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A general notion of operad is given, which includes as instances, the operads originally conceived to study loop spaces, as well as the higher operads that arise in the globular approach to higher dimensional algebra. In the framework of…
Hilbert's two-dimensional space-filling curve is appreciated for its good locality-preserving properties and easy implementation for many applications. However, Hilbert did not describe how to generalize his construction to higher…
Algebraic operations are understood as topologiztion of algebra. They become an example of simplest convergence space. In our article the convergence is a arbitrary multivalued appointment. The continuity of some mapping between two…
We consider relationships between cubic algebras and implication algebras. We first exhibit a functorial construction of a cubic algebra from an implication algebra. Then we consider an collapse of a cubic algebra to an implication algebra…
Extracting the relevant information by exploiting the spatial data warehouse becomes increasingly hard. In fact, because of the enormous amount of data stored in the spatial data warehouse, the user, usually, don't know what part of the…
We use computational linear algebra and commutative algebra to study spaces of relations satisfied by quadrilinear operations. The relations are analogues of associativity in the sense that they are quadratic (every term involves two…
In quantum mechanics, mutually unbiased bases (MUBs) represent orthonormal bases that are as "far apart" as possible, and their classification reveals rich underlying geometric structure. Given a complex inner product space, we construct…
A natural connection between rational functions of several real or complex variables, and subspace collections is explored. A new class of function, superfunctions, are introduced which are the counterpart to functions at the level of…
Understanding the global organization of complicated and high dimensional data is of primary interest for many branches of applied sciences. It is typically achieved by applying dimensionality reduction techniques mapping the considered…
We extend the known tables of pseudosquares and pseudocubes, discuss the implications of these new data on the conjectured distribution of pseudosquares and pseudocubes, and present the details of the algorithm used to do this work. Our…
Increasingly, business projects are ephemeral. New Business Intelligence tools must support ad-lib data sources and quick perusal. Meanwhile, tag clouds are a popular community-driven visualization technique. Hence, we investigate tag-cloud…
Efficient object manipulation strategies have significant impact in automation applications. In this work, the stack rearrangement in tabletop settings is studied, with a focus on augmenting the task planning domain with richer…
A fundamental operation in many vision tasks, including motion understanding, stereopsis, visual odometry, or invariant recognition, is establishing correspondences between images or between images and data from other modalities. We present…
Information inflow into a computational system is by a sequence of information items. Cognitive computing, i.e. performing transformations along that sequence, requires to represent item information as well as sequential information. Among…
This work seeks to tackle the inherent complexity of dataspaces by introducing a novel data structure that can represent datasets across multiple levels of abstraction, ranging from local to global. We propose the concept of a multilevel…
With the rapid adoption of machine learning techniques for large-scale applications in science and engineering comes the convergence of two grand challenges in visualization. First, the utilization of black box models (e.g., deep neural…
Classical algebraic structures require exact satisfaction of their defining axioms. We propose similarity algebra, a framework extending algebraic and Lie structures to settings where operations satisfy quantitative bounds up to a tolerance…
Quantum algorithms are sequences of abstract operations, performed on non-existent computers. They are in obvious need of categorical semantics. We present some steps in this direction, following earlier contributions of Abramsky, Coecke…
The topological interpretation of modal logics provides descriptive languages and proof systems for reasoning about points of topological spaces. Recent work has been devoted to model checking of spatial logics on discrete spatial…
Quantum computation is frequently mischaracterized as the simultaneous execution of exponentially many classical computations. This article offers a conceptual clarification of why this ``branchwise parallelism'' picture is misleading,…