Miracle-dz/UniFAR-FTUs huggingface dataset:
The number of points from a random lattice that lie inside a ball

This thesis contains four papers, where the first two are in the area of geometry of numbers, the third is about class group statistics and the fourth is about free path lengths. A general theme throughout the thesis is lattice points and convex bodies.In Paper A we give an asymptotic expression for the number of integer matrices with primitive row vectors and a given nonzero determinant, such that the Euclidean matrix norm is less than a given large number. We also investigate the density of matrices with primitive rows in the space of matrices with a given determinant, and determine its asymptotics for large determinants.In Paper B we prove a sharp bound for the remainder term of the number of lattice points inside a ball, when averaging over a compact set of (not necessarily unimodular) lattices, in dimensions two and three. We also prove that such a bound cannot hold if one averages over the space of all lattices.In Paper C, we give a conjectural asymptotic formula for the number of imaginary quadratic fields with class number h, for any odd h, and a conjectural asymptotic formula for the number of imaginary quadratic fields with class group isomorphic to G, for any finite abelian p-group G where p is an odd prime. In support of our conjectures we have computed these quantities, assuming the generalized Riemann hypothesis and with the aid of a supercomputer, for all odd h up to a million and all abelian p-groups of order up to a million, thus producing a large list of “missing class groups. ” The numerical evidence matches quite well with our conjectures.In Paper D, we consider the distribution of free path lengths, or the distance between consecutive bounces of random particles in a rectangular box. If each particle travels a distance R, then, as R → ∞ the free path lengths coincides with the distribution of the length of the intersection of a random line with the box (for a natural ensemble of random lines) and we determine the mean value of the path lengths. Moreover, we give an explicit formula for the probability density function in dimension two and three. In dimension two we also consider a closely related model where each particle is allowed to bounce N times, as N → ∞, and give an explicit formula for its probability density function.
Dirac equation in non-Riemannian geometries

We present the Dirac equation in a geometry with torsion and non-metricity balancing generality and simplicity as much as possible. In doing so, we use the vielbein formalism and the Clifford algebra. We also use an index-free formalism which allows us to construct objects that are totally invariant. It turns out that the previous apparatuses not only make possible a simple deduction of the Dirac equation but also allow us to exhibit some details that is generally obscure in the literature.
Pedagogical Innovations for Teaching Practicum

Teaching practicum plays a significant role in teacher education programs and helps to upgrade teachers’ professional competencies. The teaching practicum component employed by the Faculty of Education, The Open University of Sri Lanka (OUSL), and the Faculty of Education, University of Colombo provides a systematic mechanism for fostering the professional development of teachers through their Postgraduate Diploma in Education (PGDE) programmes. This comparative study was done to identify strategies and innovative methods that need to be adopted by the two universities to increase the effectiveness of teaching practicum. The participant of this study were 117 student teachers, 30 school mentors, 57 master teachers, and 5 university academics representing two universities. The data collected using questionnaires, interviews, and teaching practice records were analyzed both qualitatively and quantitatively. Findings revealed that the pedagogical knowledge and guidance provided by the universities, the collaborative atmosphere of the schools, the effective role of school mentors and master teachers, and the motivation and commitment of student teachers strongly affect the effectiveness of the teaching practice component. The establishment of a strong collaborative school-university partnership, creating a professional body of school mentors and master teachers with continuous training provisions, and improving the commitment to educational research on teaching practicum were identified as the most effective and enacting changes that need to be adopted by the two universities to cater the professional development of teachers. Overall, a new framework was developed with an innovative avenue to increase the effectiveness of teaching practicum.
An Investigation of the Fengyun-4A/B GIIRS Performance on Temperature and Humidity Retrievals

The Fengyun-4A/B (FY-4A/B) geostationary satellite carries the Geostationary Interferometric Infrared Sounder (GIIRS). The instrument parameters of the GIIRS on FY-4A and FY-4B are not exactly the same, which is crucial for the atmospheric temperature and humidity measurements. The objective of this paper is to discuss the influence of spectral range on the retrieval for the FY-4A/B GIIRS. Firstly, we performed channel selection to choose the appropriate channels for retrieval. Then, the multiple cycling utilization of the physical retrieval method is proposed and conducted for improving the accuracy, and the retrieval results of FY-4A/B GIIRS are compared. Finally, perturbation analysis is performed to discuss the sensitivity of the retrieval to temperature perturbations due to the difference in spectral range between the two GIIRS. The results show the retrieval method can realize the improvement of the average accuracy by more than 0.9 K for temperature and 3.0% for humidity. As the spectral range widens, the retrieval accuracy of FY-4B GIIRS is superior to that of FY-4A GIIRS from 130 hPa to 400 hPa. Furthermore, perturbation analysis also shows the extension of the spectral range is beneficial to the retrieval. This study could offer the usefulness of current GIIRS instruments with observed on-orbit bias, and a reference for the parameter design of the subsequent instruments.
A Lie algebraic approach to Ricci flow invariant curvature conditions and Harnack inequalities

Abstract We consider a subset S of the complex Lie algebra 𝔰𝔬﻿(n, ℂ) and the cone C﻿(S) of curvature operators which are nonnegative on S. We show that C﻿(S) defines a Ricci flow invariant curvature condition if S is invariant under AdSO﻿(n, ℂ). The analogue for Kähler curvature operators holds as well. Although the proof is very simple and short, it recovers all previously known invariant nonnegativity conditions. As an application we reprove that a compact Kähler manifold with positive orthogonal bisectional curvature evolves to a manifold with positive bisectional curvature and is thus biholomorphic to ℂℙn. Moreover, the methods can also be applied to prove Harnack inequalities.
A singular controllability problem with vanishing viscosity

The aim of this paper is to answer the question: Do the controls of a vanishing viscosity approximation of the one dimensional linear wave equation converge to a control of the conservative limit equation? Our viscous term contains the fractional power of the Dirichlet Laplace operator and it is multiplied by a small parameter devoted to tend to zero. Our analysis, based on moment problems and biorthogonal sequences, enables us to evaluate the magnitude of the controls needed for each eigenmode and to show their uniform boundedness with respect to the vanishing parameter.
Smooth Gowdy-symmetric generalized Taub–NUT solutions

We study a class of -Gowdy vacuum models with a regular past Cauchy horizon which we call smooth Gowdy-symmetric generalized Taub–NUT solutions. In particular, we prove the existence of such solutions by formulating a singular initial value problem with asymptotic data on the past Cauchy horizon. We prove that also a future Cauchy horizon exists for generic asymptotic data, and derive an explicit expression for the metric on the future Cauchy horizon in terms of the asymptotic data on the past horizon. This complements earlier results about -Gowdy models.
Thermal Behavior Modeling Based on BP Neural Network in Keras Framework for Motorized Machine Tool Spindles

This paper presents the development and evaluation of neural network models using a small input–output dataset to predict the thermal behavior of a high-speed motorized spindles. Different neural multi-output regression models were developed and evaluated using Keras, one of the most popular deep learning frameworks at the moment. ANN was developed and evaluated considering the following: the influence of the topology (number of hidden layers and neurons within), the learning parameter, and validation techniques. The neural network was simulated using a dataset that was completely unknown to the network. The ANN model was used for analyzing the effect of working conditions on the thermal behavior of the motorized grinder spindle. The prediction accuracy of the ANN model for the spindle thermal behavior ranged from 95% to 98%. The results show that the ANN model with small datasets can accurately predict the temperature of the spindle under different working conditions. In addition, the analysis showed a very strong effect of type coolant on spindle unit temperature, particularly for intensive cooling with water.
Identification of Bcl2 as a Stably Expressed qPCR Reference Gene for Human Colon Cancer Cells Treated with Cottonseed-Derived Gossypol and Bioactive Extracts and Bacteria-Derived Lipopolysaccharides

Cottonseed contains many bioactive molecules including plant polyphenols. Cottonseed value might be increased by providing high-value bioactive polyphenols for improving nutrition and health. However, there was a lack of molecular evidence for cottonseed bioactivity in mammalian cells. One widely used method for evaluating the bioactivity of natural products is quantitative real-time-PCR (qPCR). The selection of stably expressed internal reference genes is a crucial task of qPCR assay for data analysis. The rationale for reference gene selection is that a lower standard deviation of the cycle of threshold (Cq) among the treatments indicates a more stable expression of the gene. The objective of this study was to select reference genes in human colon cancer cells (COLO 205) treated with cottonseed-derived gossypol and bioactive extracts along with bacterial endotoxin lipopolysaccharides (LPS). SYBR Green qPCR was used to analyze the mRNA levels of a wide range of biomarkers involved in glucose transport, lipid biosynthesis, inflammatory response, and cancer development. qPCR data (10,560 Cq values) were generated from 55 genes analyzed from 64 treatments with triplicate per treatment for each gene. The data showed that B-cell lymphoma 2 (Bcl2) mRNA was the most stable among the 55 mRNAs analyzed in the human colon cancer cells. Glyceraldehyde 3 phosphate dehydrogenase (Gapdh) and ribosome protein L32 (Rpl32) mRNAs were not good qPCR references for the colon cancer cells. These observations were consistent regardless of the treatment comparison between gossypol and LPS, glanded and glandless seed extracts, seed coat and kernel extracts, or treatment for 8 and 24 h. These results suggest that Bcl2 is a preferable reference gene for qPCR assays in human colon cancer cells treated with cottonseed-derived gossypol and bioactive extracts as well as LPS. The extensive qPCR results firmly support the conclusion that the Bcl2 gene is stably expressed at the mRNA level in the human colon cancer cells regardless of the treatment, suggesting that Bcl2 gene expression is not regulated at the mRNA level but at the post-transcriptional level. These results should facilitate studies designated to evaluate bioactivity on gene expression regulation by cottonseed molecules and other natural and synthetic molecules for nutrition and health uses.
Derived category of moduli of pointed curves. I

This is the first paper in the sequence devoted to derived category of moduli spaces of curves of genus $0$ with marked points. We develop several approaches to describe it equivariantly with respect to the action of the symmetric group permuting marked points. We construct an equivariant full exceptional collection on the Losev-Manin space which categorifies derangements.
Wave and Dirac equations on manifolds

We review some recent results on geometric equations on Lorentzian manifolds such as the wave and Dirac equations. This includes well-posedness and stability for various initial value problems, as well as results on the structure of these equations on black-hole spacetimes (in particular, on the Kerr solution), the index theorem for hyperbolic Dirac operators and properties of the class of Green-hyperbolic operators.
Extension theorems for Hamming varieties over finite fields

We study the finite field extension estimates for Hamming varieties $H_j, j\in \mathbb F_q^*,$ defined by $H_j=\{x\in \mathbb F_q^d: \prod_{k=1}^d x_k=j\},$ where $\mathbb F_q^d$ denotes the $d$-dimensional vector space over a finite field $\mathbb F_q$ with $q$ elements. We show that although the maximal Fourier decay bound on $H_j$ away from the origin is not good, the Stein-Tomas $L^2\to L^r$ extension estimate for $H_j$ holds.
Centromere Chromatin Dynamics at a Glance

The centromere is a specialized DNA locus that ensures the faithful segregation of chromosomes during cell division. It does so by directing the assembly of an essential proteinaceous structure called the kinetochore. The centromere identity is primarily epigenetically defined by a nucleosome containing an H3 variant called CENP-A as well as by the interplay of several factors such as differential chromatin organization driven by CENP-A and H2A.Z, centromere-associated proteins, and post-translational modifications. At the centromere, CENP-A is not just a driving force for kinetochore assembly but also modifies the structural and dynamic properties of the centromeric chromatin, resulting in a distinctive chromatin organization. An additional level of regulation of the centromeric chromatin conformation is provided by post-translational modifications of the histones in the CENP-A nucleosomes. Further, H2A.Z is present in the regions flanking the centromere for heterochromatinization. In this review, we focus on the above-mentioned factors to describe how they contribute to the organization of the centromeric chromatin: CENP-A at the core centromere, post-translational modifications that decorate CENP-A, and the variant H2A.Z.
Intersection of almost complex submanifolds

We show the intersection of a compact almost complex subvariety of dimension $4$ and a compact almost complex submanifold of codimension $2$ is a $J$-holomorphic curve. This is a generalization of positivity of intersections for $J$-holomorphic curves in almost complex $4$-manifolds to higher dimensions. As an application, we discuss pseudoholomorphic sections of a complex line bundle. We introduce a method to produce $J$-holomorphic curves using the differential geometry of almost Hermitian manifolds. When our main result is applied to pseudoholomorphic maps, we prove the singularity subset of a pseudoholomorphic map between almost complex $4$-manifolds is $J$-holomorphic. Building on this, we show degree one pseudoholomorphic maps between almost complex $4$-manifolds are actually birational morphisms in pseudoholomorphic category.
Reconstruction of cracks and material losses by perimeter-like penalizations and phase-field methods: numerical results

We numerically implement the variational approach for reconstruction in the inverse crack and cavity problems developed by one of the authors. The method is based on a suitably adapted free-discontinuity problem. Its main features are the use of phase-field functions to describe the defects to be reconstructed and the use of perimeter-like penalizations to regularize the ill-posed problem. The numerical implementation is based on the solution of the corresponding optimality system by a gradient method. Numerical simulations are presented to show the validity of the method.
Magnetic domains

uniformity (with the fibre ends accurately polished References to a clear surface) is about 15-30 cm2 and in this Collier R J, Burckhardt c B, Lin L H 1971 opticar situation the quality of the hologram is satisfying. Holography (New York: Academic Press) sections 8.1. 1 Finally, figure 4 shows the virtual image of an and 8.33 off-axis hologram achieved with the experimental Shulman A B 1970 Optical Data Processing (New York: arrangement in figure 3. In this case the image was WileY) P552 reconstructed using a microscope objective. Takahara H 1978 Applied Optics 17 13
Closed almost Kähler 4-manifolds of constant non-negative Hermitian holomorphic sectional curvature are Kähler

We show that a closed almost K\"ahler 4-manifold of globally constant holomorphic sectional curvature $k\geq 0$ with respect to the canonical Hermitian connection is automatically K\"ahler. The same result holds for $k<0$ if we require in addition that the Ricci curvature is J-invariant. The proofs are based on the observation that such manifolds are self-dual, so that Chern-Weil theory implies useful integral formulas, which are then combined with results from Seiberg--Witten theory.
Distributed chaos tuned to large scale coherent motions in turbulence

It is shown, using direct numerical simulations and laboratory experiments data, that distributed chaos is often tuned to large scale coherent motions in anisotropic inhomogeneous turbulence. The examples considered are: fully developed turbulent boundary layer (range of coherence: $14 < y^{+} < 80$), turbulent thermal convection (in a horizontal cylinder), and Cuette-Taylor flow. Two ways of the tuning have been described: one via fundamental frequency (wavenumber) and another via subharmonic (period doubling). For the second way the large scale coherent motions are a natural component of distributed chaos. In all considered cases spontaneous breaking of space translational symmetry is accompanied by reflexional symmetry breaking.
Effect of Past Pharmacotherapy for Attention-Deficit/Hyperactivity Disorder on Substance Use Disorder

Background: Substance use disorders (SUDs) are a considerable public health problem. Attention-deficit/hyperactivity disorder (ADHD) frequently occurs in patients with SUD. Several studies demonstrated that ADHD constitutes a significant risk factor for the development of SUDs and suggest that childhood ADHD pharmacotherapy might help prevent development of SUD. Objectives: The study aimed to explore the effect of childhood ADHD pharmacotherapy on later life’s functional impairment and substance use patterns. Methods: Treatment-seeking SUD patients with ADHD (n = 52) were recruited from various rehabilitation facilities in South Africa. Adult ADHD individuals without SUD (n = 48) were recruited from clinicians, retail pharmacies, and the general public. SUD participants in rehabilitation facilities were screened for and diagnosed with ADHD. Lifetime substance use was assessed using self-report. ADHD-related functional impairment was assessed by the Weiss Functional Impairment Rating Scale (WFIRS). Information on present and lifetime use of ADHD medication was obtained. Clinical outcomes between those with and without a history of ADHD pharmacotherapy were compared. Results: Medicated participants (n = 59) showed lower levels of ADHD-related impairment across all functional domains (p < 0.001), compared to non-medicated participants (n = 41). They also consumed less alcohol (p = 0.04), cannabis (p < 0.001), and illicit drugs (p = 0.006) compared to the non-medicated group. Furthermore, medicated participants had a lower frequency of tobacco use compared to non-medicated participants (p = 0.04). ADHD patients without SUD also more often received medication (100% vs. 18.6%; p < 0.001) and for a longer time (121.10 vs. 9.52 months; p < 0.001). Conclusion: Childhood ADHD pharmacotherapy might be associated with a decreased risk for substance use in adulthood and lower ADHD-related impairment. Despite study limitations, these findings underline the importance of early ADHD detection and treatment, which might prevent SUD.
A geometric construction of the Witten genus, I

I give a rigorous construction of a 2-dimensional quantum field theory of maps from an elliptic curve to a compact complex manifold X, and I show that the partition function of this theory is the Witten genus of X. The results proved here were announced (in a slightly different form) in arXiv:1006.5422.
Volterra type and weighted composition operators on Fock spaces

Bounded and compact product of Volterra type integral and composition operators acting between weighted Fock spaces are described. We also estimate the norms of these operators in terms of Berezin type integral transforms on the complex plan $\mathbb{C}$. All our results are valid for weighted composition operators acting on the class of Fock spaces considered under appropriate interpretation of the weights.
The 2-Chu-Dialectica construction and the polycategory of multivariable adjunctions

Cheng, Gurski, and Riehl constructed a cyclic double multicategory of multivariable adjunctions. We show that the same information is carried by a double polycategory, in which opposite categories are polycategorical duals. Moreover, this double polycategory is a full substructure of a double Chu construction, whose objects are a sort of polarized category, and which is a natural home for 2-categorical dualities. We obtain the double Chu construction using a general "Chu-Dialectica" construction on polycategories, which includes both the Chu construction and the categorical Dialectica construction of de Paiva. The Chu and Dialectica constructions each impose additional hypotheses making the resulting polycategory representable (hence *-autonomous), but for different reasons; this leads to their apparent differences.
Strongly self-absorbing C*-dynamical systems. II

This is a continuation of the study of strongly self-absorbing actions of locally compact groups on C-algebras. Given a strongly selfabsorbing action γ : G y D, we establish permanence properties for the class of separable C-dynamical systems absorbing γ tensorially up to cocycle conjugacy. Generalizing results of both Toms-Winter and Dadarlat-Winter, it is proved that the desirable equivariant analogues of the classical permanence properties hold in this context. For the permanence with regard to equivariant extensions, we need to require a mild extra condition on γ, which replaces K1-injectivity assumptions in the classical theory. This condition turns out to be automatic for equivariantly Jiang-Su absorbing C-dynamical systems, yielding a large class of examples. It is left open whether this condition is redundant for all strongly self-absorbing actions, and we do consider examples that satisfy this condition but are not equivariantly Jiang-Su absorbing.