Stability of Systems with Stochastic Delay

Stability of systems with stochastic delays is addressed in this dissertation. A linear delay differential equation is considered where the delay takes values from a finite set of numbers according to a probability distribution function. Exact stability conditions for the resulting system are obtained. These conditions depend on the parameters of the system, the delay values and the probability distribution function governing the delay. The stability criteria are first obtained in a discretetime setting after discretizing the continuous-time system. Then, the stability conditions are obtained in a continuous-time setting where an operator description of delay differential equations is used. The stability results are applied to models of gene regulatory networks. The results can determine whether a steady state protein production is stable or oscillations in protein levels may arise as a result of stochastic fluctuations in reaction times. Finally, the interplay between noise in the gene expression level and noise in the population level in microbial consortia is investigated. The results suggest a mechanism for creating robust oscillations in multicellular environments.PHDMechanical EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/144051/1/mehsad_1.pd

A Comparison of Three and Two-Dimensional Analyses of Rockfill Dams in Narrow Valleys (A Case Study: The Vanyar Dam)

A two-dimensional analysis of the largest cross-section of earth dams may generate appropriate results provided that the dam is located in a U-shape valley. The Vanyar dam has been constructed in a narrow valley. With regard to the geometrical consideration of the valley, there is no plane strain condition throughout the long side of the dam. In this research, the results of three and two dimensional numerical analyses of the Vanyar dam are compared in terms of settlement, pore water pressure, and total vertical stress. These analyses were carried out by a finite difference method through FLAC-3D and FLAC-2D softwares. In order to verify the results of the analyses, the settlement data recorded by the instruments in the body of the dam are compared to those provided through the numerical analyses. The results of the three and two dimensional analysis show that the settlements in the upper half of the height of the dam have a suitable adaptation. Moreover, the two- dimensional analysis shows the settlements in the lower half of the height of the dam more than those shown by the three-dimensional analysis. Furthermore, in terms of total vertical stress and pore water pressure, the two-dimensional analysis shows the values throughout the height of the dam more than those shown by the threedimensional analysis

On the moment dynamics of stochastically delayed linear control systems

In this article, the dynamics and stability of a linear system with stochastic delay and additive noise are investigated. It is assumed that the delay value is sampled periodically from a stationary distribution. A semi‐discretization technique is used to time‐discretize the system and derive the mean and second‐moment dynamics. These dynamics are used to obtain the stationary moments and the corresponding necessary and sufficient stability conditions. The application of the proposed method is illustrated through the analysis of the Hayes equation with stochastic delay and additive noise. The method is also applied to the control design of a connected automated vehicle. These examples illuminate the effects of stochastic delays on the robustness of dynamical systems

Stability of Systems with Stochastic Delays and Applications to Genetic Regulatory Networks

The dynamics of systems with stochastically varying time delays are investigated in this paper. It is shown that the mean dynamics can be used to derive necessary conditions for the stability of equilibria of the stochastic system. Moreover, the second moment dynamics can be used to derive sufficient conditions for almost sure stability of equilibria. The results are summarized using stability charts that are obtained via semidiscretization. The theoretical methods are applied to simple gene regulatory networks where it is demonstrated that stochasticity in the delay can improve the stability of steady protein production

Stability of Systems with Stochastic Delays and Applications to Genetic Regulatory Networks

The dynamics of systems with stochastically varying time delays are investigated in this paper. It is shown that the mean dynamics can be used to derive necessary conditions for the stability of equilibria of the stochastic system. Moreover, the second moment dynamics can be used to derive sufficient conditions for almost sure stability of equilibria. The results are summarized using stability charts that are obtained via semidiscretization. The theoretical methods are applied to simple gene regulatory networks where it is demonstrated that stochasticity in the delay can improve the stability of steady protein production

Why INR is outside the therapeutic range in patients with acuteischemic stroke and atrial fibrillation

Introduction: Warfarin is still the primary drug used to prevent vascular events in patientswith atrial fibrillation (AF), especially in low-income countries. Therapeutic failure and non-adherenceare common causes of recurrent embolic events. The aim of this study was toinvestigate possible reasons why INR was outside the therapeutic range in patients presentingwith acute ischemic stroke and AF. Methods: This prospective study was performed over a ten-month period and all patientsadmitted with acute ischemic stroke were enrolled. Patients with AF who did not have INRwithin the therapeutic range (INR = 2-3) at the time of admission were identified. During a face-to-face interview, the reasons for INR being outside the therapeutic range were assessed basedon a prepared checklist. Results: During the study period, 810 patients had an acute ischemic stroke, of which 177 hadAF heart rhythm (22%). The median age was 76 (IQR: 71-83), and 87 (52%) were male. Of these177 patients, 44 (25%) had a previous history of AF ("previous AF" group) and 133 (75%) werediagnosed with AF during the current hospital admission ("new AF" group). Among patients onwarfarin but with INR outside the therapeutic range (29 in all), 20 (69%) did not see a physicianregularly and/or did not take medication according to the physician’s instructions. Conclusion: The most common reason for INR being outside the therapeutic range was patientslack of awareness of their heart disease (unrecognized AF). Other reasons included irregularvisits to the physician and drug non-adherence

On the moment dynamics of stochastically delayed linear control systems

In this article, the dynamics and stability of a linear system with stochastic delay and additive noise are investigated. It is assumed that the delay value is sampled periodically from a stationary distribution. A semi‐discretization technique is used to time‐discretize the system and derive the mean and second‐moment dynamics. These dynamics are used to obtain the stationary moments and the corresponding necessary and sufficient stability conditions. The application of the proposed method is illustrated through the analysis of the Hayes equation with stochastic delay and additive noise. The method is also applied to the control design of a connected automated vehicle. These examples illuminate the effects of stochastic delays on the robustness of dynamical systems

Nonlinear Vibration Of A Three-Dimensional Moving Gantry Crane Subjected To A Travelling Trolley Hoisting A Swinging Object

Nonlinear vibration of a three-dimensional moving gantry crane carrying a trolley hoisting a swinging object is studied in this paper. A finite element method is used to solve nonlinear coupled governing equations of the structure. A combinational technique (Newmark-Runge-Kutta) is employed for direct integration procedure. To develop a comprehensive parametric study and sensitivity analysis of the coupled nonlinear system, sequence of numerical simulations are carried out. Parametric study is directed to find out how different parameters like speed and acceleration of the trolley and gantry crane as well as the mass of the moving trolley and swinging object may affect the linear and nonlinear responses of the structure. It is found that the nonlinearity arises from large amplitude of three-dimensional motion of the swinging object

A survey on Diuretic Medicines based on Iranian Traditional Medicine

فرآیند گردش آب و دفع فضولات بدن از طریق کلیه‌ها، در طب سنتی ایران جایگاهی ویژه و تخصصی دارد. داروهای مدر در طب سنتی عمدتاً جهت دفع بخشی از فضولات و مواد زائد موجود در عروق و یا بافت‌ها به کمک آب و سیستم ادراری، به کار می‌روند، بدین صورت که این داروها ضمن گسیل‌داشتن بخشی از مواد زائد (به ویژه مواد زائد رقیق مائی) به سوی سیستم ادراری و با دفع این فضولات، به کنترل و یا درمان بیماری‌ها کمک می‌کنند. برخلاف داروهای دیورتیک در طب نوین که عمدتاً مسؤول دفع آب از بدن و کمک به کنترل بیماری‌هایی همچون نارسایی احتمالی قلب آسیت، ادم ریوی، ادم اندام‌ها و فشار خون بالا بوده و تبعاتی همچون برهم‌زدن تعادل الکترولیت‌ها را به دنبال دارد، داروهای مدر طب سنتی برخلاف داروهای دیورتیک در طب نوین، به تناسب نوع ماده زائد بدن، انتخاب شده و هر دارو در دفع نوع خاصی از مواد زائد تأثیر بیشتری می‌گذارد. این مطالعه، یک مطالعه کتابخانه‌ای بوده که در آن مفهوم داروهای مدر، موارد تجویز و احتیاطات استفاده از آن‌ها بر مبنای منابع طب سنتی ایران بیان شده و مکانیسم اثر آن‌ها با داروهای دیورتیک مورد استفاده در طب رایج مورد مقایسه قرار گرفته است. نتایج این مطالعه می‌تواند بینش خواننده را با گستره عملکرد داروهای مدر توسعه داده و به پزشکان در تجویز بهینه داروهای گیاهی مدر کمک نماید.There is a special notice on waste material excretion and water circulation in Persian medicine. According to Persian medicine, diuretic remedies are used for excretion of some waste humors from circulation and tissues. The target organ for this function is kidney. Diuretics excrete the fine water soluble materials and by this mechanism help to improve diseases. Diuretics in modern medicines act by water and electrolytes excretion and in this way; they are administered for conditions such as congestive heart failure, pulmonary edema, anasarca and hypertension. Each diuretic drug in Persian medicine act on a special humor. In this review, the concept of diuretics, indications, contraindications and cautions about their administration are extracted and classified based on Persian literatures. A comparison is also carried out between the diuretic mechanism in modern and Persian traditional medicines. The results of this study might expand reader’s insight about diuretic herbal remedies and help them in optimal administration of these drugs if they work based on Persian medicin