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Extreme events occur across the natural, engineering, and socioeconomic sciences, where rare but high-impact episodes can lead to disproportionate consequences that pose major challenges for prediction and risk management. Existing studies…
Frequency-dependent selection reflects the interaction between different species as they battle for limited resources in their environment. In a stochastic evolutionary game the species relative fitnesses guides the evolutionary dynamics…
Many real-life dynamical systems change abruptly followed by almost stationary periods. In this paper, we consider streams of data with such abrupt behavior and investigate the problem of tracking their statistical properties in an online…
A thermodynamic device placed outdoors, or a local ecosystem, is subject to a variety of different temperatures given by short-tem (daily) and long-term (seasonal) variations. In the long term a superstatistical description makes sense,…
Science students must deal with the errors inherent to all physical measurements and be conscious of the necessity to express their as a best estimate and a range of uncertainty. Errors are routinely classified as statistical or systematic.…
Many of life's most fascinating phenomena emerge from interactions among many elements--many amino acids determine the structure of a single protein, many genes determine the fate of a cell, many neurons are involved in shaping our thoughts…
The image of physics is connected with simple "mechanical" deterministic events: that an apple always falls down, that force equals mass times acceleleration. Indeed, applications of such concept to social or historical problems go back two…
Statistical mechanics relies on the complete though probabilistic description of a system in terms of all the microscopic variables. Its object is to derive therefrom static and dynamic properties involving some reduced set of variables.…
Abbreviated Abstract: The objective of Evolutionary Computation is to solve practical problems (e.g. optimization, data mining) by simulating the mechanisms of natural evolution. This thesis addresses several topics related to adaptation…
Turbulent dynamical systems characterized by both a high-dimensional phase space and a large number of instabilities are ubiquitous among many complex systems in science and engineering. The existence of a strange attractor in the turbulent…
These lecture notes are derived from a graduate-level course in dynamic optimization, offering an introduction to techniques and models extensively used in management science, economics, operations research, engineering, and computer…
We study the emergence of typicality in classical systems with a large number of binary state variables. We show analytically that for sufficiently large subsets of the complete state space, state functions which can be associated with…
In a complex community, species continuously adapt to each other. On rare occasions, the adaptation of a species can lead to the extinction of others, and even its own. "Adaptive dynamics" is the standard mathematical framework to describe…
Creating a study program for optimal academic completion is a complex assignment. Especially programs in the science, technology, engineering, and mathematics field are known for extended completion time as well as high drop-out rates…
In all but special circumstances, measurements of time-dependent processes reflect internal structures and correlations only indirectly. Building predictive models of such hidden information sources requires discovering, in some way, the…
The volume of phase space may grow super-exponentially ("explosively") with the number of degrees of freedom for certain types of complex systems such as those encountered in biology and neuroscience, where components interact and create…
Machine learning systems appear stochastic but are deterministically random, as seeded pseudorandom number generators produce identical realisations across repeated executions. Standard evaluation practice typically treats runs across…
Laboratory experiments with bacterial colonies, under well-controlled conditions often lead to evolutionary diversification, where at least two ecotypes emerge from an initially monomorphic population. Empirical evidence suggests that such…
Environmental science almost invariably proposes problems of extreme complexity, typically characterized by strongly nonlinear evolution dynamics. The systems under investigation have many degrees of freedom - which makes them complicated -…
It is well established that gene expression can be modeled as a Markovian stochastic process and hence proper observables might be subjected to large fluctuations and rare events. Since dynamics is often more than statics, one can work with…