Related papers: Composition and Inversion of Schema Mappings
The topic of this chapter is the role of expert programming knowledge in the understanding activity. In the "schema-based approach", the role of semantic structures is emphasized whereas, in the "control-flow approach", the role of…
A majority of shape correspondence frameworks are based on devising pointwise and pairwise constraints on the correspondence map. The functional maps framework allows for formulating these constraints in the spectral domain. In this paper,…
The problem of finding graph structure of functions commuting with a given function in terms of their functional graphs is considered. Structure of functional graphs of commuting functions is described. The problem is reduced to describing…
Data analysis and data mining are concerned with unsupervised pattern finding and structure determination in data sets. The data sets themselves are explicitly linked as a form of representation to an observational or otherwise empirical…
We introduce and study in a general setting the concept of homogeneity of an operator and, in particular, the notion of homogeneity of an integral operator. In the latter case, homogeneous kernels of such operators are also studied. The…
Meaning can be generated when information is related at a systemic level. Such a system can be an observer, but also a discourse, for example, operationalized as a set of documents. The measurement of semantics as similarity in patterns…
In this paper we give connections between mappings which generate bounded composition operators on Sobolev spaces and $Q$-mappings. On this base we obtain measure distortion properties $Q$-homeomorphisms. Using the composition operators on…
Syntactic theory has traditionally adopted a constructivist approach, in which a set of atomic elements are manipulated by combinatory operations to yield derived, complex elements. Syntactic structure is thus seen as the result or discrete…
The purpose of this paper is to give an introduction to the field of Schema Theory written by a mathematician and for mathematicians. In particular, we endeavor to to highlight areas of the field which might be of interest to a…
We develop operators for construction of proposals in probabilistic programs, which we refer to as inference combinators. Inference combinators define a grammar over importance samplers that compose primitive operations such as application…
Logic is the main formal language to perform automated reasoning, and it is further a human-interpretable language, at least for small formulae. Learning and optimising logic requirements and rules has always been an important problem in…
We consider solving a probably ill-conditioned linear operator equation, where the operator is not modeled by physical laws but is specified via training pairs (consisting of images and data) of the input-output relation of the operator. We…
Solving analytic systems using inversion can be implemented in a variety of ways. One method is to use Lagrange inversion and variations. Here we present a different approach, based on dual vector fields. For a function analytic in a…
A new notion in frame theory has been introduced recently under the name woven-weaving frames by Bemrose et. al. In the studying of frames, some operators like analysis, synthesis, Gram and frame operator play the central role. In this…
Circuit representations are becoming the lingua franca to express and reason about tractable generative and discriminative models. In this paper, we show how complex inference scenarios for these models that commonly arise in machine…
We study the complex symmetric structure of weighted composition--differentiation operators of order $n $ on the weighted Bergman spaces $A_{\alpha}^2$ with respect to some conjugations. Then we provide some examples of these operators.
The Mapper algorithm, a technique within topological data analysis (TDA), constructs a simplified graphical representation of high-dimensional data to uncover its underlying shape and structural patterns. The algorithm has attracted…
The semantic mapping problem is probably the main obstacle to computer-to-computer communication. If computer A knows that its concept X is the same as computer B's concept Y, then the two machines can communicate. They will in effect be…
Many applied time-dependent problems are characterized by an additive representation of the problem operator. Additive schemes are constructed using such a splitting and associated with the transition to a new time level on the basis of the…
Nested sums containing binomial coefficients occur in the computation of massive operator matrix elements. Their associated iterated integrals lead to alphabets including radicals, for which we determined a suitable basis. We discuss…