Terms Of P-norm Research Articles

Riemannian optimization on unit sphere with p-norm and its applications

This study deals with Riemannian optimization on the unit sphere in terms of p-norm with general $$p> 1$$ . As a Riemannian submanifold of the Euclidean space, the geometry of the sphere with p-norm is investigated, and several geometric tools used for Riemannian optimization, such as retractions and vector transports, are proposed and analyzed. Applications to Riemannian optimization on the sphere with nonnegative constraints and $$\textit{L}_{\textit{p}}$$ -regularization-related optimization are also discussed. As practical examples, the former includes nonnegative principal component analysis, and the latter is closely related to the Lasso regression and box-constrained problems. Numerical experiments verify that Riemannian optimization on the sphere with p-norm has substantial potential for such applications, and the proposed framework provides a theoretical basis for such optimization.

Una identidad de tipo Fink para la integral de funciones analíticas complejas en caminos de dominios generales

In this paper we establish an identity of Fink type for approximating the integral of analytic complex functions on paths from general domains. Error bounds for these expansions in terms of p-norms are also provided. Examples for the complex logarithm and the complex exponential are given as well.

Synchronization analysis for stochastic reaction-diffusion Cohen-Grossberg neural networks with Neumann boundary conditions via periodically intermittent control

In this paper, mathematical analysis is proposed on the synchronization problem for stochastic reaction-diffusion Cohen-Grossberg neural networks with Neumann boundary conditions. By introducing several important inequalities and using Lyapunov functional technique, some new synchronization criteria in terms of p-norm are derived under periodically intermittent control. Some previous known results in the literature are improved, and some restrictions on the mixed time-varying delays are removed. The influence of diffusion coefficients, diffusion space, stochastic perturbation and control width on synchronization is analyzed by the obtained synchronization criteria. Numerical simulations are presented to show the feasibility of the theoretical results.

Exponential synchronization of generalized neural networks with mixed time-varying delays and reaction-diffusion terms via aperiodically intermittent control.

In this paper, the exponential synchronization problem of generalized reaction-diffusion neural networks with mixed time-varying delays is investigated concerning Dirichlet boundary conditions in terms of p-norm. Under the framework of the Lyapunov stability method, stochastic theory, and mathematical analysis, some novel synchronization criteria are derived, and an aperiodically intermittent control strategy is proposed simultaneously. Moreover, the effects of diffusion coefficients, diffusion space, and stochastic perturbations on the synchronization process are explicitly expressed under the obtained conditions. Finally, some numerical simulations are performed to illustrate the feasibility of the proposed control strategy and show different synchronization dynamics under a periodically/aperiodically intermittent control.

Adaptive Exponential Synchronization for Stochastic Competitive Neural Networks with Time-Varying Leakage Delays and Reaction-Diffusion Terms

We study the exponential synchronization problem for a class of stochastic competitive neural networks with different timescales, as well as spatial diffusion, time-varying leakage delays, and discrete and distributed time-varying delays. By introducing several important inequalities and using Lyapunov functional technique, an adaptive feedback controller is designed to realize the exponential synchronization for the proposed competitive neural networks in terms of p-norm. According to the theoretical results obtained in this paper, the influences of the timescale, external stimulus constants, disposable scaling constants, and controller parameters on synchronization are analyzed. Numerical simulations are presented to show the feasibility of the theoretical results.

Exponential synchronization of Cohen-Grossberg neural networks with stochastic perturbation and reaction-diffusion terms via periodically intermittent control

In this paper, a class of Cohen-Grossberg neural networks with mixed time-varying delays, stochastic perturbation and reaction-diffusion terms is investigated. The exponential synchronization criteria in terms of p-norm are obtained based on periodically intermittent control by means of Lyapunov functional theory, mathematical induction and inequality technique. The influences of stochastic perturbation, spacial diffusion, the control rate and the control strength on the exponential synchronization are discussed according to the obtained synchronization criteria. The proposed criteria improve the previous known results in the literature and remove the restrictions on the mixed time-varying delays. Numerical simulations are carried out to illustrate the feasibility of the results. https://doi.org/10.28919/cmbn/2853

Synchronization criteria for generalized reaction-diffusion neural networks via periodically intermittent control.

In this paper, the synchronization problem for a class of generalized neural networks with time-varying delays and reaction-diffusion terms is investigated concerning Neumann boundary conditions in terms of p-norm. The proposed generalized neural networks model includes reaction-diffusion local field neural networks and reaction-diffusion static neural networks as its special cases. By establishing a new inequality, some simple and useful conditions are obtained analytically to guarantee the global exponential synchronization of the addressed neural networks under the periodically intermittent control. According to the theoretical results, the influences of diffusion coefficients, diffusion space, and control rate on synchronization are analyzed. Finally, the feasibility and effectiveness of the proposed methods are shown by simulation examples, and by choosing different diffusion coefficients, diffusion spaces, and control rates, different controlled synchronization states can be obtained.

Finite-time synchronization for fuzzy cellular neural networks with time-varying delays

In this paper, finite-time synchronization for a class of fuzzy cellular neural networks with time-varying delays is investigated based on the finite-time stability theory. By applying the inequality technique and the analysis method, some new and useful criteria of finite-time synchronization for the addressed network are derived in terms of p-norm. Finally, two examples with their numerical simulations are given to show the feasibility and effectiveness of the developed synchronization method.

Exponential synchronization for reaction-diffusion neural networks with mixed time-varying delays via periodically intermittent control

This paper deals with the exponential synchronization problem for reaction-diffusion neural networks with mixed time-varying delays and stochastic disturbance. By using stochastic analysis approaches and constructing a novel Lyapunov–Krasovskii functional, a periodically intermittent controller is first proposed to guarantee the exponential synchronization of reaction-diffusion neural networks with mixed time-varying delays and stochastic disturbance in terms of p-norm. The obtained synchronization results are easy to check and improve upon the existing ones. Particularly, the traditional assumptions on control width and time-varying delays are removed in this paper. This paper also presents two illustrative examples and uses simulated results of these examples to show the feasibility and effectiveness of the proposed scheme.

On the Decay of the Elements of Inverse Triangular Toeplitz Matrices

We consider half-infinite triangular Toeplitz matrices with slow decay of the elements and prove under a monotonicity condition that elements of the inverse matrix, as well as elements of the fundamental matrix, decay to zero. We also provide a quantitative description of the decay of the fundamental matrix in terms of p-norms. Finally, we prove that for matrices with slow log-convex decay the inverse matrix has fast decay, i.e. is bounded. The results are compared with the classical results of Jaffard and Veccio and illustrated by numerical example.

Exponential Synchronization of Stochastic Reaction-Diffusion Fuzzy Cohen-Grossberg Neural Networks With Time-Varying Delays Via Periodically Intermittent Control

In this paper, the exponential synchronization problem for fuzzy Cohen-Grossberg neural networks with time-varying delays, stochastic noise disturbance, and reaction-diffusion effects are investigated. By introducing a novel Lyapunov-Krasovskii functional with the idea of delay partitioning, a periodically intermittent controller is developed to derive sufficient conditions ensuring the addressed neural networks to be exponentially synchronized in terms of p-norm. The results extend and improve upon earlier work. A numerical example is provided to show the effectiveness of the proposed theories.

Exponential synchronization for reaction–diffusion networks with mixed delays in terms of -norm via intermittent driving

In this paper, the globally exponential synchronization for a class of reaction-diffusion neural networks with Dirichlet boundary conditions and mixed delays is investigated based on periodically intermittent control. Some new and useful synchronization criteria in terms of p-norm are derived by introducing multi-parameters, using Lyapunov functional theory. Subsequently, a feasible region of the control parameters for each neuron is derived for the realization of exponential synchronization. Besides, according to the theoretical results, the influences of diffusion strengths and diffusion spaces on synchronization are analyzed and a very interesting fact is revealed that the synchronization of neural networks with reaction-diffusions is more easily realized than those of neural networks without reaction-diffusions. Finally, a reaction-diffusion chaotic network is given to demonstrate the effectiveness of the proposed control methods.

Adaptive synchronization for stochastic competitive neural networks with mixed time-varying delays

This paper deals with the synchronization problem for competitive neural networks with different time scales, as well as mixed time-varying delays (both discrete and distributed time-varying delays) and stochastic disturbance. By using stochastic analysis approaches and constructing a novel Lyapunov–Krasovskii functional, an adaptive feedback controller is proposed to guarantee the exponential synchronization of proposed competitive neural networks in terms of p-norm. The synchronization results presented in this paper generalize and improve many known results. This paper also presents an illustrative example and uses simulated results of this example to show the feasibility and effectiveness of the theoretical results.

Exponential lag synchronization for delayed fuzzy cellular neural networks via periodically intermittent control

In this paper, lag synchronization for a class of delayed fuzzy cellular networks is investigated. By utilizing inequality technique, Lyapunov functional theory and the analysis method, some new and useful criteria of lag synchronization for the addressed networks are derived in terms of p-norm under a periodically intermittent controller. Finally, an example with simulation is given to show the effectiveness of the obtained results.

Impulsive Control and Synchronization for Delayed Neural Networks With Reaction–Diffusion Terms

This paper discuss the global exponential stability and synchronization of the delayed reaction-diffusion neural networks with Dirichlet boundary conditions under the impulsive control in terms of p-norm and point out the fact that there is no constant equilibrium point other than the origin for the reaction-diffusion neural networks with Dirichlet boundary conditions. Some new and useful conditions dependent on the diffusion coefficients are obtained to guarantee the global exponential stability and synchronization of the addressed neural networks under the impulsive controllers we assumed. Finally, some numerical examples are given to demonstrate the effectiveness of the proposed control methods.

A geometric interpretation of the multiresolution criterion in nonparametric regression

A recent approach to choosing the amount of smoothing in nonparametric regression is to select the simplest estimate for which the residuals ‘look like white noise’. This can be checked with the so-called multiresolution criterion, which Davies and Kovac [P.L. Davies and A. Kovac, Local extremes, runs, strings and multiresolutions (with discussion and rejoinder), Ann. Stat. 29 (2001), pp. 1–65.] introduced in connection with their taut-string procedure. It has also been used in several other nonparametric procedures such as spline smoothing or piecewise constant regression. We show that this criterion is related to a norm, the multiresolution norm (MR-norm). We point out some important differences between this norm and p-norms. The MR-norm is not invariant w.r.t. sign changes and permutations, and this makes it useful for detecting runs of residuals of the same sign. We also give sharp upper and lower bounds for the MR-norm in terms of p-norms.

An estimate of the mixed p-norm in terms of p-norms of smaller multiplicity

An estimate of the mixed p-norm in terms of p-norms of smaller multiplicity