相关论文: Metrics and Ambits and Sprawls, Oh My
Polyphonic music files were analyzed using the set of symbols that produced the Minimal Entropy Description which we call the Fundamental Scale. This allowed us to create a novel space to represent music pieces by developing: a) a method to…
The ability to reason with and integrate different sensory inputs is the foundation underpinning human intelligence and it is the reason for the growing interest in modelling multi-modal information within Knowledge Graphs. Multi-Modal…
The concept of depth has proved very important for multivariate and functional data analysis, as it essentially acts as a surrogate for the notion a ranking of observations which is absent in more than one dimension. Motivated by the rapid…
This paper is a continuation of Part I where the general setup was developed. Here we discuss the general equivalence problem for geometric structures and provide criteria for the equivalence, local and global, of transitive structures.…
An interesting twist of the Hirsch index is given, in terms of an index for topics and compounds. By comparing both the hb index and m for a number of compounds and topics, it can be used to differentiate between a new so-called hot topic…
Although geographic features, such as mountains and coastlines, are fractal, some studies have claimed that the fractal property is not universal. This claim, which is false, is mainly attributed to the strict definition of fractal…
The variant of calculation of functions of set and their application is offered. In particular: the new measure of system of sets generalizing classical concept of a measure is entered; the variation of set that has allowed to construct a…
This report introduces and investigates a family of metrics on sets of pointed Kripke models. The metrics are generalizations of the Hamming distance applicable to countably infinite binary strings and, by extension, logical theories or…
The thesis presents the subject of synthetic topology, especially with relation to metric spaces. A model of synthetic topology is a categorical model in which objects possess an intrinsic topology in a suitable sense, and all morphisms are…
This is the second paper in our sequence. Here, we apply our abstract Morse index formulation developed in the previous paper to study several optimization set-ups with constraints, including type I or/and type II considerations. A common…
In this paper, algebroid bundle associated to affine metrics provide an structure for unification of gravity and electromagnetism and, geometrization of matter.
We present a survey of results concerning the use of inductive constructions to study the rigidity of frameworks. By inductive constructions we mean simple graph moves which can be shown to preserve the rigidity of the corresponding…
Visual insights into a wide variety of statistical methods, for both didactic and data analytic purposes, can often be achieved through geometric diagrams and geometrically based statistical graphs. This paper extols and illustrates the…
A consecutive pattern in a permutation $\pi$ is another permutation $\sigma$ determined by the relative order of a subsequence of contiguous entries of $\pi$. Traditional notions such as descents, runs and peaks can be viewed as particular…
Classic Topic Models are built under the Bag Of Words assumption, in which word position is ignored for simplicity. Besides, symmetric priors are typically used in most applications. In order to easily learn topics with different properties…
We prove metric rigidity for complete manifolds supporting solutions of certain second order differential systems, thus extending classical works on a characterization of space-forms. In the route, we also discover new characterizations of…
Lattices are a commonly used structure for the representation and analysis of relational and ontological knowledge. In particular, the analysis of these requires a decomposition of a large and high-dimensional lattice into a set of…
Graph mining applications analyze the structural properties of large graphs, and they do so by finding subgraph isomorphisms, which makes them computationally intensive. Existing graph mining techniques including both custom graph mining…
Every metric symplectic Lie algebra has the structure of a quadratic extension. We give a standard model and describe the equivalence classes on the level of corresponding quadratic cohomology sets. Finally, we give a scheme to classify the…
We show that the set of points of an overt closed subspace of a metric completion of a Bishop-locally compact metric space is located. Consequently, if the subspace is, moreover, compact, then its collection of points is Bishop compact.