Hybrid Dynamic Variables-Dependent Event-Triggered Fuzzy Model Predictive Control

This article focuses on dynamic event-triggered mechanism(DETM)-based model predictive control(MPC) for T-S fuzzy systems.A hybrid dynamic variables-dependent DETM is carefully devised,which includes a multiplicative dynamic variable and an additive dynamic variable.The addressed DETM-based fuzzy MPC issue is described as a “min-max” optimization problem(OP).To facilitate the co-design of the MPC controller and the weighting matrix of the DETM,an auxiliary OP is proposed based on a new Lyapunov function and a new robust positive invariant(RPI) set that contain the membership functions and the hybrid dynamic variables.A dynamic event-triggered fuzzy MPC algorithm is developed accordingly,whose recursive feasibility is analysed by employing the RPI set.With the designed controller,the involved fuzzy system is ensured to be asymptotically stable.Two examples show that the new DETM and DETM-based MPC algorithm have the advantages of reducing resource consumption while yielding the anticipated performance.

Topological phases and edge modes of an uneven ladder

We investigate the topological properties of a two-chain quantum ladder with uneven legs,i.e.,the two chains differ in their periods by a factor of 2.Such an uneven ladder presents rich band structures classified by the closure of either direct or indirect bandgaps.It also provides opportunities to explore fundamental concepts concerning band topology and edge modes,including the difference of intracellular and intercellular Zak phases,and the role of the inversion symmetry(IS).We calculate the Zak phases of the two kinds and find excellent agreement with the dipole moment and extra charge accumulation.We also find that configurations with IS feature a pair of degenerate two-side edge modes emerging as the closure of the direct bandgap,while configurations without IS feature one-side edge modes emerging as not only the closure of both direct and indirect bandgaps but also within the band continuum.Furthermore,by projecting to the two sublattices,we find that the effective Bloch Hamiltonian corresponds to that of a generalized Su–Schrieffer–Heeger model or the Rice–Mele model whose hopping amplitudes depend on the quasimomentum.In this way,the topological phases can be efficiently extracted through winding numbers.We propose that uneven ladders can be realized by spin-dependent optical lattices and their rich topological characteristics can be examined by near future experiments.

Accounting for Quadratic and Cubic Invariants in Continuum Mechanics–An Overview

The differential equations of continuum mechanics are the basis of an uncountable variety of phenomena and technological processes in fluid-dynamics and related fields.These equations contain derivatives of the first order with respect to time.The derivation of the equations of continuum mechanics uses the limit transitions of the tendency of the volume increment and the time increment to zero.Derivatives are used to derive the wave equation.The differential wave equation is second order in time.Therefore,increments of volume and increments of time in continuum mechanics should be considered as small but finite quantities for problems of wave formation.This is important for calculating the generation of sound waves and water hammer waves.Therefore,the Euler continuity equation with finite time increments is of interest.The finiteness of the time increment makes it possible to take into account the quadratic and cubic invariants of the strain rate tensor.This is a new branch in hydrodynamics.Quadratic and cubic invariants will be used in differential wave equations of the second and third order in time.

Constructing Hopf Insulator from Geometric Perspective of Hopf Invariant

We propose a method to construct Hopf insulators based on the study of topological defects from the geometric perspective of Hopf invariant I.Firstly,we prove two types of topological defects naturally inhering in the inner differential structure of the Hopf mapping.One type is the four-dimensional point defects.

The Ω(2012) as a Hadronic Molecule

Recently,a new excited baryon state,Ω(2012),was observed in the invariant mass spectra of𝐾K^(-)■^(0) and K_(S)^(0)■^(-)by the Belle collaboration.This state has a narrow width(∼6 MeV)compared to other baryon states with a similar mass.Here,we provide a mini-review on the Ω(2012)state from the molecular perspective,where it appears to be a dynamically generated state with spin-parity 3/2^(−)from the coupled-channels interactions of the K■(1530)and ηΩ in s-wave and K■ in𝑑d-wave.Additionally,alternative explanations for the Ω(2012)resonance are also discussed.

Solving Invariant Problem of Cauchy Means Based on Wronskian Determinant

This paper studied the invariance of the Cauchy mean with respect to the arithmetic mean when the denominator functions satisfy certain conditions. The partial derivatives of Cauchy’s mean on the diagonal are obtained by using the method of Wronskian determinant in the process of solving. Then the invariant equation is solved by using the obtained partial derivatives. Finally, the solutions of invariant equations when the denominator functions satisfy the same simple harmonic oscillator equation or the denominator functions are power functions that have been obtained.

Solving the Three-Neutrino Problem as One of the Three-Body Problems in Physics

By using the standard PMNS (Pontecorvo-Maki-Nakagawa-Sakata) mixing matrix and applying the rule for the sum of the oscillation probabilities of three neutrinos, the equations of motion were derived in which the Dirac CP violating phase appeared as an unknown quantity. The equations of motion were separately derived for each of the three possible transitions for flavor-neutrino oscillations. Two roots of those equations were obtained in the form of two formulas for the Dirac CP violating phase with opposite signs. In the mathematical sense, the connection between those formulas was established in order to maintain the continuous process of oscillation of three neutrinos. This made it possible to calculate the numerical value for the Dirac CP violating phase, the Jarlskog invariant and to write the general form of the PMNS mixing matrix in the final form in which all its elements are defined with explicit numerical values.

A New Kind of Pre-Mean-Type Mappings and Its Gauss Iteration

A function which is reflexive is called by pre-mean, a more generalized definition of a mean. In this paper, we define a new pre-mean and study its properties, and then using the given invariant curve we consider the problem of convergence of Gauss iteration of a kind of pre-mean type mappings generated by the exponential and logarithmic functions.

Heteroclinic Cycles in a Class of 3-Dimensional Piecewise Affine Systems

This paper explores the existence of heteroclinic cycles and corresponding chaotic dynamics in a class of 3-dimensional two-zone piecewise affine systems. Moreover, the heteroclinic cycles connect two saddle foci and intersect the switching manifold at two points and the switching manifold is composed of two perpendicular planes.

Binding Energy, Root Mean Square Radius and Magnetic Dipole Moment of the Triton Nucleus

The basis functions of the translation invariant shell model are used to construct the ground state nuclear wave functions of 3H. The used residual two-body interactions consist of central, tensor, spin orbit and quadratic spin orbit terms with Gaussian radial dependence. The parameters of these interactions are so chosen in such a way that they represent the long-range attraction and the short-range repulsion of the nucleon-nucleon interactions. These parameters are so chosen to reproduce good agreement between the calculated values of the binding energy, the root mean-square radius, the D-state probability, the magnetic dipole moment and the electric quadrupole moment of the deuteron nucleus. The variation method is then used to calculate the binding energy of triton by varying the oscillator parameter which exists in the nuclear wave function. The obtained nuclear wave functions are then used to calculate the root mean-square radius and the magnetic dipole moment of the triton.

Mathematical Wave Functions and 3D Finite Element Modelling of the Electron and Positron

The wave/particle duality of particles in Physics is well known. Particles have properties that uniquely characterize them from one another, such as mass, charge and spin. Charged particles have associated Electric and Magnetic fields. Also, every moving particle has a De Broglie wavelength determined by its mass and velocity. This paper shows that all of these properties of a particle can be derived from a single wave function equation for that particle. Wave functions for the Electron and the Positron are presented and principles are provided that can be used to calculate the wave functions of all the fundamental particles in Physics. Fundamental particles such as electrons and positrons are considered to be point particles in the Standard Model of Physics and are not considered to have a structure. This paper demonstrates that they do indeed have structure and that this structure extends into the space around the particle’s center (in fact, they have infinite extent), but with rapidly diminishing energy density with the distance from that center. The particles are formed from Electromagnetic standing waves, which are stable solutions to the Schrödinger and Classical wave equations. This stable structure therefore accounts for both the wave and particle nature of these particles. In fact, all of their properties such as mass, spin and electric charge, can be accounted for from this structure. These particle properties appear to originate from a single point at the center of the wave function structure, in the same sort of way that the Shell theorem of gravity causes the gravity of a body to appear to all originate from a central point. This paper represents the first two fully characterized fundamental particles, with a complete description of their structure and properties, built up from the underlying Electromagnetic waves that comprise these and all fundamental particles.

Activation-induced pyroptosis contributes to the loss of MAIT cells in chronic HIV-1 infected patients

Background: Mucosal-associated invariant T(MAIT) cells are systemically depleted in human immunodeficiency virus type 1(HIV-1) infected patients and are not replenished even after successful combined antiretroviral therapy(cART).This study aimed to identify the mechanism underlying MAIT cell depletion.Methods: In the present study, we applied flow cytometry, single-cell RNA sequencing and immunohistochemical staining to evaluate the characteristics of pyroptotic MAIT cells in a total of 127 HIV-1 infected individuals, including 69 treatment-naive patients, 28 complete responders, 15 immunological non-responders, and 15 elite controllers, at the Fifth Medical Center of Chinese PLA General Hospital, Beijing, China.Results: Single-cell transcriptomic profiles revealed that circulating MAIT cells from HIV-1 infected subjects were highly activated, with upregulation of pyroptosis-related genes. Further analysis revealed that increased frequencies of pyroptotic MAIT cells correlated with markers of systemic T-cell activation, microbial translocation, and intestinal damage in cART-naive patients and poor CD4+ T-cell recovery in long-term cART patients. Immunohistochemical staining revealed that MAIT cells in the gut mucosa of HIV-1 infected patients exhibited a strong active gasdermin-D(GSDMD, marker of pyroptosis) signal near the cavity side, suggesting that these MAIT cells underwent active pyroptosis in the colorectal mucosa. Increased levels of the proinflammatory cytokines interleukin-12(IL-12) and IL-18 were observed in HIV-1 infected patients. In addition, activated MAIT cells exhibited an increased pyroptotic phenotype after being triggered by HIV-1 virions, T-cell receptor signals, IL-12 plus IL-18, and combinations of these factors, in vitro.Conclusions: Activation-induced MAIT cell pyroptosis contributes to the loss of MAIT cells in HIV-1 infected patients,which could potentiate disease progression and poor immune reconstitution.

The Distribution of Zeros of Quasi-Polynomials

PROFESSOR Yitang Zhang, a number theorist at the University of California, Santa Barbara, USA, has posted a paper on arXiv [1] that hints at the possibility that he may have solved the Landau-Siegel zeros conjecture. He has claimed that he has disproved a weaker version of the Landau-Siegel zeroes conjecture, an important problem related to the hypothesis.The conjecture is that there are solutions to the zeta function that do not assume the form prescribed by the Riemann hypothesis. Inspired by his work, in this Perspective, we would like to discuss about the distribution of zeros of quasi-polynomials for linear time-invariant(LTI) systems with time delays.

Multiple surface states,nontrivial band topology,and antiferromagnetism in GdAuAl_(4)Ge_(2)

Magnetic topological states of matter provide a fertile playground for emerging topological physics and phenomena.The current main focus is on materials whose magnetism stems from 3d magnetic transition elements,e.g.,MnBi_(2)Te_(4),Fe_(3)Sn_(2),and Co_(3)Sn_(2)S_(2).In contrast,topological materials with the magnetism from rare earth elements remain largely unexplored.Here we report rare earth antiferromagnet GdAuAl_(4)Ge_(2)as a candidate magnetic topological metal.Angle resolved photoemission spectroscopy(ARPES)and first-principles calculations have revealed multiple bulk bands crossing the Fermi level and pairs of low energy surface states.According to the parity and Wannier charge center analyses,these bulk bands possess nontrivial Z2 topology,establishing a strong topological insulator state in the nonmagnetic phase.Furthermore,the surface band pairs exhibit strong termination dependence which provides insight into their origin.Our results suggest GdAuAl_(4)Ge_(2)as a rare earth platform to explore the interplay between band topology,magnetism and f electron correlation,calling for further study targeting on its magnetic structure,magnetic topology state,transport behavior,and microscopic properties.

DYNAMICS OF THE STOCHASTIC g-NAVIER-STOKES EQUATIONS DRIVEN BY NONLINEAR NOISE

This paper deals with the asymptotic behavior of solutions of the stochastic g-Navier-Stokes equation driven by nonlinear noise.The existence and uniqueness of weak pullback mean random attractors for the equation in Bochner space is proven for when the diffusion terms are Lipschitz nonlinear functions.Furthermore,we also establish the existence of invariant measures for the equation.

Boundedness and liveness enforcement for labeled Petri nets using transition priority

This paper deals with the supervisory control problem of discrete event systems modeled by labeled Petri nets. The system is originally unbounded. First, the solvability of the problem is confirmed. A necessary condition is given and proven for the existence of a feasible priority-based controller based on the notions of liveness and transition invariants. Next, a cyclic behavior graph is constructed, which shows the reachable markings that guarantee the maximum liveness of the system within a given bound vector. Finally, an on-line control strategy is proposed to enforce boundedness and liveness to the given system by appending priority relations to transitions. The dynamic priority relation changes flexibly according to the current state of the system and enforces the system evolving in a bounded and live manner. In addition, numerical examples are studied to verify the validity of the proposed approach that remains the structure of the plant net and is efficient for on-line control.

Dual-stream coupling network with wavelet transform for cross-resolution person re-identification

Person re-identification is a prevalent technology deployed on intelligent surveillance.There have been remarkable achievements in person re-identification methods based on the assumption that all person images have a sufficiently high resolution,yet such models are not applicable to the open world.In real world,the changing distance between pedestrians and the camera renders the resolution of pedestrians captured by the camera inconsistent.When low-resolution(LR)images in the query set are matched with high-resolution(HR)images in the gallery set,it degrades the performance of the pedestrian matching task due to the absent pedestrian critical information in LR images.To address the above issues,we present a dualstream coupling network with wavelet transform(DSCWT)for the cross-resolution person re-identification task.Firstly,we use the multi-resolution analysis principle of wavelet transform to separately process the low-frequency and high-frequency regions of LR images,which is applied to restore the lost detail information of LR images.Then,we devise a residual knowledge constrained loss function that transfers knowledge between the two streams of LR images and HR images for accessing pedestrian invariant features at various resolutions.Extensive qualitative and quantitative experiments across four benchmark datasets verify the superiority of the proposed approach.

Invariant measures for the strong-facilitated exclusion process

Consider a generalized model of the facilitated exclusion process, which is a onedimensional exclusion process with a dynamical constraint that prevents the particle at site x from jumping to x+1 (or x-1) if the sites x-1, x-2 (or x+1, x+2) are empty. It is nongradient and lacks invariant measures of product form. The purpose of this paper is to identify the invariant measures and to show that they satisfy both exponential decay of correlations and equivalence of ensembles. These properties will play a pivotal role in deriving the hydrodynamic limit.

Invariant manifold growth formula in cylindrical coordinates and its application for magnetically confined fusion

For three-dimensional vector fields,the governing formula of invariant manifolds grown from a hyperbolic cycle is given in cylindrical coordinates.The initial growth directions depend on the Jacobians of Poincarémap on that cycle,for which an evolution formula is deduced to reveal the relationship among Jacobians of different Poincarésections.The evolution formula also applies to cycles in arbitrary finite n-dimensional autonomous continuous-time dynamical systems.Non-Möbiusian/Möbiusian saddle cycles and a dummy X-cycle are constructed analytically as demonstration.A real-world numeric example of analyzing a magnetic field timeslice on EAST is presented.

Robust Image Watermarking Using LWT and Stochastic Gradient Firefly Algorithm

Watermarking of digital images is required in diversified applicationsranging from medical imaging to commercial images used over the web.Usually, the copyright information is embossed over the image in the form ofa logo at the corner or diagonal text in the background. However, this formof visible watermarking is not suitable for a large class of applications. In allsuch cases, a hidden watermark is embedded inside the original image as proofof ownership. A large number of techniques and algorithms are proposedby researchers for invisible watermarking. In this paper, we focus on issuesthat are critical for security aspects in the most common domains like digitalphotography copyrighting, online image stores, etc. The requirements of thisclass of application include robustness (resistance to attack), blindness (directextraction without original image), high embedding capacity, high Peak Signalto Noise Ratio (PSNR), and high Structural Similarity Matrix (SSIM). Mostof these requirements are conflicting, which means that an attempt to maximizeone requirement harms the other. In this paper, a blind type of imagewatermarking scheme is proposed using Lifting Wavelet Transform (LWT)as the baseline. Using this technique, custom binary watermarks in the formof a binary string can be embedded. Hu’s Invariant moments’ coefficientsare used as a key to extract the watermark. A Stochastic variant of theFirefly algorithm (FA) is used for the optimization of the technique. Undera prespecified size of embedding data, high PSNR and SSIM are obtainedusing the Stochastic Gradient variant of the Firefly technique. The simulationis done using Matrix Laboratory (MATLAB) tool and it is shown that theproposed technique outperforms the benchmark techniques of watermarkingconsidering PSNR and SSIM as quality metrics.