Related papers: The harmony, reflection and other principles of co…
The paper is devoted to a generalization of static and dynamic mathematical models of behavior with explicitly stated reflexive models of agents' decision-making. Reflexion is considered as agent's beliefs about nature, opponents' beliefs…
Composition is a powerful principle for systems biology, focused on the interfaces, interconnections, and orchestration of distributed processes to enable integrative multiscale simulations. Whereas traditional models focus on the structure…
We review possible measures of complexity which might in particular be applicable to situations where the complexity seems to arise spontaneously. We point out that not all of them correspond to the intuitive (or "naive") notion, and that…
One may define a complex system as a system in which phenomena emerge as a consequence of multiscale interaction among the system's components and their environments. The field of Complex Systems is the study of such systems--usually…
This paper discusses system consequence, a central idea in the project to lift the theory of information flow to the abstract level of universal logic and the theory of institutions. The theory of information flow is a theory of distributed…
Abstract separation systems provide a simple general framework in which both tree-shape and high cohesion of many combinatorial structures can be expressed, and their duality proved. Applications range from tangle-type duality and tree…
Complex networks are universal, arising in fields as disparate as sociology, physics, and biology. In the past decade, extensive research into the properties and behaviors of complex systems has uncovered surprising commonalities among the…
Physical fundamentals of the self-organizing theory for the system with varying constraints are considered. A variation principle, specifically the principle of dynamic harmonization as a generalization of the Gauss-Hertz principle for the…
We introduce the class of projective reflection groups which includes all complex reflection groups. We show that several aspects involving the combinatorics and the representation theory of all non exceptional irreducible complex…
Periodic multilayers of various periods were prepared according to an algorithm proposed by the authors. The reflectivity properties of these systems were investigated using neutron reflectometry.The obtained experimental results were…
This paper aims at reviewing and analysing the method of reflections. The latter is an iterative procedure designed to linear boundary value problems set in multiply connected domains. Being based on a decomposition of the domain boundary,…
We synthesize and unify notions of regularity, both of individual sets and of collections of sets, as they appear in the convergence theory of projection methods for consistent feasibility problems. Several new characterizations of…
The representation of complex systems as networks is inappropriate for the study of certain problems. We show several examples of social, biological, ecological and technological systems where the use of complex networks gives very limited…
We introduce three families of diagonal reflection principles for matrices of stationary sets of ordinals. We analyze both their relationships among themselves and their relationships with other known principles of simultaneous stationary…
Depth is a complexity measure for natural systems of the kind studied in statistical physics and is defined in terms of computational complexity. Depth quantifies the length of the shortest parallel computation required to construct a…
Coherent control of wave transmission and reflection is crucial for applications in communication, imaging, and sensing. However, many practical scenarios involve partially coherent waves rather than fully coherent ones. We present a…
Complex spatiotemporal patterns in nature significantly challenge reductionism-based modern science. The lack of a paradigm beyond reductionism hinders our understanding of the emergence of complexity. The diversity of countless patterns…
Abstract separation systems are a new unifying framework in which separations of graph, matroids and other combinatorial structures can be expressed and studied. We characterize the abstract separation systems that have representations as…
It is a well-known empirical phenomenon that natural axiomatic theories are pre-well-ordered by consistency strength. Without a precise mathematical definition of "natural," it is unclear how to study this phenomenon mathematically. We will…
The general solutions of the reflection equation associated with Temperley-Lieb $R$-matrices are constructed. Their parametrization is defined and the Hamiltonians of corresponding integrable spin systems are given.