Monte-Carlo estimation of time-dependent statistical characteristics of random dynamical systems

The problem of estimating the time-dependent statistical characteristics of a random dynamical system is studied under two different settings. In the first, the system dynamics is governed by a differential equation parameterized by a random parameter, while in the second, this is governed by a differential equation with an underlying parameter sequence characterized by a continuous time Markov chain. We propose, for the first time in the literature, stochastic approximation algorithms for estimating various time-dependent process characteristics of the system. In particular, we provide efficient estimators for quantities such as the mean, variance and distribution of the process at any given time as well as the joint distribution and the autocorrelation coefficient at different times. A novel aspect of our approach is that we assume that information on the parameter model (i.e., its distribution in the first case and transition probabilities of the Markov chain in the second) is not available in either case. This is unlike most other work in the literature that assumes availability of such information. Also, most of the prior work in the literature is geared towards analyzing the steady-state system behavior of the random dynamical system while our focus is on analyzing the time-dependent statistical characteristics which are in general difficult to obtain. We prove the almost sure convergence of our stochastic approximation scheme in each case to the true value of the quantity being estimated. We provide a general class of strongly consistent estimators for the aforementioned statistical quantities with regular sample average estimators being a specific instance of these. We also present an application of the proposed scheme on a widely used model in population biology. Numerical experiments in this framework show that the time-dependent process characteristics as obtained using our algorithm in each case exhibit excellent agreement with exact results. (C) 2010 Elsevier Inc. All rights reserved.

Continous Time Sigma-Delta Modulator Employing a Novel Comparator Architecture

A novel comparator architecture is proposed for speed operation in low voltage environment. Performance comparison with a conventional regenerative comparator shows a speed-up of 41%. The proposed comparator is embedded in a continuous time sigma-delta ADC so as to reduce the quantizer delay and hence minimizes the excess loop delay problem. A performance enhancement of 1dB in the dynamic range of the ADC is achieved with this new comparator. We have implemented this ADC in a standard single-poly 8-Metal 0.13 mum UMC process. The entire system operates at 1.2 V supply providing a dynamic range of 32 dB consuming 720 muW of power and occupies an area of 0.1 mm2.

On continuous timed automata with input-determined guards

We consider a general class of timed automata parameterized by a set of “input-determined” operators, in a continuous time setting. We show that for any such set of operators, we have a monadic second order logic characterization of the class of timed languages accepted by the corresponding class of automata. Further, we consider natural timed temporal logics based on these operators, and show that they are expressively equivalent to the first-order fragment of the corresponding MSO logics. As a corollary of these general results we obtain an expressive completeness result for the continuous version of MTL.

Stochastic analysis of epidemics on adaptive time varying networks

Many studies investigating the effect of human social connectivity structures (networks) and human behavioral adaptations on the spread of infectious diseases have assumed either a static connectivity structure or a network which adapts itself in response to the epidemic (adaptive networks). However, human social connections are inherently dynamic or time varying. Furthermore, the spread of many infectious diseases occur on a time scale comparable to the time scale of the evolving network structure. Here we aim to quantify the effect of human behavioral adaptations on the spread of asymptomatic infectious diseases on time varying networks. We perform a full stochastic analysis using a continuous time Markov chain approach for calculating the outbreak probability, mean epidemic duration, epidemic reemergence probability, etc. Additionally, we use mean-field theory for calculating epidemic thresholds. Theoretical predictions are verified using extensive simulations. Our studies have uncovered the existence of an ``adaptive threshold,'' i.e., when the ratio of susceptibility (or infectivity) rate to recovery rate is below the threshold value, adaptive behavior can prevent the epidemic. However, if it is above the threshold, no amount of behavioral adaptations can prevent the epidemic. Our analyses suggest that the interaction patterns of the infected population play a major role in sustaining the epidemic. Our results have implications on epidemic containment policies, as awareness campaigns and human behavioral responses can be effective only if the interaction levels of the infected populace are kept in check.

Discrete time second order sliding mode observer for uncertain linear multi-output system

This paper presents a second order sliding mode observer (SOSMO) design for discrete time uncertain linear multi-output system. The design procedure is effective for both matched and unmatched bounded uncertainties and/or disturbances. A second order sliding function and corresponding sliding manifold for discrete time system are defined similar to the lines of continuous time counterpart. A boundary layer concept is employed to avoid switching across the defined sliding manifold and the sliding trajectory is confined to a boundary layer once it converges to it. The condition for existence of convergent quasi-sliding mode (QSM) is derived. The observer estimation errors satisfying given stability conditions converge to an ultimate finite bound (within the specified boundary layer) with thickness O(T-2) where T is the sampling period. A relation between sliding mode gain and boundary layer is established for the existence of second order discrete sliding motion. The design strategy is very simple to apply and is demonstrated for three examples with different class of disturbances (matched and unmatched) to show the effectiveness of the design. Simulation results to show the robustness with respect to the measurement noise are given for SOSMO and the performance is compared with pseudo-linear Kalman filter (PLKF). (C) 2013 Published by Elsevier Ltd. on behalf of The Franklin Institute

A Perspective to Adopt Continuous Dynamic Cognition for Malicious Node Detection in Heterogeneous Networks

The current day networks use Proactive networks for adaption to the dynamic scenarios. The use of cognition technique based on the Observe, Orient, Decide and Act loop (OODA) is proposed to construct proactive networks. The network performance degradation in knowledge acquisition and malicious node presence is a problem that exists. The use of continuous time dynamic neural network is considered to achieve cognition. The variance in service rates of user nodes is used to detect malicious activity in heterogeneous networks. The improved malicious node detection rates are proved through the experimental results presented in this paper. (C) 2015 The Authors. Published by Elsevier B.V.

Life Expectancy, Schooling Time and Endogenous Growth

Published as an article in: Economic Inquiry, 2004, vol. 42, issue 4, pp. 602–617.

Sampled-data gain scheduling of continuous LTV plants

This paper discusses the design of gain- scheduled sampled-data controllers for continuous-time polytopic linear parameter-varying systems. The scheduling variables are assumed to available only at the sampling instants, and a bound on the time-variation of the scheduling parameters is also assumed to be known. The resultant gain-scheduled controllers improve the maximum achieveable delay bound over previous constant-gain ones in the literature.

Optimal Time Series Momentum

We develop a continuous-time asset price model to capture the timeseries momentum documented recently. The underlying stochastic delay differentialsystem facilitates the analysis of effects of different time horizons used bymomentum trading. By studying an optimal asset allocation problem, we find thatthe performance of time series momentum strategy can be significantly improvedby combining with market fundamentals and timing opportunity with respect tomarket trend and volatility. Furthermore, the results also hold for different timehorizons, the out-of-sample tests and with short-sale constraints. The outperformanceof the optimal strategy is immune to market states, investor sentiment andmarket volatility.

Investigations on Stochastic Storage Systems with Positive Service Time

In this thesis the queueing-inventory models considered are analyzed as continuous time Markov chains in which we use the tools such as matrix analytic methods. We obtain the steady-state distributions of various queueing-inventory models in product form under the assumption that no customer joins the system when the inventory level is zero. This is despite the strong correlation between the number of customers joining the system and the inventory level during lead time. The resulting quasi-birth-anddeath (QBD) processes are solved explicitly by matrix geometric methods

Studies on Inventory with Positive Service Time Under Local Purchase Driven by N/T- Policy

In this thesis, certain continuous time inventory problems with positive service time under local purchase guided by N/T-policy are analysed. In most of the cases analysed, we arrive at stochastic decomposition of system states, that is, the joint distribution of the system states is obtained as the product of marginal distributions of the components. The thesis is divided into ve chapters

Robust strictly positive real synthesis of polynomial segments for discrete time systems

By using the result of robust strictly positive real synthesis of polynomial segments for continuous time systems, it is proved that, for any two n-th order polynomials a(z) and b(z), the Schur stability of their convex combination is necessary and sufficient for the existence of an n-th order polynomial c(z) such that c(z)/a(z) and c(z)/b(z) are both strictly positive real. We also provide the construction method of c(z). Illustrative examples are provided to show the effectiveness of this method.

Continuous corrosion rate measurement by noise resistance calculation

A commonly employed method of corrosion rate measurement is to determine the electrochemical impedance of the corroding material. One technique for estimating the impedance is the noise impedance calculation. While it has been shown to yield useful results, there are a number of problems that require attention. This paper identifies some of those problems-specifically, those of detrending and resolution-and provides a solution that allows continuous, time-varying noise resistance and noise impedance calculations to be performed with known time, frequency, and magnitude resolutions. Applications to synthetic and experimental data are included as illustrations

Survival misperception, time inconsistency, and implications for life-cycle saving and welfare

Some empirical studies firmly reveal that people tend to form overly pessimistic survival expectations for relatively less distant ages and overly optimistic survival expectations for relatively more distant ages. We incorporate this observation into a life-cycle continuous time overlapping-generations model of consumption/saving with a general form for a subjective survival function. Resulting time-inconsistent optimal control problem has been analytically solved. At the micro level, time inconsistency leads to higher consumption at young and old ages, but this alone fails to improve lifetime well-being since micro-level decisions made with a lack of information about true mortality are suboptimal. In general equilibrium, however, such time inconsistent behavior with survival misperception is conducive to aggregate capital accumulation and greater equilibrium bequest income. The latter effects can produce substantial welfare gains. We also note that empirically observed old age optimistic bias is an important phenomenon, as it helps to avoid unrealistic very old-age debt accumulation within a life-cycle model. In addition, if for a given level of optimistic bias we increase early-life pessimism, this would result in slower capital accumulation, lower bequest income, and thus be detrimental to welfare. Since recent literature reports that young-age survival pessimism has grown over time, it raises some concerns.

Dynamical analysis of neural networks with time-varying delays using the LMI approach

This study is concerned with the delay-range-dependent stability analysis for neural networks with time-varying delay and Markovian jumping parameters. The time-varying delay is assumed to lie in an interval of lower and upper bounds. The Markovian jumping parameters are introduced in delayed neural networks, which are modeled in a continuous-time along with finite-state Markov chain. Moreover, the sufficient condition is derived in terms of linear matrix inequalities based on appropriate Lyapunov-Krasovskii functionals and stochastic stability theory, which guarantees the globally asymptotic stable condition in the mean square. Finally, a numerical example is provided to validate the effectiveness of the proposed conditions.