On the Complexity of Exact Pattern Matching in Graphs: Binary Strings and Bounded Degree

Exact pattern matching in labeled graphs is the problem of searching paths of a graph $G=(V,E)$ that spell the same string as the pattern $P[1..m]$. This basic problem can be found at the heart of more complex operations on variation graphs in computational biology, of query operations in graph databases, and of analysis operations in heterogeneous networks, where the nodes of some paths must match a sequence of labels or types. We describe a simple conditional lower bound that, for any constant $\epsilon>0$, an $O(|E|^{1 - \epsilon} \, m)$-time or an $O(|E| \, m^{1 - \epsilon})$-time algorithm for exact pattern matching on graphs, with node labels and patterns drawn from a binary alphabet, cannot be achieved unless the Strong Exponential Time Hypothesis (SETH) is false. The result holds even if restricted to undirected graphs of maximum degree three or directed acyclic graphs of maximum sum of indegree and outdegree three. Although a conditional lower bound of this kind can be somehow derived from previous results (Backurs and Indyk, FOCS'16), we give a direct reduction from SETH for dissemination purposes, as the result might interest researchers from several areas, such as computational biology, graph database, and graph mining, as mentioned before. Indeed, as approximate pattern matching on graphs can be solved in $O(|E|\,m)$ time, exact and approximate matching are thus equally hard (quadratic time) on graphs under the SETH assumption. In comparison, the same problems restricted to strings have linear time vs quadratic time solutions, respectively, where the latter ones have a matching SETH lower bound on computing the edit distance of two strings (Backurs and Indyk, STOC'15).Comment: Using Lemma 12 and Lemma 13 might to be enough to prove Lemma 14. However, the proof of Lemma 14 is correct if you assume that the graph used in the reduction is a DAG. Hence, since the problem is already quadratic for a DAG and a binary alphabet, it has to be quadratic also for a general graph and a binary alphabe

Ala- ja ylärajoja merkkijonon etsinnälle verkosta

String Matching in Labelled Graphs (SMLG) is a generalisation of the classic problem of finding a match for a string into a text. In SMLG, we are given a pattern string and a graph with node labels, and we want to find a path whose node labels match the pattern string. This problem has been studied since 1992, and it was initially intended to model the problem of finding a link in a hypertext. Recently, the problem received attention due to its applications in bioinformatics, but all of the solutions, old and new, failed to run in truly sub-quadratic time. In this work, based on four published papers, we study SMLG from different angles, first proving conditional lower bounds, and then proposing efficient algorithms for special classes of graphs. In the first paper, we unveil the reason behind the hardness of SMLG, showing a quadratic conditional lower bound based on the Orthogonal Vectors Hypothesis and the Strong Exponential Time Hypothesis. The techniques that we employ come from the fine-grained complexity, and involve finding linear-time reductions from the Orthogonal Vectors problem to different variations of SMLG. In the second paper, we strengthen our findings by showing that an indexing data structure built in polynomial time is not enough to provide subquadratic time queries for SMLG. We devise a general framework for obtaining indexing lower bounds out of regular lower bounds, and we prove the indexing lower bound for SMLG as an application of this technique. In the third paper, we surpass the limitations of our lower bounds by identifying a class of graphs, called founder block graphs, which support linear time queries after subquadratic indexing. This class of graph effectively represents collections of strings called multiple sequence alignments, if gap characters are not present. In the fourth paper, we significantly improve our previous results on efficiently indexable graphs. We propose elastic founder graphs, a superset of founder block graphs, that are able to represent multiple sequence alignments with gaps. Moreover, we propose algorithms for constructing elastic founder graph, indexing them, and perform queries in linear time.Merkkijonon etsintä verkosta (engl. String Matching in Labelled Graphs, SMLG) on yleistys klassiselle ongelmalle etsiä merkkijonohahmon osumaa tekstistä. SMLG ongelmassa syötteenä ovat merkkijonohahmo ja verkko, jonka solmuilla on merkkijonotunnisteet. Tavoitteena on löytää polku, jonka solmujen tunnisteet muodostavat tekstin, joka sisältää annetun merkkijonohahmon. Ongelmaa on tutkittu vuodesta 1992 alun alkaen mallintamaan linkkien etsintää hypertekstistä. Viime aikoina ongelma on tullut uudestaan esille bioinformatiikan saralla. Sekä vanhat että uudet ratkaisut eivät ole onnistuneet oleellisesti murtamaan neliöllistä aikavaativuutta ongelman ratkaisussa. Tässä työssä SMLG ongelmaa tarkastellaan eri näkökulmista perustuen neljään julkaisuun. Ensin todistetaan ehdollinen alaraja ongelman vaativuudelle. Sitten esitetään tehokkaita ratkaisuja erilaisille verkkojen aliluokille. Ensimmäisessä julkaisussa paljastamme syyn SMLG ongelman vaikeudelle johtamalla ehdollisen alarajan perustuen kohtisuorien vektorien hypoteesiin (engl. Orthogonal Vectors Hypothesis) ja vahvaan eksponentiaalisen aikavaativuuden hypoteesiin (engl. Strong Exponential Time Hypothesis). Tähän tulokseen käytämme hienorakenteisen vaativuusteorian (engl. fine-grained complexity) tekniikoita, kuten lineaariaikaista reduktiota kohtisuorien vektoreiden ongelmasta kohdeongelmaan, tässä tapauksessa eri variaatioille SMLG ongelmasta. Toisessa julkaisussa vahvistamme edellistä tulosta osoittamalla, että polynomiaikainen verkon indeksointi ei riitä tukemaan alle neliöaikaista merkkijonohahmon etsintää. Kehitämme yleisen kehikon tämän kaltaisten indeksointialarajojen johtamiseen tavallisista alarajoista, ja todistamme SMLG ongelman alarajan sovellutuksena tästä tekniikasta. Kolmannessa julkaisussa ohitamme alarajat identifioimalla verkkojen aliluokan, kantasegmentteihin perustuvat verkot (engl. founder block graphs), joilla indeksointi onnistuu alle neliöllisessä ajassa, jonka jälkeen merkkijonohahmon etsintää voidaan suorittaa lineaarisessa ajassa. Kantasegmentteihin perustuvilla verkoilla voidaan esittää merkkijonokokoelmien monilinjaukset, mikäli linjauksessa ei tarvita poistoja ja lisäyksiä. Neljännessä julkaisussa parannamme merkittävästi aiempia tuloksiamme indeksoitavista verkoista. Laajennamme kantasegmentteihin perustuvat verkot elastisuuden käsitteellä, jolloin ne voivat esittää mielivaltaisia monilinjauksia, joissa linjauksessa sallitaan poistot ja lisäykset. Tämän lisäksi johdamme algoritmeja näiden elastisten kantasegmentteihin perustuvien verkkojen muodostamiseen, indeksointiin, sekä merkkijonohahmojen etsintään

Utility of the HPT Framework for Improving Distance Education in Nigeria

The fusion of the Internet with instructional design, and curricula delivery methods eliminated transactional distance in online learning. However, distance education (DE) in Nigeria has not aligned its pedagogy to the new reality in technology. The purposes of this non-experimental, predictive, validity study were to determine faculty and administrators\u27 perceived barriers and concerns to online adoption and to validate the behavior engineering model (BEM) instrument. Ninety-six respondents from four public universities in Nigeria completed the questionnaires. Descriptive statistics and structural equation modeling (SEM) were used respectively, to assess barriers and concerns militating against faculty and administrators\u27 online adoption, as well as validate the survey instruments. For faculty and administrators, incentive, motive, knowledge and skills influenced DE adoption. Except for age, all demographic factors influenced faculty\u27s concerns. Gender was observed to influence administrators\u27 concern. Level of online use influenced neither faculty nor administrators\u27 concerns. Technographic characteristics influenced faculty, but not administrators.\u27 Though the BEM instrument was reliable in measuring faculty and administrator\u27s stages of concern, however, the 6-factor BEM, tested at the 95% significant level, did not give a good fit. The study contributes to positive social change by identifying gaps to effective DE implementation, and recommended the appropriate interventions to transform the DE experience for students and their universities. The study also proposed the framework to fast track Nigeria\u27s vision and mission for DE

Diamine Oxidase: Kinetic Studies and Use in Organic Synthesis

The subject of this thesis is the enzyme diamine oxidase and four main topics are discussed: (1) oxidation of diamines using diamine oxidase; (2) inhibition of diamine oxidase; (3) stereochemistry and regiochemistry of the reactions catalysed by diamine oxidase; and (4) applications of diamine oxidase. (1) Oxidation of diamines using diamine oxidase. Diamine oxidase catalyses the oxidative deamination of diamines to their corresponding aminoaldehydes (Scheme A). H2N(CH2)nNH2 + H2O + O2 →Diamine Oxidase → H2N(CH2)n-1CHO + H2O2 + NH3 Scheme A n = 4 (i) n = 5 (ii) Putrescine (i) and cadaverine (ii) are the best substrates of diamine oxidase. A-Alkylputrescines and C-alkylcadaverines were synthesised and tested as substrates of diamine oxidase using an improved spectrophotometric assay. The assay involves the measurement of the hydrogen peroxide produced as a by-product of the enzymic reaction. From this assay Km and Vmax values were obtained for the oxidation of these substrates using diamine oxidase. The KM is a measure of the strength of the enzyme-substrate complex and determines the binding efficiency of the substrate to the enzyme. The Vmax is the maximal rate and is related to the turnover number of an enzyme. Analysis of these results provided information on the steric constraints of the active site. Also studied were a,w-diamines with chain lengths varying from two to twelve. Analysis of these results showed that the best binding (lowest KM value) was observed with diamines with chain lengths from five to seven and the highest Vmax value was obtained with cadaverine (ii) as the substrate (chain length five). These results suggest that formation of a cyclic diamine intermediate with the enzyme is essential for recognition and catalysis. (2) Inhibition of diamine oxidase. The oxidative deamination of diamines by diamine oxidase is a key step in polyamine metabolism. Polyamines are known to be essential for cell growth and replication. Inhibitors of the reaction catalysed by diamine oxidase should have a considerable effect on the polyamine metabolism and therefore on cell growth. Substrate analogues [eg 3,3-dimethylcadaverine (iii)] were examined as inhibitors of diamine oxidase. Compounds resembling substrates although with no primary amine groups present [eg 1,6-bis(A-piperidyl)hexane (iv)] were also tested as inhibitors. These tests were carried out using the same spectrophotometric assay as before. Most of the compounds did inhibit the diamine oxidase catalysed reaction and were shown to be competitive inhibitors. Ki values were obtained for the compounds tested as inhibitors. (3) Stereochemistry and regiochemistry of the reaction catalysed by diamine oxidase. The stereochemistry and regiochemistry of most enzymic reactions are controlled. As not a great deal is known about the stereochemistry or regiochemistry of the oxidative deamination of diamines catalysed by diamine oxidase studies were carried out to find out more. Analysis of the products of the reaction with C- alkylcadaverines was performed to determine any selectivity from the reactions. Isolation of the products was achieved by trapping the imines from the enzymic reaction using 3,4-dimethoxybenzoylacetic acid (v). The compounds examined for selectivity in the diamine oxidase catalysed oxidation were (a) 3-methylcadaverine; (b) 2-methylcadaverine; and (c) 3-phenylcadaverine. With the first two selectivity does occur although it is not yet clear if this is due to the enzyme catalysed reaction or the second reaction involving the coupling with the B-keto acid (v). Surprisingly, no product was obtained with 3-phenylcadaverine. (4) Applications of diamine oxidase. Enzymes can often be used to catalyse reactions which are difficult to carry out by other methods. The main advantages of using enzymes in synthesis are the mildness of the reaction conditions and also the possible control of the stereochemistry and regiochemistry. Diamine oxidase catalyses the oxidation of diamines to their corresponding aminoaldehydes for which there are no chemically convenient methods. Therefore the use of this enzyme in synthesis could be very favourable. The alkaloid, cryptopleurine (vi), has been synthesised using diamine oxidase in a key step. Cryptopleurine (vi) has known anti-cancer activity. Oxidation of cadaverine using diamine oxidase and subsequent coupling to 3,4-dimethoxybenzoylacetic acid (v) formed an intermediate in the synthesis of cryptopleurine (vi). Using C-alkylcadaverines and following the same procedure, a number of intermediate analogues of cryptopleurine were formed. These alkaloid analogues when made may also possess interesting biological activity. The pyrrolizidine alkaloid, trachelanthamidine (viii), was also synthesised using diamine oxidase. Oxidative deamination of homospermidine (vii) and subsequent reduction of the likely product, 1-formylpyrrolizidine produced the alkaloid (viii)

Equitable access to quality injury care; Equi-Injury project protocol for prioritizing interventions in four low- or middle-income countries : a mixed method study

Funding This research was funded by the NIHR (award number 133135) using UK aid from the UK Government to support global health research. The views expressed in this publication are those of the authors and not necessarily those of the NIHR or the UK governmentPeer reviewe

Working with words: Italian feminism and organization studies

Searching for a writing about organizations that is more real, relevant, and respondent, we propose to engage with Italian feminism of difference and the wealth of practices elaborated by small feminist groups and collectives, asso- ciated with it in the seventies. Currently undergoing a phase of rising interest, in Europe and North America, this strand of feminism—philosophically varied and complex—is characterized by the act of grounding theory in practice and articulating practices of political and personal trans- formation deeply anchored in society, yet outside in- stitutions. In this paper, we aim at presenting Italian feminism and more specifically introduce the main tenets of Italian feminism of difference (of the seventies) to organi- zation studies. We focus on a specific practice of Italian feminism of difference, namely the partire da sé (departing from oneself), prepared by the earlier practice of autoco- scienza (political consciousness‐raising). Resting particu- larly on the thinking of the philosopher Luisa Muraro, we frame the potential contribution of her theorizing the partire da sè practice in relation to existing organization research that is grounded in feminist stands

On the Complexity of String Matching for Graphs

Peer reviewe