Agreement graphs and data dependencies

The problem of deciding whether a join dependency [R] and a set F of functional dependencies logically imply an embedded join dependency [S] is known to be NP-complete. It is shown that if the set F of functional dependencies is required to be embedded in R, the problem can be decided in polynomial time. The problem is approached by introducing agreement graphs, a type of graph structure which helps expose the combinatorial structure of dependency implication problems. Agreement graphs provide an alternative formalism to tableaus and extend the application of graph and hypergraph theory in relational database research;Agreement graphs are also given a more abstract definition and are used to define agreement graph dependencies (AGDs). It is shown that AGDs are equivalent to Fagin\u27s (unirelational) embedded implicational dependencies. A decision method is given for the AGD implication problem. Although the implication problem for AGDs is undecidable, the decision method works in many cases and lends insight into dependency implication. A number of properties of agreement graph dependencies are given and directions for future research are suggested

Cyclability: Combinatorial Properties, Algorithms and Complexity

Ένα γράφημα G καλείται k-κυκλώσιμο, αν για κάθε k από τις κορυφές του υπάρχει ένας κύκλος στο G που τις περιέχει. Η κυκλωσιμότητα ενός γραφήματος G είναι ο μέγιστος ακέραιος k για τον οποίο το G είναι k-κυκλώσιμο και είναι μία παράμετρος που σχετίζεται με τη συνεκτικότητα. Σε αυτή τη διδακτορική διατριβή μελετάμε, κυρίως από τη σκοπιά της Παραμετρικής Πολυπλοκότητας, το πρόβλημα ΚΥΚΛΩΣΙΜΟΤΗΤΑ: Δεδομένου ενός γραφήματος G = (V,E) και ενός μη αρνητικού ακεραίου k (η παράμετρος), να αποφασιστεί αν η κυκλωσιμότητα του G είναι ίση με k. Το πρώτο μας αποτέλεσμα είναι αρνητικό και δείχνει ότι η ύπαρξη ενός FPT-αλγορίθμου για την επίλυση του προβλήματος ΚΥΚΛΩΣΙΜΟΤΗΤΑ είναι απίθανη (εκτός αν FPT = co- W[1], το οποίο θεωρείται απίθανο). Πιο συγκεκριμένα, αποδεικνύουμε ότι το πρόβλημα ΚΥΚΛΩΣΙΜΟΤΗΤΑ είναι co-W[1]-δύσκολο, ακόμα και αν περιορίσουμε την είσοδο στο να είναι χωριζόμενο γράφημα. Από την άλλη, δίνουμε έναν FPT-αλγόριθμο για το ίδιο πρόβλημα περιορισμένο στην κλάση των επίπεδων γραφημάτων. Για να το πετύχουμε αυτό αποδεικνύουμε μια σειρά από συνδυαστικά αποτελέσματα σχετικά με την κυκλωσιμότητα και εφαρμόζουμε μια εκδοχή δύο βημάτων της περίφημης τεχνικής της άσχετης κορυφής, που εισήχθη από τους Robertson και Seymour στη σειρά εργασιών τους για Ελλάσονα Γραφήματα, ως ένα κρίσιμο συστατικό του αλγορίθμου τους για την επίλυση του προβλήματος των ΔΙΑΚΕΚΡΙΜΕΝΩΝ ΜΟΝΟΠΑΤΙΩΝ. Για να αποδείξουμε την ορθότητα του αλγορίθμου μας εισάγουμε έννοιες, όπως αυτή των ζωτικών κυκλικών συνδέσμων, και αποδεικνύουμε αποτελέσματα με ανεξάρτητου γραφοθεωρητικού ενδιαφέροντος. Κλείνουμε τη μελέτη μας με ένα δεύτερο αρνητικό αποτέλεσμα: Αποδεικνύουμε ότι για το πρόβλημα της ΚΥΚΛΩΣΙΜΟΤΗΤΑΣ δεν υπάρχουν πολυωνυμικοί πυρήνες, ακόμα και αν περιοριστούμε σε κυβικά επίπεδα γραφήματα, εκτός και αν δεν ισχύει μια υπόθεση της κλασσικής Θεωρίας Πολυπλοκότητας (ότι NP υποσύνολο του co-NP/poly).A graph G is called k-cyclable, if for every k of its vertices there exists a cycle in G that contains them. The cyclability of G is the maximum integer k for which G is k-cyclable and it is a connectivity related graph parameter. In this doctoral thesis we study, mainly from the Parameterized Complexity point of view, the Cyclability problem: Given a graph G = (V,E) and an integer k (the parameter), decide whether the cyclability of G is equal to k. Our first result is a negative one and shows that the existence of an FPT-algorithm for solving Cyclability is unlikely (unless FPT = co-W[1], which is considered unlikely). More specifically, we prove that Cyclability is co-W[1]-hard, even if we restrict the input to be a split graph. On the other hand, we give an FPT-algorithm for the same problem when restricted to the class of planar graphs. To do this, we prove a series of combinatorial results regarding cyclability and apply a two-step version of the so called irrelevant vertex technique, which was introduced by Robertson and Seymour in their Graph Minors series (Irrelevant vertices in linkage problems) as a crucial ingredient for their algorithm solving the Disjoint Paths problem. To prove the correctness of our algorithm, we introduce notions, like the one of vital cyclic linkages, and give results of independent graph-theoretic interest. We conclude our study with a negative result: We prove that Cyclability admits no polynomial kernel, even when restricted to cubic planar graphs, unless a classical complexity theoretic assumption (that NP is a subset of co-NP/poly) fails

The Victorian Newsletter (Spring 1988)

The Victorian Newsletter is sponsored for the Victorian Group of Modern Language Association by the Western Kentucky University and is published twice annually.Inventing Victorians: Virginia Woolf's "Memoirs of a Novelist" / Mary Kaiser Loges -- Distortion Versus Revaluation: Three Twentieth-Century Responses to Victorian Fiction / Jerome Meckier -- The Dover Bitch: Victorian Duck or Modernist Duck/Rabbit / Gerhard Joseph -- Carlyle's Denial of Axiological Content in Science / Charles W. Schaefer -- Mixed Metaphor, Mixed Gender: Swinburne and the Victorian Critics / Thaïs E. Morgan -- The Humanities Tradition of Matthew Arnold / William E. Buckler -- Oliver (Un)Twisted: Narrative Strategies in Oliver Twist / Joseph Sawicki -- Representation and Homophobia in The Picture of Dorian Gray / Richard Dellamora -- Coming In The Victorian Newsletter -- Books Receive

Constructive Perspectives on Inductive Logic

Constructive (intuitionist, anti-realist) semantics has thus far been lacking an adequate concept of truth in infinity concerning factual (i.e., empirical, non-mathematical) sentences. One consequence of this problem is the difficulty of incorporating inductive reasoning in constructive semantics. It is not possible to formulate a notion for probable truth in infinity if there is no adequate notion of what truth in infinity is. One needs a notion of a constructive possible world based on sensory experience. Moreover, a constructive probability measure must be defined over these constructively possible empirical worlds. This study defines a particular kind of approach to the concept of truth in infinity for Rudolf Carnap's inductive logic. The new approach is based on truth in the consecutive finite domains of individuals. This concept will be given a constructive interpretation. What can be verifiably said about an empirical statement with respect to this concept of truth, will be explained, for which purpose a constructive notion of epistemic probability will be introduced. The aim of this study is also to improve Carnap's inductive logic. The study addresses the problem of justifying the use of an "inductivist" method in Carnap's lambda-continuum. A correction rule for adjusting the inductive method itself in the course of obtaining evidence will be introduced. Together with the constructive interpretation of probability, the correction rule yields positive prior probabilities for universal generalizations in infinite domains.Työssä tutkitaan havaintoja koskevien väitelauseiden totuutta tilanteissa, joissa havaintojen määrällä ei ainakaan tiedetysti ole ylärajaa. Filosofian ja matematiikan alaan kuuluvassa konstruktiivisessa semantiikassa eli merkitysteoriassa lauseiden merkitys määräytyy niiden todennettavuusehtojen perusteella. Äärettömän havaintomaailman tapauksessa todennettavuusehto on hankalasti muotoiltavissa, koska tällaista maailmaa koskevia yleistyksiä ei yleisessä tapauksessa voi todentaa. Tämä on yhteydessä myös induktion ongelmaan, joka koskee päättelyä menneisyyden havainnoista tulevaisuuteen. Induktiivinen päättely ei säilytä totuutta siinä mielessä, että tosista oletuksista tehtävä johtopäätös ei ole tosi loogisella välttämättömyydellä, vaan korkeintaan todennäköisesti tosi. Työssä esitetään Rudolf Carnapin (1891-1970) induktiivisen logiikan sovelluksena, kuinka äärettömiä havaintomaailmoja koskevien lauseiden totuus voidaan muotoilla konstruktiivisten periaatteiden mukaisesti. Kukin ääretön havaintoprosessi on vapaalakinen jono peräkkäisiä havaintoja, joiden muodostaman kokonaisuuden ominaisuuksia ei voida tietää prosessin äärellisissä vaiheissa. Voidaan kuitenkin tietää, vastaako prosessin annettu äärellinen vaihe jonkin ennalta määritellyn havaintojonon äärellistä vaihetta. Näin voidaan määrittää lauseen konstruktiivinen todennäköisyys äärettömille havaintojonoille: se on niiden ennalta määrättyjen havaintojonojen äärellisten vaiheiden todennäköisyyksien raja-arvo, jotka toteuttavat lauseen kussakin äärellisessä vaiheessaan tietystä vaiheesta alkaen. Tämän todennäköisyyskäsitteen ominaisuuksia tutkitaan suhteessa Carnapin esittämään asymptoottisen todennäköisyyden käsitteeseen. Lisäksi työssä tutkitaan mahdollisuutta määrittää todennäköisyys äärettömyydessä eräänlaisten havaintojonojen joukkojen eli ympäristöjen avulla. Tämän todetaan olevan ristiriidassa sen kanssa, että havaintojonoja koskevat lauseet olisivat konstruktiivisesti tosia äärettömyydessä. Induktiivisessa logiikassa lauseiden todennäköisyys määräytyy ns. induktiivisen menetelmän avulla laskettujen todennäköisyyksien mukaan. Ongelma on, että annettuun tilanteeseen parhaiten soveltuvaa induktiivsta menetelmää ei tiedetä. Etenkään ei tiedetä, onko sellainen induktiivinen menetelmä kaikkein paras, joka ei anna lainkaan painoarvoa havaitulle evidenssille esimerkiksi siten että sata havaittua mustaa korppia lisäisi 101. mustan korpin todennäköisyyttä. Työssä käsitellään myös oikean induktiivisten menetelmän valitsemisen ongelmaa ja päädytään siihen, että toisen kertaluvun todennäköisyydet eivät tarjoa tähän ratkaisua. Sen sijaan induktiivisen menetelmän itsensä päivitys annetun evidenssin nojalla tuottaa tietyin reunaehdoin annettua menetelmää paremman induktiivisen menetelmän. Toisin kuin Carnapin alkuperäisessä järjestelmässä, induktiivisen menetelmän päivitys ja konstruktiivinen semantiikka yhdessä mahdollistavat nollasta poikkeavat todennäköisyydet empiirisille yleistyksille (kuten kaikki korpit ovat mustia )

Computational aspects of knots and knot transformation

In this thesis we study the computational aspects of knots and knot trans- formations. Most of the problems of recognising knot properties (such as planarity, unknottedness, equivalence) are known to be decidable, however for many problems their precise time or space complexity is still unknown. On the other hand, their complexity in terms of computational power of devices needed to recognise the knot properties was not studied yet. In this thesis we address this problem and provide first known bounds for some knot problems within this context. In order to estimate and characterise complexity of knot problems represented by Gauss words, we consider vari- ous tools and mathematical models including automata models over infinite alphabets, standard computational models and definability in logic. In particular we show that the planarity problem of signed and unsigned Gauss words can be recognised by a two-way deterministic register au- tomata. Then we translate this result in terms of classical computational models to show that these problems belong to the log-space complexity class L, Further we consider definability questions in terms of first order logic and its extensions and show that planarity of both signed and unsigned Gauss words cannot be expressed by a formula of first-order predicate logic, while extensions of first-order logic with deterministic transitive closure operator allow to define planarity of both signed unsigned Gauss words. Follow- ing the same line of research we provide lower and upper bounds for the planarity problem of Gauss paragraphs and unknottedness. In addition we consider knot transformations in terms of string rewriting systems and provide a refined classification of Reidemeister moves formu- lated as string rewriting rules for Gauss words. Then we analyse the reach- ability properties for each type and present some bounds on the complexity of the paths between two knot diagrams reachable by a sequence of moves of the same type. Further we consider a class of non-isomorphic knot diagrams generated by type I moves from the unknot and discover that the sequence corresponding to the number of diagrams with respect to the number of crossings is equal to a sequence related to a class of Eulerian maps with respect to the number of edges. We then investigate the bijective mapping between the two classes of objects and as a result we present two algo- rithms to demonstrate the transformations from one object to the other. It is known that unknotting a knot may lead to a significant increase in number of crossings during the transformations. We consider the question of designing a set of rules that would not lead to the increase in the number of crossings during knot transformations. In particular we introduce a new set moves in this regard which can be used to substitute one of the rules of type II that increases the number of crossings. We show that such new moves coupled with Reidemeister moves can unknot all known examples of complex trivial knot diagrams without increasing number of crossings

An exploration into what works in effectively engaging young adult offenders in probation supervision: practitioners and probationers perspectives

This research explores how probation practitioners might better engage young adult offenders in order to help prevent them from re-offending. While male adults between 18 and 25 comprise around 10% of the population in England and Wales, they account for up to 40% of UK crime (House of Common Justice Committee, 2018). Evidence shows that rehabilitative interventions, rather than punishment, are generally more effective in helping offenders (including young offenders) desist from crime (Chan, 1995; Jones, & Weatherburn, 2011; MacKenzie, 2002; Monarski, 1987; Productivity Commission, 2011; Nagin et al. 2009; Weston, 2016; Nagin, D.S., Piquero, Scott, & Steinberg, 2006). Young offenders who are meaningfully engaged by probation practitioners, and who actively participate in appropriate behaviour-modification interventions, are more likely to achieve long-term positive change (Henry, Henaghan, Sanders, & Munford,2015; MOJ, 2019b: Prior, & Mason, 2010). As a significant proportion of young adult male offenders are subject to probation supervision, it would help if more positive forms of intervention for probation officers were developed. This research comprised two qualitative studies involving 15 male offenders and 15 probation officers, focusing on participants’ experiences and their perspectives on what constitutes effective engagement between young adult offenders and probation practitioners. Interviews were semi-structured and were carried out both individually and face to face. Data was transcribed verbatim and subjected to thematic analysis (Braun & Clarke, 2006, 2013). Main themes included the importance of probation officers having in-depth knowledge about offenders as individuals, being able to communicate with them, being effective motivators, and being trustworthy. Probation officers emphasised the importance of collaboratively engaging with young offenders’ families and situations, and both groups highlighted officers’ personal characteristics. Trauma was a significant issue for both groups, with officers noting the lack of information and training in this area. Practice implications and proposals are discussed, and recommendations for further research in this area of work are considered