5. M. Green, J. Schwarz, and E. Witten, Superstring theory, Cambridge Univ. Press, 1987. 6. J. Isenberg, P. Yasskin, and P. Green, Non-self-dual gauge fields, Phys. Lett. 78B (1978), 462-464. 7. B. Kostant, Graded manifolds, graded Lie theory, and prequantization, Differential Geometric Methods in Mathematicas Physics, Lecture Notes in Math., vol. 570, SpringerVerlag, Berlin and New York, 1977. 8. C. LeBrun, Thickenings and gauge fields, Class. Quantum Grav. 3 (1986), 1039-1059. 9. , Thickenings and conformai gravity, preprint, 1989. 10. C. LeBrun and M. Rothstein, Moduli of super Riemann surfaces, Commun. Math. Phys. 117(1988), 159-176. 11. Y. Manin, Critical dimensions of string theories and the dualizing sheaf on the moduli space of (super) curves, Funct. Anal. Appl. 20 (1987), 244-245. 12. R. Penrose and W. Rindler, Spinors and space-time, V.2, spinor and twistor methods in space-time geometry, Cambridge Univ. Press, 1986. 13. R. Ward, On self-dual gauge fields, Phys. Lett. 61A (1977), 81-82. 14. E. Witten, An interpretation of classical Yang-Mills theory, Phys. Lett. 77NB (1978), 394-398. 15. , Twistor-like transform in ten dimensions, Nucl. Phys. B266 (1986), 245-264. 16. , Physics and geometry, Proc. Internat. Congr. Math., Berkeley, 1986, pp. 267302, Amer. Math. Soc, Providence, R.I., 1987.

Infinite-Dimensional Dynamical Systems in Mechanics and Physics (Roger Temam)

Linked: The New Science of Networks

Neural networks

Neuromorphic computing has come to refer to a variety of brain-inspired computers, devices, and models that contrast the pervasive von Neumann computer architecture This biologically inspired approach has created highly connected synthetic neurons and synapses that can be used to model neuroscience theories as well as solve challenging machine learning problems The promise of the technology is to create a brain-like ability to learn and adapt, but the technical challenges are significant, starting with an accurate neuroscience model of how the brain works, to finding materials and engineering breakthroughs to build devices to support these models, to creating a programming framework so the systems can learn, to creating applications with brain-like capabilities In this work, we provide a comprehensive survey of the research and motivations for neuromorphic computing over its history We begin with a 35-year review of the motivations and drivers of neuromorphic computing, then look at the major research areas of the field, which we define as neuro-inspired models, algorithms and learning approaches, hardware and devices, supporting systems, and finally applications We conclude with a broad discussion on the major research topics that need to be addressed in the coming years to see the promise of neuromorphic computing fulfilled The goals of this work are to provide an exhaustive review of the research conducted in neuromorphic computing since the inception of the term, and to motivate further work by illuminating gaps in the field where new research is needed

A Survey of Neuromorphic Computing and Neural Networks in Hardware.

This paper is concerned with the problem of extended dissipativity-based state estimation for discrete-time Markov jump neural networks (NNs), where the variation of the piecewise time-varying transition probabilities of Markov chain is subject to a set of switching signals satisfying an average dwell-time property. The communication links between the NNs and the estimator are assumed to be imperfect, where the phenomena of signal quantization and data packet dropouts occur simultaneously. The aim of this paper is to contribute with a Markov switching estimator design method, which ensures that the resulting error system is extended stochastically dissipative, in the simultaneous presences of packet dropouts and signal quantization stemmed from unreliable communication links. Sufficient conditions for the solvability of such a problem are established. Based on the derived conditions, an explicit expression of the desired Markov switching estimator is presented. Finally, two illustrated examples are given to show the effectiveness of the proposed design method.

Extended Dissipative State Estimation for Markov Jump Neural Networks With Unreliable Links

In this paper, global exponential synchronization stability in an array of linearly diffusively coupled reaction-diffusion neural networks with time-varying delays is investigated by adding impulsive controller to a small fraction of nodes (pinning-impulsive controller). In order to overcome the difficulty resulting from the fact that the impulsive controller affects only the dynamical behaviors of the controlled nodes, a new analysis method is developed. By using the developed method, two known lemmas on stability of delayed functional differential equation with and without impulses, and Lyapunov stability theory, several novel and easily verified synchronization criteria guaranteeing the whole network will be pinned to a homogenous solution are derived. Moreover, the effects of the pinning-impulsive controller and the dynamics of the uncontrolled nodes and the diffusive couplings on the synchronization process are explicitly expressed in the obtained criteria. Our results also show that we can always de...

Synchronization of Coupled Reaction-Diffusion Neural Networks with Time-Varying Delays via Pinning-Impulsive Controller

Dealing with impulsive effects is one of the most challenging problems in the field of fixed-time control. In this paper, we solve this challenging problem by considering fixed-time synchronization of complex networks (CNs) with impulsive effects. By designing a new Lyapunov function and constructing comparison systems, a sufficient condition formulated by matrix inequalities is given to ensure that all the dynamical subsystems in the CNs are synchronized with an isolated system in a settling time, which is independent of the initial values of both the CNs and the isolated system. Then, by partitioning impulse interval and using the convex combination technique, sufficient conditions in terms of linear matrix inequalities are provided. Our synchronization criteria unify synchronizing and desynchronizing impulses. Compared with the existing controllers for fixed-time and finite-time techniques, the designed controller is continuous and does not include any sign function, and hence, the chattering phenomenon in most of the existing results is overcome. An optimal algorithm is proposed for the estimation of the settling time. Numerical examples are given to show the effectiveness of our new results.

Fixed-Time Synchronization of Complex Networks With Impulsive Effects via Nonchattering Control

Finite-time stochastic synchronization of complex networks

In this paper, the global exponential synchronization of delayed complex dynamical networks with nonidentical nodes and stochastic perturbations is studied. By combining adaptive control and impulsive control schemes, the considered network can be synchronized onto any given goal dynamics. The adaptive control is discontinuous and can overcome the unknown difference between dynamical nodes and goal system. As for the impulsive control, the concept named “average impulsive interval” with “elasticity number” of impulsive sequence is utilized to get less conservative synchronization criterion. Numerical simulations are given to show the effectiveness and less conservativeness of the theoretical results.

Stochastic Synchronization of Complex Networks With Nonidentical Nodes Via Hybrid Adaptive and Impulsive Control

This note considers globally finite-time synchronization of coupled networks with Markovian topology and distributed impulsive effects. The impulses can be synchronizing or desynchronizing with certain average impulsive interval. By using $M$ -matrix technique and designing new Lyapunov functions and controllers, sufficient conditions are derived to ensure the synchronization within a setting time, and the conditions do not contain any uncertain parameter. It is demonstrated theoretically and numerically that the number of consecutive impulses with minimum impulsive interval of the desynchronizing impulsive sequence should not be too large. It is interesting to discover that the setting time is related to initial values of both the network and the Markov chain. Numerical simulations are provided to illustrate the effectiveness of the theoretical analysis.

Xinsong Yang

Papers

Synchronization of Coupled Reaction-Diffusion Neural Networks with Time-Varying Delays via Pinning-Impulsive Controller

Fixed-Time Synchronization of Complex Networks With Impulsive Effects via Nonchattering Control

Finite-time stochastic synchronization of complex networks

Stochastic Synchronization of Complex Networks With Nonidentical Nodes Via Hybrid Adaptive and Impulsive Control

Finite-Time Synchronization of Coupled Networks With Markovian Topology and Impulsive Effects