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Spectral collocation method, named linear barycentric rational interpolation collocation method (LBRICM), for convection-diffusion (C-D) equation with constant coefficient is considered. We change the discrete linear equations into the matrix equation. Different from the classical methods to solve the C-D equation, we solve the C-D equation with the time variable and space variable obtained at the same time. Furthermore, the convergence rate of the C-D equation by LBRICM is proved. Numerical examples are presented to test our analysis.

In this digital, internet-based world, it is not new to face cyber attacks from time to time. A number of heavy viruses have been made by hackers, and they have successfully given big losses to our systems. In the family of these viruses, the Stuxnet virus is a well-known name. Stuxnet is a very dangerous virus that probably targets the control systems of our industry. The main source of this virus can be an infected USB drive or flash drive. In this research paper, we study a mathematical model to define the dynamical structure or the effects of the Stuxnet virus on our computer systems. To study the given dynamics, we use a modified version of the Caputo-type fractional derivative, which can be used as an old Caputo derivative by fixing some slight changes, which is an advantage of this study. We demonstrate that the given fractional Caputo-type dynamical model has a unique solution using fixed point theory. We derive the solution of the proposed non-linear non-classical model with the application of a recent version of the Predictor–Corrector scheme. We analyze various graphs at different values of the arrival rate of new computers, damage rate, virus transmission rate, and natural removal rate. In the graphical interpretations, we verify the values of fractional orders and simulate 2-D and 3-D graphics to understand the dynamics clearly. The major novelty of this study is that we formulate the optimal control problem and its important consequences both theoretically and mathematically, which can be further extended graphically. The main contribution of this research work is to provide some novel results on the Stuxnet virus dynamics and explore the uses of fractional derivatives in computer science. The given methodology is effective, fully novel, and very easy to understand.

Two-dimensional biharmonic boundary-value problems are considered by the linear barycentric rational collocation method, and the unknown function is approximated by the barycentric rational polynomial. With the help of matrix form, the linear equations of the discrete biharmonic equation are changed into a matrix equation. From the convergence rate of barycentric rational polynomial, we present the convergence rate of linear barycentric rational collocation method for biharmonic equation. Finally, several numerical examples are provided to validate the theoretical analysis.

The intersection of surfaces is a fundamental process in computational geometry and computer-aided design applications to build and interrogate complex shapes in the computer. This paper presents a novel and simple dual quaternion-based osculating circle DQOC algorithm to find the intersection curve of two regular surfaces based on the osculating circle concept and dual quaternions. Additionally, we expressed the natural equations of the intersection curve. We have also demonstrated the superiority of our method through numerical examples.

Facial expression generation has always been an intriguing task for scientists and researchers all over the globe. In this context, we present our novel approach for generating videos of the six basic facial expressions. Starting from a single neutral facial image and a label indicating the desired facial expression, we aim to synthesize a video of the given identity performing the specified facial expression. Our approach, referred to as FEV-GAN (Facial Expression Video GAN), is based on Spatio-temporal Convolutional GANs, that are known to model both content and motion in the same network. Previous methods based on such a network have shown a good ability to generate coherent videos with smooth temporal evolution. However, they still suffer from low image quality and low identity preservation capability. In this work, we address this problem by using a generator composed of two image encoders. The first one is pre-trained for facial identity feature extraction and the second for spatial feature extraction. We have qualitatively and quantitatively evaluated our model on two international facial expression benchmark databases: MUG and Oulu-CASIA NIR&VIS. The experimental results analysis demonstrates the effectiveness of our approach in generating videos of the six basic facial expressions while preserving the input identity. The analysis also proves that the use of both identity and spatial features enhances the decoder ability to better preserve the identity and generate high-quality videos. The code and the pre-trained model will soon be made publicly available.

A cubic H-Bézier geometric approximation scheme with one free parameter τis introduced for parabolic arcs. It has four control points. The control points are computed by matching the end points and end unit tangents of the two curves and provide two more free parameters. These free parameters are computed by curvature continuity constraints. Optimal value of τ is obtained by minimizing the maximum value of the distance between the cubic H-Bézier curve and the concerned parabolic arc. The method is illustrated using different numerical examples which show that the proposed method is economical, reliable and efficient.

In this article, the optimal control for nonlinear SIRC model is studied in fractional order using the Caputo fractional derivative. Graph signal flow is given of the model and simulated by Simulink/Matlab which helps in discussing the topological structure of the model. Dynamics of the system versus certain parameters are studied via bifurcation diagrams, Lyapunov exponents and Poincare maps. The existence of a uniformly stable solution is proved after control. The obtained results display the activeness and suitability of the Mittag Generalized-Leffler function method (MGLFM). The approximate solution of the fractional order SIRC model using MGLFM is explained by giving the figures of solutions before and after control. Also, we plot the 3D relationships with different alpha (fractional order) which display the originality and suitability of the results.

A particle-cluster treecode based on barycentric Hermite interpolation is presented for fast summation of electrostatic particle interactions in 3D. The interpolation nodes are Chebyshev points of the 2nd kind in each cluster. It is noted that barycentric Hermite interpolation is scale-invariant in a certain sense that promotes the treecode’s efficiency. Numerical results for the Coulomb and screened Coulomb potentials show that the treecode run time scales like O(N log N), where N is the number of particles in the system. The advantage of the barycentric Hermite treecode is demonstrated in comparison with treecodes based on Taylor approximation and barycentric Lagrange interpolation.

This document summarises the current theoretical and experimental status of the di-Higgs boson production searches, and of the direct and indirect constraints on the Higgs boson self-coupling, with the wish to serve as a useful guide for the next years. The document discusses the theoretical status, including state-of-the-art predictions for di-Higgs cross sections, developments on the effective field theory approach, and studies on specific new physics scenarios that can show up in the di-Higgs final state. The status of di-Higgs searches and the direct and indirect constraints on the Higgs self-coupling at the LHC are presented, with an overview of the relevant experimental techniques, and covering all the variety of relevant signatures. Finally, the capabilities of future colliders in determining the Higgs self-coupling are addressed, comparing the projected precision that can be obtained in such facilities. The work has started as the proceedings of the Di-Higgs workshop at Colliders, held at Fermilab from the 4th to the 9th of September 2018, but it went beyond the topics discussed at that workshop and included further developments. FERMILAB-CONF-19-468-E-T, LHCHXSWG-2019-005

In 2012 the ATLAS and CMS collaborations discovered at the LHC the Higgs boson decaying to vector bosons. This discovery has provided a strong indication that the mechanism of Electroweak Symmetry Breaking (EWSB) is similar to the one predicted by Brout-Englert-Higgs (BEH) nearly 50 years before. Since then, one of the priorities of the LHC program, as well as of the majority of the future collider proposals, is to measure directly the parameters of the EWSB potential. The goal is to identify if it has indeed the straightforward quartic shape predicted by BEH or it is more complex, as the result of an unexplored physics nature. The answer to this major scientific question will have a considerable impact on our understanding of vacuum properties and the history of the universe through the EWSB during the Big Bang. The only direct way to probe these couplings is through the measure of the production of multiple Higgs bosons, two being the simplest case. In this paper, we present a comprehensive review of the current searches and the state of the art insights on the topic. In particular, we explain why this ambitious project is even more challenging than the discovery of the Higgs boson itself. Finally, we sketch the plans of the HEP community for how to access the parameters of the BEH mechanism. This review is adapted to a curious reader familiar with particle physics in general or a scientist who wants to have a landscape overview of the topic.

Imaging methods based on the absorption or scattering of atmospheric muons, collectively named under the neologism “muography”, exploit the abundant natural flux of muons produced from cosmic-ray interactions in the atmosphere. Recent years have seen a steep rise in the development of muography methods in a variety of innovative multidisciplinary approaches to study the interior of natural or human-made structures, establishing synergies between usually disconnected academic disciplines such as particle physics, geology, and archaeology. Muography also bears promise of immediate societal impact through geotechnical investigations, nuclear waste surveys, homeland security, and natural hazard monitoring. Our aim is to provide an introduction to this vibrant research area, starting from the physical principles at the basis of the methods and describing the main detector technologies and imaging tools, including their combination with conventional techniques from other disciplines, where appropriate. Then, we discuss critically some outstanding issues that affect a broad variety of applications, and the current state of the art in addressing them. Finally, we review several recent developments in the application of muography methods to specific use cases, without any pretence of exhaustiveness.

Demonstration of the light radiation pressure on a microscopic level by A. Ashkin led to the invention of optical tweezers (OT). Applied in the studies of living systems, OT have become a preferable instrument for the noninvasive study of microobjects, allowing manipulation and measurement of the mechanical properties of molecules, organelles, and cells. In the present paper, we overview OT applications in hemorheological research, placing emphasis on red blood cells but also discussing OT applications for the investigation of the biomechanics of leukocytes and platelets. Blood properties have always served as a primary parameter in medical diagnostics due to the interconnection with the physiological state of an organism. Despite blood testing being a well-established procedure of conventional medicine, there are still many complex processes that must be unraveled to improve our understanding and contribute to future medicine. OT are advancing single-cell research, promising new insights into individual cell characteristics compared to the traditional approaches. We review the fundamental and practical findings revealed in blood research through the optical manipulation, stretching, guiding, immobilization, and inter-/intracellular force measurements of single blood cells.

The complexity of collider data analyses has dramatically increased from early colliders to the CERN LHC. Reconstruction of the collision products in the particle detectors has reached a point that requires dedicated publications documenting the techniques, and periodic retuning of the algorithms themselves. Analysis methods evolved to account for the increased complexity of the combination of particles required in each collision event (final states) and for the need of squeezing every last bit of sensitivity from the data; physicists often seek to fully reconstruct the final state, a process that is mostly relatively easy at lepton colliders but sometimes exceedingly difficult at hadron colliders to the point of requiring sometimes using advanced statistical techniques such as machine learning. The need for keeping the publications documenting results to a reasonable size implies a greater level of compression or even omission of information with respect to publications from twenty years ago. The need for compression should however not prevent sharing a reasonable amount of information that is essential to understanding a given analysis. Infrastructures like Rivet or HepData have been developed to host additional material, but physicists in the experimental Collaborations often still send an insufficient amount of material to these databases. In this manuscript I advocate for an increase in the information shared by the Collaborations, and try to define a minimum standard for acceptable level of information when reporting the results of statistical procedures in High Energy Physics publications.

This article deals with univariate binary approximating subdivision schemes and their generalization to non-tensor product bivariate subdivision schemes. The two algorithms are presented with one tension and two integer parameters which generate families of univariate and bivariate schemes. The tension parameter controls the shape of the limit curve and surface while integer parameters identify the members of the family. It is demonstrated that the proposed schemes preserve monotonicity of initial data. Moreover, continuity, polynomial reproduction and generation of the schemes are also discussed. Comparison with existing schemes is also given.

Abstract A radial basis function method for solving time-fractional KdV equation is presented. The Caputo derivative is approximated by the high order formulas introduced in Buhman (Proc. Edinb. Math. Soc. 36:319–333, 1993). By choosing the centers of radial basis functions as collocation points, in each time step a nonlinear system of algebraic equations is obtained. A fixed point predictor–corrector method for solving the system is introduced. The efficiency and accuracy of our method are demonstrated through several illustrative examples. By the examples, the experimental convergence order is approximately $$4-\alpha $$ 4-α , where $$\alpha $$ α is the order of time derivative.

This paper is devoted to Hermite interpolation with Chebyshev-Lobatto and Chebyshev-Radau nodal points. The aim of this piece of work is to establish the rate of convergence for some types of smooth functions. Although the rate of convergence is similar to that of Lagrange interpolation, taking into account the asymptotic constants that we obtain, the use of this method is justified and it is very suitable when we dispose of the appropriate information.