Miracle-dz/UniFAR-FTUs huggingface dataset:
Inversion techniques and combinatorial identities. Basic hypergeometric identities

Based on Carlitz’ q-analogue of the Gould–Hsu inverse series relations, a new insight into basic hypergeometric formulas is offered. Most q-series identities are revisited throught the embedding technique, and some new ones are demonstrated too. 0. Introduction Recently, basic hypergeometric series (q-series) computation has attracted new interest in the mathematical world for its wide application to mathematics, physics and computer science. But the basic formulas often involved in computation are so subtle that their derivation is not easy and so in most situations they are only regarded as prescribed fact. Therefore it seems desirable to gain new insight and to revisit the most well known q-series identities so that the non-specialist may recover their connections without need of reproving each individual formula. During the past few years, Hsu and the author [11] thought that the Gould–Hsu inverse relation [17] could be used to establish relations among binomial identities (ordinary hypergeometric identities according to Andrews’ view). This has been accomplished in the author’s work [9, 10] a short time ago. Now it is natural to consider the q-analogue of the work mentioned above. That is the purpose of the present paper which will show that most basic hypergeometric formulae can be reproduced in a unified manner throught the Carlitz q-analogue [8] of the Gould–Hsu inverse series relations. 1980 Mathematics Subject Classification (1985 Revision): 05A30.
Forelimb Resistance Exercise Protects Against Neuromuscular Junction Denervation in the SOD1-G93A Rat Model of ALS

Introduction The symptoms of Amyotrophic Lateral Sclerosis (ALS) include muscle weakness and eventual paralysis. These symptoms result from denervation of the neuromuscular junction (NMJ) and motor neuron cell death in the brain and spinal cord. Due to the “dying back” pattern of motor neuron degeneration, protecting NMJs should be a therapeutic priority. Although exercise has the potential to protect against NMJ denervation, its use in ALS has been controversial. Most preclinical studies have focused on aerobic exercise, which report that exercise can be beneficial at moderate intensities. The effects of resistance exercise on NMJ preservation in limb muscles have not been explored. Methods We trained male SOD1-G93A rats, which model ALS, to perform a unilateral isometric forelimb resistance exercise task. This task allows within-animal comparisons of trained and untrained forelimbs. We then determined the effects of isometric resistance exercise on NMJ denervation and AMP kinase (AMPK) activation in forelimb muscles. Results Our results revealed that SOD1-G93A rats were able to learn and perform the task similarly to wildtype rats, even after loss of body weight. SOD1-G93A rats exhibited significantly greater NMJ innervation in their trained vs their untrained forelimb biceps muscles. Measures of activated (phosphorylated) AMPK (pAMPK) were also greater in the trained vs untrained forelimb triceps muscles. Discussion These results demonstrate that isometric resistance exercise may protect against NMJ denervation in ALS. Future studies are required to determine the extent to which our findings generalize to female SOD1-G93A rats and to other subtypes of ALS.
Topology optimization design of compliant amplification mechanisms with low parasitic displacement

Compliant amplification mechanisms amplify input displacement in the desired output direction. However, owing to structural design, parasitic motion can easily be produced in an unexpected direction. The parasitic motion has a negative effect on the motion accuracy of the mechanism. To solve this problem, a topology optimization method for compliant amplification mechanisms with low parasitic displacement was proposed. Based on the variable density topology optimization method, the topology optimization model of the compliant amplification mechanism was established with the goal of increasing the output displacement and reducing the parasitic displacement. Volume ratio was set as constraint condition. The optimization criterion method were used to solve the problem and topology optimized amplification mechanisms (TOAMs) were obtained. Simultaneously, the configuration characteristics and displacement amplification ratios of the mechanism under different virtual spring stiffnesses were compared. To verify the validity of the method, the performance of the TOAM and the typical amplification mechanism (TAM) were compared using finite element simulation. The displacement amplification ratio is 5.95 and 3.17, and the relative parasitic displacement is 0.6% and 10.27%, respectively. Finally, the performance of the TOAM and the TAM was verified by experiments. The displacement amplification ratio is 5.72 and 3.06, and the relative parasitic displacement is 0.95% and 10.64%, respectively. Simulation and experimental results show that the TOAM has a larger displacement amplification ratio and a lower parasitic displacement, which verifies the validity of this method.
A lower bound on the spectrum of unimodular networks

Unimodular networks are a generalization of finite graphs in a stochastic sense. We prove a lower bound to the spectral radius of the adjacency operator and of the Markov operator of an unimodular network in terms of its average degree. This allows to prove an Alon-Boppana type bound for the largest eigenvalues in absolute value of large, connected, bounded degree graphs, which generalizes the Alon-Boppana Theorem for regular graphs. A key step is establishing a lower bound to the spectral radius of a unimodular tree in terms of its average degree. Similarly, we provide a lower bound on the volume growth rate of an unimodular tree in terms of its average degree.
Depth $0$ Nonsingular Morse Smale flows on $S^3$

In this paper, we first develope the concept of Lyapunov graph to weighted Lyapunov graph (abbreviated as WLG) for nonsingular Morse-Smale flows (abbreviated as NMS flows) on $S^3$. WLG is quite sensitive to NMS flows on $S^3$. For instance, WLG detect the indexed links of NMS flows. Then we use WLG and some other tools to describe nonsingular Morse-Smale flows without heteroclinic trajectories connecting saddle orbits (abbreviated as depth $0$ NMS flows). It mainly contains the following several directions: \begin{enumerate} \item we use WLG to list depth $0$ NMS flows on $S^3$; \item with the help of WLG, comparing with Wada's algorithm, we provide a direct description about the (indexed) link of depth $0$ NMS flows; \item to overcome the weakness that WLG can't decide topologically equivalent class, we give a simplified Umanskii Theorem to decide when two depth $0$ NMS flows on $S^3$ are topological equivalence; \item under these theories, we classify (up to topological equivalence) all depth 0 NMS flows on $S^3$ with periodic orbits number no more than 4. \end{enumerate}
Left ventricular deformation in athletes playing sports with high dynamics—insights from the three-dimensional speckle-tracking echocardiographic MAGYAR-Sport Study

Background Earlier results suggest the role of speckle-tracking echocardiography (STE)-derived left ventricular (LV) strains in screening and could help better understanding of adaptation to exercise. The present retrospective cohort study aimed to investigate three-dimensional STE-derived LV strains representing its deformation in athletes playing sports with high dynamics with different grades of static components of their training. Methods The study consisted of 67 athletes (mean age: 23.6±6.4 years, 39 males). This group of athletes was further divided into the following groups: Group C.I. (high dynamic/low static) (n=12), Group C.II. (high dynamic/moderate static) (n=22) and Group C.III. (high dynamic/high static) (n=33). The control group comprised 83 age- and gender-matched non-athletic healthy volunteers (mean age: 23.6±3.2 years, 50 males). Results Global LV longitudinal strain (LS) representing LV lengthening or shortening (−18.5%±3.0% vs. −16.3%±2.3%, P<0.05), LV circumferential strain (CS) representing LV widening or narrowing (−29.9%±5.2% vs. −28.1%±4.8%, P<0.05) and LV area strain (AS; combination of LS and CS; −43.7%±5.4% vs. −40.9%±4.8%, P<0.05) were increased in elite athletes as compared to those of non-athlete controls. All apical LV strains proved to be increased in all athletes with enhanced basal radial strain (RS, representing LV thickening and thinning) and LS and midventricular LS, AS and 3D strain (3DS, combination of RS, LS and CS). Conclusions Increased LV-LS, LV-CS and LV-AS represents enhanced LV deformation in longitudinal and circumferential directions in athletes playing sports with high dynamics. This enhancement is not related to the grade of the static component of training. Some regional differences in LV strains could be detected.
Solution of the Dirac Equation for Potential Interaction

An effective approach for solving the three-dimensional Dirac equation for spherically symmetric local interactions, which we have introduced recently, is reviewed and consolidated. The merit of the approach is in producing Schrodinger-like equation for the spinor components that could simply be solved by correspondence with well-known exactly solvable non-relativistic problems. Taking the nonrelativistic limit will reproduce the nonrelativistic problem. The approach has been used successfully in establishing the relativistic extension of all classes of shape invariant potentials as well as other exactly solvable nonrelativistic problems. These include the Coulomb, Oscillator, Scarf, Poschl-Teller, Woods-Saxon, etc.
BAYESIAN HYPER‐LASSOS WITH NON‐CONVEX PENALIZATION

The Lasso has sparked interest in the use of penalization of the log‐likelihood for variable selection, as well as for shrinkage. We are particularly interested in the more‐variables‐than‐observations case of characteristic importance for modern data. The Bayesian interpretation of the Lasso as the maximum a posteriori estimate of the regression coefficients, which have been given independent, double exponential prior distributions, is adopted. Generalizing this prior provides a family of hyper‐Lasso penalty functions, which includes the quasi‐Cauchy distribution of Johnstone and Silverman as a special case. The properties of this approach, including the oracle property, are explored, and an EM algorithm for inference in regression problems is described. The posterior is multi‐modal, and we suggest a strategy of using a set of perfectly fitting random starting values to explore modes in different regions of the parameter space. Simulations show that our procedure provides significant improvements on a range of established procedures, and we provide an example from chemometrics.
The IDEA detector concept for FCCee

The Future Circular Collider (FCC) will allow to perform detailed studies on particle physics thanks to the available high statistic and the precision with which the particle energy and beam polarization will be known. In order to exploit such opportunities, very high performance experiments have to be installed at the interaction points. The two baseline options, included in the Conceptual Design Report of FCC are CLD, based on the ILC-like detector design
Bigger Fish to Fry: The Interdependence of Earnings and ESG News in Investor Screening

We examine how investors respond to concurrent financial and ESG performance news and the implications of their response for investor screening. Our analyses reveal that investors respond more strongly to ESG performance news during earnings announcement (EA) periods than non-EA periods. We also show that negative ESG performance news is typically more salient to investors, and that investors conduct negative screening based on this dimension. In contrast, investors do not screen on ESG performance news when earnings information is negative. Collectively, our results highlight the interdependence between investor use of information from different sources, and thereby contribute to a more complete understanding of the joint importance of financial and ESG performance information in evaluating investment alternatives. JEL M41, D83, G14, G32
Remarks on motives of moduli spaces of rank 2 vector bundles on curves

Let $C$ be an algebraic curve of genus $g \geq 2$ and $M_L$ be the moduli space of rank 2 stable vector bundles on $C$ whose determinants are isomorphic to a fixed line bundle $L$ of degree 1 on $C. $ S. del Bano studied motives of moduli spaces of rank 2 vector bundles on $C$ and computed the motive of $M_L. $ In this note, we prove that his result gives an interesting decomposition of the motive of $M_L. $ This motivic decomposition is compatible with a conjecture of M. S. Narasimhan which predicts semi-orthogonal decomposition of derived category of the moduli space.
Recent Progress of Biomimetic Tactile Sensing Technology Based on Magnetic Sensors

In the past two decades, biomimetic tactile sensing technology has been a hot spot in academia. It has prospective applications in many fields such as medical treatment, health monitoring, robot tactile feedback, and human–machine interaction. With the rapid development of magnetic sensors, biomimetic tactile sensing technology based on magnetic sensors (which are called magnetic tactile sensors below) has been widely studied in recent years. In order to clarify the development status and application characteristics of magnetic tactile sensors, this paper firstly reviews the magnetic tactile sensors from three aspects: the types of magnetic sensors, the sources of magnetic field, and the structures of sensitive bodies used in magnetic tactile sensors. Secondly, the development of magnetic tactile sensors in four applications of robot precision grasping, texture characterization, flow velocity measurement, and medical treatment is introduced in detail. Finally, this paper analyzes technical difficulties and proposes prospective research directions for magnetic tactile sensors.
Buckwheat and Cardiometabolic Health: A Systematic Review and Meta-Analysis

Buckwheat (BW) is suggested to have beneficial effects, but evidence on how it affects cardiometabolic health (CMH) is not yet established. We aimed to assess the effects of BW and/or its related bioactive compounds on cardiovascular disease (CVD) risk markers in adults. Five databases were searched for eligible studies. Observational prospective studies, nonrandomized or randomized trials were considered if they assessed BW, rutin or quercetin-3-glucoside intake and CVD risk markers. We adhered to the Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA) guidelines for reporting. We selected 16 human studies based on 831 subjects with mild metabolic disturbances, such as hypercholesterolemia, diabetes and/or overweight. Eight studies, investigating primarily grain components, were included in the meta-analyses (n = 464). High study heterogeneity was present across most of our analyses. Weighted mean difference (WMD) for subjects receiving BW supplementation, compared to controls, were − 0.14 mmol/L (95% CI: −0.30; 0.02) for total cholesterol (TC), −0.03 mmol/L (95% CI: −0.22; 0.16) for LDL cholesterol, −0.14 kg (95% CI: −1.50; 1.22) for body weight, −0.04 mmol/L (95% CI: − 0.09;0.02) for HDL cholesterol, −0.02 mmol/L (95% CI: −0.15; 0.11) for triglycerides and −0.18 mmol/L (95% CI: −0.36; 0.003) for glucose. Most of the studies (66.7%) had concerns of risk of bias. Studies investigating other CVD markers were scarce and with inconsistent findings, where available. Evidence on how BW affects CMH is limited. However, the available literature indicates that BW supplementation in mild dyslipidaemia and type 2 diabetes may provide some benefit in lowering TC and glucose, albeit non-significant. Our work highlights the need for more rigorous trials, with better methodological rigor to clarify remaining uncertainties on potential effects of BW on CMH and its utility in clinical nutrition practice.
Pointwise convergence of ergodic averages of bounded measurable functions for amenable groups

Given any amenable group $G$ (with a left Haar measure $|\cdot|$ or $dg$), we can select out a \textit{F{\o}lner subnet} $\{F_\theta,\theta\in\Theta\}$ from any left F{\o}lner net in $G$, which is \textit{$L^\infty$-admissible}, namely, for any Borel $G$-space $(X,\mathscr{X})$ and any $\varphi\in L^\infty(X,\mathscr{X})$, \begin{gather*} \lim_{\theta\in\Theta}\frac{1}{|F_\theta|}\int_{F_\theta}\varphi(gx)dg=\varphi^*(x)\ \forall x\in X\quad {\textrm{and}}\quad \varphi^*=(g\varphi)^*\ \forall g\in G. \end{gather*} Moreover, if $G$ is $\sigma$-compact such as a locally compact second countable Hausdorff amenable group, then $\varphi^*\in L^\infty(X,\mathscr{X})$, $\varphi^*(gx)=\varphi^*(x)$ \textit{a.e. }, and $\varphi^*$ is \textit{a.e. } independent of the choice of the admissible F{\o}lner net $\{F_\theta,\theta\in\Theta\}$ in $G$. Consequently, we may easily obtain the ergodic disintegration of invariant probability measures for any $\sigma$-compact amenable group acting Borel on a compact metric space $X$ by continuous transformations of $X$, and the existence of $\sigma$-finite invariant Radon measures for any Borel action of an amenable group on a locally compact, $\sigma$-compact, metric space $X$ by continuous maps of $X$, and a $L^\infty$-pointwise multiple ergodic theorem.
SWFT-Net: a deep learning framework for efficient fine-tuning spot weights towards adaptive proton therapy

Objective. One critical task for adaptive proton therapy is how to perform spot weight re-tuning and reoptimize plan, both of which are time-consuming and labor intensive. We proposed a deep learning framework (SWFT-Net) to speed up such a task, a starting point for us to move towards online adaptive proton therapy. Approach. For a H&N patient case, a reference intensity modulated proton therapy plan was generated. For data augmentation, spot weights were modified to generate three datasets (DS10, DS30, DS50), corresponding to different levels of weight adjustment. For each dataset, the samples were split into the training and testing groups at a ratio of 8:2 (6400 for training, 1706 for testing). To ease the difficulty of machine learning, the residuals of dose maps and spot weights (i.e. difference relative to a reference) were used as inputs and outputs, respectively. Quantitative analyses were performed in terms of normalized root mean square error (NRMSE) of spot weights, Gamma passing rate and dose difference within the PTV. Main results. The SWFT-Net is able to generate an adapted plan in less than a second with a NVIDIA GeForce RTX 3090 GPU. For the 1706 samples in the testing dataset, the NRMSE is 0.41% (DS10), 1.05% (DS30) and 2.04% (DS50), respectively. Cold/hot spots in the dose maps after adaptation are observed. The mean relative dose difference is 0.64% (DS10), 0.92% (DS30) and 0.88% (DS50), respectively. For all three datasets, the mean Gamma passing rate is consistently over 95% for both 1 mm/1% and 3 mm/3% settings. Significance. The proposed SWFT-Net is a promising tool to help realize adaptive proton therapy. It can be used as an alternative tool to other spot fine-tuning optimization algorithms, likely demonstrating superior performance in terms of speed, accuracy, robustness and minimum human interaction. This study lays down a foundation for us to move further incorporating other factors such as daily anatomical changes and propagated PTVs, and develop a truly online adaptive workflow in proton therapy.
Brain grey and white matter structural associations with future suicidal ideation and behaviors in adolescent and young adult females with mood disorders

Abstract Background To reduce suicide in females with mood disorders, it is critical to understand brain substrates underlying their vulnerability to future suicidal ideation and behaviors (SIBs) in adolescence and young adulthood. In an international collaboration, grey and white matter structure was investigated in adolescent and young adult females with future suicidal behaviors (fSB) and ideation (fSI), and without SIBs (fnonSIB). Methods Structural (n = 91) and diffusion‐weighted (n = 88) magnetic resonance imaging scans at baseline and SIB measures at follow‐up on average two years later (standard deviation, SD = 1 year) were assessed in 92 females [age(SD) = 16.1(2.6) years] with bipolar disorder (BD, 28.3%) or major depressive disorder (MDD, 71.7%). One‐way analyses of covariance comparing baseline regional grey matter cortical surface area, thickness, subcortical grey volumes, or white matter tensor‐based fractional anisotropy across fSB (n = 40, 43.5%), fSI (n = 33, 35.9%) and fnonSIB (n = 19, 20.6%) groups were followed by pairwise comparisons in significant regions (p < 0.05). Results Compared to fnonSIBs, fSIs and fSBs showed significant decreases in cortical thickness of right inferior frontal gyrus pars orbitalis and middle temporal gyrus, fSIs of left inferior frontal gyrus, pars orbitalis. FSIs and fSBs showed lower fractional anisotropy in left uncinate fasciculus and corona radiata, and fSBs in right uncinate and superior fronto‐occipital fasciculi. Conclusions The study provides preliminary evidence of grey and white matter alterations in brain regions subserving emotional and behavioral regulation and perceptual processing in adolescent and young adult females with mood disorders with, versus without, future SIBs. Findings suggest potential targets to prevent SIBs in female adolescents and young adults.
Long pulse operation of the KAMABOKO III negative ion source

The target performance for the KAMABOKO ion source on the MANTIS test bed in Cadarache is to accelerate a beam of D− with a current density of 200 A/m2 and <1 extracted electron per accelerated D− ion, at an injected power ranging between 1 and 2 kW per liter of source volume, at a source pressure of 0.3 Pa. For ITER, a continuous neutral beam must be assured for pulse lengths of 500 s, but beams of up to 3600 s are also envisaged. During the last campaign, continuous beam pulses of duration up to 1000 s were demonstrated both in hydrogen and in deuterium. In this article, the source performance, the effect of the plasma grid temperature for long pulse operation, and the limits of the present experimental setup are described. Additionally, the effect of changing the strength of the magnetic filter in the ion source on the extracted ion and electron currents and the beam transmission is reported.
Robust, distributed and optimal control of smart grids

These lecture notes provide an overview of recent research on the modeling and control of smart grids using distributed algorithms. In particular, energy-based modeling of general AC power networks using the framework of port-Hamiltonian systems theory is presented, and the relevance of such a formulation for stability analysis and control design is discussed. Low-level control design aspects (at a physical layer) for DC microgrids are also considered, achieving objectives such as fair load sharing among distributed generation units and (average) voltage regulation using limited data and measurements from the system. Finally, general frameworks for the optimal control of smart grids are introduced to consider both physical and economic constraints and exploit the flexibility brought up by storage devices and demand response from the grid’s prosumers.