Miracle-dz/UniFAR-FTUs huggingface dataset:
An extension of the Bernoulli polynomials inspired by the Tsallis statistics

In [Arch. Math. 7, 28 (1956), Utilitas Math. 15, 51 (1979)] Carlitz introduced the degenerate Bernoulli numbers and polynomials by replacing the exponential factors in the corresponding classical generating functions with their deformed analogs: $\exp(t) \rightarrow (1+\lambda t)^{1/\lambda}$, and $\exp(tx) \rightarrow (1+\lambda t)^{x/\lambda}$. The deformed exponentials reduce to their ordinary counterparts in the $\lambda \rightarrow 0$ limit. In the present work we study the extension of the Bernoulli polynomials obtained via an alternate deformation $\exp(tx) \rightarrow (1+\lambda tx)^{1/\lambda}$ that is inspired by the concepts of $q$-exponential function and $q$-logarithm used in the nonextensive Tsallis statistics.
Stability of Equilibria for the so ( 4 ) Free Rigid Body

The stability for all generic equilibria of the Lie–Poisson dynamics of the so ( 4 ) rigid body dynamics is completely determined. It is shown that for the generalized rigid body certain Cartan subalgebras (called of coordinate type) of so (n) are equilibrium points for the rigid body dynamics. In the case of so ( 4 ) there are three coordinate type Cartan subalgebras whose intersection with a regular adjoint orbit gives three Weyl group orbits of equilibria. These coordinate type Cartan subalgebras are the analogues of the three axes of equilibria for the classical rigid body in so ( 3 ) . In addition to these coordinate type Cartan equilibria there are others that come in curves.
Jump locations of jump-diffusion processes with state-dependent rates

We propose a general framework for studying statistics of jump-diffusion systems driven by both Brownian noise (diffusion) and a jump process with state-dependent intensity. Of particular natural interest in many physical systems are the jump locations: the system evaluated at the jump times. As an example, this could be the voltage at which a neuron fires, or the so-called ‘threshold voltage’. However, the state-dependence of the jump rate provides direct coupling between the diffusion and jump components, making it difficult to disentangle the two to study individually. In this work, we provide an iterative map formulation of the sequence of distributions of jump locations. The distributions computed by this map can be used to elucidate other interesting quantities about the process, including statistics of the interjump times. Ultimately, the limit of the map reveals that knowledge of the stationary distribution of the full process is sufficient to recover (but not necessarily equal to) the distribution of jump locations. We propose two biophysical examples to illustrate the use of this framework to provide insight about a system. We find that a sharp threshold voltage emerges robustly in a simple stochastic integrate-and-fire neuronal model. The interplay between the two sources of noise is also investigated in a stepping model of molecular motor in intracellular transport pulling a diffusive cargo.
Many-Body Physics with Ultracold Gases

This paper reviews recent experimental and theoretical progress concerning many-body phenomena in dilute, ultracold gases. It focuses on effects beyond standard weak-coupling descriptions, such as the Mott-Hubbard transition in optical lattices, strongly interacting gases in one and two dimensions, or lowest-Landau-level physics in quasi-two-dimensional gases in fast rotation. Strong correlations in fermionic gases are discussed in optical lattices or near-Feshbach resonances in the BCS-BEC crossover.
First-Order Primal-Dual Method for Nonlinear Convex Cone Programming

Nonlinear Convex Cone Programming (NCCP) problems are important and have many practical applications. In this paper, we introduces a flexible first-order primal-dual algorithm called the Variant Auxiliary Problem Principle (VAPP) for solving NCCP problems when the objective function and constraints are smooth and may be nonsmooth. Each iteration of VAPP generates a nonlinear approximation to the primal problem of an augmented Lagrangian method. The approximation incorporates both linearization and a variable distance-like function, and then the iterations of VAPP provide one decomposition property for NCCP. Motivated by recent applications in big data analysis, there has been an explosive growth in interest in the convergence rate analysis of parallel computing algorithms for large scale optimization problem. This paper proposes an iteration-based error bound and linear convergence of VAPP. Some verifiable sufficient conditions of this error bound are also discussed. For the general convex case (without error bound), we establish $O(1/t)$ convergence rate for primal suboptimality, feasibility and dual suboptimality. By adaptively setting in parameters at different iterations, we show an $O(1/t^2)$ rate for the strongly convex case. We further present Forward-Backward Splitting (FBS) formulation of VAPP method and establish the connection between VAPP and other primal-dual splitting methods. Finally, we discuss some issues in the implementation of VAPP.
The Index Formula on the Moduli of G-bundles

We prove the formulae conjectured by the first author for the index of K-theory classes over the moduli stack of algebraic G-bundles on a smooth projective curve. The formulae generalise Verlinde's for line bundles and have Witten's integrals over the moduli space of stable bundles as their large level limits. As an application, we prove the Newstead-Ramanan conjecture on the vanishing of high Chern classes of certain moduli spaces of stable G-bundles.
Ion acceleration dependence on magnetic shear angle in dayside magnetopause reconnection

Magnetic reconnection at the Earth's magnetopause plays an important role in magnetospheric dynamics. Understanding the dynamics requires theory and observations. Previous theoretical work suggests that for no guide field, ions in the exhaust region on the magnetosheath side of the boundary counterstream with a velocity separation that is twice the upstream Alfvén speed (vA) and that the counterstreaming velocity decreases with increasing guide field. These theoretical predictions are tested for reconnection at the Earth's magnetopause using observations from the Cluster spacecraft. The difference between the incident and reflected ion velocities (vsep) in the magnetosheath boundary layer ion populations is used to determine the exhaust velocity. The ratio of vsep over twice the Alfvén speed (RV = vsep/2vA,L) is predicted to approach 1 for reconnection with shear angles near 180° (no guide field) but is observed to reach a value of approximately 0.84 for the magnetopause crossings analyzed with shear angles near 180°. This value is consistent with previous observations of ion velocities from reconnection at the magnetopause investigated using the Walén relation. While magnetic shear angle can contribute to the disagreement between observations and the Walén relation, it does not play a large role, given the reduced ratio for the events near 180° in this study.
Calibration and initial operation of the HIBP on the MST

For the first time, a heavy ion beam probe (HIBP) has been installed on a reversed field pinch, i.e., Madison symmetric torus (MST), to measure the plasma potential profile, potential, and electron density fluctuations, etc. The application of a HIBP on MST has presented new challenges for this diagnostic. The primary sources of difficulty are small access ports, high plasma, and, ultraviolet (UV) flux and a confining magnetic field produced largely by plasma currents. The requirement to keep ports small so as to avoid magnetic field perturbations led to the development of the cross-over sweep system. The effectiveness and calibration of this sweep system will be reported. In addition, this diagnostic is now operating with greater plasma/UV loading effects than most previous Rensselaer HIBPs. The plasma flux is reduced by using a magnetic suppression structure. The UV flux appears to be the dominant cause of the remaining loading, which is substantial. The magnetic field being largely produced by the plas.
Local wavelet transform: a cost-efficient custom processor for space image compression

Thanks to its intrinsic scalability features, the wavelet transform has become increasingly popular as decorrelator in image compression applications. Throuhgput, memory requirements and complexity are important parameters when developing hardware image compression modules. An implementation of the classical, global wavelet transform requires large memory sizes and implies a large latency between the availability of the input image and the production of minimal data entities for entropy coding. Image tiling methods, as proposed by JPEG2000, reduce the memory sizes and the latency, but inevitably introduce image artefacts. The Local Wavelet Transform (LWT), presented in this paper, is a low-complexity wavelet transform architecture using a block-based processing that results in the same transformed images as those obtained by the global wavelet transform. The architecture minimizes the processing latency with a limited amount of memory. Moreover, as the LWT is an instruction-based custom processor, it can be programmed for specific tasks, such as push-broom processing of infinite-length satelite images. The features of the LWT makes it appropriate for use in space image compression, where high throughput, low memory sizes, low complexity, low power and push-broom processing are important requirements.
Standard errors for rotation matrices with an application to the promax solution

A method of estimating the asymptotic covariance matrix for unrotated and rotated loadings and rotation matrices in factor analysis is presented. The covariance structure for common factors is expressed by the asymmetric formulation which contains unrotated and rotated loadings, and a rotation matrix. Using the restrictions for the relationships among the matrices and the restrictions from optimization of the criterion for rotation, the asymptotic covariance matrix for the parameters is obtained from an augmented information matrix. The method is applied to the models for covariances and correlations. As an application of the covariance matrix of the parameters, the asymptotic standard errors for the loadings and correlations for the rotated factors by the promax method are derived.
The Analysis of a Class of Non-Series Parallel Redundant Systems

Two analysis techniques for use in the study of a class of non-series parallel, dual channel systems are presented. The first technique is a method for obtaining an approximate solution for the system. It is based on a systematic analysis of first- and second-order failure modes and involves the use of matrix algebra. The second technique is a method for generating the exact solution from the approximate solution. This method involves a transformation which converts the system into a logically equivalent system. An exact solution for the transformed system is derived and is shown to be the exact solution for the original system.
Conformal Bootstrap Analysis for Localization: Symplectic Case

The localization phenomena due to the random potential scattering is widely discussed in the electron and photon systems, where the theoretical approach is the nonlinear $\sigma$ model with the replica method or with the supersymmetry. In this article, we discuss the application of the conformal bootstrap method to the localization by the small determinants. The possible correspondence to the symplectic Anderson localization is discussed.
CLUSTERS OF THE SMALL MAGELLANIC CLOUD. II. AGE DISTRIBUTIONS.

From a complete catalog of all star clusters in a nine-region survey of the SMC, the author uses measured cluster properties to study the rate of cluster formation and disintegration in various parts of the SMC. The mean diameters of cataloged SMC clusters is 7 pc; this value reduces to 5.8 pc for the regions for which incompleteness is not a problem. The author finds that the SMC is currently forming clusters at the rate of approximately 100 per 108years. The disintegration rate is significantly slower than for clusters in the solar neighborhood. The median age of SMC clusters is 0.9 Gyr.
Ground state solutions for fractional scalar field equations under a general critical nonlinearity

In this paper we study existence of ground state solution to the following problem \begin{document}$ (- \Delta)^{\alpha}u = g(u) \ \ \mbox{in} \ \ \mathbb{R}^{N}, \ \ u \in H^{\alpha}(\mathbb R^N) $\end{document} where \begin{document}$ (-\Delta)^{\alpha} $\end{document} is the fractional Laplacian, \begin{document}$ \alpha\in (0,1) $\end{document} . We treat both cases \begin{document}$ N\geq2 $\end{document} and \begin{document}$ N = 1 $\end{document} with \begin{document}$ \alpha = 1/2 $\end{document} . The function \begin{document}$ g $\end{document} is a general nonlinearity of Berestycki-Lions type which is allowed to have critical growth: polynomial in case \begin{document}$ N\geq2 $\end{document} , exponential if \begin{document}$ N = 1 $\end{document} .
The Ability of Lactobacillus Plantarum to Produce Exopolysaccharides with Additional Nutrients

Exopolysaccharides (EPS) are polysaccharides secreted by microbes out of cells. EPS has potential in the pharmaceutical industry as a texture and rheological agent. EPS was produced by lactic acid bacteria such as Lactobacillus plantarum using a substrate that containing glucose. The purpose of the study was to determine the ability of Lactobacillus plantarum to produce exopolysaccharides with the addition of nutrients, namely (NH4)2HPO4 and raspberry juice as a source of sugar. A fermentation process carried out the EPS production based on a growth curve for 15, 21, and 27 hours with nutrients and without adding nutrients. The additional sugar came from raspberries with concentrations of 25%, 30%, and 35%. EPS levels without the addition of (NH4)2HPO4 with a raspberry concentration of 35% at 15, 21, and 27 hours resulted in 2624, 3704, and 3928 mg/L. The results showed that EPS levels with the addition of (NH4)2HPO4 with a raspberry concentration of 35% at 15, 21, and 27 hours resulted in EPS levels of 3374, 4072, and 4792 mg/L.
Anammox bacterium ‘Candidatus Kuenenia stuttgartiensis’: a review

Anaerobic ammonium oxidation (Anammox) process is a type of biological nitrogen removal technology which is known to directly convert ammonium and nitrite to nitrogen gas. The freshwater ‘Candidatus Kuenenia stuttgartiensis’ anammox under the phylum of Planctomycetes is used to study the parameters that affect the anammox development and the metabolic pathways alongside the associated enzymes. These observations were made using state-of-the art techniques for detecting anammox bacteria based on their small-subunit ribosomal RNA genes, functional genes and unique reaction pathways. This review systematically summarizes up-to-date studies on the parameters affecting the growth of the anammox bacteria and metabolic networks driving anammox bacterial anabolism and mixotrophy beyond genome-based predictions. The K. stuttgartiensis survives in summer and winter conditions besides in the aerobic zones (dissolved oxygen >2 mg/L), which consequently contribute to better nitrogen removal in the wastewater treatment. Furthermore, the K. stuttgartiensis utilizes the Wood–Ljungdahl pathway to directly assimilate extracellular formation instead of oxidising it completely to CO2 prior reassimilation.
A practical scheme of the sigma‐point Kalman filter for high‐dimensional systems

While applying a sigma‐point Kalman filter (SPKF) to a high‐dimensional system such as the oceanic general circulation model (OGCM), a major challenge is to reduce its heavy burden of storage memory and costly computation. In this study, we propose a new scheme for SPKF to address these issues. First, a reduced rank SPKF was introduced on the high‐dimensional model state space using the truncated single value decomposition (TSVD) method (T‐SPKF). Second, the relationship of SVDs between the model state space and a low‐dimensional ensemble space is used to construct sigma points on the ensemble space (ET‐SPKF). As such, this new scheme greatly reduces the demand of memory storage and computational cost and makes the SPKF method applicable to high‐dimensional systems. Two numerical models are used to test and validate the ET‐SPKF algorithm. The first model is the 40‐variable Lorenz model, which has been a test bed of new assimilation algorithms. The second model is a realistic OGCM for the assimilation of actual observations, including Argo and in situ observations over the Pacific Ocean. The experiments show that ET‐SPKF is computationally feasible for high‐dimensional systems and capable of precise analyses. In particular, for realistic oceanic assimilations, the ET‐SPKF algorithm can significantly improve oceanic analysis and improve ENSO prediction. A comparison between the ET‐SPKF algorithm and EnKF (ensemble Kalman filter) is also tribally conducted using the OGCM and actual observations.
From high-level inference algorithms to efficient code

Probabilistic programming languages are valuable because they allow domain experts to express probabilistic models and inference algorithms without worrying about irrelevant details. However, for decades there remained an important and popular class of probabilistic inference algorithms whose efficient implementation required manual low-level coding that is tedious and error-prone. They are algorithms whose idiomatic expression requires random array variables that are latent or whose likelihood is conjugate. Although that is how practitioners communicate and compose these algorithms on paper, executing such expressions requires eliminating the latent variables and recognizing the conjugacy by symbolic mathematics. Moreover, matching the performance of handwritten code requires speeding up loops by more than a constant factor. We show how probabilistic programs that directly and concisely express these desired inference algorithms can be compiled while maintaining efficiency. We introduce new transformations that turn high-level probabilistic programs with arrays into pure loop code. We then make great use of domain-specific invariants and norms to optimize the code, and to specialize and JIT-compile the code per execution. The resulting performance is competitive with manual implementations.
The Nonpotentiality of Steady-state Coronal Magnetic Field Derived with Time-relaxation Magnetohydrodynamics Simulations Using Helioseismic and Magnetic Imager Three-component Magnetic Field Data

The steady states of the coronal magnetic field obtained with the magnetohydrodynamic (MHD) time-relaxation simulation model are examined. Our electric-field-driven model can introduce the three components of the solar surface magnetic field data maps as the boundary values of an MHD simulation, without violating the divergence-free condition of the magnetic field. The magnetic field in the simulated steady-state solar corona exhibits substantial nonpotentiality in the closed-field streamers. A few choices are allowed in our model, such as the criteria for determining whether or not the horizontal components at the weak-field region are included. The initial magnetic field configuration can be arbitrarily determined. In this work, we examined the differences between the steady states obtained with the information on the horizontal components and with several choices of the simulation setting, and compared the new steady states with those obtained without using the horizontal magnetic field components. We found that nonpotential magnetic structures in the derived steady states well correspond to the observed solar filament structures during a selected period of Carrington Rotation 2106. The difference in the steady state with different boundary treatments is found to be large. The difference caused by the initial magnetic configuration is found to be small.
Strategic framework of using drone in cities disaster response

Drone technology has been around the world more than a decade and the application has becomes more vital, especially, during the disaster event such as COVID-19 pandemic. However, some of the countries were not ready in implementating the technology due to various reasons. Thus, this study intended to identify the technological and legislative aspects of drone application for disaster response in cities environment and to propose strategic framework on optimization of drone capabilities in cities disaster response. The literature search has been conducted in order to explore the applicability of drone technology in disaster management and disaster response. Later, further investigations were carried out using the Participatory Action Research (PAR) approach. In the PAR method, the data were collected in two phases; 1) observation and discussions and 2) interview sessions. The observation and discussions were conducted to obtain the implementation process of using the drone during the disaster event by the rescue team via recorded video. To triangulate the information gathered from the discussion, a series of interview had been made. Where, six selected stakeholders from end-user, regulatory agency and supplier were interviewed. It is found that the implementation of drone technology framework in disaster consists of six perspectives, namely; actions, internal organization, external environment, needs specification and feasibility analysis. To make the framework works, stakeholders are required to function in a cohesive and collaborative manner as illustrated in the Harmonization Triangle. The strength of cohesion and collaboration has also opened up future study for a full scope disaster management cycle phases, known as response, recovery, mitigation and preparedness.
Log-biharmonicity and a Jensen formula in the space of quaternions

Given a complex meromorphic function, it is well defined its Riesz measure in terms of the laplacian of the logarithm of its modulus. Moreover, related to this tool, it is possible to prove the celebrated Jensen formula. In the present paper, using among the other things the fundamental solution for the bilaplacian, we introduce a possible generalization of these two concepts in the space of quaternions, obtaining new interesting Riesz measures and global (i.e. four dimensional), Jensen formulas.
Electronic transport of n-type CdSe quantum dot films: Effect of film treatment

Solid films of CdSe colloidal quantum dots are conductive when reduced by electrochemistry. The dark conductivity and the photoconductivity of these n-type CdSe nanocrystalline solids have been investigated as a function of film treatment. When the films are treated with NaOH, a carrier mobility of ∼10−2cm2∕Vs and a charging/discharging time of ∼10ms are obtained. Under an excitation intensity of ∼0.75mW∕cm2, a significant photoconductivity of ∼10−3Scm−1 has been observed. The high mobility allowed demonstrating the operation of a field effect transistor.
On Kernel Methods of Estimating Marginal Radial and Angular Probability Density Functions

Spatial point patterns which possess a natural origin are considered. Two ways of estimating the marginal radial and angular probability density functions associated with the stochastic process underlying such a pattern are presented. These methods are based on one and two-dimensional kernel functions respectively. The angular density estimate can be used to detect angular trend and to test for angular uniformity within a particular sector about the origin. The two methods of estimation produce essentially the same results. That based on the one-dimensional kernel is recommended because it is computationally simpler.