Related papers: Complexity and ordinary life, and some mathematics…
In this chapter the complex systems are discussed in the context of economic and business policy and decision making. It will be showed and motivated that social systems are typically chaotic, non-linear and/or non-equilibrium and therefore…
The world is changing at an ever-increasing pace. And it has changed in a much more fundamental way than one would think, primarily because it has become more connected and interdependent than in our entire history. Every new product, every…
This text consists on a series of introductory lectures on cosmology for mathematicians and physicists who are not specialized on the subject.
An introduction to applied mathematics written for students in engineering and science. Focus is on a rigorous presentation that also builds understanding by discussion, analogy, and examples. Discussion of concepts involved in modeling…
These notes, connected to a "potpourri" topics class currently underway, discuss some basic topics in analysis and connections with other areas of mathematics.
The word "complexity" is most often used as a meta--linguistic expression referring to certain intuitive characteristics of a natural system and/or its scientific description. These characteristics may include: sheer amount of data that…
This is a short introduction to Kolmogorov Complexity. The interested reader is referred to the text books by Cover & Thomas as well as Li & V\'itanyi, which cover the fields of information theory and Kolmogorov complexity in depth and with…
We explain how recent developments in the fields of realisability models for linear logic -- or geometry of interaction -- and implicit computational complexity can lead to a new approach of implicit computational complexity. This…
The outline of a programme for restructuring mathematical logic. We explain what we mean by "restructuring" and carry out exemplary parts of the programme.
The paper has a form of a talk on the given topic. It consists of three parts. The first part of the paper contains main notions, the second one is devoted to logical geometry, the third part describes types and isotypeness. The problems…
A review of various definitions of "compatibility" expressed in terms of ordinary probability, and a discussion of the occurrence of incompatibility (and the related phenomenon of interference) in non-quantal probabilistic systems.
A strong link between complexity theory and literature is possible, i.e. feasible, under one proviso, namely that total novels be considered. However, neither in literature at large nor in complexity science has been literature seriously…
Modal probabilistic logics provide a framework for reasoning about probability in modal contexts, involving notions such as knowledge, belief, time, and action. In this paper, we study a particular family of these logics, extending the…
The spatial character of territorial systems plays a crucial role in the emergence of their complexities. This contribution aims at illustrating to what extent different types of complexities can be exhibited in models of such systems. We…
We define a notion which contains numerous basic notions of Analysis as special cases, for example limit, continuity, differential, Riemann and Lebesgue integral, root and exponential functions. Properties like additivity or linearity of…
This is an extended survey of the results concerning a hierarchy of languages that is tightly connected with the quantifier alternation hierarchy within the two-variable fragment of first order logic of the linear order.
Simplicity is held by many to be the key to general intelligence. Simpler models tend to "generalise", identifying the cause or generator of data with greater sample efficiency. The implications of the correlation between simplicity and…
The aim of this essay is to propose a conception of mathematics that is fully consonant with naturalism. By that I mean the hypothesis that everything that exists is part of the natural world, which makes up a unitary whole.
Mathematics is one of the ways our species makes sense of this world and I believe that it is inherent in our thinking machinery. The mathematics we do in turn is dependent on the way we view our universe and ourselves. Lakoff and Nunez…
The emergence of a complex, large-scale organisation of cosmic matter into the Cosmic Web is a beautiful exemplification of how complexity can be produced by simple initial conditions and simple physical laws. In the epoch of Big Data in…