相关论文: Fat-Tailed Distributions and Levy Processes
Decisions are often based on imprecise, uncertain or vague information. Likewise, the consequences of an action are often equally unpredictable, thus putting the decision maker into a twofold jeopardy. Assuming that the effects of an action…
We consider stochastic growth models for populations organized in colonies and subject to uniform catastrophes. To assess population viability, we analyze scenarios in which individuals adopt dispersion strategies after catastrophic events.…
Resilience is a rehashed concept in natural hazard management - resilience of cities to earthquakes, to floods, to fire, etc. In a word, a system is said to be resilient if there exists a strategy that can drive the system state back to…
We consider a class of multiplicative processes which, added with stochastic reset events, give origin to stationary distributions with power-law tails -- ubiquitous in the statistics of social, economic, and ecological systems. Our main…
The FKG theorem says that the POSITIVE LATTICE CONDITION, an easily checkable hypothesis which holds for many natural families of events, implies POSITIVE ASSOCIATION, a very useful property. Thus there is a natural and useful theory of…
Dynamical systems in nature exhibit selfsimilar fractal fluctuations and the corresponding power spectra follow inverse power law form signifying long-range space-time correlations identified as self-organized criticality. The physics of…
A phenomenological theory of growth of the population of humankind is proposed. The theory based on the assumption about a multifractal nature of the set of number of people in temporal axis and contains control parameters. In particular…
The regularized theories are non-local at the scale of the cutoff, leading so to the usual difficulties of non-local theories. In this work the conservation laws and causality are investigated for classical field theories with multi-cluster…
It is argued that the $x-y$ cancellation model (XYCM) is a good proxy for discussions of finetuned cancellations in physical theories. XYCM is then analyzed from a statistical perspective, where it is argued that a finetuned point in the…
Resilience is a rehashed concept in natural hazard management - resilience of cities to earthquakes, to floods, to fire, etc. In a word, a system is said to be resilient if there exists a strategy that can drive the system state back to…
Laymen and sometimes even physicists think of natural sciences, in particular of theoretical and mathematical physics often as subjects, which unfold according to an intrinsic logical pattern, with the limitations being set only by the…
In this article, I would like to express some of my views on the nature of turbulence. These views are mainly drawn from the author's recent results on chaos in partial differential equations \cite{Li04}. Fluid dynamicists believe that…
In the world of modern financial theory, portfolio construction has traditionally operated under at least one of two central assumptions: the constraints are derived from a utility function and/or the multivariate probability distribution…
Learning is a process which can update decision rules, based on past experience, such that future performance improves. Traditionally, machine learning is often evaluated under the assumption that the future will be identical to the past in…
Catastrophes of all kinds can be roughly defined as short duration-large amplitude events following and followed by long periods of "ripening". Major earthquakes surely belong to the class of 'catastrophic' events. Because of the space-time…
Dynamical Systems theory generally deals with fixed point iterations of continuous functions. Computation by Turing machine although is a fixed point iteration but is not continuous. This specific category of fixed point iterations can only…
Earthquakes rank among the most destructive manifestations of the Earth's dynamics. Can they be predicted? This is often the first question students ask. To answer that right away: no, at present it is not possible to anticipate the date,…
We consider a simple control problem in which the underlying dynamics depend on a parameter that is unknown and must be learned. We exhibit a control strategy which is optimal to within a multiplicative constant. While most authors find…
Understanding human dynamics is of major scientific and practical importance and can be increasingly addressed in a quantitative fashion thanks to electronic records capturing various human activity patterns. The authors of Ref. [1] revisit…
Random population dynamics with catastrophes (events pertaining to possible elimination of a large portion of the population) has a long history in the mathematical literature. In this paper we study an ergodic model for random population…