Miracle-dz/UniFAR-FTUs huggingface dataset:
Constructions of vector-valued modular forms of rank four and level one

This paper studies modular forms of rank four and level one. There are two possibilities for the isomorphism type of the space of modular forms that can arise from an irreducible representation of the modular group of rank four, and we describe when each case occurs for general choices of exponents for the [Formula: see text]-matrix. In the remaining sections we describe how to write down the corresponding differential equations satisfied by minimal weight forms, and how to use these minimal weight forms to describe the entire graded module of holomorphic modular forms. Unfortunately, the differential equations that arise can only be solved recursively in general. We conclude the paper by studying the cases of tensor products of two-dimensional representations, symmetric cubes of two-dimensional representations, and inductions of two-dimensional representations of the subgroup of the modular group of index two. In these cases, the differential equations satisfied by minimal weight forms can be solved exactly.
Disk-sphere field duality theorem

This paper presents a new reformulated theorem for fields embedded on a sphere or a disk. We focus in particular on the associated sphere of a disk when closing its only one boundary. We call this the disk-sphere duality theorem for the study of fields topological properties. For that purpose, we use the Poincar{\'e}-Hopf theorem and the boundary number theorem to firmly support our developments. In this context, the state of a $n$-symmetry direction field will be analyzed to show that disk-sphere field duality is closely related to the behavior near the disk's boundary.
Perverse schobers and wall crossing

For a balanced wall crossing in geometric invariant theory, there exist derived equivalences between the corresponding GIT quotients if certain numerical conditions are satisfied. Given such a wall crossing, I construct a perverse sheaf of categories on a disk, singular at a point, with half-monodromies recovering these equivalences, and with behaviour at the singular point controlled by a GIT quotient stack associated to the wall. Taking complexified Grothendieck groups gives a perverse sheaf of vector spaces: I characterise when this is an intersection cohomology complex of a local system on the punctured disk.
Time‐dependent finite element simulations of a shear‐thinning viscoelastic fluid with application to blood flow

A new finite element method is developed to simulate time‐dependent viscoelastic shear‐thinning flows characterized by the generalized Oldroyd‐B model. The focus of the algorithm is improved stability through a free‐energy dissipative scheme by using low‐order piecewise‐constant finite element approximations for stress. The algorithm is further modified by incorporating a pressure‐projection method, a DG‐upwinding scheme, a symmetric interior penalty DG method to solve the elliptic pressure‐update equation and a geometric multigrid preconditioner. The improved stability and cost to accuracy is compared when using higher order discontinuous bilinear approximation, where in addition, we consider the influence of a slope limiter for these elements. The algorithm is applied to the 2D start‐up‐driven cavity problem, and the stability of the free energy is illustrated and compared between element choices. An application of the model to modelling blood in small arterioles and channels is considered by simulating pulsatile blood flow through a stenotic arteriole. The individual influences of viscoelasticity and shear‐thinning within the generalized Oldroyd‐B model are investigated by comparing results to the Newtonian, generalized Newtonian and Oldroyd‐B models. Copyright © 2014 John Wiley & Sons, Ltd.
Attitudes toward Self-Disclosure on Facebook: A Review of Perception, Emotion and Behavior in University Students

A number of social networking platforms have emerged as a result of the development of information and communication technology which have become increasingly user-friendly and full with valuable features. The social networking site with most users is Facebook. Teenagers, particularly college students use Facebook most frequently to study, gain information, entertain themselves and connect with others through self-disclosing personal information on the Facebook profile page. This quantitative study aimed to analyze the attitude of pedagogical students regarding self-disclosure on Facebook as represented through cognition, emotion and behavior concerning academic achievement. The survey was completed by 535university student’s majority in pedagogy. There were 41 students who used it for less than three years between three to five years by 218 students and 276 students who use it more than five years. The questionnaire was self-reported by participants to assess university students' attitudes toward self-disclosure on Facebook. The results indicate that pedagogical students with excellent academic achievement and more than five years of Facebook experience had the highest-level attitude toward self-disclosure on Facebook. The results indicate a positive relationship between cognition, emotion and influence factors students' Facebook attitudes. Future research on methods that enhance student positive disclosure can benefit from this study. Future research should examine how self-disclosure on Facebook relates to other aspects, such as Facebook usage time, financial state and perception of advantages and its disadvantages of Facebook in order to evaluate students' attitudes objectively.
Effect of feeding management practices on water intake in Tharparkar and Rathi cattle of Indian hot arid zone

The present study was conducted to assess the effects of grazing and stall feeding on water intake in Tharparkar and Rathi cattle in their native tract of hot arid zone. Lactating cattle (Tharparkar 10; Rathi 10) and heifers (Tharparkar 10; Rathi 10) of each breed were divided into two groups, forming grazing and stall-fed group at Jodhpur and Bikaner districts of Rajasthan. Observations were recorded for water intake, dry matter intake and milk yield in the morning and afternoon regularly, twice weekly for six weeks during each season (summer, winter and rainy) continuously for two years. Water intake in lactating cows and heifers of both the breeds followed the pattern of THI during summer season. Rathi cows had higher water intake/kg W0.75 than Tharparakar cows, however, Tharparkar heifers had higher water intake/kg W0.75 than Rathi heifers. Grazing Rathi cows had significantly higher water intake than stall-fed cows. Study revealed that Tharparkar cows had lesser water intake per kg W0.75 and per kg milk yield basis; however, Rathi heifers had lesser water intake per kg W0.75 basis in their native tract.
On Shimura's decomposition

Let k be an odd integer ≥ 3 and N be a positive integer such that 4|N. Let χ be an even Dirichlet character modulo N. Shimura decomposes the space of half-integral weight cusp forms Sk/2(N,χ) as a direct sum where F runs through all newforms of weight k - 1, level dividing N/2 and character χ2, the space Sk/2(N,χ,F) is the subspace of forms that are "Shimura equivalent" to F, and the space S0(N,χ) is the subspace spanned by single-variable theta-series. The explicit computation of this decomposition is important for practical applications of a theorem of Waldspurger relating the critical values of L-functions of quadratic twists of newforms of even integral weight to coefficients of modular forms of half-integral weight. In this paper, we give a more precise definition of the summands Sk/2(N,χ,F) whilst proving that it is equivalent to Shimura's definition. We use our definition to give a practical algorithm for computing Shimura's decomposition, and illustrate this with some examples.
Perfil de ácidos grasos en aceites de cocina de mayor venta en Medellín-Colombia

Antecedentes: el perfil de acidos grasos en los aceites de cocina tiene repercusiones en la salud humana. Objetivo: determinar el perfil de acidos grasos de algunos aceites de empleo casero, previo uso. Materiales y metodos: se seleccionaron14 marcas comerciales de aceites (oliva, canola, girasol y mezclas de aceites) segun las ventas reportadas en un hipermercado de Medellin - Colombia. El perfil de acidos grasos se determino por cromatografia de gases y se analizaron las diferencias entre los tipos de aceites. Resultados: comparando los tipos de aceites presento mayor porcentaje de acidos grasos saturados la mezcla de aceites (16,9±1,5%) (p=0,02), de monoinsaturados, oliva (78,1±0,4%) y canola (62,4±0,7%) (p=0,01) y de poliinsaturados, mezclas (54,7±2,4%) y girasol (52,4±5,2) (p=0,02). En todos los aceites los acidos grasos predominantes fueron: de saturados el palmitico, de monoinsaturados el oleico y de poliinsaturados el linoleico. El aceite de canola mostro mayor aporte de α-linolenico (8,1±1,5%) (p=0,04), mayor relacion insaturados/saturados (12,0±0,1%) (p=0,02) y menor linoleico/linolenico (2,4±0,4%) (p=0,02). El aporte de trans vario entre 0,9±0,9 y 1,8±1,3% sin diferencias significativas (p=0,17). Conclusiones: el aceite con mejor perfil de acidos grasos, por el mayor aporte de α-linolenico, mayor relacion insaturados/saturados y menor linoleico/linolenico fue el de canola.
Classification of External Zonotopal Algebras

In this paper we work with power algebras associated to hyperplane arrangements. There are three main types of these algebras, namely, external, central, and internal zonotopal algebras. We classify all external algebras up to isomorphism in terms of zonotopes. Also, we prove that unimodular external zonotopal algebras are in one to one correspondence with regular matroids. For the case of central algebras we formulate a conjecture.
Some upper bounds for the signless Laplacian spectral radius of digraphs

Let $G=(V(G) ,E(G))$ be a digraph without loops and multiarcs, where $V(G)=\{v_1,v_2,\ldots,v_n\}$ and $E(G)$ are the vertex set and the arc set of $G$, respectively. Let $d_i^{+}$ be the outdegree of the vertex $v_i$. Let $A(G)$ be the adjacency matrix of $G$ and $D(G)=\textrm{diag}(d_1^{+},d_2^{+},\ldots,d_n^{+})$ be the diagonal matrix with outdegrees of the vertices of $G$. Then we call $Q(G)=D(G)+A(G)$ the signless Laplacian matrix of $G$. The spectral radius of $Q(G)$ is called the signless Laplacian spectral radius of $G$, denoted by $q(G)$. In this paper, some upper bounds for $q(G)$ are obtained. Furthermore, some upper bounds on $q(G)$ involving outdegrees and the average 2-outdegrees of the vertices of $G$ are also derived.
Equivalent Characterizations of the Spectra of Graphs and Applications to Measures of Distance-regularity

The spectrum of a graph usually provides a lot of information about its combinatorial structure. Moreover, from the spectrum, the so-called predistance polynomials can be defined, as a generalization, for any graph, of the distance polynomials of a distance-regular graph. Going further, the preintersection numbers generalize the intersection numbers of a distance-regular graph. This paper describes, for any graph, the closed relationships between its spectrum, predistance polynomials, and preintersection numbers. Then, some applications to derive combinatorial properties of the given graph, most of them related to some fundamental characterizations of distance-regularity, are presented. In particular, the so-called `spectral excess theorem' is revisited. This result states that a connected regular graph is distance-regular if and only if its spectral excess, which is a value computed from the spectrum, equals the average excess, that is, the mean of the numbers of vertices at maximum distance from every vertex.
Completely Sidon sets in $C^*$-algebras (New title)

A sequence in a $C^*$-algebra $A$ is called completely Sidon if its span in $A$ is completely isomorphic to the operator space version of the space $\ell_1$ (i.e. $\ell_1$ equipped with its maximal operator space structure). The latter can also be described as the span of the free unitary generators in the (full) $C^*$-algebra of the free group $\F_\infty$ with countably infinitely many generators. Our main result is a generalization to this context of Drury's classical theorem stating that Sidon sets are stable under finite unions. In the particular case when $A=C^*(G)$ the (maximal) $C^*$-algebra of a discrete group $G$, we recover the non-commutative (operator space) version of Drury's theorem that we recently proved. We also give several non-commutative generalizations of our recent work on uniformly bounded orthonormal systems to the case of von Neumann algebras equipped with normal faithful tracial states.
HRQoL and nutritional well-being dissimilarities between two different online collection methods: Value for digital health implementation

Background Online health data collection has gained a reputation over the last years to record and process information about health issues for implementing digital health. Objective The research aim was to appraise two online methods (open and rewarded) to collect information about HRQoL and nutritional well-being and to compare the results between both surveyed populations. Methods This cross-sectional study is framed on the NUTRiMDEA project. Online data through two different web-based methods (open survey and rewarded survey) were retrieved to assemble data related to sociodemographic, lifestyle (diet, physical activity and sleep patterns) and general health aspects, as well as HRQoL by an evidence-based form such as the SF-12 questionnaire, the IPAQ survey, and MEDAS-14, participants were adults (>18 years old). Results Overall, 17,332 participants responded to the open survey (OS, n = 11,883) or the rewarded survey (RS, n = 5449). About 65.1% of the participants were female, while the mean age was in the range of 40–70 years. There were significant differences (p < 0.05) between surveyed populations in sociodemographic, lifestyle (diet and physical activity), health and HRQoL data. Conclusions This investigation implemented an evidence-based online questionnaire that collected demographic, lifestyle factors, phenotypic and health-related aspects as well as compared differential outcomes in HRQoL and nutritional/lifestyle well-being depending on the online mode data collection. Findings demonstrated dissimilarities in most aspects of health, HRQoL, dietary intake and physical activity records between both populations. Overall, OS sample was characterized as a healthier population with superior lifestyle habits than RS participants.
Buildings, spiders, and geometric Satake

Abstract Let $G$ be a simple algebraic group. Labelled trivalent graphs called webs can be used to produce invariants in tensor products of minuscule representations. For each web, we construct a configuration space of points in the affine Grassmannian. Via the geometric Satake correspondence, we relate these configuration spaces to the invariant vectors coming from webs. In the case of $G= \mathrm{SL} (3)$, non-elliptic webs yield a basis for the invariant spaces. The non-elliptic condition, which is equivalent to the condition that the dual diskoid of the web is $\mathrm{CAT} (0)$, is explained by the fact that affine buildings are $\mathrm{CAT} (0)$.
Estimating vaccine efficacy from small outbreaks

Let C-sub-V and C-sub-0 denote the number of cases among vaccinated and unvaccinated individuals, respectively, and let u be the proportion of individuals vaccinated. The quantity e e 1--(1--u)C-sub-Vs(uC-sub-0) e 1--(relative attack rate) is the most used estimator of the effectiveness of a vaccine to protect against infection. For a wide class of vaccine responses, a family of transmission models and three types of community settings, this paper investigates what e actually estimates. It does so under the assumption that the community is large and the vaccination coverage is adequate to prevent major outbreaks of the infectious disease, so that only data on minor outbreaks are available. For a community of homogeneous individuals who mix uniformly, it is found that e estimates a quantity with the interpretation of 1--(mean susceptibility, per contact, of vaccinees relative to unvaccinated individuals). We provide a standard error for e in this setting. For a community with some heterogeneity e can be a very misleading estimator of the effectiveness of the vaccine. When individuals have inherent differences, e estimates a quantity that depends also on the inherent susceptibilities of different types of individual and on the vaccination coverage for different types. For a community of households, e estimates a quantity that depends on the rate of transmission within households and on the reduction in infectivity induced by the vaccine. In communities that are structured, into households or age-groups, it is possible that e estimates a value that is negative even when the vaccine reduces both susceptibility and infectivity. Copyright Biometrika Trust 2004, Oxford University Press.
Quality inspection system for metal parts based on machine vision

Aiming at the problems of low accuracy and complex algorithm design for defect detection and dimensional measurement of metal parts, this paper designs a duplex inspection system using machine vision technology, which is connected to a multi-channel acquisition board and can achieve high efficiency in image acquisition and processing. The HALCON software is used to pre-process the images with algorithms such as threshold segmentation, morphological processing and image enhancement, and the MLP classifier is used to classify defects in the defect detection. The test results show that the system achieves high accuracy and high efficiency quality inspection, which brings some value to promote industrial automation and intelligent development.
Non-Singularity Conditions for Two Z-Matrix Types

A real square matrix whose non-diagonal elements are non-positive is called a Z-matrix. This paper shows a necessary and sufficient condition for non-singularity of two types of Z-matrices. The first is for the Z-matrix whose row sums are all non-negative. The non-singularity condition for this matrix is that at least one positive row sum exists in any principal submatrix of the matrix. The second is for the Z-matrix which satisfies where . Let be the ith row and the jth column element of , and be the jth element of . Let be a subset of which is not empty, and be the complement of if is a proper subset. The non-singularity condition for this matrix is such that or such that for . Robert Beauwens and Michael Neumann previously presented conditions similar to these conditions. In this paper, we present a different proof and show that these conditions can be also derived from theirs.
Preoperative Cancer Antigen 125 Level as Predictor for Complete Cytoreduction in Ovarian Cancer: A Prospective Cohort Study and Systematic Review

Simple Summary Standard treatment of advanced stage epithelial ovarian cancer consists of cytoreductive surgery (CRS) and chemotherapy. Prolonged progression free and overall survival is correlated with the amount of residual tumor after CRS. However, cytoreductive surgery is an extensive procedure with a considerable risk of postoperative complications. Therefore, it would be valuable to have parameters that can predict the surgical outcome. In this study, we evaluated the value of the blood tumor marker CA-125 to predict complete CRS to no residual tumor. The results of our study suggest that CA-125 levels ≤35 kU/L significantly predict the surgical outcome in patients who underwent interval cytoreductive surgery, but this parameter cannot be used as an independent predictor. This contrasts with the outcome of our systematic review with mainly retrospective data, which found CA-125 as an independent predictive variable. Abstract Background: The tumor marker ‘cancer antigen 125’ (CA-125) plays a role in the management of women with advanced stage ovarian cancer. This study aims to describe the predictive value of pre-treatment CA-125 level and the reduction after neoadjuvant chemotherapy (NACT) on surgical outcome. Methods: A systematic review and a prospective clinical study were performed. Multiple databases were searched from database inception to April 2022. The clinical study is part of a randomized controlled trial named “PlaComOv-study”. A regression analysis was performed to demonstrate correlations between preoperative CA-125 levels, CA-125 reduction after NACT, and surgical outcome. Results: Fourteen relevant articles were analyzed of which eleven reported that lower preoperative CA-125 levels were associated with a higher probability of complete cytoreduction. In the clinical study, 326 patients with FIGO stage IIIB-IV ovarian cancer who underwent CRS were enrolled from 2018 to 2020. Patients who underwent interval CRS with preoperative CA-125 levels ≤35 kU/L had higher odds of achieving complete CRS than patients with CA-125 level >35 kU/L (85% vs. 67%, OR 2.79, 95%CI 1.44–5.41, p = 0.002). In multivariable analysis with presence of ascites and peritoneal carcinomatosis, normalized preoperative CA-125 did not appear as a significant predictor for complete CRS. Conclusions: In literature, preoperative CA-125 levels ≤35 kU/L were associated with a significant higher percentage of complete CRS in univariable analysis. According to our cohort study, preoperative CA-125 level ≤35 kU/L cannot independently predict surgical outcome either for primary or interval CRS.
Simple permutations with order $4n + 2$ by means of Pasting and Reversing

The problem of genealogy of permutations has been solved partially by Stefan (odd order) and Acosta-Hum\'anez \& Bernhardt (power of two). It is well known that Sharkovskii's theorem shows the relationship between the cardinal of the set of periodic points of a continuous map, but simple permutations will show the behaviour of those periodic points. Recently Abdulla et al studied the structure of minimal $4n+2$-orbits of the continuous endomorphisms on the real line. This paper studies some combinatorial dynamics structures of permutations of mixed order $4n+2$, describing its genealogy, using Pasting and Reversing.
Maximum amplitudes of finite-gap solutions for the focusing Nonlinear Schr\"odinger Equation

In this paper we prove that the maximum amplitude of a finite-gap solution to the focusing Nonlinear Schr\"{o}dinger equation with given spectral bands does not exceed half of the sum of the length of all the bands. This maximum will be attained for certain choices of the initial phases. A similar result is also true for the defocusing Nonlinear Schr\"{o}dinger equation.
The loop problem for monoids and semigroups

Abstract We propose a way of associating to each finitely generated monoid or semigroup a formal language, called its loop problem. In the case of a group, the loop problem is essentially the same as the word problem in the sense of combinatorial group theory. Like the word problem for groups, the loop problem is regular if and only if the monoid is finite. We also study the case in which the loop problem is context-free, showing that a celebrated group-theoretic result of Muller and Schupp extends to describe completely simple semigroups with context-free loop problems. We consider right cancellative monoids, establishing connections between the loop problem and the structural theory of these semigroups by showing that the syntactic monoid of the loop problem is the inverse hull of the monoid.