Miracle-dz/UniFAR-FTUs huggingface dataset:
Rational approximations to generalized hypergeometric functions

In specific cases, both Bellman and Luke made certain choices of free parameters in their formal schemes and obtained rational approximations which gave excellent agreement with the true values. Except in very special cases, however, neither author proved convergence of the generated rational approximations to the desired limit. In Theorems I and II, we develop representations for the error of very general types of rational approximations to certain broad classes of generalized hypergeometric functions. As an immediate application of these representations, Corollaries II and V prove that the rational approximations developed by Bellman and Luke actually converge to the desired limit. In Section V, the efficiency of these rational approximations are displayed in two numerical examples. The representations in Theorems I and II are derived essentially by showing that the error satisfies a certain nonhomogeneous differential equation, and then representing the error in terms of the solutions of the corresponding homogeneous differential equation, using Lagrange's method of variation of parameters. The analysis is related to Lanczos r-method, see [3]-[5], and resembles in several aspects an analysis of Weber, as given in [6], concerning the Hankel functions H,{%)(z), i = 1, 2.
Computing Symmetric Positive Definite Solutions of Three Types of Nonlinear Matrix Equations

Nonlinear matrix equations arise in many practical contexts related to control theory, dynamical programming and finite element methods for solving some partial differential equations. In most of these applications, it is needed to compute a symmetric and positive definite solution. Here, we propose new iterative algorithms for solving three different types of nonlinear matrix equations. We have recently proposed a new algorithm for solving positive definite total least squares problems. Making use of an iterative process for inverse of a matrix, we convert the nonlinear matrix equation to an iterative linear one, and, in every iteration, we apply our algorithm for solving a positive definite total least squares problem to solve the linear subproblem and update the newly defined variables and the matrix inverse terms using appropriate formulas. Our proposed algorithms have a number of useful features. One is that the computed unknown matrix remains symmetric and positive definite in all iterations. As the second useful feature, numerical test results show that in most cases our proposed approach turns to compute solutions with smaller errors within lower computing times. Finally, we provide some test results showing that our proposed algorithm converges to a symmetric and positive definite solution in Matlab software environment on a PC, while other methods fail to do so.
Attenuation measurements of an ultrasonic Rayleigh wave propagating along rough surfaces

The attenuation of Rayleigh surface waves by one‐ and two‐dimensional rough surfaces is investigated on duraluminum and titanium samples. The root‐mean‐square deviation of the surface from flatness h (8.5<h<90 μm) satisfies the condition of validity of the perturbation theory approach e=h/λR≪1. The excitation frequencies of the transmitter vary from 2.2. to 10 MHz. Experimental results for one‐ and two‐dimensional rough surfaces are presented and discussed. A comparison with the theoretical calculations of Eguiluz and Maradudin [Phys. Rev. B 28, 728 (1983)] confirms the F5 dependence of the attenuation α as aq∥→0.
Canonical quadratic refinements of cohomological pairings from functorial lifts of the Wu class

As mentioned in the comments, the proposed construction of the canonical quadratic refinement on a mapping torus contains a gap. In addition, the claim in the appendix that the spin cobordism group vanishes in dimensions 4k+3 is incorrect, although it does vanish for the case of dimension 7, relevant for physics.
Investigating the contribution and effect of cash transfers to household food security of rural smallholder farmers in the Eastern Cape Province of South Africa

Abstract Shocks such as Covid-19 pandemic and natural disasters erode the resilience of many poor households against hunger by further threatening productive capacities. It is projected that over 690 million people around the world went hungry in 2019 and the COVID-19 pandemic is increasing the vulnerabilities and insufficiencies of global food systems. Food security is a human right and the government of South Africa is legally bound by the constitution to ensure food security for all. However, food insecurity in the country is owing to insufficient access to food because of structural poverty and inequality dynamics with a strong racial footprint rather than a shortage of food. Additionally, the rising cost of living, limited investment in agricultural development, and high dependency ratios especially in low-income households are some of the factors contributing to food insecurity in the country. Consequently, household-level food security is a major challenge to the South African government and policymakers. The government has strong social and economic rights commitments in place to achieve this goal and improve the lives of rural communities that are dependent on agriculture as a source of livelihood. Using household survey data, the study seeks to investigate the role played by cash transfers on household productive capacities and food security status within the context of a small pace of transition from homestead to irrigated farming in the former homelands of the Eastern Cape Province. The lower bound poverty line of R 758 (on average $57 USD), was used to determine household food security status. Simple random sampling was employed to select 158 respondents. The propensity score matching method was employed using the Nearest Neighbour and Kernel matching techniques to estimate the treatment effects and compare the outcomes of participation in irrigation farming and receipts of cash transfers in comparison with the non-irrigators. Both matching methods revealed that irrigation farming enhanced the per capita food expenditure by at least ZAR 2 738.88 and ZAR 2 790.37, which then improves household food security. The findings also revealed that cash transfers increase the farmers’ production activities by ZAR 1 467.90 and ZAR 1 478.00. Evidently, the cash transfers necessitate the purchase of more and improved production inputs and access to climate-smart practices such as irrigation, which then improves irrigators’ production capacities and, as a result, reduces vulnerability and improves livelihoods and food security.
Future Prospects of Luminescent Silicon Nanowires Biosensors

In this paper, we exploit the perspective of luminescent Si nanowires (NWs) in the growing field of commercial biosensing nanodevices for the selective recognition of proteins and pathogen genomes. We fabricated quantum confined fractal arrays of Si NWs with room temperature emission at 700 nm obtained by thin-film, metal-assisted, chemical etching with high production output at low cost. The fascinating optical features arising from multiple scattering and weak localization of light promote the use of Si NWs as optical biosensing platforms with high sensitivity and selectivity. In this work, label-free Si NW optical sensors are surface modified for the selective detection of C-reactive protein through antigen–gene interaction. In this case, we report the lowest limit of detection (LOD) of 1.6 fM, fostering the flexibility of different dynamic ranges for detection either in saliva or for serum analyses. By varying the NW surface functionalization with the specific antigen, the luminescence quenching of NW biosensors is used to measure the hepatitis B-virus pathogen genome without PCR-amplification, with an LOD of about 20 copies in real samples or blood matrix. The promising results show that NW optical biosensors can detect and isolate extracellular vesicles (EV) marked with CD81 protein with unprecedented sensitivity (LOD 2 × 105 sEV/mL), thus enabling their measurement even in a small amount of blastocoel fluid.
Metric Subregularity of Subdifferential and KL Property of Exponent 1/2

For a proper lower semicontinuous function, we study the relations between the metric subregularity of its limiting subdifferential relative to the critical set and the KL property of exponent 1/2. When the function is convex, we establish the equivalence between them. When the function is nonconvex, we show that the KL property of exponent 1/2 along with the quadratic growth on the critical set implies the metric subregularity of the subdifferential relative to the critical set; and if the function is primal-lower-nice, under an assumption on stationary values, the latter implies the former. These results provide a bridge for the two kinds of regularity and contribute to enriching each other.
Ground State Energy of the Low Density Bose Gas

Now that the properties of low temperature Bose gases at low density, ρ, can be examined exprimentally it is appropriate to revisit some of the formulas deduced by many authors four to five decades ago. One of these is that the leading term in the energy/particle is 2π ħ 2 ρa/m, where a is the scattering length. Owing to the delicate and peculiar nature of bosonic correlations, four decades of research have failed to establish this plausible formula rigorously. The only known lower bound for the energy was found by Dyson in 1957, but it was 14 times too small. The correct bound is proved here.
The sharp estimates of eigenvalues of Polyharmonic operator and higher order Stokes operator

In this paper, we establish some lower bounds for the sums of eigenvalues of the polyharmonic operator and higher order Stokes operator, which are sharper than the recent results in \cite{CSWZ13, I13}. At the same time, we obtain some certain bounds for the sums of positive and negative powers of eigenvalues of the polyharmonic operator.
Polynomials with prescribed bad primes

We tabulate polynomials in Z[t] with a given factorization partition, bad reduction entirely within a given set of primes, and satisfying auxiliary conditions associated to 0, 1, and infinity. We explain how these sets of polynomials are of particular interest because of their role in the construction of nonsolvable number fields of arbitrarily large degree and bounded ramification. Finally we discuss the similar but technically more complicated tabulation problem corresponding to removing the auxiliary conditions.
A High Precision Analog Temperature Compensated Crystal Oscillator Using a New Temperature Compensated Multiplier

The development and application of various precision electronic devices require a large number of high-precision and low-cost temperature-compensated crystal oscillators (TCXO) to generate frequency references. In order to achieve higher compensation accuracy at lower cost, a new fully integrated analog-TCXO (ATCXO) is proposed in this paper. It uses an innovative temperature-compensated multiplier to generate cubic and quintic voltages. The experimental results show that it can achieve the ultra-high fitting of the frequency-temperature characteristic curve of the crystal. This effectively improves the compensation accuracy of the TCXO. The proposed ATCXO achieves a frequency stability of ± 0.8 ppm in the temperature range of <inline-formula> <tex-math notation="LaTeX">$- 40\,\,^{\circ }\text{C}$ </tex-math></inline-formula> to 95 °C. At the same time, the gain-temperature error of the proposed temperature compensated analog multiplier is <inline-formula> <tex-math notation="LaTeX">$\le 0.13$ </tex-math></inline-formula> dB. This paper is based on SMIC 130 nm process, the core area of the chip is only 0.124 mm2. Multiple modules such as bandgap circuit, n-th power voltage generation circuit, summation circuit, gain control circuit and voltage controlled oscillator using variable capacitor array are integrated.
Oscillations de faible amplitude pour les systèmes 2×2 de lois de conservation

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Cell complexes, poset topology and the representation theory of algebras arising in algebraic combinatorics and discrete geometry

In recent years it has been noted that a number of combinatorial structures such as real and complex hyperplane arrangements, interval greedoids, matroids and oriented matroids have the structure of a finite monoid called a left regular band. Random walks on the monoid model a number of interesting Markov chains such as the Tsetlin library and riffle shuffle. The representation theory of left regular bands then comes into play and has had a major influence on both the combinatorics and the probability theory associated to such structures. In a recent paper, the authors established a close connection between algebraic and combinatorial invariants of a left regular band by showing that certain homological invariants of the algebra of a left regular band coincide with the cohomology of order complexes of posets naturally associated to the left regular band. The purpose of the present monograph is to further develop and deepen the connection between left regular bands and poset topology. This allows us to compute finite projective resolutions of all simple modules of unital left regular band algebras over fields and much more. In the process, we are led to define the class of CW left regular bands as the class of left regular bands whose associated posets are the face posets of regular CW complexes. Most of the examples that have arisen in the literature belong to this class. A new and important class of examples is a left regular band structure on the face poset of a CAT(0) cube complex. Also, the recently introduced notion of a COM (complex of oriented matroids or conditional oriented matroid) fits nicely into our setting and includes CAT(0) cube complexes and certain more general CAT(0) zonotopal complexes. A fairly complete picture of the representation theory for CW left regular bands is obtained.
QCD tree amplitudes on modern GPUs: A case study for novel event generators

For more than a decade the current generation of CPU-based matrix element generators has provided hard scattering events with excellent flexibility and good efficiency. However, they are a bottleneck of current Monte Carlo event generator toolchains, and with the advent of the HL-LHC and more demanding precision requirements, faster matrix elements are needed, especially at intermediate to large jet multiplicities. We present first results of the new BlockGen family of matrix element algorithms, featuring GPU support and novel color treatments, and discuss the best choice to deliver the performance needed for the next generation of accelerated matrix element generators.
An Energy Stable Finite-Difference Scheme for Functionalized Cahn-Hilliard Equation and its Convergence Analysis

We present and analyze an unconditionally energy stable and convergent finite difference scheme for the Functionalized Cahn-Hilliard equation. One key difficulty associated with the energy stability is based on the fact that one nonlinear energy functional term in the expansion appears as non-convex, non-concave. To overcome this subtle difficulty, we add two auxiliary terms to make the combined term convex, which in turns yields a convex-concave decomposition of the physical energy. As a result, an application of the convex splitting methodology assures both the unique solvability and the unconditional energy stability of the proposed numerical scheme. To deal with a 4-Laplacian solver in an $H^{-1}$ gradient flow at each time step, we apply an efficient preconditioned steepest descent algorithm to solve the corresponding nonlinear systems. In addition, a global in time $H_{\rm per}^2$ stability of the numerical scheme is established at a theoretical level, which in turn ensures the full order convergence analysis of the scheme. A few numerical results are presented, which confirm the stability and accuracy of the proposed numerical scheme.
Comparison of nonlocal Eulerian to Lagrangian moments for transport in an anisotropic heterogeneous aquifer with deterministic linear nonequilibrium sorption

An Eulerian perturbation scheme is applied to study transport of a reactive chemical experiencing linear nonequilibrium sorption with deterministic rate constants in a heterogeneous porous medium. Exact solutions for the mean concentrations are used to obtain mean values of spatial moments through the third moments. Comparisons are made with results obtained for the identical problem in a Lagrangian frame [Dagan and Cvetkovic, 1993]. If local‐scale dispersion is neglected in the Eulerian analysis and the fully nonlocal flux is retained, then the Eulerian and Lagrangian moments agree. However, if either the Eulerian model is localized or the local‐scale dispersion is retained, then the moments disagree. This disagreement is especially acute in the asymptotic limits. If local‐scale dispersion is included in the first‐order Lagrangian analysis, then one anticipates agreement through the third moments between the two approaches.
Ground states of a system of nonlinear Schrödinger equations with periodic potentials

ABSTRACT We are concerned with a system of coupled Schrödinger equations where F and Vi are periodic in x and 0∉σ(−Δ+Vi) for i = 1,2,…,K, where σ(−Δ+Vi) stands for the spectrum of the Schrödinger operator −Δ+Vi. We impose general assumptions on the nonlinearity F with the subcritical growth and we find a ground state solution being a minimizer of the energy functional associated with the system on a Nehari–Pankov manifold. Our approach is based on a new linking-type result involving the Nehari–Pankov manifold.
Two-Dimensional Embedded Fuzzy Data Clustering

Fuzzy $k$-means (FKM) is a popular clustering method by assigning data points into respective clusters with uncertainty measured by the membership degree. Usually, FKM performs clustering according to the distance between data points in the original space, which might contain undesirable noises and redundant features; therefore, the underlying data semantic connections cannot be accurately captured. Moreover, the vectorized representation of the two-dimensional data such as image inevitably leads to the loss of structural information. In this paper, we propose a novel FKM method termed two-dimensional embedded fuzzy data clustering (2DEFC) which has two merits. First, 2DEFC directly takes 2D data as input without vectorizing them in order to retain more structural information of data. Second, the two subspace projection matrices are jointly optimized with the data membership degree for better collaborating with each other, which effectively avoids the sub-optimality limitation caused by the conventional mode of sequentially performing dimensionality reduction and clustering. An efficient algorithm is proposed to optimize the 2DEFC objective function. Besides, we provide comprehensive analysis on 2DEFC including its convergence behavior, computational complexity, and the fuzzy weighting exponent. Extensive comparative studies on benchmark 2D data sets demonstrate that the competitive performance of 2DEFC in 2D data clustering.
Associative synthesis of geometrical scenes

In this paper we use neural network algorithms for office layout. A pixel matrix of coarse pixels is used to represent the objects of the room and their spatial relation. For each pixel the probabilities of the different objects are predicted from the neighboring pixels, assuming that the geometrical structure is mainly determined by local characteristics. Local receptive fields are employed to capture these local interactions using backpropagation networks. The reconstruction of the complete scene is achieved by an iterative process. Starting with given marginal constraints (or missing information for specific locations) each feature map performs an association with respect to its central pixel. This corresponds to the simulation of a Markov random field. External constraints on the sum of probabilities are taken into account using the iterative proportional fitting algorithm. The viability of the approach is demonstrated by an example.
2DSegFormer: 2-D Transformer Model for Semantic Segmentation on Aerial Images

Two-dimensional position information of input tokens is essential for transformer-based semantic segmentation models, especially on high-resolution aerial images. However, recent transformer-based segmentation methods use position encoding to record position information and most position encoding methods encode the 1-D positions of tokens. Therefore, we propose a 2-D semantic transformer model (2DSegFormer) for semantic segmentation on aerial images. In 2DSegFormer, we design a novel 2-D positional attention to accurately record the 2-D position information required by the transformer. Furthermore, we design the dilated residual connection and use it instead of skip connection in the deep stages to get a larger receptive field. Skip connections are used in the shallow stages of 2DSegFormer to pass the details to the corresponding stages in the decoder. Experimental results on UAVid, Vaihingen, and AeroScapes datasets demonstrate the effectiveness of 2DSegFormer. Compared with the state-of-the-art methods, 2DSegFormer shows better performance and great robustness on three different datasets. In particular, 2DSegFormer-B2 achieves first place in the public ranking on the UAVid test set.
Control-Centric Living Laboratory for Management of Distributed Energy Resources

Variability and uncertainty of renewable distributed generation increase power grid complexity, necessitating the development of advanced control strategies. demonstrates a real-world testbed and the implementation of control strategies on it to mitigate the challenges associated with variability and uncertainty of renewable distributed generation. This control-centric testbed includes 4.6 MW of controllable building loads, a 1 MW solar array, and a 125 kW / 130 kWh battery energy storage system (BESS). The capabilities of the testbed are illustrated by highlighting the implementation of three specific scenarios relevant to future smart grid infrastructures. In the first scenario, photovoltaic output variability is mitigated with the BESS using adaptive moving average and adaptive state of charge control methods. The second and third scenarios demonstrate peak load management and load following control to manage uncertainty using the Intelligent Load Control (ILC) algorithm. The ILC modifies controllable loads using a prioritization matrix and an analytical hierarchy process. The three scenarios all operate at a different time-constant, and are each effectively addressed, demonstrating the versatility and flexibility of the presented testbed. This demonstrated ability to rapidly test the efficacy of alternate control algorithms on a real system is crucial to the maturation of future smart-grid.