Miracle-dz/UniFAR-FTUs huggingface dataset:
Staggered Time Average Algorithm for Stochastic Non-smooth Optimization with O(1/T) Convergence

Stochastic non-smooth convex optimization constitutes a class of problems in machine learning and operations research. This paper considers minimization of a non-smooth function based on stochastic subgradients. When the function has a locally polyhedral structure, a staggered time average algorithm is proven to have O(1/T) convergence rate. A more general convergence result is proven when the locally polyhedral assumption is removed. In that case, the convergence bound depends on the curvature of the function near the minimum. Finally, the locally polyhedral assumption is shown to improve convergence beyond O(1/T) for a special case of deterministic problems.
SINGULARITIES OF THE BIEXTENSION METRIC FOR FAMILIES OF ABELIAN VARIETIES

In this paper we study the singularities of the invariant metric of the Poincaré bundle over a family of abelian varieties and their duals over a base of arbitrary dimension. As an application of this study we prove the effectiveness of the height jump divisors for families of pointed abelian varieties. The effectiveness of the height jump divisor was conjectured by Hain in the more general case of variations of polarized Hodge structures of weight $-1$ .
Task Offloading Strategy for Ocean Based on MEC

With the development of marine business, the diversification of marine business has produced more and more delay-sensitive and computing-intensive tasks, and the demand for marine communication is becoming more and more obvious. Establish a task offloading model between ship users, select offload nodes based on the connectivity probability between ship users, in order to alleviate the problem of data congestion during transmission, use orthogonal frequency division multiple access technology to divide channels, and propose subtasks and Algorithm for subchannel matching. Ship users use solar energy to supply energy, and propose a penalty strategy for insufficient energy collection and a penalty strategy for task delay, so that the system can minimize the actual energy consumption and establish an objective function under the condition of satisfying the delay constraint. The local transmit power is optimized, and the gray wolf optimization algorithm is improved to obtain a better data offloading ratio. The simulation results of EdgeCloudSim show that, compared with other methods, the proposed method can achieve the best performance while guaranteeing the delay.
Averaging Fourth‐Rank Tensors with Weight Functions

The problem of averaging fourth‐rank tensors with texture describing weight functions has been solved for orthotropic physical symmetry and for orthorhombic crystal symmetry. The results are presented in tabular form. The procedure for extending the tabular results to tetragonal, hexagonal, and cubic crystal symmetries is indicated. The solution requires the coefficients of the generalized spherical harmonic expansion of the weight function up to fourth order, and entails only those approximations required to obtain such coefficients from experimental data.
Molecular Dipolar Crystals as High Fidelity Quantum Memory for Hybrid Quantum Computing

We study collective excitations of rotational and spin states of an ensemble of polar molecules, which are prepared in a dipolar crystalline phase, as a candidate for a high-fidelity quantum memory. While dipolar crystals are formed in the high-density limit of cold clouds of polar molecules under one- and two-dimensional trapping conditions, the crystalline structure protects the molecular qubits from detrimental effects of short-range collisions. We calculate the lifetime of the quantum memory by identifying the dominant decoherence mechanisms, and estimate their effects on gate operations, when a molecular ensemble qubit is transferred to a superconducting strip line cavity (circuit QED). In the case of rotational excitations coupled by dipole-dipole interactions we identify phonons as the main limitation of the lifetime of qubits. We study specific setups and conditions, where the coupling to the phonon modes is minimized. Detailed results are presented for a one-dimensional dipolar chain.
Phase-Based Motion Magnification for Structural Vibration Monitoring at a Video Streaming Rate

Here we propose a novel approach to image magnification that enables frame-by-frame motion magnification application at a video streaming rate of around 30 fps. This novel approach can be used instead of batch processing an image file in conventional phase-based magnification (PBM). This new PBM method can instantly show a magnified video streaming on display at 30 fps, which is helpful for vibration measurement and for monitoring tasks where magnified images need to be viewed simultaneously. To accomplish video streaming-rate magnification, the proposed PBM uses time-domain convolution in temporal bandpass filtering for frame-by-frame operation whereas conventional PBM employs a frequency-domain filter that is applied to the entire image file at once. An experiment was conducted to monitor the vibration of a cantilever using a webcam streaming at the same frame rate, and data were collected simultaneously using a laser Doppler vibrometer for comparison. The experiment confirmed that the proposed PBM approach is more effective than the conventional magnification method and it also analyzed the system performance for vibration measurement. Additionally, the proper orthogonal mode could be found through the singular value decomposition from vibration displacement data of the cantilever that was collected instantly from the magnified image frames. Furthermore, the dominant mode could be effectively extracted from excitation at the resonance frequency. Because of magnification factors, the vibration displacements from the proposed method were estimated using linear regression and the accuracy of the estimated displacements was within the permissible error bound. Since the proposed PBM is a frame-by-frame operation, instantaneous adjustment of magnification parameters is available, even while the magnification is being processed. In addition, the proposed PBM is independently adjustable to the number of image frames for temporal FIR filter order.
Discretization of Lorentz Force Term

This article investigates three discretization methods (C1 method, C2 method, and CIM) for the Lorentz force term from the viewpoint of accuracy in magnetohydrodynamic (MHD) flow calculation. The three methods are tested against a fully developed two-dimensional laminar channel flow within a uniform magnetic field having an analytic solution. The results show that the CIM is in good agreement with the analytic solution in the Hartman number range considered (Ha = 0–1,000), whereas the C1 and C2 methods produce numerical errors, which are greatly increased as the Hartman number increases.
Existence of Solutions to Split Variational Inequality Problems and Split Minimization Problems in Banach Spaces

In this paper, we extend the concept of split variational inequality problems from Hilbert spaces to Banach spaces. Then we apply the Fan-KKM theorem to prove the existence of solutions to some split variational inequality problems and some split minimization problems in Banach spaces. We also apply fixed point theorems on Chain complete posets to show the solvability of some split variational inequality problems in partially ordered Banach space.
Patterns in random fractals

abstract:We characterize the existence of certain geometric configurations in the fractal percolation limit set $A$ in terms of the almost sure dimension of $A$. Some examples of the configurations we study are: homothetic copies of finite sets, angles, distances, and volumes of simplices. In the spirit of relative Szemer\'{e}di theorems for random discrete sets, we also consider the corresponding problem for sets of positive $\nu$-measure, where $\nu$ is the natural measure on $A$. In both cases we identify the dimension threshold for each class of configurations. These results are obtained by investigating the intersections of the products of $m$ independent realizations of $A$ with transversal planes and, more generally, algebraic varieties, and extend some well-known features of independent percolation on trees to a setting with long-range dependencies.
A method for solving nonlinear differential equations: an application to $\lambda\phi^4$ model

Recently, it has been great interest in the development of methods for solving nonlinear differential equations directly. Here, it is shown an algorithm based on Pad\'e approximants for solving nonlinear partial differential equations without requiring a one-dimensional reduction. This method is applied to the $\lambda\phi^4$ model in 4 dimensions and new solutions are obtained.
Can Shared Control Improve Overtaking Performance? Combining Human and Automation Strengths for a Safer Maneuver

The Shared Control (SC) cooperation scheme, where the driver and automated driving system control the vehicle together, has been gaining attention through the years as a promising option to improve road safety. As a result, advanced interaction methods can be investigated to enhance user experience, acceptance, and trust. Under this perspective, not only the development of algorithms and system applications are needed, but it is also essential to evaluate the system with real drivers, assess its impact on road safety, and understand how drivers accept and are willing to use this technology. In this sense, the contribution of this work is to conduct an experimental study to evaluate if a previously developed shared control system can improve overtaking performance on roads with oncoming traffic. The evaluation is performed in a Driver-in-the-Loop (DiL) simulator with 13 real drivers. The system based on SC is compared against a vehicle with conventional SAE-L2 functionalities. The evaluation includes both objective and subjective assessments. Results show that SC proved to be the best solution for assisting the driver during overtaking in terms of safety and acceptance. The SC’s longer and smoother control transitions provide benefits to cooperative driving. The System Usability Scale (SUS) and the System Acceptance Scale (SAS) questionnaire show that the SC system was perceived as better in terms of usability, usefulness, and satisfaction.
Convergence rates of nonlinear inverse problems in Banach spaces via Holder stability estimates

In this paper, we analyze the convergence rates of well known Tikhonov regularization scheme for solving the nonlinear ill-posed problems by using the Holder stability estimates. In particular, we obtain the convergence rates via two different approaches. The first approach is the standard one via Bregman distances and the second one is in terms of weaker norms. The important aspect in the second approach is that the regularization is only used to constrain the regularized solutions to a set where stability holds. Moreover, a novel smoothness condition is introduced termed as approximate Holder estimates which is further exploited to obtain the convergence rates. At the end, we also discuss the convergence rates for Tikhonov regularization with sparsity constraints by incorporating the Holder stability estimates.
Evaluation of the Rate of Convergence in the PIA

Folklore says that Howard's Policy Improvement Algorithm converges extraordinarily fast, even for controlled diffusion settings. In a previous paper, we proved that approximations of the solution of a particular parabolic partial differential equation obtained via the policy improvement algorithm show a quadratic local convergence. In this paper, we show that we obtain the same rate of convergence of the algorithm in a more general setup. This provides some explanation as to why the algorithm converges fast. We provide an example by solving a semilinear elliptic partial differential equation numerically by applying the algorithm and check how the approximations converge to the analytic solution.
Full Stability for a Class of Control Problems of Semilinear Elliptic Partial Differential Equations

We investigate full Lipschitzian and full H\"olderian stability for a class of control problems governed by semilinear elliptic partial differential equations, where all the cost functional, the state equation, and the admissible control set of the control problems undergo perturbations. We establish explicit characterizations of both Lipschitzian and H\"olderian full stability for the class of control problems. We show that for this class of control problems the two full stability properties are equivalent. In particular, the two properties are always equivalent in general when the admissible control set is an arbitrary fixed nonempty, closed, and convex set.
A topological proof of the non-degeneracy of harmonic structures on Sierpinski Gaskets

We present a direct proof of the non-degeneracy of the harmonic structures on the level-$n$ Sierpinski gaskets for any $n\geq 2$, which was conjectured by Hino in [H1,H2] and confirmed to be true by Tsougkas [T] very recently using Tutte's spring theorem.
Scattering results for Dirac Hartree-type equations with small initial data

We consider the Dirac equations with cubic Hartree-type nonlinearity which are derived by uncoupling the Dirac-Klein-Gordon systems. We prove small data global well-posedness and scattering results in the full scaling subcritical regularity regime. The strategy of the proof relies on the localized Strichartz estimates and bilinear estimates in \begin{document}$ V^2 $\end{document} spaces, together with the use of the null structure that the nonlinear term exhibits. This result is shown to be almost optimal in the sense that the iteration method based on Duhamel's formula fails over the supercritical range.
A Hierarchical Heterogeneous Graph for Unsupervised SAR Image Change Detection

This letter presents a novel graph-driven synthetic aperture radar (SAR) image change detection approach. A hierarchical heterogeneous graph (HHG) is proposed, combining two distinct graphs: a weighted graph based on adjacency of superpixels of an initial over-segmentation, and the dual-weighted heterogeneous graph. The superpixel-based regional affinities are coupled with pixel-based heterogeneous affinities, being embedded into the structure of HHG. The difference image generation relies on the matching of the bitemporal graphs, as well as the multiscale features of vertex domain. Finally, traditional graph cuts algorithm is applied to separate the difference image into changed and unchanged areas. Experiments on three real SAR datasets show that the proposed approach outperforms other experimental approaches and is a good candidate for SAR image change detection tasks.
Stability of Riemannian manifolds with Killing spinors

Riemannian manifolds with non-zero Killing spinors are Einstein manifolds. Klaus Kroncke proved that all complete Riemannian manifolds with imaginary Killing spinors are (linearly) strictly stable in \cite{Kro15}. In this paper, we obtain a new proof for this stability result by using a Bochner type formula in \cite{DWW05} and \cite{Wan91}. Moreover, existence of real Killing spinors is closely related to the Sasaki-Einstein structure. A regular Sasaki-Einstein manifold is essentially the total space of a certain principal $S^{1}$-bundle over a Kahler-Einstein manifold. We prove that if the base space is a product of two Kahler-Einstein manifolds then the regular Sasaki-Einstein manifold is unstable. This provides us many new examples of unstable manifolds with real Killing spinors.
AN INCOMPRESSIBLE NAVIER-STOKES MODEL IMPLEMENTED ON NONSTAGGERED GRIDS

The present study aims to develop an effective finite-difference model for solving incompressible Navier-Stokes equations. For the sake of programming simplicity, discretization of equations is made on nonstaggered grids without oscillatory solutions arising from the decoupling of the velocity and pressure fields. For the sake of computational efficiency, both segregated and alternating direction implicit (ADI) solution algorithms are employed to reduce the matrix size and, in turn, the CPU time. For the sake of numerical accuracy, a convection-diffusion-reaction finite-difference scheme is employed to provide nodally exact solutions in each ADI solution step. The convective instability problem is thus eliminated, since each convective term is modeled analytically even in multidimensional cases. The validity of the proposed numerical model is rigorously justified by solving one- and two-dimensional problems, which are amenable to analytical solutions. The simulated solutions for the scalar prototype equation agree well with the exact solutions and provide a very high spatial rate of convergence. The same is true for the simulated results of the Navier-Stokes equations.
From ``Dirac Combs'' to Fourier-positivity

Motivated by various problems in physics and applied mathematics, we look for constraints and properties of real Fourier-positive functions, i.e. with positive Fourier transforms. Properties of the "Dirac comb" distribution and of its tensor products in higher dimensions lead to Poisson resummation, allowing for a useful approximation formula of a Fourier transform in terms of a limited number of terms. A connection with the Bochner theorem on positive definiteness of Fourier-positive functions is discussed. As a practical application, we find simple and rapid analytic algorithms for checking Fourier-positivity in 1- and (radial) 2-dimensions among a large variety of real positive functions. This may provide a step towards a classification of positive positive-definite functions.
A connection between MAX $\kappa$-CUT and the inhomogeneous Potts spin glass in the large degree limit

Abstract. We study the asymptotic behavior of the Max κ-cut on a family of sparse, inhomogeneous random graphs. In the large degree limit, the leading term is a variational problem, involving the ground state of a constrained inhomogeneous Potts spin glass. We derive a Parisi type formula for the free energy of this model, with possible constraints on the proportions, and derive the limiting ground state energy by a suitable zero temperature limit.
Researched on Maximum Power Point Tracking of PV Power System

To the oscillation and misjudgment problem of the traditional perturbation and observation algorithm, a novel three-point comparison method was proposed. This method applied Constant Voltage Tracking (CVT) method and variable-step perturbation method to solve the problem between tracking accuracy and speed, and applied double-direction perturbation method to make sure the reliability of action to avoid the misjudgment when external conditions fast changing. Restraining the oscillation near the maximum power point effectively was another merit of this proposed method. Finally, the experimental results demonstrate effectiveness of proposed method with PV experimental platform.
Statistical analysis of Pisarenko's method for sinusoidal frequency estimation

Statistical analysis is performed for Pisarenko's method of sinusoidal frequency estimation by using the periodogram technique. Under the assumption that the data consist of several sinusoids plus white noise, we give an asymptotic expression of the error variance of the sinusoidal frequency estimator. Also, a modified method is proposed. This is computationally efficient but the statistical property is not improved. We also present simulation results and compare them to the theoretical ones. Lastly, we point out that the Pisarenko's method can be implemented as an (on-line) bias compensated least-squares algorithm, thus avoiding the eigenvalue and eigenvector calculations.
Performance of the Fourier transform reconstructor for the European Extremely Large Telescope

The forthcoming Extremely Large Telescopes, and the new generation of Extreme Adaptive Optics systems, carry on a boost in the number of actuators that makes the real-time correction of the atmospheric aberration computationally challenging. It is necessary to study new algorithms for performing Adaptive Optics at the required speed. Among the last generation algorithms that are being studied, the Fourier Transform Reconstructor (FTR) appears as a promising candidate. Its feasibility to be used for Single-Conjugate Adaptive Optics has been extensively proved by Poyneer et al.[1] As part of the activities supported by the ELT Design Study (European Community's Framework Programme 6) we have studied the performance of this algorithm applied to the case of the European ELT, in two different cases: single-conjugate and ground-layer adaptive optics and we are studying different approaches to apply it to the more complex multi-conjugate case. The algorithm has been tested on ESO's OCTOPUS software, which simulates the atmosphere, the deformable mirror, the sensor and the closed-loop control. The performance has been compared with other algorithms as well as their response in the presence of noise and with various atmospheric conditions. The good results on performance and robustness, and the possibility of parallelizing the algorithm (shown by Rodríguez-Ramos and Marichal-Hernández) make it an excellent alternative to the typically used Matrix-Vector Multiply algorithm.
Homotopy limits of model categories and more general homotopy theories

Generalizing a definition of homotopy fiber products of model categories, we give a definition of the homotopy limit of a diagram of left Quillen functors between model categories. As has been previously shown for homotopy fiber products, we prove that such a homotopy limit does in fact correspond to the usual homotopy limit, when we work in a more general model for homotopy theories in which they can be regarded as objects of a model category.
Discrete Painlevé equations and random matrix averages

The τ-function theory of Painleve systems is used to derive recurrences in the rank n of certain random matrix averages over U(n). These recurrences involve auxiliary quantities which satisfy discrete Painleve equations. The random matrix averages include cases which can be interpreted as eigenvalue distributions at the hard edge and in the bulk of matrix ensembles with unitary symmetry. The recurrences are illustrated by computing the value of a sequence of these distributions as n varies, and demonstrating convergence to the value of the appropriate limiting distribution.
Asymptotic of Number of Similarity Classes of Commuting Tuples

We have for positive integers $n$, $k$ and finite field $\mathbb{F}_q$, $c(n,k,q)$, as the number of simultaneous similarity classes of $k$-tuples of commuting $n\times n$ matrices over the $\mathbb{F}_q$. In this paper, it has been shown that $c(n,k,q)$ as a function of $k$ for fixed $n$ and $q$ is asymptotically $q^{m(n)k}$, where $m(n) = \left[\frac{n^2}{4}\right] + 1$, which is the dimension of the maximal commutative subalgebra of $M_n(\mathbb{F}_q)$ (the algebra of $n\times n$ matrices over $\mathbb{F}_q$).
On locally $n \times n$ grid graphs

We investigate locally $n \times n$ grid graphs, that is, graphs in which the neighbourhood of any vertex is the Cartesian product of two complete graphs on $n$ vertices. We consider the subclass of these graphs for which each pair of vertices at distance two is joined by sufficiently many paths of length $2$. The number of such paths is known to be at most $2n$ by previous work of Blokhuis and Brouwer. We show that if each distance two pair is joined by at least $n-1$ paths of length $2$ then the diameter is bounded by $O(\log(n))$, while if each pair is joined by at least $2(n-1)$ such paths then the diameter is at most $3$ and we give a tight upper bound on the order of the graphs. We show that graphs meeting this upper bound are distance-regular antipodal covers of complete graphs. We exhibit an infinite family of such graphs which are locally $n \times n$ grid for odd prime powers $n$, and apply these results to locally $5 \times 5$ grid graphs to obtain a classification for the case where either all $\mu$-graphs have order at least $8$ or all $\mu$-graphs have order $c$ for some constant $c$.