1,686 research outputs found
Opening the system to the environment: new theories and tools in classical and quantum settings
The thesis is organized as follows. Section 2 is a first, unconventional, approach to the topic of EPs. Having grown interest in the topic of combinatorics and graph theory, I wanted to exploit its very abstract and mathematical tools to reinterpret something very physical, that is, the EPs in wave scattering. To do this, I build the interpretation of scattering events from a graph theory perspective and show how EPs can be understood within this interpretation. In Section 3, I move from a completely classical treatment to a purely quantum one. In this section, I consider two quantum resonators coupled to two baths and study their dynamics with local and global master equations. Here, the EPs are the key physical features used as a witness of validity of the master equation. Choosing the wrong master equation in the regime of interest can indeed mask physical and fundamental features of the system. In Section 4, there are no EPs. However I transition towards a classical/quantum framework via the topic of open systems. My main contribution in this work is the classical stochastic treatment and simulation of a spin coupled to a bath. In this work, I show how a natural quantum--to--classical transition occurs at all coupling strengths when certain limits of spin length are taken. As a key result, I also show how the coupling to the environment in this stochastic framework induces a classical counterpart to quantum coherences in equilibrium. After this last topic, in Section 5, I briefly present the key features of the code I built (and later extended) for the latter project. This, in the form of a Julia registry package named SpiDy.jl, has seen further applications in branching projects and allows for further exploration of the theoretical framework. Finally, I conclude with a discussion section (see Sec. 5) where I recap the different conclusions gathered in the previous sections and propose several possible directions.Engineering and Physical Sciences Research Council (EPSRC
Planarity in cubic intuitionistic graphs and their application to control air traffic on a runway
Fuzzy modeling plays a pivotal role in various fields, including science, engineering, and medicine. In comparison to conventional models, fuzzy models offer enhanced accuracy, adaptability, and resemblance to real-world systems and help researchers to always make the best choice in complex problems. A type of fuzzy graph that is widely used in medical and psychological sciences is the cubic intuitionistic fuzzy graph, which plays an important role in various fields such as computer science, psychology, medicine, and political sciences. It is also used to find effective people in an organization or social institution. In this research endeavor, we embark upon elucidating the innovative notion of a cubic intuitionistic planar graph, delving into its intricate properties and attributes. Additionally, we unveil the novel concept of a cubic intuitionistic dual graph, thus enriching the realm of graph theory with further profundity. Furthermore, our exploration encompasses the elucidation of other pertinent terminologies, such as cubic intuitionistic multi-graphs, along with the categorization of edges into the distinct classifications of strong and weak edges. Moreover, we discern the concept of the degree of planarity within the context of CIPG and unveil the notion of strong and weak faces. Additionally, we delve into the construction of cubic intuitionistic dual graphs, which can be realized in cases where the initial graph is planar or possesses a degree of planarity ≥0.67. Notably, we furnish the exposition with a comprehensive discussion on noteworthy findings and substantial results pertaining to these captivating topics, contributing valuable insights on the field of graph theory. Last, we shall endeavor to exemplify the practical relevance and importance of our research by presenting an illuminating real-world application, thus demonstrating the tangible impact and significance of our endeavors in this research article
Planar Disjoint Paths, Treewidth, and Kernels
In the Planar Disjoint Paths problem, one is given an undirected planar graph
with a set of vertex pairs and the task is to find pairwise
vertex-disjoint paths such that the -th path connects to . We
study the problem through the lens of kernelization, aiming at efficiently
reducing the input size in terms of a parameter. We show that Planar Disjoint
Paths does not admit a polynomial kernel when parameterized by unless coNP
NP/poly, resolving an open problem by [Bodlaender, Thomass{\'e},
Yeo, ESA'09]. Moreover, we rule out the existence of a polynomial Turing kernel
unless the WK-hierarchy collapses. Our reduction carries over to the setting of
edge-disjoint paths, where the kernelization status remained open even in
general graphs.
On the positive side, we present a polynomial kernel for Planar Disjoint
Paths parameterized by , where denotes the treewidth of the input
graph. As a consequence of both our results, we rule out the possibility of a
polynomial-time (Turing) treewidth reduction to under the same
assumptions. To the best of our knowledge, this is the first hardness result of
this kind. Finally, combining our kernel with the known techniques [Adler,
Kolliopoulos, Krause, Lokshtanov, Saurabh, Thilikos, JCTB'17; Schrijver,
SICOMP'94] yields an alternative (and arguably simpler) proof that Planar
Disjoint Paths can be solved in time , matching the
result of [Lokshtanov, Misra, Pilipczuk, Saurabh, Zehavi, STOC'20].Comment: To appear at FOCS'23, 82 pages, 30 figure
Towards an Unsupervised Bayesian Network Pipeline for Explainable Prediction, Decision Making and Discovery
An unsupervised learning pipeline for discrete Bayesian networks is proposed to facilitate prediction, decision making, discovery of patterns, and transparency in challenging real-world AI applications, and contend with data limitations. We explore methods for discretizing data, and notably apply the pipeline to prediction and prevention of preterm birth
A grammar of Ulwa (Papua New Guinea)
Synopsis:
This book is a grammatical description of Ulwa, a Papuan language spoken by about 600 people living in four villages in the East Sepik Province of Papua New Guinea. Ulwa belongs to the Keram language family. This grammatical description is based on a corpus of recorded texts and elicited sentences that were collected during a total of about twelve months of research carried out between 2015 and 2018. The book aims to detail as many aspects of Ulwa grammar as possible, including matters of phonology, morphology, and syntax. It also contains a lexicon with over 1,400 entries and three fully glossed and translated texts. The book was written with a typologically oriented audience in mind, and should be of interest to Papuan specialists as well as to general linguists. It may be useful to those working on the history or classification of Papuan languages as well as those conducting typological research on any number of grammatical features
Longest Path and Cycle Transversal and Gallai Families
A longest path transversal in a graph G is a set of vertices S of G such that every longest path in G has a vertex in S. The longest path transversal number of a graph G is the size of a smallest longest path transversal in G and is denoted lpt(G). Similarly, a longest cycle transversal is a set of vertices S in a graph G such that every longest cycle in G has a vertex in S. The longest cycle transversal number of a graph G is the size of a smallest longest cycle transversal in G and is denoted lct(G). A Gallai family is a family of graphs whose connected members have longest path transversal number 1. In this paper we find several Gallai families and give upper bounds on lpt(G) and lct(G) for general graphs and chordal graphs in terms of |V(G)|
Developing Socially-Just Teachers Through A Proposed Alternative Curriculum For Initial Teacher Education
Problems of teacher burnout, low job satisfaction and high rates of teacher attrition are not specific to England but are also global concerns and symptomatic of a profession in crisis. In England, teacher education is a highly regulated sector and, in recent years, has become increasingly complex, fragmented and marketised. Increased government control over what pre-service teachers learn during their initial training phase has resulted in a centralised teacher training curriculum which is both reductionist and situates teachers as technicians. Universities have always played a distinctive role in teacher education, but the marketisation of the sector in recent years has led to a de-professionalisation and re-professionalisation of university teacher educators. The disappearance of universities from teacher training policy discourse and the tightening of government control over what is taught to pre-service teachers reflects a lack of trust in the university teacher education sector.
Given this aggressive policy context, it is not surprising that some higher education institutions in England have withdrawn their teacher education courses. Courses which were once the ‘bread and butter’ of many institutions are now viewed as a reputational risk. Inspection regimes seek to enforce the government prescribed curriculum and there are heavy penalties that are imposed on institutions where the prescribed curriculum is not being delivered in its entirety or where it is not being taught in sufficient depth. The government curriculum is reductionist and produces teachers as technicians who believe in and can implement the prescribed approaches.
This thesis presents 13 published papers. Implications to support the development of an alternative teacher education curriculum are drawn from the findings. The findings of the papers demonstrate that matters of inclusion and social justice need to be given greater emphasis in teacher education to enable pre-service teachers to respond to the professional challenges that they will face in classrooms. Key broad themes drawn from the papers include teacher identity, social justice and inclusion as critical components of a teacher education curriculum. These themes are used to develop a proposed curriculum framework for initial teacher education, which aims to situate teachers as critical thinkers who can challenge government policy, advance equality and prioritise both their own mental health and the mental health of their students. In addition, a framework for a mentor curriculum is also proposed to support the implementation of the teacher education curriculum in schools
Scalable Learning of Bayesian Networks Using Feedback Arc Set-Based Heuristics
Bayesianske nettverk er en viktig klasse av probabilistiske grafiske modeller. De består av en struktur (en rettet asyklisk graf) som beskriver betingede uavhengighet mellom stokastiske variabler og deres parametere (lokale sannsynlighetsfordelinger). Med andre ord er Bayesianske nettverk generative modeller som beskriver simultanfordelingene på en kompakt form.
Den største utfordringen med å lære et Bayesiansk nettverk skyldes selve strukturen, og på grunn av den kombinatoriske karakteren til asyklisitetsegenskapen er det ingen overraskelse at strukturlæringsproblemet generelt er NP-hardt. Det eksisterer algoritmer som løser dette problemet eksakt: dynamisk programmering og heltalls lineær programmering er de viktigste kandidatene når man ønsker å finne strukturen til små til mellomstore Bayesianske nettverk fra data. På den annen side er heuristikk som bakkeklatringsvarianter ofte brukt når man forsøker å lære strukturen til større nettverk med tusenvis av variabler, selv om disse heuristikkene vanligvis ikke har teoretiske garantier og ytelsen i praksis kan bli uforutsigbar når man arbeider med storskala læring.
Denne oppgaven tar for seg utvikling av skalerbare metoder som takler det strukturlæringsproblemet av Bayesianske nettverk, samtidig som det forsøkes å opprettholde et nivå av teoretisk kontroll. Dette ble oppnådd ved bruk av relaterte kombinatoriske problemer, nemlig det maksimale asykliske subgrafproblemet (maximum acyclic subgraph) og det duale problemet (feedback arc set). Selv om disse problemene er NP-harde i seg selv, er de betydelig mer håndterbare i praksis. Denne oppgaven utforsker måter å kartlegge Bayesiansk nettverksstrukturlæring til maksimale asykliske subgrafforekomster og trekke ut omtrentlige løsninger for det første problemet, basert på løsninger oppnådd for det andre.
Vår forskning tyder på at selv om økt skalerbarhet kan oppnås på denne måten, er det adskillig mer utfordrende å opprettholde den teoretisk forståelsen med denne tilnærmingen. Videre fant vi ut at å lære strukturen til Bayesianske nettverk basert på maksimal asyklisk subgraf kanskje ikke er den beste metoden generelt, men vi identifiserte en kontekst - lineære strukturelle ligningsmodeller - der vi eksperimentelt kunne validere fordelene med denne tilnærmingen, som fører til rask og skalerbar identifisering av strukturen og med mulighet til å lære komplekse strukturer på en måte som er konkurransedyktig med moderne metoder.Bayesian networks form an important class of probabilistic graphical models. They consist of a structure (a directed acyclic graph) expressing conditional independencies among random variables, as well as parameters (local probability distributions). As such, Bayesian networks are generative models encoding joint probability distributions in a compact form.
The main difficulty in learning a Bayesian network comes from the structure itself, owing to the combinatorial nature of the acyclicity property; it is well known and does not come as a surprise that the structure learning problem is NP-hard in general. Exact algorithms solving this problem exist: dynamic programming and integer linear programming are prime contenders when one seeks to recover the structure of small-to-medium sized Bayesian networks from data. On the other hand, heuristics such as hill climbing variants are commonly used when attempting to approximately learn the structure of larger networks with thousands of variables, although these heuristics typically lack theoretical guarantees and their performance in practice may become unreliable when dealing with large scale learning.
This thesis is concerned with the development of scalable methods tackling the Bayesian network structure learning problem, while attempting to maintain a level of theoretical control. This was achieved via the use of related combinatorial problems, namely the maximum acyclic subgraph problem and its dual problem the minimum feedback arc set problem. Although these problems are NP-hard themselves, they exhibit significantly better tractability in practice. This thesis explores ways to map Bayesian network structure learning into maximum acyclic subgraph instances and extract approximate solutions for the first problem, based on the solutions obtained for the second.
Our research suggests that although increased scalability can be achieved this way, maintaining theoretical understanding based on this approach is much more challenging. Furthermore, we found that learning the structure of Bayesian networks based on maximum acyclic subgraph/minimum feedback arc set may not be the go-to method in general, but we identified a setting - linear structural equation models - in which we could experimentally validate the benefits of this approach, leading to fast and scalable structure recovery with the ability to learn complex structures in a competitive way compared to state-of-the-art baselines.Doktorgradsavhandlin
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