Combinatorial-topological framework for the analysis of global dynamics

We discuss an algorithmic framework based on efficient graph algorithms and algebraic-topological computational tools. The framework is aimed at automatic computation of a database of global dynamics of a given m-parameter semidynamical system with discrete time on a bounded subset of the n-dimensional phase space. We introduce the mathematical background, which is based upon Conley's topological approach to dynamics, describe the algorithms for the analysis of the dynamics using rectangular grids both in phase space and parameter space, and show two sample applications. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4767672]

The dynamics of leniency application and the knock-on effect of cartel enforcement. Bruegel Working Paper 2016/02, February 2016

The authors study the timing of leniency applications using a novel application of multi-spell discrete-time survival analysis for a sample of cartels prosecuted by the European Commission between 1996 and 2014. The start of a Commission investigation does not affect the rate by which conspirators apply for leniency in the market investigated, but increases the rate of application in separate markets in which a conspirator in the investigated market also engaged in collusion. The revision of the Commission’s leniency programme in 2002 increased the rate of pre-investigation applications. Our results shed light on enforcement efforts against cartels and other forms of

Modeling Depression Progression Dynamics from Electronic Health Record

Thesis (Master's)--University of Washington, 2016-06

Description and training of neural network dynamics

Attractor properties of a popular discrete-time neural network model are illustrated through numerical simulations. The most complex dynamics is found to occur within particular ranges of parameters controlling the symmetry and magnitude of the weight matrix. A small network model is observed to produce fixed points, limit cycles, mode-locking, the Ruelle-Takens route to chaos, and the period-doubling route to chaos. Training algorithms for tuning this dynamical behaviour are discussed. Training can be an easy or difficult task, depending whether the problem requires the use of temporal information distributed over long time intervals. Such problems require training algorithms which can handle hidden nodes. The most prominent of these algorithms, back propagation through time, solves the temporal credit assignment problem in a way which can work only if the relevant information is distributed locally in time. The Moving Targets algorithm works for the more general case, but is computationally intensive, and prone to local minima.

Steps and bumps:precision extraction of discrete states of molecular machines

We report statistical time-series analysis tools providing improvements in the rapid, precision extraction of discrete state dynamics from time traces of experimental observations of molecular machines. By building physical knowledge and statistical innovations into analysis tools, we provide techniques for estimating discrete state transitions buried in highly correlated molecular noise. We demonstrate the effectiveness of our approach on simulated and real examples of steplike rotation of the bacterial flagellar motor and the F1-ATPase enzyme. We show that our method can clearly identify molecular steps, periodicities and cascaded processes that are too weak for existing algorithms to detect, and can do so much faster than existing algorithms. Our techniques represent a step in the direction toward automated analysis of high-sample-rate, molecular-machine dynamics. Modular, open-source software that implements these techniques is provided.

Evolutionary dynamics under various modes of reproduction

Thesis (Ph.D.)--University of Washington, 2016-08

Age-Specific Fertility Dynamics: Sub-Saharan African Fertility in a Global Context

Thesis (Ph.D.)--University of Washington, 2016-08

Influence of memory in deterministic walks in random media: Analytical calculation within a mean-field approximation

Consider a random medium consisting of N points randomly distributed so that there is no correlation among the distances separating them. This is the random link model, which is the high dimensionality limit (mean-field approximation) for the Euclidean random point structure. In the random link model, at discrete time steps, a walker moves to the nearest point, which has not been visited in the last mu steps (memory), producing a deterministic partially self-avoiding walk (the tourist walk). We have analytically obtained the distribution of the number n of points explored by the walker with memory mu=2, as well as the transient and period joint distribution. This result enables us to explain the abrupt change in the exploratory behavior between the cases mu=1 (memoryless walker, driven by extreme value statistics) and mu=2 (walker with memory, driven by combinatorial statistics). In the mu=1 case, the mean newly visited points in the thermodynamic limit (N >> 1) is just < n >=e=2.72... while in the mu=2 case, the mean number < n > of visited points grows proportionally to N(1/2). Also, this result allows us to establish an equivalence between the random link model with mu=2 and random map (uncorrelated back and forth distances) with mu=0 and the abrupt change between the probabilities for null transient time and subsequent ones.

A novel continuous time representation for the scheduling of pipeline systems with pumping yield rate constraints

Pipeline systems play a key role in the petroleum business. These operational systems provide connection between ports and/or oil fields and refineries (upstream), as well as between these and consumer markets (downstream). The purpose of this work is to propose a novel MINLP formulation based on a continuous time representation for the scheduling of multiproduct pipeline systems that must supply multiple consumer markets. Moreover, it also considers that the pipeline operates intermittently and that the pumping costs depend on the booster stations yield rates, which in turn may generate different flow rates. The proposed continuous time representation is compared with a previously developed discrete time representation [Rejowski, R., Jr., & Pinto, J. M. (2004). Efficient MILP formulations and valid cuts for multiproduct pipeline scheduling. Computers and Chemical Engineering, 28, 1511] in terms of solution quality and computational performance. The influence of the number of time intervals that represents the transfer operation is studied and several configurations for the booster stations are tested. Finally, the proposed formulation is applied to a larger case, in which several booster configurations with different numbers of stages are tested. (C) 2007 Elsevier Ltd. All rights reserved.

On the Filtering Problem for Continuous-Time Markov Jump Linear Systems with no Observation of the Markov Chain

We consider in this paper the optimal stationary dynamic linear filtering problem for continuous-time linear systems subject to Markovian jumps in the parameters (LSMJP) and additive noise (Wiener process). It is assumed that only an output of the system is available and therefore the values of the jump parameter are not accessible. It is a well known fact that in this setting the optimal nonlinear filter is infinite dimensional, which makes the linear filtering a natural numerically, treatable choice. The goal is to design a dynamic linear filter such that the closed loop system is mean square stable and minimizes the stationary expected value of the mean square estimation error. It is shown that an explicit analytical solution to this optimal filtering problem is obtained from the stationary solution associated to a certain Riccati equation. It is also shown that the problem can be formulated using a linear matrix inequalities (LMI) approach, which can be extended to consider convex polytopic uncertainties on the parameters of the possible modes of operation of the system and on the transition rate matrix of the Markov process. As far as the authors are aware of this is the first time that this stationary filtering problem (exact and robust versions) for LSMJP with no knowledge of the Markov jump parameters is considered in the literature. Finally, we illustrate the results with an example.

Swapping space for time and unfair tests of ecological models

Testing ecological models for management is an increasingly important part of the maturation of ecology as an applied science. Consequently, we need to work at applying fair tests of models with adequate data. We demonstrate that a recent test of a discrete time, stochastic model was biased towards falsifying the predictions. If the model was a perfect description of reality, the test falsified the predictions 84% of the time. We introduce an alternative testing procedure for stochastic models, and show that it falsifies the predictions only 5% of the time when the model is a perfect description of reality. The example is used as a point of departure to discuss some of the philosophical aspects of model testing.

Economic and environmental impacts of pollution control in a system of environment and economic interdependence

The importance of the rate of change of the pollution stock in determining the damage to the environment has been an issue of increasing concern in the literature. This paper uses a three-sector (economy, population and environment), non-linear, discrete time, calibrated model to examine pollution control. The model explicitly links economic growth to the health of the environment. The stock of natural resources is affected by the rate of pollution flows, through their impact on the regenerative capacity of the natural resource stock. This can shed useful insights into pollution control strategies, particularly in developing countries where environmental resources are crucial for production in many sectors of the economy. Simulation exercises suggested that, under plausible assumptions, it is possible to reverse undesirable transient dynamics through pollution control expenditure, but this is dependent upon the strategies used for control. The best strategy is to spend money fostering the development of production technologies that reduce pollution rather than spending money dealing with the effects of the pollution flow into the environment. (C) 2001 Elsevier Science Ltd. All rights reserved.

Fractional order modelling of fractional-order holds

Discrete time control systems require sample- and-hold circuits to perform the conversion from digital to analog. Fractional-Order Holds (FROHs) are an interpolation between the classical zero and first order holds and can be tuned to produce better system performance. However, the model of the FROH is somewhat hermetic and the design of the system becomes unnecessarily complicated. This paper addresses the modelling of the FROHs using the concepts of Fractional Calculus (FC). For this purpose, two simple fractional-order approximations are proposed whose parameters are estimated by a genetic algorithm. The results are simple to interpret, demonstrating that FC is a useful tool for the analysis of these devices.

Optimal tuning of fractional controllers using genetic algorithms

This study addresses the optimization of fractional algorithms for the discrete-time control of linear and non-linear systems. The paper starts by analyzing the fundamentals of fractional control systems and genetic algorithms. In a second phase the paper evaluates the problem in an optimization perspective. The results demonstrate the feasibility of the evolutionary strategy and the adaptability to distinct types of systems.

Controling delayed transitions with applications to prevent single species extinctions

A new method is proposed to control delayed transitions towards extinction in single population theoretical models with discrete time undergoing saddle-node bifurcations. The control method takes advantage of the delaying properties of the saddle remnant arising after the bifurcation, and allows to sustain populations indefinitely. Our method, which is shown to work for deterministic and stochastic systems, could generally be applied to avoid transitions tied to one-dimensional maps after saddle-node bifurcations.