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This document is both a synthesis of current notions about complex systems, and a practical approach description. A disambiguation is proposed and exposes possible reasons for controversies related to causation and emergence. Theoretical…
Several recent works have developed a new, probabilistic interpretation for numerical algorithms solving linear systems in which the solution is inferred in a Bayesian framework, either directly or by inferring the unknown action of the…
This paper presents a series of general results about the optimal estimation of physical transformations in a given symmetry group. In particular, it is shown how the different symmetries of the problem determine different properties of the…
After a quick review of the representation theory of the symmetric group, we give an exposition of the tools brought about by the so-called half-infinite wedge representation of the infinite symmetric group. We show how these can be applied…
This article is an expository account of the theory of twisted commutative algebras, which simply put, can be thought of as a theory for handling commutative algebras with large groups of linear symmetries. Examples include the coordinate…
We give a broad survey of recent results in Enumerative Combinatorics and their complexity aspects.
In this paper, we introduce a natural classification of bar and joint frameworks that possess symmetry. This classification establishes the mathematical foundation for extending a variety of results in rigidity, as well as infinitesimal or…
Computational simulations are a popular method for testing hypotheses about the emergence of communication. This kind of research is performed in a variety of traditions including language evolution, developmental psychology, cognitive…
We present a perturbative technique for modeling the scattering of light by a nonlinear material. This approach eliminates the need for an iterative algorithm to solve the fully coupled nonlinear problem. We demonstrate its effectiveness in…
The relation between representations and positive definite functions is a key concept in harmonic analysis on topological groups. Recently this relation has been studied on topological groupoids. This is the first in a series of papers in…
In this paper, by using the method of Contour Integral Representations and the Theorem of Residues and integral representations of series, we discuss the analytic representa- tions of parametric Euler sums that involve harmonic numbers…
This short note proposes a symbolic approach for representing and reasoning about quantum circuits using complex, vector or matrix-valued Boolean expressions. A major benefit of this approach is that it allows us to directly borrow the…
We present a symbolic method for organizing the representation theory of one-dimensional superalgebras. This relies on special objects, which we have called adinkra symbols, which supply tangible geometric forms to the still-emerging…
We investigate the concept of symmetry and its role in problem solving. This paper first defines precisely the elements that constitute a "problem" and its "solution," and gives several examples to illustrate these definitions. Given…
We propose a set of compositional design patterns to describe a large variety of systems that combine statistical techniques from machine learning with symbolic techniques from knowledge representation. As in other areas of computer science…
In this paper we explore a new method of analysis of associative algebras.
Symbolic integration deals with the evaluation of integrals in closed form. We present an overview of Risch's algorithm including recent developments. The algorithms discussed are suited for both indefinite and definite integration. They…
A new deformed canonical commutation relation, generalizing various known deformations, is defined together with its structure function of deformation. Then, the related irreducible representations are characterized and classified. Finally,…
Recent research in molecular discovery has primarily been devoted to small, drug-like molecules, leaving many similarly important applications in material design without adequate technology. These applications often rely on more complex…
This is an elementary introduction to the representation theory of finite semigroups. We illustrate the Clifford-Munn correspondence between the representations of a semigroup and the representations of its maximal subgroups. The emphasis…