Miracle-dz/UniFAR-FTUs huggingface dataset:
Strong Proximities on Smooth Manifolds and Vorono\" i Diagrams

This article introduces strongly near smooth manifolds. The main results are (i) second countability of the strongly hit and far-miss topology on a family $\mathcal{B}$ of subsets on the Lodato proximity space of regular open sets to which singletons are added, (ii) manifold strong proximity, (iii) strong proximity of charts in manifold atlases implies that the charts have nonempty intersection. The application of these results is given in terms of the nearness of atlases and charts of proximal manifolds and what are known as Vorono\" i manifolds.
Improving Communication with Parents in the NICU during the COVID-19 Pandemic, a Study and Review of the Literature

Background: Communication with parents of sick premature and term infants in the NICU is complicated and challenging. Multiple efforts have been made to improve it, including the introduction of new electronic-based measures. Aim: We aimed to study the influence of implementation of a new communication technology on parents’ satisfaction with care in the NICU during the COVID-19 pandemic. Methods: Infants were video-recorded in their incubators or cots without being disturbed. These short films, with voice updates on the infant’s condition, were sent on a daily basis to their parents via a WhatsApp application. Results: Parents who chose to join the new communication project (study group) were older, and their infants were more premature. Parents were satisfied with this new communication modality. Satisfaction scores in both study and control groups were high, but not significantly different. Conclusions: Although the implementation of the new communication project was successful, we could not demonstrate significant improvement in satisfaction scores that were high in study and control groups, reflecting baseline high satisfaction. Further studies are needed employing other assessment tools in order to evaluate other aspects of parents’ satisfaction with new modalities of communication introduced to the NICU, and their effects on parents’ bonding with their infants.
A New Randomized Block-Coordinate Primal-Dual Proximal Algorithm for Distributed Optimization

This paper proposes Triangularly Preconditioned Primal- Dual algorithm, a new primal-dual algorithm for minimizing the sum of a Lipschitz-differentiable convex function and two possibly nonsmooth convex functions, one of which is composed with a linear mapping. We devise a randomized block-coordinate (BC) version of the algorithm which converges under the same stepsize conditions as the full algorithm. It is shown that both the original as well as the BC scheme feature linear convergence rate when the functions involved are either piecewise linear-quadratic, or when they satisfy a certain quadratic growth condition (which is weaker than strong convexity). Moreover, we apply the developed algorithms to the problem of multiagent optimization on a graph, thus obtaining novel synchronous and asynchronous distributed methods. The proposed algorithms are fully distributed in the sense that the updates and the stepsizes of each agent only depend on local information. In fact, no prior global coordination is required. Finally, we showcase an application of our algorithm in distributed formation control.
Miniaturized Wideband CP Antenna Using Hybrid Embedded Metasurface Structure

In this study, a hybrid embedded metasurface (MTS) structure is proposed and applied to realize a miniaturized MTS antenna. In contrast to the conventional periodic rectangular MTS, the proposed MTS structure is formed by hybrid embedded patches composed of several X and rectangle metal patches. The gap between the hybrid patches introduces additional capacitances, which can reduce the resonance frequency of the MTS antenna and achieve significant miniaturization. Characteristic mode analysis (CMA) is then utilized to analyze the MTS operating mechanism and guide the best possible feeding positions for wideband circularly polarized (CP) radiation. Subsequently, a cross-slot and microstrip line are used to excite a pair of degenerate modes to obtain CP radiation and broadband impedance matching. Finally, for demonstration, the proposed MTS antenna was fabricated and measured with an overall aperture of 0.46 $\lambda _{0}\times0.46\,\,\lambda _{0} \times0.07\,\,\lambda _{0}$ at 5 GHz. The measured 3 dB axial ratio bandwidth (ARBW) is 21.40%. Thus, it can be demonstrated that the proposed antenna can radiate effectively with significant miniaturization and the desired wideband CP radiation patterns, revealing promising prospects for wireless communication systems.
Source estimation with incoherent waves in random waveguides

We study an inverse source problem for the acoustic wave equation in a random waveguide. The goal is to estimate the source of waves from measurements of the acoustic pressure at a remote array of sensors. The waveguide effect is due to boundaries that trap the waves and guide them in a preferred (range) direction, the waveguide axis, along which the medium is unbounded. The random waveguide is a model of perturbed ideal waveguides which have flat boundaries and are filled with known media that do not change with range. The perturbation consists of fluctuations of the boundary and of the wave speed due to numerous small inhomogeneities in the medium. The fluctuations are uncertain in applications, which is why we model them with random processes, and they cause significant cumulative scattering at long ranges from the source. The scattering effect manifests mathematically as an exponential decay of the expectation of the acoustic pressure, the coherent part of the wave. The incoherent wave is modeled by the random fluctuations of the acoustic pressure, which dominate the expectation at long ranges from the source. We use the existing theory of wave propagation in random waveguides to analyze the inverse problem of estimating the source from incoherent wave recordings at remote arrays. We show how to obtain from the incoherent measurements high fidelity estimates of the time resolved energy carried by the waveguide modes, and study the invertibility of the system of transport equations that model energy propagation in order to estimate the source.
Character varieties with Zariski closures of GL_n-conjugacy classes at punctures

In a previous paper (joint with Hausel and Rodriguez-Villegas) we gave a conjectural formula for the mixed Hodge polynomials of character varieties with generic semisimple conjugacy classes at punctures and we prove a formula for the E-polynomial. We also proved that these character varieties are irreducible. In this paper we extend the above results to character varieties with Zariski closures of arbitrary generic conjugacy classes at punctures working with intersection cohomology. We also study Weyl group action on the intersection cohomology of the partial resolutions of these character varieties and give a conjectural formula for the two-variables polynomials that encode the trace of the elements of the Weyl group on the subquotients of the weight filtration. Finally, we compute the generating function of the stack count of character varieties with Zariski closure of unipotent regular conjugacy class at punctures.
Hybrid individualized assistance-oriented learning system framework for STEM-Education

The imparting of knowledge and skills in STEM education, especially under the influence of the Covid-19 pandemic, is increasingly taking place online and through digital formats. The partially asynchronous instruction eliminates, on the one hand, the social relation in the learning process and, on the other hand, the direct experience with physical objects. Here, the digital learning systems provide learning tools and controls to support the learning process on a general basis. Existing methods for simulating physical objects (digital twins) are also used to a minimal extent. The following approach presents a learning system framework that enables individualized learning, including all dimensions (social, physical). Implementing a concept that uses a personalized assistance system to orchestrate the individual learning steps enables efficient and effective learning. Applying the learning system framework exemplifies the STEM education at Reutlingen University in the logistics learning factory Werk150.
Silverman's conjecture for additive polynomial mappings

Let $F : \mathrm{End}_{\mathbb{F_p}}(\mathbb{G}_{a/K}^d)$ be an additive polynomial mapping over a global function field $K/\mathbb{F}_q$, and let $P \in \mathbb{G}_a^d(K)$. Following Silverman, consider $\delta := \lim_{n \in \mathbb{N}} (\deg{F^{n}})^{1/n}$ the dynamic degree of $F$ and $\alpha(P) := \limsup_{n \in \mathbb{N}} h_K(F^{n}P)^{1/n}$ the arithmetic degree of $F$ at $P$. We have $\alpha(P) \leq \delta$, and extending a conjecture of Silverman from the number field case, it is expected that equality holds if the orbit of $P$ is Zariski-dense. We prove a weaker form of this conjecture: if $\delta > 1$ and the orbit of $P$ is Zariski-dense, then also $\alpha(P) > 1$. We obtain furthermore a more precise result concerning the growth along the orbit of $P$ of the heights of the individual coordinates, and formulate a few related open problems motivated by our results, including a generalization "with moving targets" of Faltings's theorem back in the number field case.
Prospective Randomized Double-Blind Placebo-Controlled Study of Oral Pomegranate Extract on Skin Wrinkles, Biophysical Features, and the Gut-Skin Axis

(1) Background: The pomegranate fruit (Punica granatum L.) has been widely used in traditional medicine and has increasingly gained popularity among consumers in order to manage different facets of health. The objective of this study was to evaluate the effects of the fruit extract of P. granatum L. on different parameters of skin health. (2) Methods: A prospective, double-blind placebo-controlled study was conducted on both healthy males and females aged 25–55 years. Subjects were supplemented with a standardized punicalagin enriched oral pomegranate extract [Pomella® (Verdure Science, Noblesville, IN, USA), PE group] or a placebo (control group) daily for four weeks. Changes in wrinkle severity, facial biophysical properties, skin microbiome, and the gut microbiome were assessed. (3) Results: The PE group had significant reductions in wrinkle severity (p < 0.01) and a decreasing trend in the forehead sebum excretion rate (p = 0.14). The participants in the PE group with a higher relative abundance of Eggerthellaceae in the gut had a decrease in their facial TEWL (p < 0.05) and wrinkle severity (p = 0.058). PE supplementation led to an increase in the Staphylococcus epidermidis species and the Bacillus genus on the skin. (4) Conclusions: Overall, the study demonstrated improvements in several biophysical properties, wrinkles, and shifts in the skin microbiome with oral PE supplementation in healthy subjects.
On Dris Conjecture about Odd Perfect Numbers

The Euler's form of odd perfect numbers, if any, is $n=\pi^{\alpha}N^2$, where $\pi$ is prime, $(\pi,N)=1$ and $\pi\equiv \alpha \equiv 1 \pmod{4}$. Dris conjecture states that $N>\pi^{\alpha}$. We find that $N^2>\frac{1}{2}\pi^{\gamma}$, with $\gamma=max\{\omega(n)-1,\alpha\}$; $\omega(n)\geq 9$ is the number of distinct prime factors of $n$.
Convergence of the mirror to a rational elliptic surface

The construction introduced by Gross, Hacking and Keel in (Several Complex Variables (Springer, New York, NY, 1976))allows one to construct a formal mirror family to a pair (S,D) where S is a smooth rational projective surface and D a certain type of Weil divisor supporting an ample or anti‐ample class. In that paper, they proved two convergence results when the intersection matrix of D is not negative semi‐definite and when the matrix is negative definite. In the original version of that paper, they claimed that if the intersection matrix were negative semi‐definite, then family extends over an analytic neighbourhood of the origin but gave an incorrect proof. In this paper, we correct this error. We reduce the construction of the mirror to such a surface to calculating certain log Gromov–Witten invariants. We then relate these invariants to the invariants of a new space where we can find explicit formulae for the invariants. From this we deduce analytic convergence of the mirror family, at least when the original surface has an I4 fibre.
Improved Winding Losses Calculation Based on Bessel Functions

In this article, an approach combining semi-empirical equations and the method of images is proposed for round conductor layer windings with un-gapped core. The new equation for proximity effect can convert the constant field strength from the magneto-motive force (MMF) across the core window into a frequency-dependent uniform background magnetic field strength, which can take partly the interaction between conductors into account. Geometric factors are introduced by fitting the finite element method (FEM) results to improve the accuracy. The method of images is used to calculate the field strength in order to counteract the impact of the 2-D edge effect. The new method is compared with the 2-D FEM, analytical methods, and is also validated by measurements with EE core transformers. The proposed method shows good accuracy (< 10% error) compared with 2-D FEM for both high and low porosity factor windings. Therefore, it can handle more winding configurations than other 1-D analytical methods.
ROLE: Rotated Lorentzian Graph Embedding Model for Asymmetric Proximity

Graph embedding, which aims to learn low-dimensional node representations to preserve original graph structures, has attracted extensive research interests. However, most existing graph embedding models represent nodes in Euclidean spaces, which cannot effectively preserve complex patterns, e.g., hierarchical structures. Very recently, several hyperbolic embedding models have been proposed to preserve the hierarchical information in negative curvature spaces. Nevertheless, existing hyperbolic models fail to model the asymmetric proximity between nodes. To address this, we investigate a new asymmetric hyperbolic network representation problem, which targets at jointly preserving the hierarchical structures and asymmetric proximity for general directed graphs. We solve this problem by proposing a novel Rotated Lorentzian Embedding (ROLE) model, which yields two main benefits. First, our model can effectively capture both implicit and explicit hierarchical structures that come from the network topology and category information of nodes, respectively. Second, it can model the asymmetric proximity using rotation transformations. Specifically, we represent each node with a Lorentzian embedding vector, and learn two rotation matrices to reflect the direction of edges. We conduct extensive experiments on four real-world directed graph datasets. Empirical results demonstrate that the proposed approach consistently outperforms various state-of-the-art embedding models. In particular, ROLE achieves HR@1 scores up to 19.8% higher and NDCG@5 scores up to 11.3% higher than the best baselines on the task of node recommendation.
Generative Adversarial Neural Machine Translation for Phonetic Languages via Reinforcement Learning

Neural Machine Translation (NMT) heavily depends on the context vectors generated via attention network for the target word prediction. Existing works primarily focus on generating context vectors from words or subwords of sentences, limiting NMT models' ability to learn sufficient information about the source sentence representations. These situations are even worse when languages belong to extremely low-resource categories due to rare word problem. To improve the learning of source sentence representations and handle the rare word problem of Low Resource Languages (LRLs), we propose a novel improvement in Generative Adversarial Networks (GAN)-NMT by incorporating deep reinforcement learning-based optimised attention in generator and convolutional neural network in discriminator. We also create the novel joint embedding of subwords and sub-phonetic representation of sentences as input to GAN that helps models to learn the better representations and generate suitable context vectors compared to existing traditional approaches for LRLs. To show the effectiveness of our method, we demonstrate experiments on LRLs pairs, e.g., Gujarati <inline-formula><tex-math notation="LaTeX">$\leftrightarrow$</tex-math></inline-formula> Hindi, Nepali <inline-formula><tex-math notation="LaTeX">$\leftrightarrow$</tex-math></inline-formula> Hindi, Punjabi <inline-formula><tex-math notation="LaTeX">$\leftrightarrow$</tex-math></inline-formula> Hindi, Maithili <inline-formula><tex-math notation="LaTeX">$\leftrightarrow$</tex-math></inline-formula> Hindi and Urdu <inline-formula><tex-math notation="LaTeX">$\leftrightarrow$</tex-math></inline-formula> Hindi. Our proposed novel approach suppress the existing state-of-the-art techniques with considerable improvement.
Serving students with disabilities in K-12 online learning: daily practices of special educators during the COVID-19 pandemic

Abstract Online and distance education strategies offer a path for closing opportunity gaps for students with disabilities because of digital technologies’ flexibility and capacity for differentiation, but fully online schooling does always guarantee an inclusive education. The COVID-19-induced shift to remote learning highlighted the need for more insight into inclusive practices for students with disabilities in online contexts, especially at the K-12 levels. The present study describes special education teachers’ online teaching practices with students with disabilities and the necessary conditions for special educator use of technology in K-12 remote learning. Using in-depth interview (N = 2 0) and survey data with special educators teaching during the COVID-19 pandemic, findings highlight specific strategies special educators use to differentiate instruction as well as innovations in hybrid content experiences and home-school partnerships across K-12 schooling. The practices of special educators teaching in online environments provide insights into how all educators can support learners with or without disabilities in K-12 distance education settings.
Stable Invariants for Multidimensional Persistence

In this paper we explain how to convert discrete invariants into stable ones via what we call hierarchical stabilization. We illustrate this process by constructing stable invariants for multi parameter persistence modules with respect to so called simple noise systems. For one parameter we recover the standard bar code information. For more than one parameter we prove that the constructed invariants are in general NP-hard to calculate.
Urological Management of the Spinal Cord-Injured Patient: Suggestions for Improving Intermittent Catheterization and Reflex Voiding

Spinal cord injury can either be complete with no neural communication across the injury level or incomplete with limited communication. Similarly, motor neuron injuries above the sacral spinal cord are classified as upper motor neuron injuries, while those inside the sacral cord are classified as lower motor neuron injuries. Specifically, we provide recommendations regarding the urological management of complete upper motor neuron spinal cord injuries; however, we also make limited comments related to other injuries. The individual with a complete upper motor neuron injury may encounter five lower urinary tract conditions: first, neurogenic detrusor overactivity causing urinary incontinence; second, neurogenic detrusor underactivity resulting in high post-void residual volumes; third, detrusor sphincter dyssynergia, which is contraction of striated and/or smooth muscle urethral sphincters during detrusor contractions; fourth, urinary tract infection; and fifth, autonomic dysreflexia during detrusor contractions, which produces high blood pressure as well as smooth muscle detrusor sphincter dyssynergia. Intermittent catheterization is the recommended urinary management method because it addresses the five lower urinary tract conditions and has good long-term outcomes. This method uses periodic catheterizations to drain the bladder, but also needs bladder inhibitory interventions to prevent urinary incontinence between catheterizations. Primary limitations associated with this management method include difficulties with the multiple catheterizations, side effects of bladder inhibitory medications, and urinary tract infections. Three suggestions to address these concerns include the use of low-friction catheters, wireless, genital-nerve neuromodulation for bladder inhibition, and consideration of urine egress into the urethra as a risk factor for UTI as well as egress treatment. The second management method is reflex voiding. This program uses external condoms for urine collection in males and diapers for females. Suprapubic tapping is used to promote bladder contractions. This method is not recommended because it has high rates of medical complications. In particular, it is associated with high detrusor pressure, which can lead to ureteral reflux and kidney pathology. Botulinum toxin injection into the urethral striated sphincter can manage detrusor sphincter dyssynergia, reduce voiding pressures, and risks to the kidney. We suggest a modified method for botulinum toxin injections as well as five additional methods to improve reflex voiding outcomes. Finally, the use of intermittent catheterization and reflex voiding for individuals with incomplete spinal injuries, lower motor neuron injuries and multiple scleroses are briefly discussed.
Invariant meshless discretization schemes

A method is introduced for the construction of meshless discretization schemes which preserve Lie symmetries of the differential equations that these schemes approximate. The method exploits the fact that equivariant moving frames provide a way of associating invariant functions with non-invariant functions. An invariant meshless approximation of a nonlinear diffusion equation is constructed. Comparative numerical tests with a non-invariant meshless scheme are presented. These tests yield that invariant meshless schemes can lead to substantially improved numerical solutions compared to numerical solutions generated by non-invariant meshless schemes.