Miracle-dz/UniFAR-FTUs huggingface dataset:
A precolouring extension of Vizing's theorem

Fix a palette K of Δ+1 colors, a graph with maximum degree Δ , and a subset M of the edge set with minimum distance between edges at least 9 . If the edges of M are arbitrarily precoloured from K , then there is guaranteed to be a proper edge‐coloring using only colors from K that extends the precolouring on M to the entire graph. This result is a first general precolouring extension form of Vizing's theorem, and it proves a conjecture of Albertson and Moore under a slightly stronger distance requirement. We also show that the condition on the distance can be lowered to 5 when the graph contains no cycle of length 5 .
On Hamilton cycles in Erd\H{o}s-R\'{e}nyi subgraphs of large graphs

Given a graph $\Gamma = (V, E)$ on $n$ vertices and $m$ edges, we define the Erd\H{o}s-R\'{e}nyi graph process with host $\Gamma$ as follows. A permutation $e_1,\dots,e_m$ of $E$ is chosen uniformly at random, and for $t\leq m$ we let $\Gamma_t = (V, \{e_1,\dots,e_t\})$. Suppose the minimum degree of $\Gamma$ is $\delta(\Gamma) \geq (1/2 + \varepsilon)n$ for some constant $\varepsilon > 0$. Then with high probability, $\Gamma_t$ becomes Hamiltonian at the same moment that its minimum degree becomes at least two. Given $0\leq p\leq 1$ we let $\Gamma_p$ be the Erd\H{o}s-R\'{e}nyi subgraph of $\Gamma$, obtained by retaining each edge independently with probability $p$. When $\delta(\Gamma)\geq (1/2 + \varepsilon)n$, we provide a threshold function $p_0$ for Hamiltonicity, such that if $(p-p_0)n\to -\infty$ then $\Gamma_p$ is not Hamiltonian whp, and if $(p-p_0)n\to\infty$ then $\Gamma_p$ is Hamiltonian whp.
Matrices over a commutative ring as sums of three idempotents or three involutions

Abstract Motivated by Hirano-Tominaga’s work on rings for which every element is a sum of two idempotents and by de Seguins Pazzis’s results on decomposing every matrix over a field of positive characteristic as a sum of idempotent matrices, we address decomposing every matrix over a commutative ring as a sum of three idempotent matrices and, respectively, as a sum of three involutive matrices.
Preconditioning ideas for the Augmented Lagrangian method

A preconditioning strategy for the Powell-Hestenes-Rockafellar Augmented Lagrangian method (ALM) is presented. The scheme exploits the structure of the Augmented Lagrangian Hessian. It is a modular preconditioner consisting of two blocks. The first one is associated with the Lagrangian of the objective while the second administers the Jacobian of the constraints and possible low-rank corrections to the Hessian. The proposed updating strategies take advantage of ALM convergence results and avoid frequent refreshing. Constraint administration takes into account complementarity over the Lagrange multipliers and admits relaxation. The preconditioner is designed for problems where constraint quantity is small compared to the search space. A virtue of the scheme is that it is agnostic to the preconditioning technique used for the Hessian of the Lagrangian function. The strategy described can be used for linear and nonlinear preconditioning. Numerical experiments report on spectral properties of preconditioned matrices from Matrix Market while some optimization problems where taken from the CUTEst collection. Preliminary results indicate that the proposed scheme could be attractive and further experimentation is encouraged.
Structural anomalies at the magnetic transition in centrosymmetric BiMnO 3

The structural properties of ${\mathrm{BiMnO}}_{3}$ were determined from neutron powder diffraction data as a function of temperature and magnetic field. The structure at all temperatures was found to be centrosymmetric with space group $C2∕c$, which is incompatible with ferroelectricity. At ${T}_{C}\ensuremath{\simeq}100\phantom{\rule{0.3em}{0ex}}\mathrm{K}$, we observed the onset of a large magnetoelastic strain, proportional to the square of the magnetization. We interpret this structural rearrangement, together with the previously observed magnetodielectric anomalies, due to the need to optimize the partially frustrated magnetic interactions.
Critical Thinking Instruction Incorporated in Cross-Cultural Communication Course Design: A Needs Analysis Report Based on Voices of Chinese International College Undergraduates

Critical thinking represents one of the most absolutely vital talents for every individual, both in the workplace and in their personal lives. Critical thinking has become a primary concern for all educational institution students in recent decades, particularly Chinese undergraduates. The intention of this study was to investigate the needs analysis of Chinese international college undergraduates’ perceptions of critical thinking skills incorporated into a cross-cultural communication course, as well as their expectations of critical thinking skills instructional coursework throughout the cross-cultural communication context. Throughout this mixed-methods investigation, 78 Chinese international college students volunteered to complete a critical thinking disposition inventory (CTDI) as the primary research instrument, in addition to a semi-structured interview. The research uncovered that Chinese international undergraduates exhibited unclear notions of critical thinking abilities. As a byproduct of China’s education system, the majority of Chinese international college undergraduates were flooded with dismissive attitudes toward critical thinking abilities. In order to control their academic advancement in a more critical and analytical fashion, Chinese students expressed a pressing need for critical thinking skills to be included in their cross-cultural communication course.
Tropical Geometry over Higher Dimensional Local Fields

We introduce the tropicalization of closed subschemes of a torus defined over a higher dimensional local field. We study the basic invariants of such tropicalizations. This is a generalization of the results of Einslieder, Kapranov, Lind, Speyer and Sturmfels to higher local fields.
A study of the chromospherically active, short-period binary VZ piscium

The short-period binary VZ Piscium is unusual in that it has a high space velocity, indicating that it is old, and a high mass ratio, suggesting that it is presently evolving into contact with little mass exchange having occurred between the components. In this study, we obtained IUE and visible spectra to investigate Mg II h + k and Ca II H and K emission strengths. Both features are found to be strong and variable. From the visible spectra, radial velocities were measured, and a new mass ratio of q = 0.80 was deter-mined. This mass ratio was used in a new light-curve analysis, and the system was found to be in marginal contact, with the secondary component slightly detached. A model with bright (hot) regions on the inner hemisphere of the slightly detached, less massive component was found to fit well with the variety of spectroscopic and photometric observations of the system. The masses determined for the components are compatible with normal K dwarfs.
Predicting Chemotherapy Resistance in Gestational Trophoblastic Neoplasia: Ratio of Neutrophils, Lymphocytes, Monocytes, and Platelets

Background Neutrophil-to-lymphocyte ratio (NLR), lymphocyte-to-monocyte ratio (LMR), and platelet-to-lymphocyte ratio (PLR) have recently been used as inflammatory biomarkers for cancer patients. This study aims to determine the role of pretreatment NLR, LMR, and PLR in predicting chemoresistance in gestational trophoblastic neoplasia (GTN) patients. Material/Methods A total of 129 low-risk and high-risk GTN patients who had received first-line chemotherapy were enrolled in this historical cohort study. The pretreatment NLR, LMR, and PLR values were analyzed to predict the resistance to first-line chemotherapy in low-risk and high-risk GTN patients. Results Chemoresistant patients had significantly higher NLR than chemosensitive patients in low-risk and high-risk GTN patients (P<0.05). In high-risk GTN, patients with lower LMR and higher PLR tended to have chemoresistance to first-line chemotherapy (P=0.008, P=0.001). Univariate analysis revealed that the NLR, LMR, and PLR cut-off points of 2.654, 3.8, and 192.174, respectively, were associated with chemoresistance in high-risk GTN (P=0.0001, P=0.011, P=0.0001). The combination of NLR, PLR, and FIGO score in high-risk GTN was the best combination among other combinations with cut-off value >17 (P=0.001). Conclusions Higher NLR, lower LMR, and higher PLR were associated with chemoresistance for high-risk GTN patients. Furthermore, NLR, LMR, and PLR can improve the accuracy of predicting resistance to first-line chemotherapy in high-risk GTN.
Distributions of Traces of Frobenius for Smooth Plane Curves Over Finite Fields

ABSTRACT We analyze the variation around the mean of the distribution of the number of rational points on non-hyperelliptic genus 3 curves over finite fields, by extrapolating from results on the distribution of traces of Frobenius for plane curves whose degree is small with respect to the cardinality of their finite base field. We put our results in perspective with a numerical study for prime fields of characteristic 11 ⩽ p ⩽ 53. Our methods shed some new light on the asymmetry of the distribution around its mean value, which is related to the Serre obstruction.
Does Melatonin Associated with Nanostructured Calcium Phosphate Improve Alveolar Bone Repair?

Background and objectives: Calcium phosphates have been widely used as bone substitutes, but their properties are limited to osteoconduction. The association of calcium phosphates with osteoinductive bioactive molecules has been used as a strategy in regenerative medicine. Melatonin has been studied due to its cell protection and antioxidant functions, reducing osteoclastic activity and stimulating newly formed bone. This study aimed to evaluate the effect of topical application of melatonin associated with nanostructured carbonated hydroxyapatite microspheres in the alveolar bone repair of Wistar rats through histological and histomorphometric analysis. Materials and Methods: Thirty female Wistar rats (300 g) were used, divided randomly into three experimental groups (n = 10), G1: nanostructured carbonated hydroxyapatite microspheres associated with melatonin gel (CHA-M); G2: nanostructured carbonated hydroxyapatite (CHA); G3: blood clot (without alveolar filling). The animals were euthanized after 7 and 42 days of the postoperative period and processed for histological and histomorphometric evaluation. Kruskal–Wallis and Dunn’s post-test were applied to investigate statistical differences between the groups at the same time point for new bone and connective tissue variables. Mann–Whitney was used to assess statistical differences between different time points and in the biomaterial variable. Results: Results showed a greater volume of residual biomaterial in the CHA-M than the CHA group (p = 0.007), and there were no significant differences in terms of newly formed bone and connective tissue between CHA and CHA-M after 42 days. Conclusions: This study concluded that both biomaterials improved alveolar bone repair from 7 to 42 days after surgery, and the association of CHA with melatonin gel reduced the biomaterial’s biodegradation at the implanted site but did not improve the alveolar bone repair.
Characterization of finitely generated infinitely iterated wreath products

Abstract. Given a sequence of of finite transitive groups of degree ni, let be the inverse limit of the iterated permutational wreath products . We prove that is (topologically) finitely generated if and only if is finitely generated and the growth of the minimal number of generators of Gi is bounded by for a constant d. Moreover we give a criterion to decide whether is positively finitely generated.
Implementation of feedback in smoothed particle hydrodynamics: towards concordance of methods

We perform simulations of feedback from supernovae and black holes with smoothed particle hydrodynamics. Such strong perturbations are inaccurately handled with standard time integration schemes, leading to poor energy conservation, a problem that is commonly overlooked. We show for the first time that, in the absence of radiative cooling, concordance of thermal and kinetic feedback are achieved when using an accurate time integration. In order to preserve the concordance of feedback methods when using a more efficient time integration scheme – as for instance the hierarchical time-step scheme – we implement a modified version of the time-step limiter proposed by Saitoh & Makino. We apply the limiter to general test cases, and first show that this scheme violates energy conservation up to almost 4 orders of magnitude when energy is injected at random times. To tackle this issue, we find it necessary not only to ensure a fast information propagation, but also to enforce a prompt response of the system to the energy perturbation. The method proposed here to handle strong feedback events enables us to achieve energy conservation at per cent level in all tests, even if all the available energy is injected into only one particle. We argue that concordance of feedback methods can be achieved in numerical simulations only if the time integration scheme preserve a high energy conservation level.
Non-uniform and dynamic torsion of elastic beams Part 1: Governing equations and particular solutions

Abstract The double torsion fracture test has been widely used in the past for measuring resistance to crack growth under static loading and, more recently, under high-loading-rate conditions. Specimen deformation in this test is conventionally analysed on the basis of a one-dimensional torsion equation. Under dynamic conditions, it is imperative to establish an accurate torsion equation which can be used to model the double torsion test. The present paper describes the development, in this context, of a dynamic fourth-order partial differential equation for one-dimensional torsion, based on Barr's equation. The equation obtained in this paper accounts for the axial inertia associated with cross-sectional warping and the axial stresses which arise when warping is constrained. The equation can also accommodate non-linear elasticity. The equation is validated, using Barr's own data, for the torsional resonance problem which he studied and, using finite-element analysis, for a problem of constrained static torsion analysed by Timoshenko.
Improving the spin-up of regional EnKF for typhoon assimilation and forecasting with Typhoon Sinlaku (2008)

The Running-In-Place (RIP) method is implemented in the framework of the Local Ensemble Transform Kalman Filter (LETKF) coupled with the Weather Research and Forecasting (WRF) model. RIP aims at accelerating the spin-up of the regional LETKF system when the WRF ensemble is initialised from a global analysis, which is obtained at a coarser resolution and lacks features related to the underlying mesoscale evolution. The RIP method is further proposed as an outer-loop scheme to improve the nonlinear evolution of the ensemble when the characteristics of the error statistics change rapidly owing to strong nonlinear dynamics. The impact of using RIP as an outer-loop for the WRF-LETKF system is evaluated for typhoon assimilation and prediction with Typhoon Sinlaku (2008) as a case study. For forecasts beyond one day, the typhoon track prediction is significantly improved after RIP is applied, especially during the spin-up period of the LETKF assimilation when Sinlaku is developing rapidly from a severe tropical storm to a typhoon. The impact of the dropsondes is significantly increased by RIP at early assimilation cycles. Results suggest that these improvements are because of the positive impact on the environmental condition of the typhoon. Results also suggest that using the RIP scheme adaptively allows RIP to be used as an outer-loop for the WRF-LETKF with further improvements.
Streamline Upwind Finite-Element Method for Overland Flow

A streamline upwind, finite-element method is proposed to solve the two-dimensional (2D) kinematic wave and shallow water wave equations for overland flow problems. The spatial domain is discretized into a network of quadrilateral, bilinear finite elements, and time derivatives are treated by a three-point finite-difference scheme to increase numerical stability. Solutions computed by the streamline upwind method are compared to those of the Galerkin method. Streamline upwind and Galerkin solutions of the kinematic wave equation exhibited good agreement with an analytic solution for flow over an inverted cone. However, the Galerkin solution exhibited oscillations during the steady portion of the runoff hydrograph. Galerkin solutions of the shallow water wave equations for inverted cone and bowl-shaped surfaces displayed oscillations in time and space, while the streamline upwind method exhibited no oscillatory behavior. Results generated by the streamline upwind method agreed well with experimental data sets and simulations conducted with the MacCormack finite-difference method.
Multiple unfoldings of orbifold singularities: Engineering geometric analogies to unification

Katz and Vafa [Nucl. Phys. B497, 146 (1997)] showed how charged matter can arise geometrically by the deformation of ADE-type orbifold singularities in type IIa, M-theory, and F-theory compactifications. In this paper we use those same basic ingredients, used there to geometrically engineer specific matter representations, here to deform the compactification manifold itself in a way which naturally compliments many features of unified model building. We realize this idea explicitly by deforming a manifold engineered to give rise to an SU{sub 5} grand unified model into a one giving rise to the standard model. In this framework, the relative local positions of the singularities giving rise to standard model fields are specified in terms of the values of a small number of complex structure moduli which deform the original manifold, greatly reducing the arbitrariness of their relative positions.
Derived length of zero entropy groups acting on compact Kahler manifolds

Let X be a compact Kahler manifold of dimension n. Let G be a group of zero entropy automorphisms of X. Let G0 be the set of elements in G which are isotopic to the identity. We prove that after replacing G by a suitable finite-index subgroup, G/G0 is a unipotent group of derived length at most n-1. This is a corollary of an optimal upper bound of length involving the Kodaira dimension of X. We also study the algebro-geometric structure of X when it admits a group action with maximal derived length n-1.
2D simulation of a silicon MESFET with a nonparabolic hydrodynamical model based on the maximum entropy principle

A hydrodynamical model for electron transport in silicon semiconductors, which is free of any fitting parameters, has been formulated on the basis of the maximum entropy principle. The model considers the energy band to be described by the Kane dispersion relation and includes electron-nonpolar optical phonon and electron-acoustic phonon scattering. The set of balance equations of the model forms a quasilinear hyperbolic system and for its numerical integration a recent high-order shock-capturing central differencing scheme has been employed. Simulations of an n+-n-n+ silicon diode have been presented and comparison with Monte Carlo data shows the good accuracy of the model and performance of the numerical scheme. Here the results of simulations of a silicon MESFET in the two-dimensional case are presented. Both the model and the numerical scheme demonstrate their accuracy and efficiency as CAD tools for modeling realistic submicron electron devices.
Symplectic resolutions of Quiver varieties and character varieties

In this article, we consider Nakajima quiver varieties from the point of view of symplectic algebraic geometry. We prove that they are all symplectic singularities in the sense of Beauville and completely classify which admit symplectic resolutions. Moreover we show that the smooth locus coincides with the locus of canonically $\theta$-polystable points, generalizing a result of Le Bruyn, and we describe the Namikawa Weyl group. An interesting consequence of our results is that not all symplectic resolutions of quiver varieties appear to come from variation of GIT. We apply this to the $G$-character variety of a compact Riemann surface of genus $g > 0$, when $G$ is $\mathrm{SL}(n,\mathbb{C})$ or $\mathrm{GL}(n,\mathbb{C})$. We show that these varieties are symplectic singularities and classify when they admit symplectic resolutions: they do when $g = 1$ or $(g,n)=(2,2)$ (assuming $n \geq 2$). This is analogous to the case of a quiver with one vertex, $g$ arrows, and dimension vector $(n)$. We note that our results show that existence of proper and projective symplectic resolutions are equivalent for the varieties in question. This does not seem to be known in general.
Continuous cohomology of topological quandles

A continuous cohomology theory for topological quandles is introduced, and compared to the algebraic theories. Extensions of topological quandles are studied with respect to continuous 2-cocycles, and used to show the differences in second cohomology groups for specific topological quandles. A method of computing the cohomology groups of the inverse limit is applied to quandles.
iKnight–Guarding IoT Infrastructure Using Generative Adversarial Networks

With the phenomenal growth of IoT devices and their exponentially increasing applications at the edge of the network, it has become imminent to provide secure, flexible, and programmable network services to support user privacy, security, and quality of service. However, such services can only be enabled and effectively applied when the edge systems automatically identify these devices. Existing IoT classification systems are based on supervised training methods that require labeled data and manual feature extraction. Such approaches suffer from many challenges, such as privacy, labeling efforts, and adaptability to new devices. This paper develops a multistage multi-class classifier based on semi-supervised generative adversarial networks that perform automatic feature extraction with minimal labeled data. The classifier can identify devices with 96% accuracy when only 3% of the training data is labeled. Moreover, the classifier can correctly infer the device type (IoT, non-IoT, and anomaly) of any new device with 90% accuracy. We also show how our model can support various features such as noise robustness, continual learning ability, and novelty detection, such as zero-day malware attacks. Finally, we integrate our classifier with a software-defined network to enable smart IoT network services at the edge.
Pediatric Low-Grade Glioma Surgery with Sodium Fluorescein: Efficient Localization for Removal and Association with Intraoperative Pathological Sampling

Low-grade gliomas are among the most common CNS lesions in pediatrics and surgery is often the first-line treatment. Intraoperative tools have been developed to maximize the results of surgery, and in particular dyes such as sodium fluorescein (SF) have been investigated in high-grade adult lesions. The use of SF in pediatric low-grade gliomas is still unclear. We retrospectively reviewed 22 pediatric CNS low-grade gliomas operated on with SF from September 2021 to October 2022. A total of 86% of lesions showed SF uptake, which was helpful intraoperatively (confirmation of initial localization of the tumor, or identification of tumor remnants) in 74% of them. The intraoperative fluorescence seems associated with gadolinium enhancement at the preoperative MRI. Interestingly, the extemporaneous pathological sampling (EPS) was informative in every case showing SF uptake, whereas in cases without SF uptake, the EPS was non-informative, although the tissue was later confirmed as pathological. These findings highlight the interest of SF for perioperative diagnosis of tumor tissue and may suggest in which cases the differentiation of tumor–healthy tissue could be especially blurred, posing difficulties for the pathologist.