Romanovski polynomials present in denominators, the regularity of the constructed potentials is checked by taking advantage of the disconjugacy properties of second-order differential equations of Schr\"odinger type. It is also shown that on going from Scarf I to Scarf II or from Rosen-Morse II to Rosen-Morse I potentials, the variety of rational extensions is narrowed down from types I, II, and III to type III only.
Algebraic cycles and triple $K3$ burgers

We consider surfaces of geometric genus $3$ with the property that their transcendental cohomology splits into $3$ pieces, each piece coming from a $K3$ surface. For certain families of surfaces with this property, we can show there is a similar splitting on the level of Chow groups (and Chow motives).
DGSSC: A Deep Generative Spectral-Spatial Classifier for Imbalanced Hyperspectral Imagery

In recent years, hyperspectral image classification (HSIC) has achieved impressive progress with emerging studies on deep learning models. However, the classification performance downgrades due to the limited number of annotated samples, especially for minority classes. Notably, the imbalanced data dilemma is familiar in remote sensing hyperspectral image because the ground objects are commonly distributed without evenness. Therefore, this paper proposes a novel deep generative spectral-spatial classifier (DGSSC) for addressing the issues of imbalanced HSIC. Specifically, the DGSSC comprises three components, a two-stage encoder, a decoder, and a classifier, which are trained in an end-to-end manner. In particular, to exploit the abundant spectral-spatial features with relatively low computational complexity, the first stage of the encoder comprises successive three-dimensional (3D) and two-dimensional (2D) convolutions, exploring the spectral-spatial and deep spatial information. In addition, the second stage involves the deep latent variable model to achieve minority-class data augmentation. Furthermore, a patch distance-based reconstruction loss function is designed to facilitate the outputs of the decoder being more similar to the input 3D patch samples. The proposed DGSSC can outperform the state-of-the-art methods on three benchmark datasets, especially with its more robust prediction results. For instance, the DGSSC achieves a remarkable 97.85% mean overall accuracy with 0.24% standard deviation over ten independent runs with randomly selected imbalanced 1% training samples on the University of Pavia dataset.
Advances in Research on Bioactivity, Toxicity, Metabolism, and Pharmacokinetics of Usnic Acid In Vitro and In Vivo

Lichens are among the most widely distributed plants on earth and have the longest growth cycle. Usnic acid is an abundant characteristic secondary metabolite of lichens and the earliest lichen compound used commercially. It has diverse pharmacological activities, such as anti-inflammatory, antibacterial, antiviral, anticancer, antioxidant, and photoprotective effects, and promotes wound healing. It is widely used in dietary supplements, daily chemical products (fodder, dyes, food, perfumery, and cosmetics), and medicine. However, some studies have found that usnic acid can cause allergic dermatitis and drug-induced liver injury. In this paper, the bioactivity, toxicity, in vivo and in vitro metabolism, and pharmacokinetics of usnic acid were summarized. The aims were to develop and utilize usnic acid and provide reference for its future research.
An analytic family of representations for the mapping class group of punctured surfaces

We use quantum invariants to define an analytic family of representations for the mapping class group Mod.U/ of a punctured surface U. The representations depend on a complex number A withjAj6 1 and act on an infinite-dimensional Hilbert space. They are unitary when A is real or imaginary, bounded whenjAj< 1, and only densely defined whenjAjD 1 and A is not a root of unity. When A is a root of unity distinct from 1 and i the representations are finite-dimensional and isomorphic to the “Hom” version of the well-known TQFT quantum representations. The unitary representations in the interval a 1;0c interpolate analytically between two natural geometric unitary representations, the SU.2/‐character variety representation studied by Goldman and the multicurve representation induced by the action of Mod.U/ on multicurves. The finite-dimensional representations converge analytically to the infinite-dimensional ones. We recover Marche and Narimannejad’s convergence theorem, and Andersen, Freedman, Walker and Wang’s asymptotic faithfulness, that states that the image of a noncentral mapping class is always nontrivial after some level r0 . When the mapping class is pseudo-Anosov we give a simple polynomial estimate of the level r0 in terms of its dilatation. 57R56; 57M27, 22D10
Forest: A Lightweight Semantic Image Descriptor for Robust Visual Place Recognition

Visual place recognition (VPR) is the process of identifying previously visited places using visual information. It is crucial for a robot to achieve fast and accurate VPR under appearance and viewpoint changes. Inspired by human perception intuition, this letter proposes a lightweight semantic image descriptor called Forest for robust VPR. Specifically, for each semantic object in the image, three most recognizable reference objects are first found and ranked in descending order according to a customized measure. And then, categories, position and area of the semantic object itself, along with the categories of the three recognized reference objects, are used to encode the local descriptor of the object. As a result, the set of local descriptors is used as the global descriptor of the image. Performance of the proposed descriptor is evaluated and compared with six state-of-the-art VPR methods, Ibow-LCD, CoHOG, NetVLAD, LOST-X, Region VLAD, Patch-NetVLAD, over four public datasets of urban scenes, Extended-CMU Season, RobotCar Seasons v2, SYNTHIA and Kitti, using three Precision-Recall based metrics, AUC(Area Under Curve), Recall@100%Precision and Precision@100%Recall. The results show that our method maintains competitive accuracy in scenes with appearance and viewpoint changes and exhibits high robustness. At the same time, our method is robust to the noise of semantic segmentation and exhibits high real-time performance.
Smale Strategies for Network Prisoner's Dilemma Games

Smale’s approach [13] to the classical two-players repeated Prisoner’s Dilemma game is revisited here for N-players and Network games in the framework of Blackwell’s approachability, stochastic approximations and differential inclusions. MSC: 91A06, 91A26, 62L20, 34G25, 37B25,
Dietary Oregano Essential Oil Supplementation Influences Production Performance and Gut Microbiota in Late-Phase Laying Hens Fed Wheat-Based Diets

Simple Summary Essential oils (EOs) are antibacterial and anti-inflammatory, and are called natural antibiotics. Within the great variety of EOs, oregano essential oil(OEO) is known for its antimicrobial activity. So, we focused on comparing the effect of flavomycin and OEO on the egg-laying performance and intestinal flora of laying hens. This study found that OEO improved the egg-production performance and altered microbial composition. The results revealed that OEO could be an effective alternative to flavomycin. Abstract This study aimed to investigate the potential effects of OEO on production performance, egg quality, fatty acid composition in yolk, and cecum microbiota of hens in the late phase of production. A total of 350 58-week-old Jing Tint Six laying hens were randomly divided into five groups: (1) fed a basal diet (control); (2) fed a basal diet + 5 mg/kg flavomycin (AGP); (3) fed a basal diet + 100 mg/kg oregano essential oil + 20 mg/kg cinnamaldehyde (EO1); (4) fed a basal diet + 200 mg/kg oregano essential oil + 20 mg/kg cinnamaldehyde (EO2); (5) fed a basal diet + 300 mg/kg oregano essential oil + 20 mg/kg cinnamaldehyde (EO3). Compared to the control group, group EO2 exhibited higher (p < 0.05) egg production during weeks 5–8 and 1–8. EO2 had a lower feed conversion ratio than the control group during weeks 1–8. The content of monounsaturated fatty acid (MUFA) in EO2 was higher (p < 0.05) than that of the control and AGP groups. EO2 increased (p < 0.05) the abundance of Actinobacteriota and decreased the abundance of Desulfovibri in the cecum. The abundances of Anaerofilum, Fournierella, Fusobacterium, and Sutterella were positively correlated with egg production, feed conversion ratio, and average daily feed intake, while the abundances of Bacteroides, Desulfovibrio, Lactobacillus, Methanobrevibacter, and Rikenellaceae_RC9_gut_group were negatively correlated with egg production, feed conversion ratio, and average daily feed intake. Dietary supplementation with 200 mg/kg OEO and 20 mg/kg cinnamaldehyde could improve egg-production performance, decrease feed conversion ratio, and alter the fatty acid and microbial composition of eggs from late-phase laying hens.
Finite trees inside thin subsets of ${\Bbb R}^d$

Bennett, Iosevich and Taylor proved that compact subsets of ${\Bbb R}^d$, $d \ge 2$, of Hausdorff dimensions greater than $\frac{d+1}{2}$ contain chains of arbitrary length with gaps in a non-trivial interval. In this paper we generalize this result to arbitrary tree configurations.
A Pohozaev-type formula and Quantization of Horizontal Half-Harmonic Maps

In a recent paper the first and the third authors introduced the notion of horizontal \alpha-harmonic map, with respect to a given C^1 planes distribution P_T on all R^m. The goal of this paper is to investigate compactness and quantization properties of sequences of horizontal 1/2- harmonic maps u_k in 1D. The quantization analysis is obtained through a precise asymptotic development of the energy of u_k in the neck regions and a subtle application of new Pohozaev-type formulae.
Edge effect on vascular epiphytes in a subtropical Atlantic Forest fragment

Epiphytes are efficient indicators of environmental quality. The Atlantic Forest is a hotspot for epiphyte richness; however, it is experiencing one of the highest rates of degradation, exposing epiphytes to edge effects. This study aimed to evaluate the floristic composition and richness of vascular epiphytes and their relationship with phorophyte features and microenvironmental variables at the edge and in the interior of a subtropical Atlantic Forest fragment in Brazil. Twenty-five trees were analyzed, respectively, at the edge and in the interior of the fragment. Height and diameter of phorophytes, temperature, relative air humidity, photosynthetically active radiation and canopy opening were measured. A total of 41 epiphytic species were recorded, 40 occurring in the interior and 23 at the edge. Orchidaceae, Bromeliaceae, and Polypodiaceae were the richest families, representing 75% of all species. The average number of species per tree in the interior was twice that for the edge. Pleopeltis pleopeltifolia, Microgramma squamulosa, M. vacciniifolia and Rhipsalis teres concentrated great biomass in both environments, with twice as much in the interior. Epiphyte richness and biomass was lower on thinner trees with more open canopies at the edge. Our results indicate that the forest interior is more beneficial for epiphytes, which are sensitive to environmental changes caused by the edge effect. The contrast between the epiphytic communities of the edge and the interior reveals the need to increase richness and abundance of native trees and prevent cattle grazing, the planting of exotic species and more human settlements in the habitat matrix.
The framed little 2‐discs operad and diffeomorphisms of handlebodies

The framed little 2‐discs operad is homotopy equivalent to a cyclic operad. We show that the derived modular envelope of this cyclic operad (that is, the modular operad freely generated in a homotopy invariant sense) is homotopy equivalent to the modular operad made from classifying spaces of diffeomorphism groups of 3‐dimensional handlebodies with marked discs on their boundaries. A modification of the argument provides a new and elementary proof of Costello's theorem that the derived modular envelope of the associative operad is homotopy equivalent to the ‘open string’ modular operad made from moduli spaces of Riemann surfaces with marked intervals on the boundary. Our technique also recovers a theorem of Braun that the derived modular envelope of the cyclic operad that describes associative algebras with involution is homotopy equivalent to the modular operad made from moduli spaces of unoriented Klein surfaces with open string gluing.
An approximation algorithm for blocking of an experimental design

Blocked randomized designs are used to improve the precision of treatment effect estimates compared to a completely randomized design. A block is a set of units that are relatively homogeneous and consequently would tend to produce relatively similar outcomes if the treatment had no effect. The problem of finding the optimal blocking of the units into equal sized blocks of any given size larger than two is known to be a difficult problem—there is no polynomial time method guaranteed to find the optimal blocking. All available methods to solve the problem are heuristic methods. We propose methods that run in polynomial time and guarantee a blocking that is provably close to the optimal blocking. In all our simulation studies, the proposed methods perform better, create better homogeneous blocks, compared with the existing methods. Our blocking method aims to minimize the maximum of all pairwise differences of units in the same block. We show that bounding this maximum difference ensures that the error in the average treatment effect estimate is similarly bounded for all treatment assignments. In contrast, if the blocking bounds the average or sum of these differences, the error in the average treatment effect estimate can still be large in several treatment assignments.
An isoperimetric inequality on the ℓp balls

The normalised volume measure on the $\ell_p^n$ unit ball ($1\leq p\leq 2$) satisfies the following isoperimetric inequality: the boundary measure of a set of measure $a$ is at least $cn^{1/p}\tilde{a}\log^{1-1/p}(1/\tilde{a})$, where $\tilde{a}=\min(a,1-a)$.
Twisted patterns in large subsets of $\mathbb{Z}^N$

Let $E \subset \mathbb{Z}^N$ be a set of positive upper Banach density and let $\Gamma < \operatorname{GL}_N(\mathbb{Z})$ be a finitely generated, strongly irreducible subgroup whose Zariski closure in $\operatorname{GL}_N(\mathbb{R})$ is a Zariski connected semisimple group with no compact factors. Let $Y$ be any set and suppose that $\Psi : \mathbb{Z}^N \rightarrow Y$ is a $\Gamma$-invariant function. We prove that for every positive integer $m$, there exists a positive integer $k$ with the property that for every finite set $F \subset \mathbb{Z}^N$ with $|F| = m$, we have \[ \Psi(kF) \subset \Psi(E-b) \quad \textrm{for some $b \in E$}. \] Furthermore, if $E$ is an aperiodic Bohr$_o$-set, we can choose $k = 1$ and $b = 0$. As one of many applications of this result, we show that if $E_o \subset \mathbb{Z}$ has positive upper Banach density, then, for any integer $m$, there exists an integer $k$ with the property for \emph{every} finite set $F \subset \mathbb{Z}$, we can find $x,y,z \in E_o$ such that \[ k^2 F \subset \big\{ (u-x)^2 + (v-y)^2 - (w-z)^2 \, : \, u,v,w \in E_o \big\}. \] In particular, if $E_o \subset \mathbb{Z}$ is an aperiodic Bohr$_o$-set, then every integer can be written on the form $u^2 + v^2 - w^2$ for some $u,v,w \in E_o$. Our techniques use recent results by Benoist-Quint and Bourgain-Furman-Lindenstrauss-Mozes on equidistribution of random walks on automorphism groups of tori.
The nonlinear stability of the trivial solution to the Maxwell-Born-Infeld system

In this article, we use an electromagnetic gauge-free framework to establish the existence of small-data global solutions to the Maxwell-Born-Infeld (MBI) system on the Minkowski spacetime background in 1+3 dimensions. Because the nonlinearities in the system have a special null structure, we are also able to show that these solutions decay at least as fast as solutions to the linear Maxwell-Maxwell system. In addition, we show that on any Lorentzian manifold, the MBI system is hyperbolic in the interior of the field-strength regime in which its Lagrangian is real-valued.
Typical points and families of expanding interval mappings

We study parametrised families of piecewise expanding interval mappings $T_a \colon [0,1] \to [0,1]$ with absolutely continuous invariant measures $\mu_a$ and give sufficient conditions for a point $X(a)$ to be typical with respect to $(T_a, \mu_a)$ for almost all parameters $a$. This is similar to a result by D. Schnellmann, but with different assumptions.
The non-linear sewing lemma I: weak formulation

We introduce a new framework to deal with rough differential equations based on flows and their approximations. Our main result is to prove that measurable flows exist under weak conditions, even solutions to the corresponding rough differential equations are not unique. We show that under additional conditions of the approximation, there exists a unique Lipschitz flow. Then, a perturbation formula is given. Finally, we link our approach to the additive, multiplicative sewing lemmas and the rough Euler scheme.
Educational Intervention in Promoting Fatty Liver Preventive Behaviors in Women: Using the Protection Motivation Theory

Background: The aim of this study was to determine the effect of educational intervention on improving the preventive behaviors of fatty liver in women referring to comprehensive health service centers in Bardaskan using the protection motivation theory (PMT). Materials and Methods: This quasi-experimental study was conducted on women aged 18-59 in Bardaskan in 2020. The sample size was determined as 128 according to the suggestion (Cohen), including 64 experimental and 64 control samples. The participants completed a researcher-made questionnaire consisting of three parts (demographic variables, constructs of PMT, and fatty liver prevention behaviors). The educational intervention for the experimental group was performed in 12 one-hour sessions over 4 weeks using lectures, group discussions, questions and answers, brainstorming, substitution experiences, and delivery of the designed educational booklet. Two months after the completion of the educational intervention, the questionnaire was completed again by all participants. The obtained data were analyzed by SPSS 21 using descriptive statistics, Chi-square test, independent t test, paired t test, ANCOVA test, and linear regression test. Results: There was a significant difference between the mean scores of perceived susceptibility (P<0.001), perceived severity (P=0.002), perceived external and internal rewards (P=0.010), response efficiency (P=0.010), perceived cost (P<0.001), and behavior (P=0.028) between the experimental and control groups after the educational intervention. Conclusion: Educational intervention based on PMT led to behavior modifications to promote the preventive behaviors of the fatty liver.
A new statistical damage model for true triaxial pre-and post-peak behaviors of rock considering intermediate principal stress and initial compaction effects

Deep underground engineering excavation will induce complex change in the true three-dimensional stress state of the surrounding rock, causing rock damage and then leading to a change in mechanical properties. In this research, the true triaxial compression tests are conducted to study the influence of σ2 and σ3 on the mechanical properties of marble, such as the characteristic strength (crack initiation stress σci, damage stress σcd, peak strength σp, and residual strength σr), post-peak deformation, ductility and brittleness. The peak strength σp, crack initiation stress σci and damage stress σcd of rock increase with the increase in σ2, while the variation of residual strength σr with σ2 is different from that of peak strength. As σ2 increases or σ3 decreases, the pre-peak plasticity of the rock decreases, the post-peak curve shape of the rock changes significantly, and the overall shape of the post-peak curve transforms from Class I to Class II. The Mogi-Coulomb strength criterion with intermediate principal stress effect was used to characterize the rock microelement strength, and then the new statistical damage constitutive model considering the initial compaction effect and damage threshold was proposed, and the model validation was carried out based on the experimental results and the effects of the proposed model parameters m and F0 on the rock strength and post-peak curve morphology were further explored.
Characteristic varieties of algebraic curves

A procedure for calculation of fundamental groups for the complements to algebraic curves in complex projective plane was found by Zariski and van Kampen ([Z],[vK]). Their methods yielded several important calculations and results on the fundamental groups of the complements (cf. for example [L2] for references). However, only limited information was obtained about their algebraic structure or what actually affects the complexity of these fundamental groups. This paper is a result of attempts to find alternative ways for calculating the fundamental groups of the complements or at least some invariants of these groups. The invariants of the fundamental groups, which we consider here, are certain subvarieties of complex tori C. They were called characteristic varieties in [L3]. These subvarieties are unions of translated subtori, as follows from recent work [Ar]. We calculate these subtori in terms of local type of singularities and dimensions of linear systems which we attach to the configuration of singularities of the curve. These characteristic varieties can be defined as follows. Let C = ∪1≤i≤rCi be an algebraic curve in C and π1 = π1(C 2 − C) be the fundamental group of its complement. Then π1/π ′ 1 is isomorphic to Z r and acts on π 1/π ′′ 1 by conjugation. This makes π 1/π ′′ 1 into a module over the group ring of π1/π ′ 1. The latter is just the ring of Laurent polynomials Z[t1, t −1 1 , . , tr, t −1 r ]. After tensoring with C, we obtain a C[π1/π ′ 1]-module π ′ 1/π ′′ 1 ⊗C. The support of