On robust stability of stochastic genetic regulatory networks with time delays: A delay fractioning approach

Copyright [2009] IEEE. This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of Brunel University's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to [email protected]. By choosing to view this document, you agree to all provisions of the copyright laws protecting it.Robust stability serves as an important regulation mechanism in system biology and synthetic biology. In this paper, the robust stability analysis problem is investigated for a class of nonlinear delayed genetic regulatory networks with parameter uncertainties and stochastic perturbations. The nonlinear function describing the feedback regulation satisfies the sector condition, the time delays exist in both translation and feedback regulation processes, and the state-dependent Brownian motions are introduced to reflect the inherent intrinsic and extrinsic noise perturbations. The purpose of the addressed stability analysis problem is to establish some easy-to-verify conditions under which the dynamics of the true concentrations of the messenger ribonucleic acid (mRNA) and protein is asymptotically stable irrespective of the norm-bounded modeling errors. By utilizing a new Lyapunov functional based on the idea of “delay fractioning”, we employ the linear matrix inequality (LMI) technique to derive delay-dependent sufficient conditions ensuring the robust stability of the gene regulatory networks. Note that the obtained results are formulated in terms of LMIs that can easily be solved using standard software packages. Simulation examples are exploited to illustrate the effectiveness of the proposed design procedures

APPLICATION OF GROUP TESTING FOR ANALYZING NOISY NETWORKS

My dissertation focuses on developing scalable algorithms for analyzing large complex networks and evaluating how the results alter with changes to the network. Network analysis has become a ubiquitous and very effective tool in big data analysis, particularly for understanding the mechanisms of complex systems that arise in diverse disciplines such as cybersecurity [83], biology [15], sociology [5], and epidemiology [7]. However, data from real-world systems are inherently noisy because they are influenced by fluctuations in experiments, subjective interpretation of data, and limitation of computing resources. Therefore, the corresponding networks are also approximate. This research addresses these issues of obtaining accurate results from large noisy networks efficiently. My dissertation has four main components. The first component consists of developing efficient and scalable algorithms for centrality computations that produce reliable results on noisy networks. Two novel contributions I made in this area are the development of a group testing [16] based algorithm for identification of high centrality vertices which is extremely faster than current methods, and an algorithm for computing the betweenness centrality of a specific vertex. The second component consists of developing quantitative metrics to measure how different noise models affect the analysis results. We implemented a uniform perturbation model based on random addition/ deletion of edges of a network. To quantify the stability of a network we investigated the effect that perturbations have on the top-k ranked vertices and the local structure properties of the top ranked vertices. The third component consists of developing efficient software for network analysis. I have been part of the development of a software package, ESSENS (Extensible, Scalable Software for Evolving NetworkS) [76], that effectively supports our algorithms on large networks. The fourth component is a literature review of the various noise models that researchers have applied to networks and the methods they have used to quantify the stability, sensitivity, robustness, and reliability of networks. These four aspects together will lead to efficient, accurate, and highly scalable algorithms for analyzing noisy networks

Power flow and small signal stability analysis on the interconnected Philippine power grid

SummaryThe Philippines, as one of the developing nations in south-east Asia, has isolated power system networks which bring forth challenges in its operational systems, especially when subjected to a deregulated environment. This paper presents an analysis on the power flow and small signal stability of the interconnected three isolated Philippine Power Grid. To achieve this, eigenvalue analysis is employed to probe the small signal stability of the main power grids. The free software, Power Systems Analysis Toolbox (PSAT), is used to develop the model using MATLAB®/Simulink®. There have been no publicly available studies regarding stability of the proposed link between the major grid and the Mindanao (south island) grid. Participation factors were further studied to determine which states contributes most with the variety of modes. The lowest oscillatory damping modes are also assessed to better understand the systems characteristics

Investigation into voltage and angle stability of a hybrid HVAC-HVDC power network

This study investigates the power stability problems of HVDC and VSC-HVDC interactions on their hybrid networks with HV AC link, with the intention of bringing out their weaknesses and strengths. The knowledge of this will assist network planners to be informed on ways of improving the efficiency and quality of power systems network. The simulations for this study was done using DIgSILENT Powerfactory software version 14.0.515. This study encapsulates the three major stability problems affecting power systems network, namely, the voltage stability, transient stability and small signal stability. The voltage stability study was conducted using series of load flows at various levels to plot the VP and QV curves, and the results were used to analyze the systems proximity and sensitivity to voltage collapse, as well as the maximum loading point (MPL) of the network. Furthermore, the voltage angle, and terminal voltage responses during a three-phase short circuit disturbance was also used to analyze the voltage stability of the networks. For the transient stability study, several case studies were investigated and their dynamic performances during three-phase short circuit perturbations were analyzed. The small signal stability investigation was done using modal analysis to determine the small signal stability of the three transmission schemes mentioned above. The transient and small signal stability, which are both subsets of rotor angle stability, were further investigated to show the effect of power systems stabilizer (PSS) and automatic voltage regulator (A VR) on rotor angle stability. The results of the analyses show that the HVDC transmission scheme provides the best alternative for bulk power transmission over a long distance. The VSC-HVDC transmission network is suitable for interconnections where the tie with HV AC networks have a low short circuit ratio (SCR). Other conclusions reached with the investigations are explained in chapter ten

Analisis Rumah Kabel Bawah Tanah pada Proyek Pekerjaan Jaringan Utilitas Sktt 150 Kv Plumpang - Gambir

Underground cable distribution channels to be excellent especially in big cities like Jakarta. This is because the underground cable distribution is a solution to the difficulty of land acquisition that will be used for top cable networks. Nevertheless, there is an important factor to be considered in implementing the underground cable distribution channel that is the condition of the soil through which the cable. This study aims to determine the dimensions of the cable house was safe from the soil instability. The soil instability are the stability of bolsters and the shear stability and take into account the carrying capacity of the foundation used. The data used as a reference in the analysis using research data that has been done previously. In stability analysis and foundation bearing capacity used Geo5 software demo version aid. The results obtained from the analysis, with variations on the dimensions of the cable house used are 2 mx 2 m, 2.5 mx 2.5 m and 3 mx 3 m, it is seen that the greater the dimensions used then the security number of stability bolsters, soil shear stability and the carrying capacity of the foundation decreases. This is due to the greater the dimensions of the cable house used, the greater the burden borne by the soil

Historia en las redes, las redes de humanistas en el Renacimiento

Se realiza un censo de los humanistas del Renacimiento a partir de enciclopedias y listas de humanistas. La lista resultante se dividió en periodos de 30 años y se conformó una red social con los personajes que resultaron contemporáneos, se obtuvieron 8 redes. Cada una de las redes se analizó con el software para análisis de redes sociales Pajek y por medio de software escrito ad hoc en lenguaje M. Resultados: las redes de humanistas son redes complejas en virtud de sus propiedades topológicas. Planteamos que los parámetros topológicos de las redes sociales son la medida de su complejidad. Las redes de humanistas ganaron en robustez gradualmente hasta alcanzar su máximo en el periodo de 1493-1523, para luego declinar. Todas las redes estudiadas mantuvieron las propiedades topológicas asociadas con la velocidad de transmisión de información, facilidad de transmisión y estabilidad hasta el fin del Renacimiento. Como algunos miembros de las redes de humanistas conformaron también las llamadas redes de filósofos de la naturaleza es factible plantear que estas últimas heredaron las propiedades de las primeras. El humanista más relevante del periodo Renacentista resulto ser Erasmo de Rotterdam por el valor que alcanzo en su intermediación durante 3 periodos consecutivos.A census of Renaissance's humanists was conducted by consulting encyclopedias and humanists lists. The resulting list was divided in periods of 30 years, yielding 8 different networks. Social network analysis of each network was performed by means of the Pajek software and by ad hoc software written in M language. Results: the humanist's networks are complex networks by virtue of their topological properties. We state that these topological properties are the measure of the social network complexity. From the analysis of the individual networks topological features some conclusions were drawed: the humanists' networks gained in robustness as time passed by until reaching an acme at period 5 (1493-1523) then a declining robustness ensued. Al the resulting networks maintained topological properties associated to stability and speed of information transfer until the end of the Renaiscance. This last fact suggest that nature philosophers inherited this properties from the humanists' ones, since by the end of Renaiscance members of the humanists networks became also members of the nature philosophers networks. The most prominent humanist of the period, according to its betweenness value was Erasmus of Rotterdam

Nonlinear dynamics of blood flow in simple microvascular networks

It has been found that spontaneous oscillations of nodal pressures, hematocrit, and blood velocity can occur in microvascular networks in the absence of biological control. In this paper, both analytical and numerical methods have been used to investigate the nonlinear dynamics of microvascular blood flow in simple networks. First, the steady state solutions for the system are found. Then the governing coupled PDE\u27s are transformed into state dependent time delay differential equations, DDE\u27s. The DDE\u27s are then linearized about a steady state and normalized. The characteristic equation for the network is found by assuming the linearized DDE\u27s have a nontrivial exponential solution. The solutions of the characteristic equation are also called the eigenvalues for the network dynamics at that steady state. It is known that the steady state is unstable when the real part of the rightmost eigenvalue is positive. Thus, a theoretical prediction of the stability of the blood flow in the network can be based on the rightmost eigenvalues. The analysis has been performed on the networks with two node topology and with three node topology. Due to the nonlinearity of the characteristic equation, solutions are found numerically using a software package called DDE-BIFTOOL . After the eigenvalues are found, predictions of the stability of steady states are compared to direct numerical simulations for blood flow in the networks. Effects of physical parameters and inlet conditions on hemodynamics are investigated in the two node microvascular networks and the three node microvascular networks (2 inlets). For the two node networks, the region of instability in parameter space is quite narrow. This means that experimental verification of spontaneous blood flow oscillations will be very difficult for the two node topology. The numerical results for the three node networks showed the three node system has instabilities over a much wider parameter ranges than the two node network. However, one of the most critical parameters, inlet hematocrit, is still quite high. This means such experiments are still very challenging. Future work may involve continuing the search in wider parameter ranges and testing more complicated topologies to find realized conditions. Then in vitro experiments may be conducted to verify results of the linear stability analysis