New Exponential Stability Results for Neutral Stochastic Systems with Distributed Delays

This paper studies the stability problem of a grey neutral stochastic system with distributed delays. The main feature of a grey system is that the parameters of system are evaluated by grey numbers, and system has the strong background in engineering applications. However, the literature dealing with the stability problem for grey system seems to be scarce. The main aim of this paper is to fill the gap. Based on the Lyapunov stability theorem and Itô’s formula, especially, using the decomposition technique of the continuous matrix-covered sets of grey matrix, we propose several novel sufficient conditions, which ensure our considered grey system in mean-square exponential stability and almost surely exponential stability. Furthermore, two examples are provided to show the effectiveness of the obtained results

Spectrum analysis of LTI continuous-time systems with constant delays: A literature overview of some recent results

In recent decades, increasingly intensive research attention has been given to dynamical systems containing delays and those affected by the after-effect phenomenon. Such research covers a wide range of human activities and the solutions of related engineering problems often require interdisciplinary cooperation. The knowledge of the spectrum of these so-called time-delay systems (TDSs) is very crucial for the analysis of their dynamical properties, especially stability, periodicity, and dumping effect. A great volume of mathematical methods and techniques to analyze the spectrum of the TDSs have been developed and further applied in the most recent times. Although a broad family of nonlinear, stochastic, sampled-data, time-variant or time-varying-delay systems has been considered, the study of the most fundamental continuous linear time-invariant (LTI) TDSs with fixed delays is still the dominant research direction with ever-increasing new results and novel applications. This paper is primarily aimed at a (systematic) literature overview of recent (mostly published between 2013 to 2017) advances regarding the spectrum analysis of the LTI-TDSs. Specifically, a total of 137 collected articles-which are most closely related to the research area-are eventually reviewed. There are two main objectives of this review paper: First, to provide the reader with a detailed literature survey on the selected recent results on the topic and Second, to suggest possible future research directions to be tackled by scientists and engineers in the field. © 2013 IEEE.MSMT-7778/2014, FEDER, European Regional Development Fund; LO1303, FEDER, European Regional Development Fund; CZ.1.05/2.1.00/19.0376, FEDER, European Regional Development FundEuropean Regional Development Fund through the Project CEBIA-Tech Instrumentation [CZ.1.05/2.1.00/19.0376]; National Sustainability Program Project [LO1303 (MSMT-7778/2014)

Heritable Stochastic Switching Revealed by Single-Cell Genealogy

The partitioning and subsequent inheritance of cellular factors like proteins and RNAs is a ubiquitous feature of cell division. However, direct quantitative measures of how such nongenetic inheritance affects subsequent changes in gene expression have been lacking. We tracked families of the yeast Saccharomyces cerevisiae as they switch between two semi-stable epigenetic states. We found that long after two cells have divided, they continued to switch in a synchronized manner, whereas individual cells have exponentially distributed switching times. By comparing these results to a Poisson process, we show that the time evolution of an epigenetic state depends initially on inherited factors, with stochastic processes requiring several generations to decorrelate closely related cells. Finally, a simple stochastic model demonstrates that a single fluctuating regulatory protein that is synthesized in large bursts can explain the bulk of our results

Time metrology in Global Navigation Satellite Systems

Precise timekeeping is at the basis of any Global Navigation Satellite System. In this thesis, after an extensive introduction on time and frequency metrology, some of the basic time-related aspects of navigation systems are discussed, and new ideas and solutions are presented. In the first part of the work, the most relevant innovative contributions are related to the mathematical clock model and to the stability analysis of atomic clocks affected by frequency jumps, as well as to the development of a new averaging algorithm for the generation of a robust time scale from an ensemble of atomic clocks. In the second part, devoted to the role of timekeeping in satellite navigation systems, the innovative contributions are mainly about: a revision of the relativistic corrections; the development and testing of a new composite clock, which could be used as a system time scale for the Galileo system; a study on the impact of the light-shift effect on the timing performance of GPS rubidium clocks; the development of a new recursive clock anomalies detector, as well as a discussion about the possible implementations of a clock anomalies detector and a compensation system for on-board applications

New Progress of Grey System Theory in The New Millennium

Purpose – The purpose of this paper is to summarize the progress in grey system research during 2000- 2015, so as to present some important new concepts, models, methods and a new framework of grey system theory. Design/methodology/approach –The new thinking, new models and new methods of grey system theory and their applications are presented in this paper. It includes algorithm rules of grey numbers based on the “Kernel” and the degree of greyness of grey numbers, the concept of general grey numbers, the synthesis axiom of degree of greyness of grey numbers and their operations; the general form of buffer operators of grey sequence operators; the four basic models of GM(1,1), such as Even Grey Model(EGM), Original Difference Grey Model(ODGM), Even Difference Grey Model(EDGM), Discrete Grey Model(DGM) and the suitable sequence type of each basic model, and suitable range of most used grey forecasting models; the similarity degree of grey incidences, the closeness degree of grey incidences and the three dimensional absolute degree of grey incidence of grey incidence analysis models; the grey cluster model based on center-point and end-point mixed triangular whitenization functions; the multi-attribute intelligent grey target decision model, the two stages decision model with grey synthetic measure of grey decision models; grey game models, grey input-output models of grey combined models; and the problems of robust stability for grey stochastic time-delay systems of neutral type, distributed-delay type and neutral distributed-delay type of grey control, etc. And the new framework of grey system theory is given as well. Findings –The problems which remain for further studying are discussed at the end of each section. The reader could know the general picture of research and developing trend of grey system theory from this paper. Practical implications – A lot of successful practical applications of the new models to solve various problems have been found in many different areas of natural science, social science, and engineering, including spaceflight, civil aviation, information, metallurgy, machinery, petroleum, chemical industry, electrical power, electronics, light industries, energy resources, transportation, medicine, health, agriculture, forestry, geography, hydrology, seismology, meteorology, environment protection, architecture, behavioral science, management science, law, education, military science, etc. These practical applications have brought forward definite and noticeable social and economic benefits. It demonstrates a wide range of applicability of grey system theory, especially in the situation where the available information is incomplete and the collected data are inaccurate. Originality/value –The reader is given a general picture of grey systems theory as a new model system and a new framework for studying problems where partial information is known; especially for uncertain systems with few data points and poor information. The problems remaining for further studying are identified at the end of each section. Keywords Grey systems theory, Operations of grey numbers, Buffer operators, Grey forecasting models, Grey incidence analysis models, Grey cluster evaluation models, Grey decision models, Combined grey models, Grey contro

Rhythms and Evolution: Effects of Timing on Survival

The evolution of metabolism regulation is an intertwined process, where different strategies are constantly being developed towards a cognitive ability to perceive and respond to an environment. Organisms depend on an orchestration of a complex set of chemical reactions: maintaining homeostasis with a changing environment, while simultaneously sending material and energetic resources to where they are needed. The success of an organism requires efficient metabolic regulation, highlighting the connection between evolution, population dynamics and the underlying biochemistry. In this work, I represent organisms as coupled information-processing networks, that is, gene-regulatory networks receiving signals from the environment and acting on chemical reactions, eventually affecting material flows. I discuss the mechanisms through which metabolism control is improved during evolution and how the nonlinearities of competition influence this solution-searching process. The propagation of the populations through the resulting landscapes generally point to the role of the rhythm of cell division as an essential phenotypic feature driving evolution. Subsequently, as it naturally follows, different representations of organisms as oscillators are constructed to indicate more precisely how the interplay between competition, maturation timing and cell-division synchronisation affects the expected evolutionary outcomes, not always leading to the \"survival of the fastest\"