Enumerations of rooted trees with an application to group presentations

AbstractThe combinatorial properties of the set of rooted trees can be viewed algrebraically by considering this set as an algebra with one unary and one binary operation. This viewpoint yields solutions to several enumeration problems. In particular, using a correspondence between rooted trees and presentations of finite abelian p-groups devised by A.W. Hales, I enumerate all presentations of a given group

Tamari Lattices and the symmetric Thompson monoid

We investigate the connection between Tamari lattices and the Thompson group F, summarized in the fact that F is a group of fractions for a certain monoid F+sym whose Cayley graph includes all Tamari lattices. Under this correspondence, the Tamari lattice operations are the counterparts of the least common multiple and greatest common divisor operations in F+sym. As an application, we show that, for every n, there exists a length l chain in the nth Tamari lattice whose endpoints are at distance at most 12l/n.Comment: 35page

LDA Topic Modeling: Contexts for the History & Philosophy of Science

In this paper we discuss the application of LDA topic modeling to questions that interest historians & philosophers of science, which we illustrate primarily through our own work on modeling Charles Darwin's reading and writing behavior. We discuss the need to go beyond simplistic presentations of topic models that tend to give scholars the idea that the algorithms produce results that are superficial and perhaps unreliable. The ways in which topic models are often misrepresented and misunderstood frame our attempt to convince readers that, despite appearances, topic modeling provides a lot more of value to HPS research than merely providing for enhanced search and information retrieval from large sets of documents. Rather than "topics" we prefer to think of these topic models as revealing contexts for individual reading and wrote, leading us to ask questions about the individual exploration and exploitation of the materials to which a scientist such as Darwin had access. We discuss the use of topic models as tools for identifying influence and measuring creativity within those contexts and conclude that the interplay between human intelligence and sophisticated algorithms will expand the range of questions about science that HPS scholars will ask, and can answer

A first-order axiomatization of the theory of finite trees

We provide first-order axioms for the theories of finite trees with bounded branching and finite trees with arbitrary (finite) branching. The signature is chosen to express, in a natural way, those properties of trees most relevant to linguistic theories. These axioms provide a foundation for results in linguistics that are based on reasoning formally about such properties. We include some observations on the expressive power of these theories relative to traditional language complexity classes

Extrakce znalostních grafů z projektové dokumentace

Název práce: Extrakce znalostních grafů z projektové dokumentace Autor: Bc. Tomáš Helešic Katedra: Katedra softwarového inženýrství Vedoucí diplomové práce: Mgr. Martin Nečaský, Ph.D. Abstrakt: Cílem této práce je prozkoumat možnosti automatické extrakce infor- mací z firemní projektové dokumentace s využitím nástroje pro strojové zpra- cování přirozeného jazyka a analýza přesnosti lingvistického zpracování těchto dokumentů. Dále navrhnout metody, jak získat klíčové pojmy a vazby mezi nimi. Z těchto pojmů a vazeb se vytváří znalostní grafy, které se uchovávají ve vhodném úložisti s vyhledávací službou. Práce se snaží propojit již ex- istující technologie, implementovat je do jednoduché aplikace a ověřit jejich připravenost pro praktické využití. Cílem je inspirovat budoucí výzkum v této oblasti, identifikovat kritická místa a navhrnout zlepšení. Hlavní přínos tkví v propojení zpracování přirozeného jazyka, metod extrakce informací, sémantické vyhledávání s firemnímy dokumenty. Přínos praktické části spočívá ve způsobu identifikace důležitých informací, které popisují jednotlivé dokumenty a jejich využití ve vyhledávání. Klíčová slova: Znalostní grafy, Extrakce informace, Zpracování...Title: Knowledge Graph Extraction from Project Documentation Author: Bc. Tomáš Helešic Department: Department of Software Engineering Supervisor: Mgr. Martin Nečaský, Ph.D. Abstract: The goal of this thesis is to explore the possibilities of automatic in- formation extraction from company project documentation with the use of ma- chine natural language processing and the analysis of the precision of linguistic processing of these documents. Furthermore suggest methods how acquire key terms and dependencies between them. From this terms and dependencies cre- ate knowledge graphs, that are stored in an appropriate database with search engine. The work is trying to interconnect already existing technologies in a shape of a simple application and test their readiness for a practical use. The goal is to inspire future research in this field, identify critical parts and propose improvements. The main gain is in the interconnection between natural lan- guage processing, methods of information extraction and semantic searching in corporate documents. The gain of the practical part reside in the way how to identify key information that is uniquely describing each document and its use in search. Keywords: Knowledge graphs, Information extraction, Natural language pro- cessing, Resource Description Framework 1Katedra softwarového inženýrstvíDepartment of Software EngineeringMatematicko-fyzikální fakultaFaculty of Mathematics and Physic

Combinatorics of the Permutahedra, Associahedra, and Friends

I present an overview of the research I have conducted for the past ten years in algebraic, bijective, enumerative, and geometric combinatorics. The two main objects I have studied are the permutahedron and the associahedron as well as the two partial orders they are related to: the weak order on permutations and the Tamari lattice. This document contains a general introduction (Chapters 1 and 2) on those objects which requires very little previous knowledge and should be accessible to non-specialist such as master students. Chapters 3 to 8 present the research I have conducted and its general context. You will find: * a presentation of the current knowledge on Tamari interval and a precise description of the family of Tamari interval-posets which I have introduced along with the rise-contact involution to prove the symmetry of the rises and the contacts in Tamari intervals; * my most recent results concerning q, t-enumeration of Catalan objects and Tamari intervals in relation with triangular partitions; * the descriptions of the integer poset lattice and integer poset Hopf algebra and their relations to well known structures in algebraic combinatorics; * the construction of the permutree lattice, the permutree Hopf algebra and permutreehedron; * the construction of the s-weak order and s-permutahedron along with the s-Tamari lattice and s-associahedron. Chapter 9 is dedicated to the experimental method in combinatorics research especially related to the SageMath software. Chapter 10 describes the outreach efforts I have participated in and some of my approach towards mathematical knowledge and inclusion.Comment: 163 pages, m\'emoire d'Habilitation \`a diriger des Recherche

Travelling knowledges: urban poverty and slum/shack dwellers international

The relationship between knowledge and development is of growing importance in development theory and practice. Despite the growth in interest, there are significant issues that have not been explored in detail. I will focus on some of these issues, including: the ways in which knowledge and learning are conceived and created in development; the ways in which knowledge travels; the opportunities for learning between 'North' and 'South'; and the political spaces that are created through different kinds of knowledge. To explore these issues, I examine a network of non-governmental organisations (NGOs) and community-based organisations (CBOs) called Slum/Shack Dwellers International (SDI). This network seeks to reconfigure the governance of urban poverty reduction strategies and encourage poor' people to re-think their own capacities and potentials. In particular, I draw on interview-based fieldwork conducted on one key member of this group, the Indian Alliance based in Mumbai. I critically examine some of the possibilities and challenges of various forms of 'travelling knowledges'. These are strategies that have travelled through exchanges, wherein groups of poor people travel from one settlement to another to share stories and experiences with other poor people in what amounts to an informal 'training' process. By examining exchanges between SDI and groups in the UK, I critically discuss the broader potential in development to move beyond barriers of North and South that limit learning. I adopt a broadly post-rationalist approach to the concerns in the thesis. Through this, I argue the importance of considering knowledge and learning as produced through relations of near and far, social and material, and as driven by routines and practices. A post-rationalist approach helps us to understand and appreciate the importance of geography for knowledge and learning in the SDI network. This approach draws attention to power. It encourages a critical consciousness that is alert to the kinds of knowledge conceived for development, and that recognizes the various ways in which different knowledges help create different types of politics. A post-rationalist approach also cautions against conceptions of knowledge and learning that risk marginalizing geography and power in development more generally. The thesis demonstrates the need to give further consideration of how knowledge is conceived as a development strategy, and what the potential possibilities and pitfalls of travelling knowledges are