Related papers: Prediction
Detecting rare events, those defined to give rise to high impact but have a low probability of occurring, is a challenge in a number of domains including meteorological, environmental, financial and economic. The use of machine learning to…
The paper describes a theoretical model of the generation of electromagnetic emissions detected prior to the earthquake, a scheme of the earthquake prediction methodology, the possible methods, which are capable of simultaneous…
A model for fault dynamics consisting of two rough and rigid brownian profiles that slide one over the other is introduced. An earthquake occurs when there is an intersection between the two profiles. The energy release is proportional to…
We review the close link between intermittent events ('quakes') and extremal noise fluctuations which has been advocated in recent numerical and theoretical work. From the idea that record-breaking noise fluctuations trigger the quakes, an…
In this paper, we focus on the influence of heterogeneity and stochasticity of the population on the dynamical structure of a basic susceptible-infected-susceptible (SIS) model. First we prove that, upon a suitable mathematical…
An attempt to construct a phenomenological theory of earthquakes is being undertaken by a small research team, which includes the author. We have only taken the first steps towards goal, but the results already obtained convincingly…
This two-part paper presents a new approach to predictive analysis for social processes. Part I identifies a class of social processes, called positive externality processes, which are both important and difficult to predict, and introduces…
We comment on some recent, yet unpublished results concerning instabilities in complex systems and their applications. In particular, we briefly describe main observations during extensive computer simulations of two lattice nonequilibrium…
The new field of complex systems supports the view that a number of systems arising from disciplines as diverse as physics, biology, engineering, and economics may have certain quantitative features that are intriguingly similar. The earth…
We consider a nonlinear pendulum whose suspension point undergoes stochastic vibrations in its plane of motion. Stochastic vibrations are constructed by stochastic differential equations with random periodic solutions. Averaging over these…
In statistical and nonlinear systems, two qualitatively distinct parameter regions are typically identified: the regular region, characterized by smooth behavior of key quantities, and the critical region, where these quantities exhibit…
We present a variety of results analyzing the behavior of a class of stochastic processes --- referred to as Stochastic Hybrid Systems (SHSs) --- in or near equilibrium, and determine general conditions on when the moments of the process…
An important challenge in several disciplines is to understand how sudden changes can propagate among coupled systems. Examples include the synchronization of business cycles, population collapse in patchy ecosystems, markets shifting to a…
Hawkes process is a class of simple point processes that is self-exciting and has clustering effect. The intensity of this point process depends on its entire past history. It has wide applications in finance, insurance, neuroscience,…
The synchronization of coupled chaotic systems represents a fundamental example of self organization and collective behavior. This well-studied phenomenon is classically characterized in terms of macroscopic parameters, such as Lyapunov…
Epileptic seizure forecasting, combined with the delivery of preventative therapies, holds the potential to greatly improve the quality of life for epilepsy patients and their caregivers. Forecasting seizures could prevent some potentially…
The stochastic self-propagating star-formation (SSPSF) model is an important theoretical framework for explaining how localised star-formation events trigger subsequent activity across galactic discs. While widely used to interpret spiral…
Point processes have been dominant in modeling the evolution of seismicity for decades, with the Epidemic Type Aftershock Sequence (ETAS) model being most popular. Recent advances in machine learning have constructed highly flexible point…
Epilepsy is a disease in which frequent seizures occur due to abnormal activity of neurons. Patients affected by this disease can be treated with the help of medicines or surgical procedures. However, both of these methods are not quite…
The objective of this work is the investigation of complexity, asymmetry, stochasticity and non-linearity of the financial and economic systems by using the tools of statistical mechanics and information theory. More precisely, this thesis…