Miracle-dz/UniFAR-FTUs huggingface dataset:
A NURBS-based Discontinuous Galerkin method for CAD compliant flow simulations

In this work, we explain how a classical nodal Discontinuous Galerkin (DG) method for conservation laws can be modified to be geometrically exact with respect to CAD (Computer-Aided Design) data. The proposed approach relies on the use of rational Bezier elements, that can exactly match geometries defined by NURBS (Non-Uniform Rational B-Splines) after some basic transformations. It has been found convenient to use the same basis to describe the solution, yielding a so-called isogeometric formulation. The resulting method exhibits optimal convergence rates and facilitates couplings with geometry, e.g. for local refinement, shape sensitivity analysis, or moving computational domains. Illustrations are provided for two-dimensional compressible Euler and Navier-Stokes equations.
On Convergence for Piecewise Affine Models of Gene Regulatory Networks via a Lyapunov Approach

In this paper, we analyse convergence and stability properties for piecewise affine models of gene regulatory networks, by means of piecewise quadratic Lyapunov functions. In the first part, we present the piecewise affine model of a gene regulatory network then, after proving a result on the existence of a minimal, attractive, and positively invariant box, we describe a linear matrix inequalitie framework to construct a Lyapunov function for the system. In the second part of the work, after a characterization of the system solutions when considering also isolated Zeno behavior of the trajectories, a monotonicity property of the so found Lyapunov function is formally proved, together with a result on the convergence of the trajectories, in the sense of measure. Finally, we present two examples, showing the applicability and utility of the main theoretical results previously explained.
Stellar Relaxation Processes Near the Galactic Massive Black Hole

The massive black hole (MBH) in the Galactic Center and the stars around it form a unique stellar dynamics laboratory for studying how relaxation processes affect the distribution of stars and compact remnants and lead to close interactions between them and the MBH. Recent theoretical studies suggest that processes beyond "minimal" two-body relaxation may operate and even dominate relaxation and its consequences in the Galactic Center. I describe loss-cone refilling by massive perturbers, strong mass segregation and resonant relaxation; review observational evidence that these processes play a role in the Galactic Center; and discuss some cosmic implications for the rates of gravitational wave emission events from compact remnants inspiraling into MBHs, and the coalescence timescales of binary MBHs.
Induced representations of the modular group PSL(2,Z) and the transfer operator for its subgroups of finite index

In the transfer operator approach to Selberg’s zeta function for a subgroup Γ of finite index in PSL(2, Z) and character χ the space F (s; Γ; χ) of eigenfunctions of the transfer operator L s for the eigenvalue 1 with certain asymptotics at zero is in bijection with the space S(s; Γ, χ) of Maass cusp forms of Γ and χ respectively the space S(s; Γ; χ) of period functions of Lewis and Zagier. Selberg’s zeta function Z(s; Γ; χ) gets thereby expressed in terms of the Fredholm determinant of L s . We extend this approach to the case χ an arbitrary unitary representation of Γ. We show that also the symmetries of the transfer operator with unitary representation can be related to the automorphisms of the corresponding Maass cusp forms. According to the Jacquet-Langlands correspondence the space S(s;On) of Maass cusp forms for On, the unit group of an indefinite quaternion devision algebra of discriminant n, is in bijection with the space Snew(s; Γ0(n)) of new forms for the Hecke congruence group Γ0(n), when n is square free and a product of an even number of primes. The expectation, that the restriction of the transfer operator to the corresponding subspace Fnew(s; Γ0(n)) of the eigenfunctions, coincides with this operator corresponding to one of the irreducible components of UΓ0(n) is not true as we show in the case Γ0(6). By a result of Millington, the representation UΓ0(n) of PSL(2, Z) appearing in the transfer operator L0 s and induced from the trivial representation of Γ0(n), can be identified with a permutation representation of the finite group Q(n) = PSL(2, Z)/H(n) with H(n) = kerUΓ0(n). By applying results of the theory of finite groups it follows that for coprime n and m, UΓ0(nm) = UΓ0(n)⊗UΓ0(m) and for p prime UΓ0(p) ∼= Ut⊕Up where Ut is the trivial 1-dim. representation and Up is a certain p-dimensional irreducible representation of PSL(2, Z). This leads to a decomposition of the transfer operator and the space of its eigenfunctions. In the special case n = 6 the representation UΓ0(6) contains the irreducible representation U2⊗U3, which characterizes a subspace of F (s; Γ0(6)) describing a mixture of old and new eigenfunctions including the space Fnew(s; Γ0(6)). In the case of the principal congruence subgroup Γ(2) the induced representation UΓ(2) on the other hand contains a 1-dim. subrepresentation Usgn characterizing exactly the space Fnew(s; Γ(2)). Finally it is proved, that a character χ on Γ is congruence iff the representation ρχ of PSL(2, Z) induced from χ is congruence. Applying this to the representation ρχα induced from Selberg’s family of characters χα, for Γ0(4), yields besides the α-values for which χα is congruence, also certain non-congruence subgroups to which Zograf’s criterion can not be applied.
Shared-Aperture Antennas Based on Even- and Odd-Mode Spoof Surface Plasmon Polaritons

In this communication, we propose a method of designing shared-aperture antennas based on excitations of both even- and odd-mode spoof surface plasmon polaritons (SSPPs). The antenna consists of a feeding monopole and a tapered SSPPs structure, both of which are placed vertically on a metallic ground. Due to tilted electric vectors of the monopole in near fields, both even- and odd-mode SSPPs can be excited. Standing waves of even-mode SSPPs on the SSPPs structure will enable broadside or tilted radiation, while traveling waves of odd-mode SSPPs on the tapered end will enable endfire radiation. Therefore, such an antenna configuration can achieve broadside, tilted, and endfire radiations. As an example, a shared-aperture antenna operating in $C/X$ /Ku-bands was designed, fabricated, and measured. Both the simulated and measured results verify that the antenna can achieve broadside radiation in 4.68–4.83 GHz, tilted radiation in 8.51–8.82 GHz, and endfire radiation in 11.00–17.38 GHz, with peak gains about 2.7, 3.5, and 6.8 dB, respectively. The antenna itself can work in multiple bands with customized radiation patterns, without using several antenna radiators and complex feeding network. This communication provides an effective method of designing shared-aperture antennas in future lightweight and multifunctional wireless communication systems.
Addressing collinearity and class imbalance in logistic regression for statistical fraud detection

We study how one can improve upon a logistic regression model for statistical fraud detection. Fraud data are often characterized by uneven class distributions as well as high dependence among covariates. With a focus on recreating such dependence structures found in fraud data, we propose a stochastic model from which we can generate data. The model utilizes copulas to create a highly flexible framework for generating dependent covariates. This allows for a wide range of dependence structures among the covariates, and does not put any restrictions on the marginal distributions for the covariates themselves. We use this data generation scheme to conduct a simulation study of which regularization methods for logistic regression are best suited when covariates are highly dependent. We evaluate this in terms of both prediction and variable selection. The second problem, namely an uneven class distribution, introduces challenges as well. First, selection of an appropriate measure of predictive performance is important. Secondly, it has been demonstrated that some methods may struggle with poor predictive performance on the under-represented class. We study how such a class imbalance affects the predictive performance and variable selection capabilities of the penalized logistic regression methods. In the last part of this thesis we model tax fraud on a real-life data set provided by The Norwegian Tax Administration. Our results show that penalized logistic regression can be a helpful tool for detecting tax fraud.
On bias of LS estimators of the parameters in autoregressive model AR(2)

Summary: In this article, presented the formula for bias of the conditional LS estimator of the parameters of autoregressive model of lag two with null constant parameter based on four observations. It has been shown that the crucial role in determining the bias of LS estimators in AR(2) models plays the random variable (cid:1851) = (cid:2869) (cid:3028)(cid:2878)(cid:3030)(cid:3084) (cid:3295) , where (cid:1853) and (cid:1855) are constants and (cid:2013) (cid:3047) is a random term of the autoregressive equation. The formula for the bias of the LS estimators is supplemented by its approximation with the boundary of the error of approximation.
Comparison of TVcDM and DDcTV algorithms in image reconstruction

ABSTRACT The total variation (TV) minimization algorithms is a classical representative of the optimization algorithms and have been widely used for their simpleness, robustness, expandability and their potential of accurately reconstructing images from sparse data or noisy data. The commonly used constrained TV (cTV) program is the data-divergence constrained TV (DDcTV) minimization. The other recently proposed cTV program is the TV constrained data-divergence minimization (TVcDM). In the work, we compare the two programs the convergence rate and the reconstruction accuracy via the sparse-view projection set and the noisy projection set in the context of CT. Further, we compare their reconstruction accuracy via real data in electron paramagnetic resonance imaging (EPRI). The studies show that TVcDM has much faster convergence rate relative to DDcTV and that TVcDM may achieve higher accuracy in most cases no matter in sparse-view projections CT reconstructions or in noisy projections CT reconstructions or in EPRI sparse reconstructions. From a comprehensive perspective, TVcDM has superior convergence and accurate reconstruction performance relative to DDcTV and should be recommended in the application of TV reconstruction algorithms. The knowledge and insights gained in the work may be extended to the performance analysis of other optimization-based reconstruction algorithms.
Pharmacologic Treatment of Impulse Control Disorders

toward rapid, unplanned reactions to either internal or external stimuli with diminished regard for negative consequences. Given this definition, multiple psychiatric disorders might be characterized as exhibiting problems with impulse control. In the fourth edition of the Diagnostic and Statistical Manual of the American Psychiatric Association (DSM-IV-TR), the category “impulse control disorders not elsewhere classified” includes pathologic gambling (PG), trichotillomania, intermittent explosive disorder (IED), kleptomania, and pyromania. Despite high prevalence rates in the general population, impulse control disorders have been relatively understudied. The disorder that arguably has been the best researched (i.e., PG) has been systematically investigated only recently with respect to empirically supported pharmacologic treatments. Because rigorous research is particularly limited for pyromania, this article will review the available research on the treatment of PG, trichotillomania, IED, and kleptomania. PATHOLOGIC GAMBLING PG is characterized by persistent and recurrent maladaptive patterns of gambling behavior and is associated with impaired functioning, reduced quality of life, decreased work productivity, and high rates of bankruptcy and relationship problems. PG usually begins in adolescence or early adulthood, with males tending to start at an earlier age. In epidemiologic studies, women represent approximately 32% After reading this article, the practitioner should be able to:
Qualitative and quantitative determination of potassium aluminum sulfate dodecahydrate in potato starch based on terahertz spectroscopy

Terahertz time‐domain spectroscopy (THz‐TDS) was used to study the additive potassium aluminum sulfate dodecahydrate (PASD) in potato starch. The terahertz time‐domain and frequency domain spectra of potato starch potato starch and PASD were obtained. The absorption coefficient spectrum and refractive index spectrum of the above two substances is calculated. The absorption coefficient spectrum shows that potassium aluminum sulfate dodecahydrate has obvious characteristic absorption peak in terahertz band. THz‐TDS technique can be used to identify the characteristics of potassium aluminum sulfate dodecahydrate in starch. Terahertz time‐domain spectra of potato starch doped with different percentage (mass fraction) potassium aluminum sulfate dodecahydrate were obtained. It was found that with the increase of the content of PASD, the amplitude of the absorption peak decreased and the refractive index decreased gradually, which indicated that THz‐TDS technique could be used for qualitative identification and quantitative detection of PASD in potato starch.
Estimation of models and cycles in time series applying fractal geometry

A time series, also called a time series or chronological series, consists of a set of data, coming from realizations of a random variable that are observed successively in time. Its analysis involves the use of statistical methods to adjust models to explain their behavior and make reliable forecasts. In this article integrated autoregressive models of moving average are adjusted to the studied series, complemented with specific methods of fractal geometry as support for the detection of the existence of random cycles in the series. The present investigation implies the realization of simulations, in a first phase and, later, the analysis of temporal series of economic and social variables of the country and the region.
Flow‐dependent stochastic coupling for climate models with high ocean‐to‐atmosphere resolution ratio

This study introduces a new flow‐dependent distribution sampling (FDDS) scheme for air–sea coupling. The FDDS scheme is implemented in a climate model and used to improve the simulated mean and variability of atmospheric and oceanic surface fields and thus air–sea fluxes. Most coupled circulation models use higher resolutions in the sea ice and ocean compared to the atmospheric model component, thereby explicitly simulating the atmospheric subgrid‐scale at the interface. However, the commonly applied averaging of surface fields and air–sea fluxes tends to smooth fine‐scale structures, such as oceanic fronts. The stochastic FDDS scheme samples the resolved spatial ocean (and sea ice) subgrid distribution that is usually not visible to a coarser‐resolution atmospheric model. Randomly drawn nodal ocean values are passed to the corresponding atmospheric boxes for the calculation of surface fluxes, aiming to enhance surface flux variability. The resulting surface field perturbations of the FDDS scheme are based on resolved dynamics, displaying pronounced seasonality with realistic magnitude. The AWI Climate Model is used to test the scheme on interannual time‐scales. Our set‐up features a high ocean‐to‐atmosphere resolution ratio in the Tropics, with grid‐point ratios of about 60:1. Compared to the default deterministic averaging, changes are largest in the Tropics leading to an improved spatial distribution of precipitation with bias reductions of up to 50%. Enhanced sea‐surface temperature variability in boreal winter further improves the seasonal phase locking of temperature anomalies associated with the El Niño–Southern Oscillation. Mean 2m temperature, sea ice thickness and concentration react with a contrasting dipole pattern between hemispheres but a joint increase of monthly and interannual variability. This first approach to implement a flow‐dependent stochastic coupling scheme shows considerable benefits for simulations of global climate, and various extensions and modifications of the scheme are possible.
Mean-field Behaviour of Neural Tangent Kernel for Deep Neural Networks

Recent influential work by Jacot et al. (2018) has shown that training a neural1network of any kind with gradient descent in parameter space is strongly related to kernel gradient descent in function space with respect to the Neural Tangent Kernel (NTK). Lee et al. (2019) built on this result by establishing that the output of a neural network trained using gradient descent can be approximated by a linear model for wide networks. In parallel, a recent line of studies (Schoenholz et al., 2017; Hayou et al., 2019) has suggested that a special initialization known as the Edge of Chaos improves training. In this paper, we bridge the gap between these two concepts by quantifying the impact of the initialization and the activation function on the NTK when the network depth becomes large. In particular, we show that the performance of wide deep neural networks cannot be explained by the NTK regime and we provide experiments illustrating our theoretical results.
Diurnal Variation of Rainfall in a Tropical Coastal Region with Complex Orography

We examined the diurnal cycle of the rainfall in a coastal tropical mountainous region in central Veracruz State, Mexico (18°–21° N, 95.5°–98.5° W), featuring a striking topographic gradient running from sea level at the Gulf of Mexico coast to 5000 m above sea level (m.a.s.l.) in less than 100 km horizontal distance. During the summer, this unique location leads to regular the interaction between the easterly moisture inflow and the mountainous barrier. Over the complex terrain, forced ascent leads the occurrence of maximum rainfall during the afternoon (16–19 local time, LT ≈ 1½ hours ahead of solar time in summer), first along the slope and later over the coast. Along the coastal plain, the precipitation continues until the early morning consistent with there being convergence between land breezes and the trade winds. Observations obtained during a measurement campaign from 28 June to 3 July 2015, indicate that during the early evening downslope winds move against easterly flow, likely due to katabatic outflows previously observed over the region. These features are confirmed using spatial (0.88°) and temporal (30 min) resolution CMORPH rainfall estimates, since we observed evening episodes initiating along the slope during the afternoon (14–17 LT) moving later towards the coast.
Stability and control of uncertain ICPT system considering time‐varying delay and stochastic disturbance

This paper studies the problem of robust exponential stability for uncertain inductively coupled power transfer (ICPT) system considering time‐varying delay and stochastic disturbance. Firstly, the model of the system is set up via a time domain method. Secondly, based on the Newton‐Leibnitz formula and stability theory, a new stability analysis of the ICPT system with uncertain parameter and time‐varying delay or stochastic disturbance is presented respectively. The proposed approach can be applied for analyzing other similar systems, and the obtained results can be also used for estimating convergence rate and region of stability. Thirdly, based on the Lyapunov‐Krasovskii functional (LKF) approach and the stochastic stability theory, robust exponential stability criteria in the mean square are derived and the relevant controller is designed. The proposed method can further reduce conservatism. Finally, the correctness and effectiveness of the obtained results are verified by an example and simulations indicate that the larger time delay, the slower attenuation. Simultaneously, the uncertain parameter and the stochastic disturbance have a significant influence on the region of stability. In addition, in respect of reducing conservatism, the effectiveness of the proposed method is demonstrated by comparing with other papers. In addition, the designed controller shows better performance for the ICPT system with the parameter uncertainty, the time‐varying delay, and the stochastic disturbance.
Ion and Electron Dynamics in the Presence of Mirror, Electromagnetic Ion Cyclotron, and Whistler Waves

The wave–particle cyclotron interaction is a basic process in collisionless plasmas, which results in the redistribution of the energy between plasma waves and charged particles. This paper presents an event observation in order to explore the dynamics of charged particles and plasma waves, i.e., mirror, electromagnetic ion cyclotron (EMIC), and whistler waves, in the Earth’s magnetosheath. It shows that when ions have a high-speed streaming velocity parallel to the magnetic field, EMIC waves arise. We also find that the frequency distribution of nearly parallel and nearly antiparallel whistler waves depends on the parallel streaming velocity of electrons. Based on the linear kinetic theory and the fitting plasma parameters, we show that the differential flows among ion components can enhance the ion cyclotron anisotropy instability that is even stronger than the mirror instability. The differential electron flows induce an asymmetry of the growth rate of counter-propagating whistler waves in the electron cyclotron anisotropy instability. On the other hand, the low-frequency EMIC and transverse electromagnetic waves modulate the ion pitch angle distribution. Moreover, when charged particles flow across the magnetic field, both low- and high-energy electrons are deeply trapped by mirror waves. These results illustrate new features of the observed plasma waves and charged particles in the Earth’s magnetosheath, which could inspire improvement of the wave models therein.
SOA Pre-Amplified 100 Gb/s/λ PAM-4 TDM-PON Downstream Transmission Using 10 Gbps O-Band Transmitters

We experimentally demonstrate the downstream transmission of a 100 Gb/s/λ time division multiplexed passive optical network (TDM-PON) based on four-level pulsed amplitude modulation (PAM-4) in the O-band using 10 Gbps transmitters with semiconductor optical amplifier (SOA) and digital signal processing (DSP) at the receiver. Considering the soft-decision FEC (SD-FEC) threshold (1 × 10−2), power budget of 30.3 dB and 29.3 dB have been achieved after 22 km and 50 km fiber transmission, respectively. There is no observable dispersion penalty after 22 km and 50 km transmission. The possibility of 100 Gb/s/λ PON is first investigated using intensity modulation and direct detection (IM/DD) schemes rather than coherent detection schemes.