Related papers: Linearization and categorification
In this paper we study the problem of quantizing theories defined over a nonclassical configuration space. If one follows the path-integral approach, the first problem one is faced with is the one of definition of the integral over such…
Majorisation, also called rearrangement inequalities, yields a type of stochastic ordering in which two or more distributions can be compared. In this paper we argue that majorisation is a good candidate as a theory for uncertainty. We…
The Euler characteristic can be defined as a special kind of valuation on finite distributive lattices. This work begins with some brief consideration on the role of the Euler characteristic on NM algebras, the algebraic counterpart of…
The third quantization formalism of quantum cosmology adds simplicity and conceptual insight into the quantum description of the multiverse. Within such a formalism, the existence of squeezed and entangled states raises the question of…
We introduce the characterization of a class of quantum PageRank algorithms in a scenario in which some kind of quantum network is realizable out of the current classical internet web, but no quantum computer is yet available. This class…
Motivated by questions in theoretical computer science and quantum information theory, we study the classical problem of determining linear spaces of matrices of bounded rank. Spaces of bounded rank three were classified in 1983, and it has…
This note discusses an interesting matrix factorization called the CUR Decomposition. We illustrate various viewpoints of this method by comparing and contrasting them in different situations. Additionally, we offer a new characterization…
We review remarkable results in several mathematical scenarios, including graph theory, division algebras, cross product formalism and matroid theory. Specifically, we mention the following subjects: (1) the Euler relation in graph theory,…
We define a model for linear logic based on two well-known ingredients: games and simulations. This model is interesting in the following respect: while it is obvious that the objects interpreting formulas are games and that everything is…
Learning to rank -- producing a ranked list of items specific to a query and with respect to a set of supervisory items -- is a problem of general interest. The setting we consider is one in which no analytic description of what constitutes…
We examine the use of classes to formulate several categorical notions. This leads to two proposals: an explicit structure for working with subobjects, and a hierarchy of $k$-classes. We apply the latter to both ordinary and higher…
Linear discrimination, from the point of view of numerical linear algebra, can be treated as solving an ill-posed system of linear equations. In order to generate a solution that is robust in the presence of noise, these problems require…
A construction of the noncommutative-geometric counterparts of classical classifying spaces is presented, for general compact matrix quantum structure groups. A quantum analogue of the classical concept of the classifying map is introduced…
Category, or property generalization is a central function in the human cognition. It plays a crucial role in a variety of domains, such as learning, everyday reasoning, specialized reasoning, and decision making. Judging the content of a…
We introduce layer systems for proving generalizations of the modularity of confluence for first-order rewrite systems. Layer systems specify how terms can be divided into layers. We establish structural conditions on those systems that…
Recent developments concerning canonical quantisation and gauge invariant quantum mechanical systems and quantum field theories are briefly discussed. On the one hand, it is shown how diffeomorphic covariant representations of the…
Categorization systems are widely studied in psychology, sociology, and organization theory as information-structuring devices which are critical to decision-making processes. In the present paper, we introduce a sound and complete…
Parametric models in vector spaces are shown to possess an associated linear map. This linear operator leads directly to reproducing kernel Hilbert spaces and affine- / linear- representations in terms of tensor products. From the…
We formulate a refined theory of linear systems, using the methods of a previous paper, "A Theory of Branches for Algebraic Curves", and use it to give a geometric interpretation of the genus of an algebraic curve. Using principles of…
We present an approach to the canonical quantization of systems with equations of motion that are historically called non-Lagrangian equations. Our viewpoint of this problem is the following: despite the fact that a set of differential…