Related papers: Constructions for cyclic sieving phenomena
These are lecture notes for various Summer and Winter schools that I have given. The notes describe the methodology called Variational Modelling, and focus on the application to the modelling of gradient-flow systems. I describe the…
Cycloids are particular Petri nets for modelling processes of actions or events. They belong to the fundaments of Petri's general systems theory and have very different interpretations, ranging from Einstein's relativity theory and…
The idea of a parsing of a stationary process according to a collection of words is introduced, and the basic framework required for the asymptotic analysis of these parsings is presented. We demonstrate how the pointwise ergodic theorem…
A linear recurrence sequence in a cyclotomic field produces a sequence of the generating fields of each term. We show that the later sequence is periodic after removing the first finite terms, and give a bound of its period. This can be…
Representation theorems relate seemingly complex objects to concrete, more tractable ones. In this paper, we take advantage of the abstraction power of category theory and provide a general representation theorem for a wide class of…
Graphs are a basic tool for the representation of modern data. The richness of the topological information contained in a graph goes far beyond its mere interpretation as a one-dimensional simplicial complex. We show how topological…
We model problems as presheaves that assign sets of certificates to input instances, and we show how to use presheaf \v{C}ech cohomology to capture the precise ways in which local solutions fail to patch into global ones. Applied to…
We prove that the generalised non-crossing partitions associated to well-generated complex reflection groups of exceptional type obey two different cyclic sieving phenomena, as conjectured by Armstrong, respectively by Bessis and Reiner.…
We derive various interesting properties of complex equiangular cyclic frames for many pairs (n, k) using Gauss sums and number theory. We further use these results to study the random and burst errors of some special cases of complex…
We present an alternative cyclic proof system for Peano arithmetic that could be simpler than the existing ones and well-adapted both for proof analysis and for automatizing inductive proof search. In addition, we will show how various…
In this paper we present new, short and elementary proofs of the famous projection and section theorems that are used in Stochastic Calculus.
In this introductory article we present the basics of an approach to implementing computational interpreting of natural language aiming to model the meanings of words and phrases. Unlike other approaches, we attempt to define the meanings…
Co-occurrence statistics based word embedding techniques have proved to be very useful in extracting the semantic and syntactic representation of words as low dimensional continuous vectors. In this work, we discovered that dictionary…
We survey some results that provide different versions of classical results through different summability methods. Specifically, in order to adapt such classical results, we analyze which properties should satisfy the summability methods.…
Human perception is structured around objects which form the basis for our higher-level cognition and impressive systematic generalization abilities. Yet most work on representation learning focuses on feature learning without even…
The $k$-symplectic structures appear in the geometric study of the partial differential equations of classical field theories. Meanwhile, we present a new application of the $k$-symplectic structures to investigate a type of systems of…
Causal discovery aims to recover information about an unobserved causal graph from the observable data it generates. Layerings are orderings of the variables which place causes before effects. In this paper, we provide ways to recover…
This study provides a summary of the theory which enables the analysis of extreme values, i.e., of measurements acquired from the observation of extraordinary/rare physical phenomena. The formalism is developed in a transparent way,…
Recurrence is a fundamental characteristic of dynamical systems with complicated behavior. Understanding the inner structure of recurrence is challenging, especially if the system has many degrees of freedom and is subject to noise. We…
This document develops general concepts useful for extracting knowledge embedded in large graphs or datasets that have pair-wise relationships, such as cause-effect-type relations. Almost no underlying assumptions are made, other than that…