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We explore a general method based on trees of elementary submodels in order to present highly simplified proofs to numerous results in infinite combinatorics. While countable elementary submodels have been employed in such settings already,…
Two-sample inference for the difference of population means typically relies upon a Central Limit Theorem approximation. When data are drawn from a Negative Binomial distribution, previous work of Shilane et al. (2010) showed that a Normal…
We develop an explicit covering theory for complexes of groups, parallel to that developed for graphs of groups by Bass. Given a covering of developable complexes of groups, we construct the induced monomorphism of fundamental groups and…
The concentration of a distribution toward a lower bound is a conceptually simple property that closely relates to concepts of rarity and poverty, but that lacks a global descriptive statistic. We term this property 'shift' and define it as…
Can you decide if there is a coincidence in the numbers counting two different combinatorial objects? For example, can you decide if two regions in $\mathbb{R}^3$ have the same number of domino tilings? There are two versions of the…
We give a definition of thickness in $\mathbb{R}^d$ that is useful even for totally disconnected sets, and prove a Gap Lemma type result. We also guarantee an interval of distances in any direction in thick compact sets, relate thick sets…
I investigate the scattering properties of transformation devices as the traditional impedance matching criteria are altered. This is demonstrated using simple theory and augmented by numerical simulations that investigate the role of…
Dimensionality reduction is a popular preprocessing and a widely used tool in data mining. Transparency, which is usually achieved by means of explanations, is nowadays a widely accepted and crucial requirement of machine learning based…
We study the uniform computational content of the Vitali Covering Theorem for intervals using the tool of Weihrauch reducibility. We show that a more detailed picture emerges than what a related study by Giusto, Brown, and Simpson has…
A series of detailed quantitative results is established for the family of demi-distributions which is a large extension of the family of usual distributions.
We discuss the frequent pattern mining problem in a general setting. From an analysis of abstract representations, summarization and frequent pattern mining, we arrive at a generalization of the problem. Then, we show how the problem can be…
A class of subsets designated as very thin subsets of natural numbers has been studied and seen that theory of convergence may be rediscovered if very thin sets are given to play main role instead of thin or finite sets which removes some…
Recent works on word representations mostly rely on predictive models. Distributed word representations (aka word embeddings) are trained to optimally predict the contexts in which the corresponding words tend to appear. Such models have…
We generalize the dual notions of "expansion" and "collapse" so they can be applied to arbitrary metric spaces. We also expand the theory to allow for infinitely many such moves. Those tools are then employed to prove a variety of…
Computational materials design often profits from the fact that some complicated contributions are not calculated for the real material, but replaced by results of models. We turn this approximation into a very general and in principle…
Potts models, which can be used to analyze dependent observations on a lattice, have seen widespread application in a variety of areas, including statistical mechanics, neuroscience, and quantum computing. To address the intractability of…
Over time, clinical trials have increasingly incorporated complex design and analysis elements such as interim analyses, adaptations, multiple endpoints, and sophisticated multiplicity schemes for multiple endpoints and/or treatment arms…
Soft set theory serves as a mathematical framework for handling uncertain information, and hesitant fuzzy sets find extensive application in scenarios involving uncertainty and hesitation. Hesitant fuzzy sets exhibit diverse membership…
The techniques of dispersion relations match very well with those of effective field theory. I describe the techniques for using dispersion relations effectively, and give some pedagogical examples to illustrate the range of applications.
In complex systems, it is often the case that the region of interest forms only one part of a much larger system. The idea of joining two different quantum simulations - a high level calculation on the active region of interest, and a low…