Stabilization of reaction-diffusion fractional-order memristive neural networks.

This paper investigates the stabilization control of fractional-order memristive neural networks with reaction-diffusion terms. With regard to the reaction-diffusion model, a novel processing method based on Hardy-Poincarè inequality is introduced, as a result, the diffusion terms are estimated associated with the information of the reaction-diffusion coefficients and the regional feature, which may be beneficial to obtain conditions with less conservatism. Then, based on Kakutani's fixed point theorem of set-valued maps, new testable algebraic conclusion for ensuring the existence of the system's equilibrium point is obtained. Subsequently, by means of Lyapunov stability theory, it is concluded that the resulting stabilization error system is global asymptotic/Mittag-Leffler stable with a prescribed controller. Finally, an illustrative example about is provided to show the effectiveness of the established results.

Exponential Synchronization Control of Reaction-Diffusion Fuzzy Memristive Neural Networks: Hardy-Poincarè Inequality.

This article is devoted to solving the exponential synchronization problem of a new type of fuzzy memristive neural network with reaction-diffusion terms. By introducing adaptive laws, two controllers are designed. After combining the inequality technique with the Lyapunov function approach, some easily verified sufficient conditions are established to ensure the exponential synchronization of the reaction-diffusion fuzzy memristive system under the proposed adaptive scheme. In addition, by using the Hardy-Poincarè inequality, the diffusion terms are estimated associated with the information of the reaction-diffusion coefficients and the regional feature, which improves some existing conclusions. Finally, an illustrative example is presented to demonstrate the validity of the theoretical results.

Passivity and Dissipativity of Fractional-Order Quaternion-Valued Fuzzy Memristive Neural Networks: Nonlinear Scalarization Approach.

In this article, the problem of passivity and dissipativity analysis is investigated for a class of fractional-order quaternion-valued fuzzy memristive neural networks. Based on the famous nonlinear scalarizing function, a nonlinear scalarization method is developed, which can be employed to compare the "size" of two different quaternions. In this way, the convex closure proposed by the quaternion-valued connection weights is meaningful. By constructing proper Lyapunov functional, several improved passivity criteria and dissipativity conclusions are established, which can be checked efficiently by utilizing some standard mathematical calculations. Finally, the obtained results are validated by simulation examples.

Exponential H∞ State Estimation for Memristive Neural Networks: Vector Optimization Approach.

This article presents the theoretical results on the H∞ state estimation problem for a class of discrete-time memristive neural networks. By utilizing a Lyapunov-Krasovskii functional, sufficient conditions are derived to guarantee that the error system is exponentially mean-square stable; subsequently, the prespecified H∞ disturbance rejection attenuation level is also guaranteed. It should be noted that the vector optimization method is employed to find the maximum bound of function and the minimum disturbance turning simultaneously. Finally, the corresponding simulation results are included to show the effectiveness of the proposed methodology.

Exponential State Estimation for Stochastically Disturbed Discrete-Time Memristive Neural Networks: Multiobjective Approach.

The state estimation of the discrete-time memristive model is studied in this article. By applying the stochastic analysis technique, sufficient formulas are established to ensure the exponentially mean-square stability of the error model. Moreover, the derived control gain matrix can be calculated via the linear matrix inequality (LMI). It should be mentioned that, by extending the derived conclusion to a multiobjective optimization problem, the maximum bound of the active function and the minimum bound of the disturbance attenuation are derived. The corresponding simulation figures are provided in the end.

Finite-Time Stability Analysis for Markovian Jump Memristive Neural Networks With Partly Unknown Transition Probabilities.

This paper is concerned with the finite-time stochastically stability (FTSS) analysis of Markovian jump memristive neural networks with partly unknown transition probabilities. In the neural networks, there exist a group of modes determined by Markov chain, and thus, the Markovian jump was taken into consideration and the concept of FTSS is first introduced for the memristive model. By introducing a Markov switching Lyapunov functional and stochastic analysis theory, an FTSS test procedure is proposed, from which we can conclude that the settling time function is a stochastic variable and its expectation is finite. The system under consideration is quite general since it contains completely known and completely unknown transition probabilities as two special cases. More importantly, a nonlinear measure method was introduced to verify the uniqueness of the equilibrium point; compared with the fixed point Theorem that has been widely used in the existing results, this method is more easy to implement. Besides, the delay interval was divided into four subintervals, which make full use of the information of the subsystems upper bounds of the time-varying delays. Finally, the effectiveness and superiority of the proposed method is demonstrated by two simulation examples.

Drosophila TRPML is required for TORC1 activation.

Loss-of-function mutations in TRPML1 (transient receptor potential mucolipin 1) cause the lysosomal storage disorder, mucolipidosis type IV (MLIV). Here, we report that flies lacking the TRPML1 homolog displayed incomplete autophagy and reduced viability during the pupal period--a phase when animals rely on autophagy for nutrients. We show that TRPML was required for fusion of amphisomes with lysosomes, and its absence led to accumulation of vesicles of significantly larger volume and higher luminal Ca(2+). We also found that trpml(1) mutant cells showed decreased TORC1 (target of rapamycin complex 1) signaling and a concomitant upregulation of autophagy induction. Both of these defects in the mutants were reversed by genetically activating TORC1 or by feeding the larvae a high-protein diet. The high-protein diet also reduced the pupal lethality and the increased volume of acidic vesicles. Conversely, further inhibition of TORC1 activity by rapamycin exacerbated the mutant phenotypes. Finally, TORC1 exerted reciprocal control on TRPML function. A high-protein diet caused cortical localization of TRPML, and this effect was blocked by rapamycin. Our findings delineate the interrelationship between the TRPML and TORC1 pathways and raise the intriguing possibility that a high-protein diet might reduce the severity of MLIV.

Dependence on a retinophilin/myosin complex for stability of PKC and INAD and termination of phototransduction.

Normal termination of signaling is essential to reset signaling cascades, especially those such as phototransduction that are turned on and off with great rapidity. Genetic approaches in Drosophila led to the identification of several proteins required for termination, including protein kinase C (PKC), NINAC (neither inactivation nor afterpotential C) p174, which consists of fused protein kinase and myosin domains, and a PDZ (postsynaptic density-95/Discs Large/zona occludens-1) scaffold protein, INAD (inactivation no afterpotential D). Here, we describe a mutation affecting a poorly characterized but evolutionarily conserved protein, Retinophilin (Retin), which is expressed primarily in the phototransducing compartment of photoreceptor cells, the rhabdomeres. Retin and NINAC formed a complex and were mutually dependent on each other for expression. Loss of retin resulted in an age-dependent impairment in termination of phototransduction. Mutations that affect termination of the photoresponse typically lead to a reduction in levels of the major rhodopsin (Rh1) to attenuate signaling. Consistent with the slower termination in retin(1), the mutant photoreceptor cells exhibited increased endocytosis of Rh1 and a decline in Rh1 protein. The slower termination in retin(1) was a consequence of a cascade of defects, which began with the reduction in NINAC p174 levels. The diminished p174 concentration caused a decrease in INAD. Because PKC requires interaction with INAD for protein stability, this leads to reduction in PKC levels. The decline in PKC was age dependent and paralleled the onset of the termination phenotype in retin(1) mutant flies. We conclude that the slower termination of the photoresponse in retin(1) resulted from a requirement for the Retin/NINAC complex for stability of INAD and PKC.

Light-induced translocation of Drosophila visual Arrestin2 depends on Rac2.

Photoreceptor cells are remarkable in their ability to adjust their sensitivity to light over a wide range of intensities. Rapid termination of the photoresponse is achieved in part by shuttling proteins in and out of the light-transducing compartment of the photoreceptor cells. One protein that undergoes light-dependent translocation is the rhodopsin regulatory protein arrestin. However, the mechanisms coupling rhodopsin to arrestin movement are poorly understood. Here we show that light-dependent shuttling of the major arrestin in Drosophila photoreceptor cells, Arrestin2 (Arr2), occurs independently of known elements of the phototransduction cascade. Disruptions of the trimeric G protein, phospholipase Cbeta, the TRP channel, or the Na(+)/Ca(2+) exchanger did not influence Arr2 localization. Rather, we found that loss of the small GTPase Rac2 severely impaired Arr2 movement and prolonged the termination of the photoresponse. Our findings demonstrate that light-induced translocation of Arr2 occurs through a noncanonical rhodopsin/Rac2 pathway, which is distinct from the classical phototransduction cascade.