Exponential stability of delayed recurrent neural networks with Markovian jumping parameters

This is the post print version of the article. The official published version can be obtained from the link below - Copyright 2006 Elsevier Ltd.In this Letter, the global exponential stability analysis problem is considered for a class of recurrent neural networks (RNNs) with time delays and Markovian jumping parameters. The jumping parameters considered here are generated from a continuous-time discrete-state homogeneous Markov process, which are governed by a Markov process with discrete and finite state space. The purpose of the problem addressed is to derive some easy-to-test conditions such that the dynamics of the neural network is stochastically exponentially stable in the mean square, independent of the time delay. By employing a new Lyapunov–Krasovskii functional, a linear matrix inequality (LMI) approach is developed to establish the desired sufficient conditions, and therefore the global exponential stability in the mean square for the delayed RNNs can be easily checked by utilizing the numerically efficient Matlab LMI toolbox, and no tuning of parameters is required. A numerical example is exploited to show the usefulness of the derived LMI-based stability conditions.This work was supported in part by the Engineering and Physical Sciences Research Council (EPSRC) of the UK under Grant GR/S27658/01, the Nuffield Foundation of the UK under Grant NAL/00630/G, and the Alexander von Humboldt Foundation of Germany

Exponential synchronization of complex networks with Markovian jump and mixed delays

This is the post print version of the article. The official published version can be obtained from the link - Copyright 2008 Elsevier LtdIn this Letter, we investigate the exponential synchronization problem for an array of N linearly coupled complex networks with Markovian jump and mixed time-delays. The complex network consists of m modes and the network switches from one mode to another according to a Markovian chain with known transition probability. The mixed time-delays are composed of discrete and distributed delays, both of which are mode-dependent. The nonlinearities imbedded with the complex networks are assumed to satisfy the sector condition that is more general than the commonly used Lipschitz condition. By making use of the Kronecker product and the stochastic analysis tool, we propose a novel Lyapunov–Krasovskii functional suitable for handling distributed delays and then show that the addressed synchronization problem is solvable if a set of linear matrix inequalities (LMIs) are feasible. Therefore, a unified LMI approach is developed to establish sufficient conditions for the coupled complex network to be globally exponentially synchronized in the mean square. Note that the LMIs can be easily solved by using the Matlab LMI toolbox and no tuning of parameters is required. A simulation example is provided to demonstrate the usefulness of the main results obtained.This work was supported in part by the Biotechnology and Biological Sciences Research Council (BBSRC) of the UK under Grants BB/C506264/1 and 100/EGM17735, the Engineering and Physical Sciences Research Council (EPSRC) of the UK under Grants GR/S27658/01 and EP/C524586/1, an International Joint Project sponsored by the Royal Society of the UK, the Natural Science Foundation of Jiangsu Province of China under Grant BK2007075, the National Natural Science Foundation of China under Grant 60774073, and the Alexander von Humboldt Foundation of Germany

Deciphering microbiomes dozens of meters under our feet and their edaphoclimatic and spatial drivers

Microbes inhabiting deep soil layers are known to be different from their counter-part in topsoil yet remain under investigation in terms of their structure, function, and how their diversity is shaped. The microbiome of deep soils (>1 m) is expected to be relatively stable and highly independent from climatic conditions. Much less is known, however, on how these microbial communities vary along climate gradients. Here, we used amplicon sequencing to investigate bacteria, archaea, and fungi along fifteen 18-m depth profiles at 20–50-cm intervals across contrasting aridity condi-tions in semi-arid forest ecosystems of China's Loess Plateau. Our results showed that bacterial and fungal α diversity and bacterial and archaeal community similarity de-clined dramatically in topsoil and remained relatively stable in deep soil. Nevertheless, deep soil microbiome still showed the functional potential of N cycling, plant-derived organic matter degradation, resource exchange, and water coordination. The deep soil microbiome had closer taxa–taxa and bacteria–fungi associations and more influ-ence of dispersal limitation than topsoil microbiome. Geographic distance was more influential in deep soil bacteria and archaea than in topsoil. We further showed that aridity was negatively correlated with deep-soil archaeal and fungal richness, archaeal community similarity, relative abundance of plant saprotroph, and bacteria–fungi associations, but increased the relative abundance of aerobic ammonia oxidation,manganese oxidation, and arbuscular mycorrhizal in the deep soils. Root depth, com-plexity, soil volumetric moisture, and clay play bridging roles in the indirect effects of aridity on microbes in deep soils. Our work indicates that, even microbial communi-ties and nutrient cycling in deep soil are susceptible to changes in water availability, with consequences for understanding the sustainability of dryland ecosystems and the whole-soil in response to aridification. Moreover, we propose that neglecting soil depth may underestimate the role of soil moisture in dryland ecosystems under future climate scenarios

Overexpression of LcSABP, an Orthologous Gene for Salicylic Acid Binding Protein 2, Enhances Drought Stress Tolerance in Transgenic Tobacco

Salicylic acid (SA) plays an essential role in the growth and development of plants, and in their response to abiotic stress. Previous studies have mostly focused on the effects of exogenously applied SA on the physiological response of plants to abiotic stresses; however, the underlying genetic mechanisms for the regulatory functions of endogenous SA in the defense response of plants remain unclear. In plants, SA binding protein 2 (SABP2), possessing methyl salicylate (MeSA) esterase activity, catalyzes the conversion of MeSA to SA. Herein, a SABP2-like gene, LcSABP, was cloned from Lycium chinense, which contained a complete open reading frame of 795 bp and encoded a protein of 264 amino acids that shared high sequence similarities with SABP2 orthologs from other plants. Overexpression of LcSABP enhanced the drought tolerance of transgenic tobacco plants. The results indicated that increased levels of LcSABP transcripts and endogenous SA content were involved in the enhanced drought tolerance. Physiological and biochemical studies further demonstrated that higher chlorophyll content, increased photosynthetic capacity, lower malondialdehyde content, and higher activities of superoxide dismutase, peroxidase, and catalase enhanced the drought tolerance of transgenic plants. Moreover, overexpression of LcSABP also increased the expression of reactive oxygen species (ROS)- and stress-responsive genes under drought stress. Overall, our results demonstrate that LcSABP plays a positive regulatory role in drought stress response by enhancing the endogenous SA content, promoting the scavenging of ROS, and regulating of the expression of stress-related transcription factor genes. Our findings indicate that LcSABP functions as a major regulator of the plant’s response to drought stress through a SA-dependent defense pathway

State estimation for jumping recurrent neural networks with discrete and distributed delays

This is the post print version of the article. The official published version can be obtained from the link - Copyright 2009 Elsevier LtdThis paper is concerned with the state estimation problem for a class of Markovian neural networks with discrete and distributed time-delays. The neural networks have a finite number of modes, and the modes may jump from one to another according to a Markov chain. The main purpose is to estimate the neuron states, through available output measurements, such that for all admissible time-delays, the dynamics of the estimation error is globally asymptotically stable in the mean square. An effective linear matrix inequality approach is developed to solve the neuron state estimation problem. Both the existence conditions and the explicit characterization of the desired estimator are derived. Furthermore, it is shown that the traditional stability analysis issue for delayed neural networks with Markovian jumping parameters can be included as a special case of our main results. Finally, numerical examples are given to illustrate the applicability of the proposed design method.This work was supported in part by the Engineering and Physical Sciences Research Council (EPSRC) of the UK under Grants GR/S27658/01, an International Joint Project sponsored by the Royal Society of the UK, the National Natural Science Foundation of China under Grants 60774073 and 60804028, the Natural Science Foundation of Jiangsu Province of China under Grant BK2007075, and the Alexander von Humboldt Foundation of Germany

Microbial assemblies associated with temperature sensitivity of soil respiration along an altitudinal gradient

10 páginas.. 4 figuras.- referencias.- Supplementary data to this article can be found online at https://doi. org/10.1016/j.scitotenv.2022.153257Identifying the drivers of the response of soil microbial respiration to warming is integral to accurately forecasting the carbon-climate feedbacks in terrestrial ecosystems. Microorganisms are the fundamental drivers of soil microbial respiration and its response to warming; however, the specific microbial communities and properties involved in the process remain largely undetermined. Here, we identified the associations between microbial community and temperature sensitivity (Q10) of soil microbial respiration in alpine forests along an altitudinal gradient (from 2974 to 3558 m) from the climate-sensitive Tibetan Plateau. Our results showed that changes in microbial community composition accounted for more variations of Q10 values than a wide range of other factors, including soil pH, moisture, substrate quantity and quality, microbial biomass, diversity and enzyme activities. Specifically, co-occurring microbial assemblies (i.e., ecological clusters or modules) targeting labile carbon consumption were negatively correlated with Q10 of soil microbial respiration, whereas microbial assemblies associated with recalcitrant carbon decomposition were positively correlated with Q10 of soil microbial respiration. Furthermore, there were progressive shifts of microbial assemblies from labile to recalcitrant carbon consumption along the altitudinal gradient, supporting relatively high Q10 values in high-altitude regions. Our results provide new insights into the link between changes in major microbial assemblies with different trophic strategies and Q10 of soil microbial respiration along an altitudinal gradient, highlighting that warming could have stronger effects on microbially-mediated soil organic matter decomposition in high-altitude regions than previously thought.This research was supported by the National Natural Science Foundation of China (32071595 and 41830756). We also thank the Fundamental Research Funds for the Central Universities (Program no. 2662019PY010 and 2662019QD055), Natural Science Fund of Hubei Province (2019CFA094), and the Strategic Priority Research Program (A) of the Chinese Academy of Sciences (Grant No. XDA20040502). We thank Hailong Li for his assistance in field sampling, and Jinhuang Lin for mapping sample locations. M.D-B. is supported by a Ramón y Cajal grant from the Spanish Government (agreement no. RYC2018-025483-I). ReferencesPeer reviewe

On short cycles in triangle-free oriented graphs

summary:An orientation of a simple graph is referred to as an oriented graph. Caccetta and Häggkvist conjectured that any digraph on $n$ vertices with minimum outdegree $d$ contains a directed cycle of length at most $\lceil n / d\rceil$. In this paper, we consider short cycles in oriented graphs without directed triangles. Suppose that $\alpha _0$ is the smallest real such that every $n$-vertex digraph with minimum outdegree at least $\alpha _0n$ contains a directed triangle. Let $\epsilon < {(3-2\alpha _0)}/{(4-2\alpha _0)}$ be a positive real. We show that if $D$ is an oriented graph without directed triangles and has minimum outdegree and minimum indegree at least $(1/{(4-2\alpha _0)}+\epsilon )|D|$, then each vertex of $D$ is contained in a directed cycle of length $l$ for each $4\le l< {(4-2\alpha _0)\epsilon |D|}/{(3-2\alpha _0)}+2$

The Full m Index Sets of P2×Pn

Shiu and Kwong (2008) studied the full friendly index set of P2×Pn, which only addressed the cases where m=0 or 1. In this paper, we significantly extend their work by determining the full m index set MP2×Pn for all values of m. Our key approach is to utilize graph embedding and recursion methods to deduce MP2×Pn for general m. In particular, we embed small graphs like C4 and K2 into P2×Pn and apply recursive techniques to prove the main results. This work expands the scope of previous graph labeling studies and provides new insights into determining the full m index set of product graphs. Given the broad range of applications for labeled graphs, this research can potentially impact fields like coding theory, communication network design, and more