Related papers: On the Structure of Behaviors
The present paper is devoted to the study of dimonoids, algebraic structures with two associative binary operations that satisfy a prescribed system of axioms. We investigate the properties of dual dimonoids. In the class of noncommutative…
Complex environments, processes and systems may exhibit several distinct modes of physical behaviour or operation. Thus, for example, in their design, a set of mathematical models may be needed, each model having its own domain of…
We describe a systematic way of the generalization, to models with non-linear duality, of the space-time covariant and duality-invariant formulation of duality-symmetric theories in which the covariance of the action is ensured by the…
Opacity is an information flow property that captures the notion of plausible deniability in dynamic systems, that is whether an intruder can deduce that "secret" behavior has occurred. In this paper we provide a general framework of…
In this paper, we mainly focus on formal deformation theory of module homomorphisms. We first introduce the cohomology of module homomorphisms and study formal one-parameter deformation. We obtain some properties about obstructions. Then we…
This is a very brief survey of some results in the geometry of string duality delivered at a lecture given at ICM 1998, Berlin. String Duality is the statement that one kind of string theory compactified on one space is equivalent in some…
Most engineering models contain several parameters, and the map from input parameters to model output can be viewed as a multivariate function. An active subspace is a low-dimensional subspace of the space of inputs that explains the…
Open discrete mappings with a modulus condition in metric spaces are considered. Some results related to local behavior of mappings as well as theorems about continuous extension to a boundary are proved.
Biological systems exhibit two structural features on many levels of organization: sparseness, in which only a small fraction of possible interactions between components actually occur; and modularity - the near decomposability of the…
The monodromy group is an invariant for parameterized systems of polynomial equations that encodes structure of the solutions over the parameter space. Since the structure of real solutions over real parameter spaces are of interest in many…
It is proposed that the physical universe is an instance of a mathematical structure which possesses a dual structure, and that this dual structure is the collection of all possible knowledge of the physical universe. In turn, the physical…
We investigate the space of quantum operations, as well as the larger space of maps which are positive, but not completely positive. A constructive criterion for decomposability is presented. A certain class of unistochastic operations,…
Frame theory is recently an active research area in mathematics, computer science and engineering with many exciting applications in a variety of different fields. This theory has been generalized rapidly and various generalizations of…
We introduce a notion of Q-algebra that can be considered as a generalization of the notion of Q-manifold (a supermanifold equipped with an odd vector field obeying {Q,Q} =0). We develop the theory of connections on modules over Q-algebras…
An old idea in optimization theory says that since the gradient is a dual vector it may not be subtracted from the weights without first being mapped to the primal space where the weights reside. We take this idea seriously in this paper…
A new behavior descriptive entity type called spec is proposed, which combines the traditional interface with test rules and test cases, to completely specify the desired behavior of each method, and to enforce the behavior-wise correctness…
For a Lie algebra L over an algebraically closed field of non-zero characteristic, every finite-dimensional L-module can be decomposed into a direct sum of submodules such that all composition factors of a summand have the same character.…
If $M$ is an $R$-module, we study the submodules $K\leq M$ with the property that $K$ is invariant with respect to all monomorphisms $K\rightarrow M$. Such submodules are called \textsl{strictly invariant}. For the case of $%…
We consider a dynamic social network model in which agents play repeated games in pairings determined by a stochastically evolving social network. Individual agents begin to interact at random, with the interactions modeled as games. The…
We introduce refinement in the function-behaviour-structure framework for design, as described by John Gero, in order to deal with complexity. We do this by connecting the frameworks for the design of two models, one the refinement of the…