Miracle-dz/UniFAR-FTUs huggingface dataset:
$\infty$-categorical monadicity and descent

Riehl and Verity have introduced an "$\infty$-cosmic" framework in which they redevelop the category theory of $\infty$-categories using 2-categorical arguments. In this paper, we begin with a self-contained review of the parts of their theory needed to discuss adjunctions and monadicity. This is applied in order to extend to the $\infty$-categorical context the classical criterion for fully faithfulness of the comparison functor induced by an adjunction. We discuss the relation with previous work in the literature---which primarily uses model-categorical techniques---and indicate applications to descent theory.
Genetic Evaluation and Phenotypic Trend for Some Lactation Traits of Dromedary Camels

: There is a paucity of published work on genetic evaluation of lactation traits in camels using modern methodologies such as MTDFREML (Maximum Likelihood Restricted by Multiple Trait Derivatives Free of Maximum). The current study aimed to estimate the genetic parameters (direct heritability, repeatability and breeding values), and to estimate the phenotypic trend. The studies were including total milk yield (TMY/kg), day milk yield (DMY/ kg) and length of lactation period (LP). Actual means of TMY, DMY and LP were 1464.90 kg, 4.00 and 418.84, respectively. LP was significantly (P≤0.05) affected by the year and season of calving. Additive heritability (h2a) estimates for TMY, DMY and LP was 0.25, 0.30 and 0.17, respectively. These are promising values for the potential of genetic improvement. Repeatability (t) values recorded a medium value for LP (0.19), while the values were high for both TMY (0.36) and DMY (0.43). The range of predicted breeding values (PBVs) of animals for TMY, DMY and LP were 143.07 kg, 1.5 kg and 113.9 days, respectively. Regression coefficients for she-camels showed a negative annual phenotypic trend (PT) of about -3.58 kg and -0.012 kg per year for TMY and DMY, respectively. A genetic improvement program should be followed to allow exploiting the higher estimates of genetic parameters by relying on animals with positive breeding values.
The $L^p$ Carleman estimate and a partial data inverse problem

We construct an explicit Green's function for the conjugated Laplacian $e^{-\omega \cdot x/h}\Delta e^{-\omega \cdot x/h}$, which let us control our solutions on roughly half of the boundary. We apply the Green's function to solve a partial data inverse problem for the Schr\"odinger equation with potential $q \in L^{n/2}$. We also use this Green's function to derive $L^p$ Carleman estimates similar to the ones in Kenig-Ruiz-Sogge \cite{krs}, but for functions with support up to part of the boundary.
On the semiclassical Laplacian with magnetic field having self-intersecting zero set

This paper is devoted to the spectral analysis of the Neumann realization of the 2D magnetic Laplacian with semiclassical parameter h > 0 in the case when the magnetic field vanishes along a smooth curve which crosses itself inside a bounded domain. We investigate the behavior of its eigenpairs in the limit h $\rightarrow$ 0. We show that each crossing point acts as a potential well, generating a new decay scale of h 3/2 for the lowest eigenvalues, as well as exponential concentration for eigenvectors around the set of crossing points. These properties are consequences of the nature of associated model problems in R 2 for which the zero set of the magnetic field is the union of two straight lines. In this paper we also analyze the spectrum of model problems when the angle between the two straight lines tends to 0.
Long-time behavior of a nonlocal Cahn-Hilliard equation with reaction

In this paper we study the long-time behavior of a nonlocal Cahn-Hilliard system with singular potential, degenerate mobility, and a reaction term. In particular, we prove the existence of a global attractor with finite fractal dimension, the existence of an exponential attractor, and convergence to equilibria for two physically relevant classes of reaction terms.
Affection Deprivation and Weathering: An Exploratory Study of Black and African Americans’ Well-Being during COVID-19*

This study investigates factors related to the well-being of African Americans during the COVID-19 pandemic, specifically, reports of discrimination, perceived stress, and affection deprivation through the lenses of Affection Exchange Theory and the Weathering Framework. Sixty-six individuals participated in a cross-sectional survey study through an online Qualtrics questionnaire. We predicted that Black and African American participants would report experiencing more discrimination during the pandemic than other people of color (POC) due to several overlapping pathways of racism (e.g., stereotype effect, internalized racism, and systemic racism) affecting Black individuals more than others. We also predicted affection deprivation for Black and African American participants would be directly related to their perceived stress. Results from an independent samples t-test indicated no significant difference of discrimination between Black and non-Black participants. However, in post hoc analysis, there was a significant difference of discrimination between Black and White participants, illustrating the greater strain on Black individuals during the pandemic when compared to their White counterparts. Finally, correlational analysis revealed a significant positive association between affection deprivation and perceived stress for Black participants. We believe this relationship reflects an important health problem Black Americans are facing during the COVID-19 pandemic, in which isolation through COVID-19 protective measures (e.g., quarantine) are exacerbating the burden of stress they already bear. increase in perceived stress for Black and African American individuals. These findings suggest that increases in supportive communication can act as a buffer for Black and African American individuals to help reduce the negative effects of weathering and pandemic-related stress.
Axial Compression of a Thin Elastic Cylinder: Bounds on the Minimum Energy Scaling Law

We consider the axial compression of a thin elastic cylinder placed about a hard cylindrical core. Treating the core as an obstacle, we prove upper and lower bounds on the minimum energy of the cylinder that depend on its relative thickness and the magnitude of axial compression. We focus exclusively on the setting where the radius of the core is greater than or equal to the natural radius of the cylinder. We consider two cases: the “large mandrel” case, where the radius of the core exceeds that of the cylinder, and the “neutral mandrel” case, where the radii of the core and cylinder are the same. In the large mandrel case, our upper and lower bounds match in their scaling with respect to thickness, compression, and the magnitude of pre‐strain induced by the core. We construct three types of axisymmetric wrinkling patterns whose energy scales as the minimum in different parameter regimes, corresponding to the presence of many wrinkles, few wrinkles, or no wrinkles at all. In the neutral mandrel case, our upper and lower bounds match in a certain regime in which the compression is small as compared to the thickness; in this regime, the minimum energy scales as that of the unbuckled configuration. We achieve these results for both the von Kármán–Donnell model and a geometrically nonlinear model of elasticity. © 2017 Wiley Periodicals, Inc.
Linear collective collocation and Galerkin approximations for parametric and stochastic elliptic PDEs

Consider the parametric elliptic problem \begin{equation} - \operatorname{dv} \big(a(y)(x)\nabla u(y)(x)\big) \ = \ f(x) \quad x \in D, \ y \in [-1,1]^\infty, \quad u|_{\partial D} \ = \ 0, \end{equation} where $D \subset {\mathbb R}^m$ is a bounded Lipschitz domain, $[-1,1]^\infty$, $f \in L_2(D)$, and the diffusions $a$ satisfy the uniform ellipticity assumption and are affinely dependent with respect to $y$. The parametric variable $y$ may be deterministic or random. In the present paper, a central question to be studied is as follows. Assume that we have an approximation property that there is a sequence of finite element approximations with a certain error convergence rate in energy norm of the space $V:=H^1_0(D)$ for the nonparametric problem $- \operatorname{dv} \big(a(y_0)(x)\nabla u(y_0)(x)\big) = f(x)$ at every point $y_0 \in [-1,1]^\infty$. Then under what assumptions does this sequence induce a sequence of finite element approximations with the same error convergence rate for the parametric elliptic problem in the norm of the Bochner spaces $L_\infty([-1,1]^\infty,V)$ or $L_2([-1,1]^\infty,V)$? We solved this question by linear collective Taylor, collocation and Galerkin methods, based on Taylor expansions, Lagrange polynomial interpolations and Legendre polynomials expansions, respectively, on the parametric domain $[-1,1]^\infty$. Under very light conditions, we show that all these approximation methods give the same error convergence rate as that by the sequence of finite element approximations for the nonparametric elliptic problem. The parametric infinite-variate part completely disappears from the convergence rate and influences only the constant. Hence the curse of dimensionality is broken by linear methods.
Neighboring Optimal Guidance for Low-Thrust Multi-Burn Orbital Transfers

This paper presents a novel neighboring extremal approach to establish the neighboring optimal guidance (NOG) strategy for fixed-time low-thrust multi-burn orbital transfer problems. Unlike the classical variational methods which define and solve an accessory minimum problem (AMP) to design the NOG, the core of the proposed method is to construct a parameterized family of neighboring extremals around a nominal one. A geometric analysis on the projection behavior of the parameterized neighboring extremals shows that it is impossible to establish the NOG unless not only the typical Jacobi condition (JC) between switching times but also a transversal condition (TC) at each switching time is satisfied. According to the theory of field of extremals, the JC and the TC, once satisfied, are also sufficient to ensure a multi-burn extremal trajectory to be locally optimal. Then, through deriving the first-order Taylor expansion of the parameterized neighboring extremals, the neighboring optimal feedbacks on thrust direction and switching times are obtained. Finally, to verify the development of this paper, a fixed-time low-thrust fuel-optimal orbital transfer problem is calculated.
Nutritional Qualities, Physical and Organoleptic Characteristics of Cookies Resulting from the Substitution of Wheat Flour by Caterpillar Powder (Imbrasia Oyemensis)

The present work aims to study the nutritional properties of cookies, resulting from the substitution of wheat flour by caterpillar powder (Imbrasia oyemensis) . The different substitution rates were 0%, 5%, 10%, 15% and 20%. The physicochemical composition of the cookies was determined by standard methods (AOAC). A significant improvement (p<0.05) in the protein (10.1 ± 0.3 to 17.5 ± 0.6%), fat (15.1 ± 0.4 to 18.2 ± 0.1%), ash (0.57 ± 0.1 to 1.66 ± 0.8%), and fiber (0.1 ± 0.06 to 1.2 ± 0.05%) content of the cookies was observed with the substitution level. On the other hand, there was a significant decrease (p<0.05) in carbohydrate content (68.93 to 60.7 %) and a significant increase (p<0.05) in energy values (453.4 to 476.6 Kcal). At the level of the physical parameters of the cookies, it is noted on the one hand a decrease of the diameter (6.8 ± 0.05 to 6.2 ± 0.02 cm), of the spread ratio (12.84 ± 0.76 to 8.12 ± 0.43) and on the other hand an increase of the thickness (0.53 ± 0.03 to 0.76 ± 0.2 cm) and of the weight (20.37 ± 0.4 to 21.03 ± 0.3 g), as the level of substitution increases. The descriptive parameters of the cookies (color, texture, crispness, flavor, aroma, sweet taste) were also influenced with the substitution level. The hedonic test indicates that the 100% wheat cookie (BFB) was the most preferred by tasters, followed by BFC5 and BFC10. The substitution of wheat flour by caterpillar (Imbrasia oyemensis) powder has improved the nutritional properties of the cookies compared to cookies made only with wheat flour. These cookies could therefore be an alternative in the fight against protein-energy malnutrition.
On commuting matrices and exponentials

Let A and B be matrices of M_n(C). We show that if exp(A)^k exp(B)^l=exp(kA+lB) for all integers k and l, then AB=BA. We also show that if exp(A)^k exp(B)=exp(B)exp(A)^k=exp(kA+B)$ for every positive integer k, then the pair (A,B) has property L of Motzkin and Taussky. As a consequence, if G is a subgroup of (M_n(C),+) and M -> exp(M) is a homomorphism from G to (GL_n(C),x), then G consists of commuting matrices. If S is a subsemigroup of (M_n(C),+) and M -> exp(M) is a homomorphism from S to (GL_n(C),x), then the linear subspace Span(S) of M_n(C) has property L of Motzkin and Taussky.
Browkin’s discriminator conjecture

Let $q\ge 5$ be a prime and put $q^*=(-1)^{(q-1)/2}\cdot q$. We consider the integer sequence $u_q(1),u_q(2),\ldots,$ with $u_q(j)=(3^j-q^*(-1)^j)/4$. No term in this sequence is repeated and thus for each $n$ there is a smallest integer $m$ such that $u_q(1),\ldots,u_q(n)$ are pairwise incongruent modulo $m$. We write $D_q(n)=m$. The idea of considering the discriminator $D_q(n)$ is due to Browkin (2015) who, in case $3$ is a primitive root modulo $q,$ conjectured that the only values assumed by $D_q(n)$ are powers of $2$ and of $q$. We show that this is true for $n\neq 5$, but false for infinitely many $q$ in case $n=5$. We also determine $D_q(n)$ in case 3 is not a primitive root modulo $q$. Browkin's inspiration for his conjecture came from earlier work of Moree and Zumalac\'arregui (2016), who determined $D_5(n)$ for $n\ge 1$, thus establishing a conjecture of Salajan. For a fixed prime $q$ their approach is easily generalized, but requires some innovations in order to deal with all primes $q\ge 7$ and all $n\ge 1$. Interestingly enough, Fermat and Mirimanoff primes play a special role in this.
Integrating Extensive Reading into School Curriculum: A Veteran EFL Teacher’s Perspective

Numerous studies have tested the effects of extensive reading (ER) on L2 acquisition, while limited research has investigated the implementation of ER, especially in secondary L2 teaching contexts. In line with the advocacy of integrating ER into L2 curriculum, this qualitative case study explores a veteran EFL teacher’s perceptions of ER implementation and his practice of integrating ER into the school curriculum. As the English department leader of a middle school in downtown Beijing, the teacher participant, with rich experience in EFL teaching and ER implementation, initiated the compilation of several textbooks and study guides as part of the school curriculum, accompanied by in-class activities and after-class assignments. Data were collected from three in-depth interviews with the teacher participant, respectively at the beginning, in the middle, and at the end of the school year. Other sources of data include related study materials and students’ assignments. Findings of this study indicate that school-based textbooks, complemented with in-class activities and reinforced by assignments, contribute to school curriculum development and ER implementation. Based on the results of the study, an ER-curriculum integration model was proposed for further discussion and exploration.
ACCESS - II. A complete census of star formation in the Shapley supercluster - UV and IR luminosity functions

We present panoramic Spitzer/MIPS mid- and far-infrared (MIR/FIR) and GALEX ultraviolet imaging of the most massive and dynamically active system in the local Universe, the Shapley supercluster at z = 0.048, covering the five clusters that make up the supercluster core. We combine these data with existing spectroscopic data from 814 confirmed supercluster mem- bers to produce the first study of a local rich cluster including both ultraviolet and infrared luminosity functions (LFs). This joint analysis allows us to produce a complete census of star formation (both obscured and unobscured), extending down to star formation rates (SFRs) ∼0.02-0.05 Myr −1 , and quantify the level of obscuration of star formation among cluster galaxies, providing a local benchmark for comparison to ongoing and future studies of cluster galaxies at higher redshifts with Spitzer and Herschel . T heGALEX near-ultraviolet (NUV) and far-ultraviolet (FUV) luminosity functions (LFs) obtained have steeper faint-end slopes than the local field population, due largely to the contribution of massive, quiescent galaxies at MFUV −16. The 24- and 70-µm galaxy LFs for the Shapley supercluster instead have shapes fully consistent with those obtained for the Coma cluster and for the local field galaxy pop- ulation. This apparent lack of environmental dependence for the shape of the FIR luminosity function suggests that the bulk of the star-forming galaxies that make up the observed cluster infrared LF have been recently accreted from the field and have yet to have their star forma- tion activity significantly affected by the cluster environment. We estimate a global SFR of 327 Myr −1 over the whole supercluster core, of which just ∼20 per cent is visible directly in the ultraviolet continuum and ∼80 per cent is reprocessed by dust and emitted in the infrared. The level of obscuration (LIR/LFUV) in star-forming galaxies is seen to increase linearly with LK over 2 orders of magnitude in stellar mass.
Research Paper Return to Sports Activity in Anterior Cruciate Ligament Reconstruction: 4-Strand Hamstring vs Quad riceps Tendon

Background: Graft type selection is still a controversial issue in anterior cruciate ligament (ACL) reconstruction. The type of graft is a determinant of return to sport and its quality. Objectives: This study aims to evaluate results and rate of return to sport using quadriceps autograft compared to hamstring autograft. Methods: The present prospective cohort study investigated the results of using quadriceps and hamstring autografts in athletes with an ACL tear. Our variables included age, sex, and body mass index, type of sports activity, infection, meniscus tear and chondral lesion, time and quality of return to sport, range of motion, KT-1000, Lachman and knee injury and osteoarthritis outcome score, international knee documentation committee grade, and Lysholm score. Results: A total of 71 out of 139 studied patients were operated on hamstring autografts and 68 patients by quadriceps autografts. The patients showed no significant differences (P>0.05) in terms of age, sex, body mass index, sports group, and meniscus tear. In the final follow-up, the chondral lesion was 26.47 vs 16.90, anterior knee pain was 5.8 vs 2.81, and the return to sport was 71.64 vs 78.87 in the quadriceps group vs the hamstring group. The extension loss involved 2 patients per group. The scores of the international knee documentation committee and knee injury and osteoarthritis outcome, the Lysholm test, KT-1000, and the Lachman test had no significant differences in the two groups. Conclusion: The results of the present study indicated that the use of both quadriceps and hamstring autografts was appropriate for the ACL tear. Also, the orthopedic surgeon should be responsible for deciding to select one of the two grafts.
CLAN CULTURE AND FAMILY OWNERSHIP IN CHINA

This study explores a cultural determinant of family ownership concentration in China’s private business. Exploiting regional variations in local clan culture intensity, we find robust evidence that stronger clan culture influences are associated with higher family ownership concentration. Relying on the existence of movers, we separate the impact of inherited clan culture from that of external environmental factors and show that the former remains significantly positive. Our IV estimates further establish the causal effect of Chinese clan culture on family ownership concentration. In the end, we also provide additional evidence for underlying mechanisms.
On harmonic Bloch-type mappings

Let f be a complex-valued harmonic mapping defined in the unit disk . We introduce the following notion: we say that f is a Bloch-type function if its Jacobian satisfies This gives rise to a new class of functions which generalizes and contains the well-known analytic Bloch space. We give estimates for the schlicht radius, the growth and the coefficients of functions in this class. We establish an analogue of the theorem which, roughly speaking, states that for analytic is Bloch if and only if is univalent.
Randomized Sampling for Basis Function Construction in Generalized Finite Element Methods

In the context of generalized finite element methods for elliptic equations with rough coefficients $a(x)$, efficiency and accuracy of the numerical method depend critically on the use of appropriate basis functions. This work explores several random sampling strategies for construction of basis functions, and proposes a quantitative criterion to analyze and compare these sampling strategies. Numerical evidence shows that the optimal basis functions can be well approximated by a random projection of generalized eigenvalue problem onto subspace of $a$-harmonic functions.
Gravitational wave production by collisions: more bubbles

We re-examine the production of gravitational waves by bubble collisions during a first-order phase transition. The spectrum of the gravitational radiation is determined by numerical simulations using the ‘envelope approximation’. We find that the spectrum rises as f3.0 for small frequencies and decreases as f−1.0 for high frequencies. Thus, the fall-off at high frequencies is significantly slower than previously stated in the literature. This result has direct impact on detection prospects for gravity waves originating from a strong first-order electroweak phase transition at space-based interferometers, such as LISA and BBO. In addition, we observe a slight dependence of the peak frequency on the bubble wall velocity.
A GENERAL RELATIVISTIC EXTERNAL COMPTON-SCATTERING MODEL FOR TeV EMISSION FROM M87

M87 is the first detected non-blazar extragalactic tera-electron-volt (TeV) source with rapid variation and a very flat spectrum in the TeV band. To explain the two peaks in the spectral energy distribution of the nucleus of M87, which is similar to that of blazars, the most commonly adopted models are the synchrotron self-Compton-scattering models and the external inverse Compton (EIC) scattering models. Considering that there is no correlated variation in the soft band (from radio to X-ray) matching the TeV variation and that the TeV sources should not suffer from γγ absorption due to the flat TeV spectrum, the EIC models are advantageous in modeling the TeV emission from M87. In this paper, we propose a self-consistent EIC model to explain the flat TeV spectrum of M87 within the framework of fully general relativity, where the background soft photons are from the advection-dominated accretion flow around the central black hole, and the high-energy electrons are from the mini-jets that are powered by the magnetic reconnection in the main jet. In our model, both the TeV flares observed in the years 2005 and 2008 could be well explained: the γγ absorption for TeV photons is very low, even inside the region very close to the black hole 20Rg ∼ 50Rg; at the same region, the average EIC cooling time (∼102 ∼ 103 s) is short, which is consistent with the observed timescale of the TeV variation. Furthermore, we also discuss the possibility that the accompanying X-ray flare in 2008 is due to the direct synchrotron radiation of the mini-jets.