Constantinos I. Siettos

Coarse Brownian dynamics for nematic liquid crystals: Bifurcation, projective integration, and control via stochastic simulation

We demonstrate how time integration of stochastic differential equations (i.e., Brownian dynamics simulations) can be combined with continuum numerical analysis techniques to analyze the dynamics of liquid crystalline polymers (LCPs). Sidestepping the necessity of obtaining explicit closures, the approach analyzes the (unavailable in closed form) “coarse” macroscopic equations, estimating the necessary quantities through appropriately initialized, short “bursts” of Brownian dynamics simulation. Through this approach, both stable and unstable branches of the equilibrium bifurcation diagram are obtained for the Doi model of LCPs and their “coarse stability” is estimated. Additional macroscopic computational tasks enabled through this approach, such as coarse projective integration and coarse stabilizing controller design, are also demonstrated.

A cellular automata model for forest fire spread prediction: The case of the wildfire that swept through Spetses Island in 1990

We present and illustrate the simulation results of a cellular automata model describing the dynamics of a forest fire spread on a mountainous landscape taking into account factors such as the type and density of vegetation, the wind speed and direction and the spotting phenomenon. The model is used to simulate the wildfire that broke up on Spetses in August of 1990 and destroyed a major part of the Island’s forest. We used a black-box non-linear optimization approach to fine-tune some of the model’s parameters based on a geographical information system incorporating available data from the real forest fire. The comparison between the simulation and the actual-observed results showed that the proposed model predicts in a quite adequate manner the evolution characteristics in space and time of the real incident and as such could be potentially used to develop a fire risk-management tool for heterogeneous landscapes.

Classification of aged wine distillates using fuzzy and neural network systems

The classification of aged wine distillates is a non-linear, multi-criteria decision-making problem characterized by overwhelming complexity, non-linearity and lack of objective information regarding the desired final product qualitative characteristics. The most efficient solution for the evaluation of aged wine distillates estimations with emphasis on the properties of the aroma and the taste, when an appropriate mathematical model cannot be found, is to develop adequate and reliable expert systems based on fuzzy logic and neural networks. A fuzzy classifier and a neural network are proposed for the classification of wine distillates for each of two distinct features of the products namely the aroma and the taste. The fuzzy classifier is based on the fuzzy k-nn algorithm while the neural system is a feedforward sigmoidal multilayer network which is trained using the back-propagation method. The results show that both fuzzy and neural classification systems performed remarkably well in the evaluation of the aroma and the taste of the products.

Mathematical modeling of infectious disease dynamics

Over the last years, an intensive worldwide effort is speeding up the developments in the establishment of a global surveillance network for combating pandemics of emergent and re-emergent infectious diseases. Scientists from different fields extending from medicine and molecular biology to computer science and applied mathematics have teamed up for rapid assessment of potentially urgent situations. Toward this aim mathematical modeling plays an important role in efforts that focus on predicting, assessing, and controlling potential outbreaks. To better understand and model the contagious dynamics the impact of numerous variables ranging from the micro host–pathogen level to host-to-host interactions, as well as prevailing ecological, social, economic, and demographic factors across the globe have to be analyzed and thoroughly studied. Here, we present and discuss the main approaches that are used for the surveillance and modeling of infectious disease dynamics. We present the basic concepts underpinning their implementation and practice and for each category we give an annotated list of representative works.

Wildland fire spread modelling using cellular automata: evolution in large-scale spatially heterogeneous environments under fire suppression tactics

We show how microscopic modelling techniques such as Cellular Automata linked with detailed geographical information systems (GIS) and meteorological data can be used to efficiently predict the evolution of fire fronts on mountainous and heterogeneous wild forest landscapes. In particular, we present a lattice-based dynamic model that includes various factors, ranging from landscape and earth statistics, attributes of vegetation and wind field data to the humidity of the fuel and the spotting transfer mechanism. We also attempt to model specific fire suppression tactics based on air tanker attacks utilising technical specifications as well as operational capabilities of the aircrafts. We use the detailed model to approximate the dynamics of a large-scale fire that broke out in a region on the west flank of the Greek National Park of Parnitha Mountain in June of 2007. The comparison between the simulation and the actual results showed that the proposed model predicts the fire-spread characteristics in an adequate manner. Finally, we discuss how such a detailed model can be exploited in order to design and develop, in a systematic way, fire risk management policies.

Modeling the 2014 Ebola Virus Epidemic - Agent-Based Simulations, Temporal Analysis and Future Predictions for Liberia and Sierra Leone.

We developed an agent-based model to investigate the epidemic dynamics of Ebola virus disease (EVD) in Liberia and Sierra Leone from May 27 to December 21, 2014. The dynamics of the agent-based simulator evolve on small-world transmission networks of sizes equal to the population of each country, with adjustable densities to account for the effects of public health intervention policies and individual behavioral responses to the evolving epidemic. Based on time series of the official case counts from the World Health Organization (WHO), we provide estimates for key epidemiological variables by employing the so-called Equation-Free approach. The underlying transmission networks were characterized by rather random structures in the two countries with densities decreasing by ~19% from the early (May 27-early August) to the last period (mid October-December 21). Our estimates for the values of key epidemiological variables, such as the mean time to death, recovery and the case fatality rate, are very close to the ones reported by the WHO Ebola response team during the early period of the epidemic (until September 14) that were calculated based on clinical data. Specifically, regarding the effective reproductive number Re, our analysis suggests that until mid October, Re was above 2.3 in both countries; from mid October to December 21, Re dropped well below unity in Liberia, indicating a saturation of the epidemic, while in Sierra Leone it was around 1.9, indicating an ongoing epidemic. Accordingly, a ten-week projection from December 21 estimated that the epidemic will fade out in Liberia in early March; in contrast, our results flashed a note of caution for Sierra Leone since the cumulative number of cases could reach as high as 18,000, and the number of deaths might exceed 5,000, by early March 2015. However, by processing the reported data of the very last period (December 21, 2014-January 18, 2015), we obtained more optimistic estimates indicative of a remission of the epidemic in Sierra Leone, as reflected by the derived Re (~0.82, 95% CI: 0.81-0.83).

Design of a model identification fuzzy adaptive controller and stability analysis of nonlinear processes

This paper deals with the design of a model identification fuzzy adaptive controller with real-time scaling factors adjustment and the stability analysis of nonlinear distributed parameter systems. The solution branch of such systems frequently contains limit points (or turning points) which represent the boundary between stability and instability of the system. Hence, stability analysis is required for the determination of the stable and unstable operating regions. The performance of the proposed fuzzy self-tuning controller is compared to an equivalent conventional adaptive controller, over a wide range of step disturbances and operating regions. The proposed fuzzy adaptive scheme in comparison with the conventional adaptive scheme exhibits a much robust response, shorter settling times, overshooting less the controlled variable and smaller IAE of the manipulated variable for the entire range of step disturbances.

Focusing revisited: a renormalization/bifurcation approach

The nonlinear Schrodinger (NLS) equation is a ubiquitous example of an envelope wave equation for conservative, dispersive systems. We revisit here the problem of self-similar focusing of waves in the case of the focusing NLS equation through the prism of a template-based dynamic renormalization technique that factors out self-similarity and yields a bifurcation view of the onset of focusing. As a result, identifying the focusing self-similar solution becomes a steady-state problem. The steady states are subsequently obtained and their linear stability is numerically examined. The calculations are performed in the setting of variable index of refraction, in which the onset of focusing appears as a supercritical bifurcation of a novel type of mixed Hamiltonian-dissipative dynamical system (reminiscent, to some extent, of a pitchfork bifurcation).

Can social microblogging be used to forecast intraday exchange rates

The Efficient Market Hypothesis (EMH) is widely accepted to hold true under certain assumptions. One of its implications is that the prediction of stock prices at least in the short run cannot outperform the random walk model. Yet, recently many studies stressing the psychological and social dimension of financial behavior have challenged the validity of the EMH. Toward this aim, over the last few years, internet-based communication platforms and search engines have been used to extract early indicators of social and economic trends. Here, we used Twitter’s social networking platform to model and forecast the EUR/USD exchange rate in a high-frequency intradaily trading scale. Using time series and trading simulations analysis, we provide some evidence that the information provided in social microblogging platforms such as Twitter can in certain cases enhance the forecasting efficiency regarding the very short (intradaily) forex.

A systems-based approach to multiscale computation: Equation-free detection of coarse-grained bifurcations

We discuss certain basic features of the equation-free (EF) approach to modeling and computation for complex/multiscale systems. We focus on links between the equation-free approach and tools from systems and control theory (design of experiments, data analysis, estimation, identification and feedback). As our illustrative example, we choose a specific numerical task (the detection of stability boundaries in parameter space) for stochastic models of two simplified heterogeneous catalytic reaction mechanisms. In the equation-free framework the stochastic simulator is treated as an experiment (albeit a computational one). Short bursts of fine scale simulation (short computational experiments) are designed, executed, and their outputs processed and fed back to the process, in integrated protocols aimed at performing the particular coarse-grained task (the detection of a macroscopic instability). Two distinct approaches are presented; one is a direct translation of our previous protocol for adaptive detection of instabilities in laboratory experiments [Rico-Martinez, R., Krisher, K., Flatgen, G., Anderson, J. S., & Kevrekidis, I. G. (2003). Adaptive detection of instabilities: An experimental feasibility study. Physica D, 176, 1–18]; the second approach is motivated from numerical bifurcation algorithms for critical point detection. A comparison of the two approaches brings forth a key feature of equation-free computation: computational experiments can be easily initialized at will, in contrast to laboratory ones.