Miracle-dz/UniFAR-FTUs huggingface dataset:
Center-focus determination and limit cycles bifurcation for $p:q$ homogeneous weight singular point

The quasi-homogeneous (and in general non-homogeneous) polynomial differential systems have been studied from many different points of view. In this paper, Center-focus determination and limit cycles bifurcation for $p:q$ homogeneous weight singular point are investigated. Some prosperities of Successive function and focus values are discussed, furthermore, the method of computing focal values is given. As an example, center-focus determination and limit cycle bifurcation for $2:3$ homogeneous weight singular point are studied, three or five limit cycles in the neighborhood of origin can be obtained by different perturbations.
Topological Quantum Computation with Gapped Boundaries

This paper studies fault-tolerant quantum computation with gapped boundaries. We first introduce gapped boundaries of Kitaev's quantum double models for Dijkgraaf-Witten theories using their Hamiltonian realizations. We classify the elementary excitations on the boundary, and systematically describe the bulk-to-boundary condensation procedure. We also provide a commuting Hamiltonian to realize defects between boundaries in any quantum double model. Next, we present the algebraic/categorical structure of gapped boundaries and boundary defects, which will be used to describe topologically protected operations and obtain quantum gates. To demonstrate a potential physical realization, we provide quantum circuits for surface codes that can perform all basic operations on gapped boundaries. Finally, we show how gapped boundaries of the abelian theory $\mathfrak{D}(\mathbb{Z}_3)$ can be used to perform universal quantum computation.
Complete Monotonicity Properties of a Function Involving the Polygamma Function

In this paper, we study completete monotonicity properties of the function $f_{a,k}(x)=\psi^{(k)}(x+a) - \psi^{(k)}(x) - \frac{ak! }{x^{k+1}}$, where $a\in(0,1)$ and $k\in \mathbb{N}_0$. Specifically, we consider the cases for $k\in \{ 2n: n\in \mathbb{N}_0 \}$ and $k\in \{ 2n+1: n\in \mathbb{N}_0 \}$. Subsequently, we deduce some inequalities involving the polygamma functions.
THE LOW-MASS, HIGHLY ACCRETING BLACK HOLE ASSOCIATED WITH THE ACTIVE GALACTIC NUCLEUS 2XMM J123103.2+110648

Optical spectra and images taken with the Baade 6.5 m Magellan telescope confirm that 2XMM J123103.2+110648, a highly variable X-ray source with an unusually soft spectrum, is indeed associated with a type 2 (narrow-line) active nucleus at a redshift of z = 0.11871. The absence of broad Hα or Hβ emission in an otherwise X-ray unabsorbed source suggests that it intrinsically lacks a broad-line region. If, as in other active galaxies, the ionized gas and stars in J1231+1106 are in approximate virial equilibrium, and the MBH − σ* relation holds, the exceptionally small velocity dispersion of σ = 33.5 km s−1 for [O iii] λ5007 implies that MBH ≈ 105 M☉, among the lowest ever detected. Such a low black hole mass is consistent with the general characteristics of the host, a small, low-luminosity, low-mass disk galaxy. We estimate the Eddington ratio of the black hole to be ≳0.5, in good agreement with expectations based on the X-ray properties of the source.
Treatment of Jumper’s Knee with Extracorporeal Shockwave Therapy: A Systematic Review and Meta-Analysis

Abstract The aim of this systematic review and meta-analysis was to determine the therapeutic efficacy of extracorporeal shockwave therapy (ESWT) for athletes with patellar tendinopathy. We searched PubMed, EBSCOHost and Ovid for randomized controlled trials (RCTs) which evaluated the therapeutic efficacy of ESWT in athletes with jumper’s knee. The methodological quality of RCTs was rated with the Physiotherapy Evidence Database scale. Data in the meta-analysis were expressed as standardized mean difference (SMDs) and 95% confidence intervals (CIs). Heterogeneity was assessed with I2 statistics. Of 192 records identified, a total of seven articles met the inclusion criteria. The ESWT and control groups with any other conservative treatment did not differ significantly with respect to the Visual Analogue Scale (VAS) long-term scores obtained at ≥ 6 months of therapy completion (SMD: -0.33; 95% CI: -4.64 to 3.98; p = 0.87; I2= 98%). Furthermore, no significant differences were found between the ESWT and control groups regarding the pooled Victorian Institute of Sports Assessment for Patella (VISA-P) scores for long-term outcomes (SMD: 8.21; 95% CI: -39.3 to 55.73; p = 0.73; I2= 99%). The ESWT and control groups did not differ significantly on the VAS and VISA-P scores for long-term outcomes. In both cases, heterogeneity was considered to be high. Hence, no clear and generalized conclusions can be drawn regarding ESWT effectiveness in athletes with patellar tendinopathy.
Ultrahigh energy collision with neither black hole nor naked singularity

We explore the collision between two concentric spherical thin shells. The inner shell is charged, whereas the outer one is either neutral or charged. In the situation we consider, the charge of the inner shell is larger than its gravitational mass, and the inside of it is empty and regular. Hence the domain just outside it is described by the overcharged Reissner-Nordstrom geometry whereas the inside of it is Minkowski. First, the inner shell starts to shrink form infinity with finite kinetic energy, and then the outer shell starts to shrink from infinity with vanishing kinetic energy. The inner shell bounces on the potential wall and collides with the ingoing outer shell. The energy of collision between these shells at "their center of mass frame" does not exceed the total energy of the system. By contrast, by virtue of the very large gamma factor of the relative velocity of the shells, the energy of collision between two of the constituent particles of these shells at their center of mass frame can be much larger than the Planck scale. This result suggests that the black hole or naked singularity is not necessary for ultra-high energy collision of particles.
Forced gradings in integral quasi-hereditary algebras with applications to quantum groups

Let $\sO$ be a discrete valuation ring with fraction field $K$ and residue field $k$. A quasi-hereditary algebra $\wA$ over $\sO$ provides a bridge between the representation theory of the quasi-hereditary algebra $\wA_K:=K\otimes \wA$ over the field $K$ and the quasi-hereditary algebra $A_k:=k\otimes_\sO\wA$ over $k$. In one important example, $\wA_K$--mod is a full subcategory of the category of modules for a quantum enveloping algebra while $\wA_k$--mod is a full subcategory of the category of modules for a reductive group in positive characteristic. This paper considers first the question of when the positively graded algebra $\gr \wA:= \bigoplus_{n\geq 0}(\wA\cap\rad^n\wA_K)/(\wA\cap\rad^{n+1}\wA_K)$ is quasi-hereditary. A main result gives sufficient conditions that $\gr\wA$ be quasi-hereditary. The main requirement is that each graded module $\gr\wDelta(\lambda)$ arising from a $\wA$-standard (Weyl) module $\wDelta(\lambda)$ have an irreducible head. An additional hypothesis requires that the graded algebra $\gr \wA_K$ be quasi-hereditary, a property recently proved by us to hold in some important cases involving quantum enveloping algebras. In the case where $\wA$ arises from regular dominant weights for a quantum enveloping algebra at a primitive $p$th root of unity for a prime $p>2h-2$ (where $h$ is the Coxeter number), a second main result shows that $\gr\wA$ is quasi-hereditary. The proof depends on previous work of the authors, including a continuation of the methods there involving tightly graded subalgebras, and a development of a quantum deformation theory over $\sO$, worthy of attention in its own right, extending the work of Andersen-Jantzen-Soergel. As we point out, this work provides an essential step in our work on $p$-filtrations of Weyl modules for reductive algebraic groups over fields of positive characteristic.
Local well-posedness for quadratic Schr\"odinger equations in $\mathbf{R^{1+1}}$: a normal form approach

For the Schr\"odinger equation $u_t+i u_{xx}=\nab^\be[u^2]$, $\be\in (0,1/2)$, we establish local well-posedness in $H^{\be-1+}$ (note that if $\be=0$, this matches, up to an endpoint, the sharp result of Bejenaru-Tao, \cite{BT}). Our approach differs significantly from the previous ones in that we use normal form transformation to analyze the worst interacting terms in the nonlinearity and then show that the remaining terms are (much) smoother. In particular, this allows us to conclude that $u-e^{-i t \p_x^2} u(0)\in H^{-\f{1}{2}}(\rone)$, even though $u(0)\in H^{\be-1+}$. In addition and as a byproduct of our normal form analysis, we obtain a Lipschitz continuity property in $H^{-\f{1}{2}}$ of the solution operator (which originally acts on $H^{\be-1+}$), which is new even in the case $\be=0$. As an easy corollary, we obtain local well-posedness results for $u_t+ i u_{xx} = [\nab^{\beta} u]^2$. Finally, we sketch an approach to obtain similar statements for the equations $u_t+i u_{xx}=\nab^\be[u\bar{u}]$ and $u_t+i u_{xx}=\nab^\be[\bar{u}^2]$.
Machine learning models can predict the presence of variants in hemoglobin: artificial neural network-based recognition of human hemoglobin variants by HPLC

Abstract Objectives This article presents the use of machine learning techniques such as artificial neural networks, K-nearest neighbors (KNN), naive Bayes, and decision trees in the prediction of hemoglobin variants. To the best of our knowledge, this is the first study using machine learning models to predict suspicious cases with HbS or HbD Los Angeles carriers state. Methods We had a dataset of 238 observations, of which 128 were HbD carriers, and 110 were HbS carriers. The features were age, sex, RBC, Hb, HTC, MCV, MCH, RDW, serum iron, TIBC, ferritin, HbA2, HbF, HbA0, retention time (RT) of the abnormal peak, and the area under the peak of the abnormal peak. KNN, naive Bayes, decision tree models, and artificial neural network models were trained. Model performances were estimated using 7-fold cross-validation. Results When RT, the key point of differentiation used in high-performance liquid chromatography (HPLC), was included as a feature, all models performed well. When RT was excluded (eliminated), the deep learning model performed the best (Accuracy: 0.99; Specificity: 0.99; Sensitivity: 0.99; F1 score: 0.99), while the naive Bayes model performed the worst (Accuracy: 0.94; Specificity: 0.97; Sensitivity: 0.90; F1 score: 0.93). Conclusions Deep learning and decision tree models have demonstrated high performance and have the potential to be integrated into medical laboratory work practices as a tool for hemoglobinopathy detection. These outcomes suggest that when machine learning models are fed enough data, they can detect a wide range of hemoglobin variants. However, more comprehensive studies with data from a larger number of patients and hemoglobinopathies will be useful for validating our models.
The Mechanical and Efficiency Constraints When Swimming Front Crawl with the Aquanex System

Abstract The aim of this study was to compare the mechanical and efficiency constraints between free swim and swimming with differential pressure sensors (Aquanex System). These conditions were also analysed to understand the differences between sexes. Thirty young swimmers, 14 boys and 16 girls (12.31 ± 0.67 years) performed three 25-m front crawl maximal bouts under each condition: free swim and swimming with sensors. Under the condition with sensors, swimmers carried the Aquanex System composed of two hand pressure sensors (v.4.1, Model DU2, Type A, Swimming Technology Research, Richmond, VA, USA). The 25-m time (T25) was assessed as a swimming performance variable. The swimming velocity (v), stroke rate (SR), and stroke length (SL) were assessed and calculated as stroke mechanics variables. Thereafter, the stroke index (SI) and arm stroke efficiency (ηF) were estimated for swimming efficiency. Statistical significance was set at p ≤ 0.05. Swimming performance was impaired when swimmers swam with sensors (overall: p = 0.03, d = 0.14; Δ = 1.30%) and a significant decrease in v was found for overall (p = 0.04, d = 0.14; Δ = 1.42%) and the girls’ group (p < 0.01, d = 0.39; Δ = -1.99%). The remaining stroke mechanics variables showed no differences between conditions, as well as for swimming efficiency. Furthermore, there were no differences between girls and boys in free swim and with sensors for all variables. Swimming with the Aquanex System seems not to impose constraints in the mechanics and efficiency of young swimmers, despite differences in swimming performance and v.
‘We don’t speak the same language:’ language choice and identity on a Tunisian internet forum

Abstract The linguistic situation in the Arab world is in an important state of transition, with the “spoken” vernaculars increasingly functioning as written languages as well. While this fact is widely acknowledged and the subject of a growing body of qualitative literature, there is little quantitative research detailing the process in action. The current project examines this development as it is occurring in Tunisia: I present the findings from a corpus study comparing the frequency of Tunisian Arabic–Standard Arabic equivalent pairs in online forum posts from 2010 with those from 2021. The findings show that the proportion of Tunisian lexical items, compared to their Standard Arabic equivalents, increased from a minority (19.7%) to a majority (69.9%) over this period. At the same time, metalinguistic comments on the forum reveal that, although its status is still contentious, Tunisian has become unmarked as a written language. These changes can be attributed to major developments in Tunisian society over the period of study – including internet access and the 2011 revolution. These findings suggest destabilization of the diglossic language situation in Tunisia and a privileging of national identity vis-à-vis the rest of the Arab world.
A Fourier-based Picard-iteration approach for a class of McKean–Vlasov SDEs with Lévy jumps

We consider a prototype class of Lévy-driven stochastic differential equations (SDEs) with McKean–Vlasov (MK–V) interaction in the drift coefficient. It is assumed that the drift coefficient is affine in the state variable, and only measurable in the law of the solution. We study the equivalent functional fixed-point equation for the unknown time-dependent coefficients of the associated linear Markovian SDE. By proving a contraction property for the functional map in a suitable normed space, we infer existence and uniqueness results for the MK–V SDE, and derive a discretized Picard iteration scheme that approximates the law of the solution through its characteristic function. Numerical illustrations show the effectiveness of our method, which appears to be appropriate to handle the multi-dimensional setting.
Onsager symmetries in U(1)-invariant clock models

We show how the Onsager algebra, used in the original solution of the two-dimensional Ising model, arises as an infinite-dimensional symmetry of certain self-dual models that also have a symmetry. We describe in detail the example of nearest-neighbour n-state clock chains whose symmetry is enhanced to . As a consequence of the Onsager-algebra symmetry, the spectrum of these models possesses degeneracies with multiplicities 2N for positive integer N. We construct the elements of the algebra explicitly from transfer matrices built from non-fundamental representations of the quantum-group algebra . We analyse the spectra further by using both the coordinate Bethe ansatz and a functional approach, and show that the degeneracies result from special exact n-string solutions of the Bethe equations. We also find a family of commuting chiral Hamiltonians that break the degeneracies and allow an integrable interpolation between ferro- and antiferromagnets.
Adaptive Stochastic Variance Reduction for Subsampled Newton Method with Cubic Regularization

The cubic regularized Newton method of Nesterov and Polyak has become increasingly popular for nonconvex optimization because of its capability of finding an approximate local solution with a second order guarantee and its low iteration complexity. Several recent works extend this method to the setting of minimizing the average of N smooth functions by replacing the exact gradients and Hessians with subsampled approximations. It is shown that the total Hessian sample complexity can be reduced to be sublinear in N per iteration by leveraging stochastic variance reduction techniques. We present an adaptive variance reduction scheme for a subsampled Newton method with cubic regularization and show that the expected Hessian sample complexity is [Formula: see text] for finding an [Formula: see text]-approximate local solution (in terms of first and second order guarantees, respectively). Moreover, we show that the same Hessian sample complexity is retained with fixed sample sizes if exact gradients are used. The techniques of our analysis are different from previous works in that we do not rely on high probability bounds based on matrix concentration inequalities. Instead, we derive and utilize new bounds on the third and fourth order moments of the average of random matrices, which are of independent interest on their own.
Systems for Socially-Challenging Information Management

In collaborative settings, information management becomes even more challenging. In addition to the classic challenge of information management (i.e. information overload), collaboration also introduces social barriers between group members; this entails asymmetric roles, where different stakeholders have different levels of motivation, knowledge, social capital, authority, or time. To successfully manage their information, groups of people need to coordinate their needs and resources. In my thesis, I focus on building interfaces for lowering social burdens to negotiate and communicate the distribution of resources. I develop coordination systems that guide interaction for collaborative information-management tasks. I first introduce a system called Ziva, which supports interdisciplinary teams by coordinating information exchange. Then, I describe TaskLight, which aims to support information management during the help-seeking process. Lastly, I present challenges of coordinating tool preferences and a resulting system called CollaboRanger.
Owl: performance-aware scheduling for resource-efficient function-as-a-service cloud

This work documents our experience of improving the scheduler in Alibaba Function Compute, a public FaaS platform. It commences with our observation that memory and CPU are under-utilized in most FaaS sandboxes. A natural solution is to overcommit VM resources when allocating sandboxes, whereas the ensuing contention may cause performance degradation and compromise user experience. To complicate matters, the degradation in FaaS can arise from external factors, such as failed dependencies of user functions. We design Owl to achieve both high utilization and performance stability. It introduces a customizable rule system for users to specify their toleration of degradation, and overcommits resources with a dual approach. (1) For less-invoked functions, it allocates resources to the sandboxes with usage-based heuristic, keeps monitoring their performance, and remedies any detected degradation. It differentiates whether a degraded sandbox is affected externally by separating a contention-free environment and migrating the affected sandbox into there as a comparison baseline. (2) For frequently-invoked functions, Owl profiles the interference patterns among collocated sandboxes and place the sandboxes under the guidance of profiles. The collocation profiling is designed to tackle the constraints that profiling has to be conducted in production. Owl further consolidates idle sandboxes to reduce resource waste. We prototype Owl in our production system and implement a representative benchmark suite to evaluate it. The results demonstrate that the prototype could reduce VM cost by 43.80% and effectively mitigate latency degradation, with negligible overhead incurred.
Putting Users in Control of Social Platforms for Better Content Credibility

My research is on re-imagining the design of social media and more broadly the web to achieve greater end user empowerment. I believe one of the implications of this greater user empowerment can be higher credibility of content. In this pursuit, I investigate alternative designs to the status quo of the existing social media platforms which prioritize engagement over accuracy. It is known that misinformation—especially that which promotes outrage—can generate substantial engagement [3]. Therefore, platforms, despite their visible efforts to combat misinformation, may in fact be reluctant to succeed in increasing accuracy. In fact, their prioritization of engagement over accuracy can at times undermine users’ own efforts to combat misinformation on the platforms. For instance, a user who encounters an incorrect post and then leaves a comment refuting it may in fact be inadvertently disseminating it farther because the system considers the comment as engagement. Another related failure in design is the lack of clear signals for capturing and displaying content credibility, leading engagement metrics such as the number of likes and shares to affect users’ perception of content credibility [2]. Yet another suboptimal design decision is an emphasis on low barriers to sharing that allows users to share content without much attention to its accuracy or potential negative consequences, simply to receive social feedback or elevated engagement [4, 7].
Arax: a runtime framework for decoupling applications from heterogeneous accelerators

Today, using multiple heterogeneous accelerators efficiently from applications and high-level frameworks, such as Tensor-Flow and Caffe, poses significant challenges in three respects: (a) sharing accelerators, (b) allocating available resources elastically during application execution, and (c) reducing the required programming effort. In this paper, we present Arax, a runtime system that decouples applications from heterogeneous accelerators within a server. First, Arax maps application tasks dynamically to available resources, managing all required task state, memory allocations, and task dependencies. As a result, Arax can share accelerators across applications in a server and adjust the resources used by each application as load fluctuates over time. Additionally, Arax offers a simple API and includes Autotalk, a stub generator that automatically generates stub libraries for applications already written for specific accelerator types, such as NVIDIA GPUs. Consequently, Arax applications are written once without considering physical details, including the number and type of accelerators. Our results show that applications, such as Caffe, TensorFlow, and Rodinia, can run using Arax with minimum effort and low overhead compared to native execution, about 12% (geometric mean). Arax supports efficient accelerator sharing, by offering up to 20% improved execution times compared to NVIDIA MPS, which supports NVIDIA GPUs only. Arax can transparently provide elasticity, decreasing total application turn-around time by up to 2X compared to native execution without elasticity support.