Miracle-dz/UniFAR-FTUs huggingface dataset:
Solving 𝑆-unit, Mordell, Thue, Thue–Mahler and Generalized Ramanujan–Nagell Equations via the Shimura–Taniyama Conjecture

In the first part we construct algorithms (over Q \mathbb {Q} ) which we apply to solve S S -unit, Mordell, cubic Thue, cubic Thue–Mahler and generalized Ramanujan–Nagell equations. As a byproduct we obtain alternative practical approaches for various classical Diophantine problems, including the fundamental problem of finding all elliptic curves over Q \mathbb {Q} with good reduction outside a given finite set of rational primes. The first type of our algorithms uses modular symbols, and the second type combines explicit height bounds with efficient sieves. In particular we construct a refined sieve for S S -unit equations which combines Diophantine approximation techniques of de Weger with new geometric ideas. To illustrate the utility of our algorithms we determined the solutions of large classes of equations, containing many examples of interest which are out of reach for the known methods. In addition we used the resulting data to motivate various conjectures and questions, including Baker’s explicit a b c abc -conjecture and a new conjecture on S S -integral points of any hyperbolic genus one curve over Q \mathbb {Q} . In the second part we establish new results for certain old Diophantine problems (e.g. the difference of squares and cubes) related to Mordell equations, and we prove explicit height bounds for cubic Thue, cubic Thue–Mahler and generalized Ramanujan–Nagell equations. As a byproduct, we obtain here an alternative proof of classical theorems of Baker, Coates and Vinogradov–Sprindžuk. In fact we get refined versions of their theorems, which improve the actual best results in many fundamental cases. We also conduct some effort to work out optimized height bounds for S S -unit and Mordell equations which are used in our algorithms of the first part. Our results and algorithms all ultimately rely on the method of Faltings (Arakelov, Paršin, Szpiro) combined with the Shimura–Taniyama conjecture, and they all do not use lower bounds for linear forms in (elliptic) logarithms. In the third part we solve the problem of constructing an efficient sieve for the S S -integral points of bounded height on any elliptic curve E E over Q \mathbb {Q} with given Mordell–Weil basis of E ( Q ) E(\mathbb {Q}) . Here we combine a geometric interpretation of the known elliptic logarithm reduction (initiated by Zagier) with several conceptually new ideas. The resulting “elliptic logarithm sieve” is crucial for some of our algorithms of the first part. Moreover, it considerably extends the class of elliptic Diophantine equations which can be solved in practice: To demonstrate this we solved many notoriously difficult equations by combining our sieve with known height bounds based on the theory of logarithmic forms.
Motivations behind Vaccine Hesitancy: Examining Altruism and Government Distrust across Job Sectors during COVID-19

Abstract This article examines vaccination and vaccine hesitancy during the COVID-19 pandemic by focusing on the role of altruism and distrust in government across different job sectors. Using the Household Pulse Survey, a nationally representative and near real-time dataset administered by the United States Census Bureau, our findings suggest that there is a clear difference in vaccine take-up and vaccine hesitancy across job sectors. We find that government and nonprofit employees are more likely to receive vaccines and, if not vaccinated yet, are less vaccine-hesitant than private-sector employees. Additionally, motivations behind vaccine hesitancy, particularly altruism and distrust in government, varied according to one’s sector affiliation. Government and nonprofit employees, compared to private employees, were more likely to be vaccine hesitant for altruistic motivations. Differences in government distrust across sectors bore unexpected results, as we found no difference between government and private employees, while nonprofit employees were less likely to be vaccine hesitant due to government distrust. We discuss the implications and contributions of this article and suggest future agenda for COVID-19 research and sector comparison literature.
Neonatal Death in Women with Severe Preeclampsia Receiving Conservative Management: Literature Review

Introduction: In developing countries that still have places with inadequate supporting facilities, equipment and limited trained personnel, infants less than 37 weeks may still be at high risk for severe complications and even death if active management or termination is carried out, so conservative care is recommended. Object: The aim of this study was to analyze the perinatal outcome of neonatal mortality in women with severe preeclampsia who received conservative management. Method: This study uses a literature review method which includes searching for articles in electroncic research journal databases. Search articles using Scopus and Google Scholar with no year limit. The keywords used in the search were Preeclampsia, Conservative Management, Expectative Management, and Perinatal Outcomes. A total of 637 articles were obtained, and six articles were analyzed based on the research setting, design study, samples characteristics, and research results for each article. Results and Discussion: of this study are conservative management of women with severe preeclampsia can reduce neonatal mortality rates in care in developed countries, but still shows high rates of care in developing countries. Conclusion: of the results, this study indicate that conservative management can improve maternal outcomes in the form of neonatal mortality in developed countries
The effect of sentence length on question comprehension in children with cochlear implants

Objectives The present study investigated the comprehension of subject and object who and which questions in children with cochlear implants (CI). Methods Growth Curve Analysis (GCA) was used to compare eye gaze fixations and gaze patterns to the appropriate subject or object nouns within a four-picture array between 16 children with CI and 31 children with typical hearing (aged 7;0-12;0) on wh-questions with and without added adjectives to increase length. Offline accuracy was also compared. Results Findings indicated children with typical hearing exhibited more fixations to the target noun across all conditions, supporting higher comprehension accuracy. Both groups of children demonstrated more fixations to the target noun in object questions and questions without added length. Patterns of eye movement were significantly different between groups, suggesting different patterns of eye gaze across the array before fixation on the target noun. Children with CI exhibited fewer fixations, slower speed to fixation, and differences in gaze patterns that may imply the presence of processing limitations. Error analyses also suggested that children with CI frequently fixated on a picture similar to the target noun. Conclusions Results indicate children with CI comprehend questions more slowly than their hearing peers, which may be related to limitations in working memory.
Staffing Large Service Systems Under Arrival-rate Uncertainty

We consider the problem of staffing large-scale service systems with multiple customer classes and multiple dedicated server pools under joint quality-of-service (QoS) constraints. We first analyze the case in which arrival rates are deterministic and the QoS metric is the probability a customer is queued, given by the Erlang-C formula. We use the Janssen-Van Leeuwaarden-Zwart bounds to obtain asymptotically optimal solutions to this problem. The second model considered is one in which the arrival rates are not completely known in advance (before the server staffing levels are chosen), but rather are known via a probability distribution. In this case, we provide asymptotically optimal solutions to the resulting stochastic integer program, leveraging results obtained for the deterministic arrivals case.
Smooth Schubert varieties and generalized Schubert polynomials in algebraic cobordism of Grassmannians

We provide several ingredients towards a generalization of the Littlewood-Richardson rule from Chow groups to algebraic cobordism. In particular, we prove a simple product-formula for multiplying classes of smooth Schubert varieties with any Bott-Samelson class in algebraic cobordism of the grassmannian. We also establish some results for generalized Schubert polynomials for hyperbolic formal group laws.
On the Schmidt subspace theorem for algebraic points

We study extensions and generalizations of the Schmidt Subspace Theorem in various settings. In particular, we prove results for algebraic points of bounded degree, giving a sharp version of Schmidt's theorem for quadratic points in the projective plane and a more general result that resolves a conjecture of Schlickewei.
On Constructions Preserving the Asymptotic Topology of Metric Spaces

We prove that graph products constructed over infinite graphs with bounded clique number preserve finite asymptotic dimension. We also study the extent to which Dranishnikov's asymptotic property C and Dranishnikov and Zarichnyi's straight finite decomposition complexity are preserved by constructions such as unions, free products, and group extensions.
Numbers and functions in quantum field theory

We review recent results in the theory of numbers and single-valued functions on the complex plane which arise in quantum field theory. We use the results to calculate the renormalization functions $\beta$, $\gamma$, $\gamma_m$ of dimensionally regularized $\phi^4$ theory in the minimal subtraction scheme up to seven loops.
Deep Learning Inversion of Electrical Resistivity Data by One-Sided Mapping

Recently, deep learning-based electrical resistivity inversion (DL-ERI) became popular for its potential to achieve high-accuracy imaging of the subsurface's electrical properties. The most typical way is to directly learn the mapping from apparent resistivity data to the resistivity model with DNN. Therefore, they are doing cross-domain mapping, which usually causes learning difficulty. In this work, we propose to do DL-ERI by one-sided domain mapping that uses gradients domain as the input and target. Specifically, the target is represented as residuals between the resistivity model and a uniform initial model, while input is the gradients calculated from the first step of the traditional linear inversion method. Then, we could obtain the inversion results by adding the predicted target to the initial model. From experiments, our one-sided domain mapping method shows clear superiority over the cross-domain mapping baseline and demonstrates promising performance on physical experimental data.
Meta-Analysis of Repeat Hepatectomy versus Radiofrequency Ablation for Recurrence of Hepatocellular Carcinoma

Simple Summary Development of intrahepatic recurrence of HCC is common even following index curative-intent hepatectomy. Multiple studies have demonstrated that repeat hepatectomy (RH) or radiofrequency ablation (RFA) may be performed in patients with recurrent disease. This systematic review and meta-analysis aimed to compare short- and long-term outcomes of patients undergoing RHR versus RFA for recurrent HCC. Abstract Hepatocellular carcinoma (HCC) is the most common primary hepatic malignancy and a leading cause of cancer-related death in both the developed and developing world. Recurrent HCC (rHCC) develops in a significant proportion of patients even following curative-intent resection. In the absence of a structured treatment algorithm, a number of treatment options including repeat hepatectomy (RH) and radiofrequency ablation (RFA) have been utilized in select patients with rHCC. The aim of this systematic review and meta-analysis was to compare short- and long-term outcomes of patients undergoing RHR versus RFA for rHCC. Four electronic databases were screened until September 2022. A total of 17 studies were included in the meta-analysis. Overall and disease-free survival were comparable among the two groups. Patients undergoing RH were less likely to develop a second recurrence (RR 0.89, 95% C.I. 0.81 to 0.98, p = 0.02). Overall and major morbidity were significantly increased in the RH group (RR 3.01, 95% C.I. 1.98 to 4.56, p < 0.001 and RR 3.65, 95% C.I. 2.07 to 6.43, p < 0.001, respectively), while mortality was similar between RFA and RH. The data demonstrated that RFA is a safe and efficient alternative to RH for selected patients with rHCC. Nevertheless, despite higher morbidity associated with RH, repeat resection remains the preferred treatment option whenever feasible, as it allows for better local disease control.
Fixed-points in the cone of traces on a C*-algebra

Nicolas Monod introduced the class of groups with the fixed-point property for cones, characterized by always admitting a non-zero fixed point whenever acting (suitably) on proper weakly complete cones. He proved that his class of groups contains the class of groups with subexponential growth and is contained in the class of supramenable groups. In this paper we investigate what Monod's results say about the existence of invariant traces on (typically non-unital) C*-algebras equipped with an action of a group with the fixed-point property for cones. As an application of these results we provide results on the existence (and non-existence) of traces on the (non-uniform) Roe algebra.
Quality of Music Education in Croatian Music Schools: Students' Attitudes

The purpose of this paper is to investigate how higher secondary music school students experience teaching, programs, and educational processes in music schools, which are the shortcomings and what are the suggestions for improving the system. The results show high satisfaction with attending music school related to the purpose of future professional orientation. Students see improvements in choosing more modern teaching topics, greater connection with practice, more time for student creativity, and work on improving teachers’ pedagogical skills. The results of this research could be used to accelerate the introduction of curriculum teaching and the National Curriculum for Art Education as a relevant document in music schools in the Republic of Croatia. Also, regardless of the inertia of the educational system, teachers can plan their teaching according to these results that will reconcile their ideas, methodological and didactic laws, and student expectations to contribute to greater motivation of their students.
A Fourier Integrator for the Cubic Nonlinear Schrödinger Equation with Rough Initial Data

Standard numerical integrators suffer from an order reduction when applied to nonlinear Schrodinger equations with low-regularity initial data. For example, standard Strang splitting requires the boundedness of the solution in $H^{r+4}$ in order to be second-order convergent in $H^r$, i.e., it requires the boundedness of four additional derivatives of the solution. We present a new type of integrator that is based on the variation-of-constants formula and makes use of certain resonance based approximations in Fourier space. The latter can be efficiently evaluated by fast Fourier methods. For second-order convergence, the new integrator requires two additional derivatives of the solution in one space dimension, and three derivatives in higher space dimensions. Numerical examples illustrating our convergence results are included. These examples demonstrate the clear advantage of the Fourier integrator over standard Strang splitting for initial data with low regularity.
Adaptive Similar Triangles Method: a Stable Alternative to Sinkhorn's Algorithm for Regularized Optimal Transport

In this paper, we are motivated by two important applications: entropy-regularized optimal transport problem and road or IP traffic demand matrix estimation by entropy model. Both of them include solving a special type of optimization problem with linear equality constraints and objective given as a sum of an entropy regularizer and a linear function. It is known that the state-of-the-art solvers for this problem, which are based on Sinkhorn's method (also known as RSA or balancing method), can fail to work, when the entropy-regularization parameter is small. We consider the above optimization problem as a particular instance of a general strongly convex optimization problem with linear constraints. We propose a new algorithm to solve this general class of problems. Our approach is based on the transition to the dual problem. First, we introduce a new accelerated gradient method with adaptive choice of gradient's Lipschitz constant. Then, we apply this method to the dual problem and show, how to reconstruct an approximate solution to the primal problem with provable convergence rate. We prove the rate $O(1/k^2)$, $k$ being the iteration counter, both for the absolute value of the primal objective residual and constraints infeasibility. Our method has similar to Sinkhorn's method complexity of each iteration, but is faster and more stable numerically, when the regularization parameter is small. We illustrate the advantage of our method by numerical experiments for the two mentioned applications. We show that there exists a threshold, such that, when the regularization parameter is smaller than this threshold, our method outperforms the Sinkhorn's method in terms of computation time.
Interface Engineering for Steep Slope Cryogenic MOSFETs

In this work, we study experimentally the impact of different gate dielectric stacks on the subthreshold behavior of cryogenic MOSFETs. While in room temperature devices, silicon nitride deteriorates the off-state of MOSFETs it turns out that at cryogenic temperatures an appropriately thin, grown silicon nitride layer in combination with a high-k gate dielectric counteracts the saturation of the inverse subthreshold slope and inflection phenomena. As a result, steep slope cryogenic MOSFETs with strongly improved subthreshold behavior are demonstrated.
Local-in-time Physical Solutions of the Incompressible Semi-Geostrophic Equations in Eulerian Coordinates

We prove the existence of local-in-time smooth solutions of the incompressible semi-geostrophic equations expressed in Eulerian co-ordinates in 3-dimensional smooth bounded simply-connected domains. Our solutions adhere to Cullen's Stability Principle in that the geopotential is guaranteed to be a convex map for all times of its existence. We achieve our results by appealing to the theory of so-called div-curl systems (or Hodge systems), making use of recent results of Wang, which yield useful estimates on the ageostrophic velocity field. To our knowledge, this work constitutes the first time that any notion of bounded solution of the semi-geostrophic equations in Eulerian co-ordinates has been constructed on a bounded domain. Indeed, our work solves an open problem as highlighted by, among others, A. Figalli in his CIME lectures on the semi-geostrophic equations. Our methods are largely elementary. We discuss the application of the novel ideas in this work to the case of variable Coriolis force in the final section of the article.
The Classification of Subfactors with Index at Most 5\frac{1}4

Subfactor standard invariants encode quantum symmetries. The small index subfactor classification program has been a rich source of interesting quantum symmetries. We give the complete classification of subfactor standard invariants to index 5 1 4 5\frac {1}{4} , which includes 3 + 5 3+\sqrt {5} , the first interesting composite index.
Characterization of generalized quasi-arithmetic means

In this paper we characterize generalized quasi-arithmetic means, that is means of the form M ( x _1,., x _n) ≔ ( f _1 + ⋯ + f _n)^−1( f _1( x _1) + … + f _n( x _n)), where f _1,. , f _n: I → ℝ are strictly increasing and continuous functions. Our characterization involves the Gauss composition of the cyclic meantype mapping induced by M and a generalized bisymmetry equation.
Type A quiver loci and Schubert varieties

We describe a closed immersion from each representation space of a type A quiver with bipartite (i.e., alternating) orientation to a certain opposite Schubert cell of a partial flag variety. This "bipartite Zelevinsky map" restricts to an isomorphism from each orbit closure to a Schubert variety intersected with the above-mentioned opposite Schubert cell. For type A quivers of arbitrary orientation, we give the same result up to some factors of general linear groups. These identifications allow us to recover results of Bobinski and Zwara; namely we see that orbit closures of type A quivers are normal, Cohen-Macaulay, and have rational singularities. We also see that each representation space of a type A quiver admits a Frobenius splitting for which all of its orbit closures are compatibly Frobenius split.
Polynomially convex embeddings of even-dimensional compact manifolds

We show that, for $k>1$, any $2k$-dimensional compact submanifold of $\mathbb{C}^{3k-1}$ can be perturbed to be polynomially convex and totally real except at a finite number of points. This lowers the known bound on the number of smooth functions required on every $2k$-manifold $M$ to generate a dense subalgebra of $\mathcal{C}(M)$. We also show that the obstruction to isotropic embeddability of all $2k$-dimensional manifolds in $\mathbb{C}^{3k-1}$ does not persist if we allow for K\"ahler forms with isolated degeneracies.
A Bloch transform based numerical method for the rough surface scattering problems

In this paper, we will study the Bloch transformed rough surface scattering problems, and propose a numerical method based on the Bloch transformed problems. Based on the mathematical theory of the scattering problems from locally perturbed periodic surfaces, the same techniques will be applied to the rough surface scattering problems, and an equivalent coupled family of quasi-periodic scattering problems in one periodic cell will be established. The most important result obtained in this paper is on the finite Fourier series approximation of the Bloch transformed field with respect to the quasi-periodicity parameter. It will be proved that the finite series is exactly the Bloch transformed solution corresponds to truncated rough surfaces. Thus the truncation provides a reasonable approximation, and could be applied to the numerical solutions. Based on the approximation, a numerical method is proposed for the rough surface scattering problems. The convergence of the numerical method is proved and illustrated by the numerical experiments. The method provides a completely new perspective for the rough surface scattering problems. There is possibility that some high order method will be developed based on this new method.
Random Hermitian matrices and Gaussian multiplicative chaos

We prove that when suitably normalized, small enough powers of the absolute value of the characteristic polynomial of random Hermitian matrices, drawn from one-cut regular unitary invariant ensembles, converge in law to Gaussian multiplicative chaos measures. We prove this in the so-called $$L^2$$L2-phase of multiplicative chaos. Our main tools are asymptotics of Hankel determinants with Fisher–Hartwig singularities. Using Riemann–Hilbert methods, we prove a rather general Fisher–Hartwig formula for one-cut regular unitary invariant ensembles.