Related papers: Three applications of coverings to difference patt…
Two-dimensional patterns are used in many research areas in computer science, ranging from image processing to specification and verification of complex software systems (via scenarios). The contribution of this paper is twofold. First, we…
Covering model provides a general framework for granular computing in that overlapping among granules are almost indispensable. For any given covering, both intersection and union of covering blocks containing an element are exploited as…
This article introduces a general statistical modeling principle called "Density Sharpening" and applies it to the analysis of discrete count data. The underlying foundation is based on a new theory of nonparametric approximation and…
We propose a multi-scale extension of conformal prediction, an approach that constructs prediction sets with finite-sample coverage guarantees under minimal statistical assumptions. Classic conformal prediction relies on a single notion of…
Covering theory is an important tool in representation theory of algebras, however, the results and the proofs are scattered in the literature. We give an introduction to covering theory at a level as elementary as possible.
We describe and analyze different approaches to represent ordinal patterns. All of these can be found in the literature. The most important representations (plus sub-classes) are compared in terms of their applicability from different…
Approximation theory is concerned with the ability to approximate functions by simpler and more easily calculated functions. The first question we ask in approximation theory concerns the {\it possibility of approximation}. Is the given…
In this article we generalize packing density problems from permutations to patterns with repeated letters and generalized patterns. We are able to find the packing density for some classes of patterns and several other short patterns.
We present a class of models that, via a simple construction, enables exact, incremental, non-parametric, polynomial-time, Bayesian inference of conditional measures. The approach relies upon creating a sequence of covers on the…
Difference sets and their generalisations to difference families arise from the study of designs and many other applications. Here we give a brief survey of some of these applications, noting in particular the diverse definitions of…
We introduce a general notion of covering property, of which many classical definitions are particular instances. Notions of closure under various sorts of convergence, or, more generally, under taking kinds of accumulation points, are…
Dependent pattern matching is a key feature in dependently typed programming. However, there is a theory-practice disconnect: while many proof assistants implement pattern matching as primitive, theoretical presentations give semantics to…
The closure and the partitioning principles have been used to build various multiple testing procedures in the past three decades. The essence of these two principles is based on parameter space partitioning. In this article, we propose a…
In the mixture models problem it is assumed that there are $K$ distributions $\theta_{1},\ldots,\theta_{K}$ and one gets to observe a sample from a mixture of these distributions with unknown coefficients. The goal is to associate instances…
Difference triangle sets are useful in many practical problems of information transmission. This correspondence studies combinatorial and computational constructions for difference triangle sets having small scopes. Our algorithms have been…
We show that a language model's ability to predict text is tightly linked to the breadth of its embedding space: models that spread their contextual representations more widely tend to achieve lower perplexity. Concretely, we find that…
We generalize Roth's theorem on three term arithmetic progressions to translation invariant quadratic forms in at least 17 variables. We use Fourier-analysis, restriction theory, uniformity norms and Roth's density increment method to show…
We introduce layers to modal type theories, which subsequently enables type theories for pattern matching on code in meta-programming and clean and straightforward semantics.
The results of difference sequences theory are applied to analytic function theory and Diophantine equations. As a result we have the equation which connects the $n$-th derivative of a function with the difference sequence for the values of…
This dissertation presents a multifaceted look into the structural decomposition of permutation classes. The theory of permutation patterns is a rich and varied field, and is a prime example of how an accessible and intuitive definition…