Bad News for Chordal Partitions

Reed and Seymour [1998] asked whether every graph has a partition into induced connected non-empty bipartite subgraphs such that the quotient graph is chordal. If true, this would have significant ramifications for Hadwiger's Conjecture. We prove that the answer is `no'. In fact, we show that the answer is still `no' for several relaxations of the question

Highly parallel sparse Cholesky factorization

Several fine grained parallel algorithms were developed and compared to compute the Cholesky factorization of a sparse matrix. The experimental implementations are on the Connection Machine, a distributed memory SIMD machine whose programming model conceptually supplies one processor per data element. In contrast to special purpose algorithms in which the matrix structure conforms to the connection structure of the machine, the focus is on matrices with arbitrary sparsity structure. The most promising algorithm is one whose inner loop performs several dense factorizations simultaneously on a 2-D grid of processors. Virtually any massively parallel dense factorization algorithm can be used as the key subroutine. The sparse code attains execution rates comparable to those of the dense subroutine. Although at present architectural limitations prevent the dense factorization from realizing its potential efficiency, it is concluded that a regular data parallel architecture can be used efficiently to solve arbitrarily structured sparse problems. A performance model is also presented and it is used to analyze the algorithms

Engine Structures Analysis Software: Component Specific Modeling (COSMO)

A component specific modeling software program has been developed for propulsion systems. This expert program is capable of formulating the component geometry as finite element meshes for structural analysis which, in the future, can be spun off as NURB geometry for manufacturing. COSMO currently has geometry recipes for combustors, turbine blades, vanes, and disks. Component geometry recipes for nozzles, inlets, frames, shafts, and ducts are being added. COSMO uses component recipes that work through neutral files with the Technology Benefit Estimator (T/BEST) program which provides the necessary base parameters and loadings. This report contains the users manual for combustors, turbine blades, vanes, and disks

Product structure of graph classes with bounded treewidth

We show that many graphs with bounded treewidth can be described as subgraphs of the strong product of a graph with smaller treewidth and a bounded-size complete graph. To this end, define the "underlying treewidth" of a graph class $\mathcal{G}$ to be the minimum non-negative integer $c$ such that, for some function $f$, for every graph ${G \in \mathcal{G}}$ there is a graph $H$ with ${\text{tw}(H) \leq c}$ such that $G$ is isomorphic to a subgraph of ${H \boxtimes K_{f(\text{tw}(G))}}$. We introduce disjointed coverings of graphs and show they determine the underlying treewidth of any graph class. Using this result, we prove that the class of planar graphs has underlying treewidth 3; the class of $K_{s,t}$-minor-free graphs has underlying treewidth $s$ (for ${t \geq \max\{s,3\}}$); and the class of $K_t$-minor-free graphs has underlying treewidth ${t-2}$. In general, we prove that a monotone class has bounded underlying treewidth if and only if it excludes some fixed topological minor. We also study the underlying treewidth of graph classes defined by an excluded subgraph or excluded induced subgraph. We show that the class of graphs with no $H$ subgraph has bounded underlying treewidth if and only if every component of $H$ is a subdivided star, and that the class of graphs with no induced $H$ subgraph has bounded underlying treewidth if and only if every component of $H$ is a star

Exploring the topical structure of short text through probability models : from tasks to fundamentals

Recent technological advances have radically changed the way we communicate. Today’s communication has become ubiquitous and it has fostered the need for information that is easier to create, spread and consume. As a consequence, we have experienced the shortening of text messages in mediums ranging from electronic mailing, instant messaging to microblogging. Moreover, the ubiquity and fast-paced nature of these mediums have promoted their use for unthinkable tasks. For instance, reporting real-world events was classically carried out by news reporters, but, nowadays, most interesting events are first disclosed on social networks like Twitter by eyewitness through short text messages. As a result, the exploitation of the thematic content in short text has captured the interest of both research and industry. Topic models are a type of probability models that have traditionally been used to explore this thematic content, a.k.a. topics, in regular text. Most popular topic models fall into the sub-class of LVMs (Latent Variable Models), which include several latent variables at the corpus, document and word levels to summarise the topics at each level. However, classical LVM-based topic models struggle to learn semantically meaningful topics in short text because the lack of co-occurring words within a document hampers the estimation of the local latent variables at the document level. To overcome this limitation, pooling and hierarchical Bayesian strategies that leverage on contextual information have been essential to improve the quality of topics in short text. In this thesis, we study the problem of learning semantically meaningful and predictive representations of text in two distinct phases: • In the first phase, Part I, we investigate the use of LVM-based topic models for the specific task of event detection in Twitter. In this situation, the use of contextual information to pool tweets together comes naturally. Thus, we first extend an existing clustering algorithm for event detection to use the topics learned from pooled tweets. Then, we propose a probability model that integrates topic modelling and clustering to enable the flow of information between both components. • In the second phase, Part II and Part III, we challenge the use of local latent variables in LVMs, specially when the context of short messages is not available. First of all, we study the evaluation of the generalization capabilities of LVMs like PFA (Poisson Factor Analysis) and propose unbiased estimation methods to approximate it. With the most accurate method, we compare the generalization of chordal models without latent variables to that of PFA topic models in short and regular text collections. In summary, we demonstrate that by integrating clustering and topic modelling, the performance of event detection techniques in Twitter is improved due to the interaction between both components. Moreover, we develop several unbiased likelihood estimation methods for assessing the generalization of PFA and we empirically validate their accuracy in different document collections. Finally, we show that we can learn chordal models without latent variables in text through Chordalysis, and that they can be a competitive alternative to classical topic models, specially in short text.Els avenços tecnològics han canviat radicalment la forma que ens comuniquem. Avui en dia, la comunicació és ubiqua, la qual cosa fomenta l’ús de informació fàcil de crear, difondre i consumir. Com a resultat, hem experimentat l’escurçament dels missatges de text en diferents medis de comunicació, des del correu electrònic, a la missatgeria instantània, al microblogging. A més de la ubiqüitat, la naturalesa accelerada d’aquests medis ha promogut el seu ús per tasques fins ara inimaginables. Per exemple, el relat d’esdeveniments era clàssicament dut a terme per periodistes a peu de carrer, però, en l’actualitat, el successos més interessants es publiquen directament en xarxes socials com Twitter a través de missatges curts. Conseqüentment, l’explotació de la informació temàtica del text curt ha atret l'interès tant de la recerca com de la indústria. Els models temàtics (o topic models) són un tipus de models de probabilitat que tradicionalment s’han utilitzat per explotar la informació temàtica en documents de text. Els models més populars pertanyen al subgrup de models amb variables latents, els quals incorporen varies variables a nivell de corpus, document i paraula amb la finalitat de descriure el contingut temàtic a cada nivell. Tanmateix, aquests models tenen dificultats per aprendre la semàntica en documents curts degut a la manca de coocurrència en les paraules d’un mateix document, la qual cosa impedeix una correcta estimació de les variables locals. Per tal de solucionar aquesta limitació, l’agregació de missatges segons el context i l’ús d’estratègies jeràrquiques Bayesianes són essencials per millorar la qualitat dels temes apresos. En aquesta tesi, estudiem en dos fases el problema d’aprenentatge d’estructures semàntiques i predictives en documents de text: En la primera fase, Part I, investiguem l’ús de models temàtics amb variables latents per la detecció d’esdeveniments a Twitter. En aquest escenari, l’ús del context per agregar tweets sorgeix de forma natural. Per això, primer estenem un algorisme de clustering per detectar esdeveniments a partir dels temes apresos en els tweets agregats. I seguidament, proposem un nou model de probabilitat que integra el model temàtic i el de clustering per tal que la informació flueixi entre ambdós components. En la segona fase, Part II i Part III, qüestionem l’ús de variables latents locals en models per a text curt sense context. Primer de tot, estudiem com avaluar la capacitat de generalització d’un model amb variables latents com el PFA (Poisson Factor Analysis) a través del càlcul de la likelihood. Atès que aquest càlcul és computacionalment intractable, proposem diferents mètodes d estimació. Amb el mètode més acurat, comparem la generalització de models chordals sense variables latents amb la del models PFA, tant en text curt com estàndard. En resum, demostrem que integrant clustering i models temàtics, el rendiment de les tècniques de detecció d’esdeveniments a Twitter millora degut a la interacció entre ambdós components. A més a més, desenvolupem diferents mètodes d’estimació per avaluar la capacitat generalizadora dels models PFA i validem empíricament la seva exactitud en diverses col·leccions de text. Finalment, mostrem que podem aprendre models chordals sense variables latents en text a través de Chordalysis i que aquests models poden ser una bona alternativa als models temàtics clàssics, especialment en text curt.Postprint (published version

On the topology Of network fine structures

Multi-relational dynamics are ubiquitous in many complex systems like transportations, social and biological. This thesis studies the two mathematical objects that encapsulate these relationships --- multiplexes and interval graphs. The former is the modern outlook in Network Science to generalize the edges in graphs while the latter was popularized during the 1960s in Graph Theory. Although multiplexes and interval graphs are nearly 50 years apart, their motivations are similar and it is worthwhile to investigate their structural connections and properties. This thesis look into these mathematical objects and presents their connections. For example we will look at the community structures in multiplexes and learn how unstable the detection algorithms are. This can lead researchers to the wrong conclusions. Thus it is important to get formalism precise and this thesis shows that the complexity of interval graphs is an indicator to the precision. However this measure of complexity is a computational hard problem in Graph Theory and in turn we use a heuristic strategy from Network Science to tackle the problem. One of the main contributions of this thesis is the compilation of the disparate literature on these mathematical objects. The novelty of this contribution is in using the statistical tools from population biology to deduce the completeness of this thesis's bibliography. It can also be used as a framework for researchers to quantify the comprehensiveness of their preliminary investigations. From the large body of multiplex research, the thesis focuses on the statistical properties of the projection of multiplexes (the reduction of multi-relational system to a single relationship network). It is important as projection is always used as the baseline for many relevant algorithms and its topology is insightful to understand the dynamics of the system.Open Acces

Nexus Portfolio for Snare Drum: Performance Practice and Historical Perspective

The literature for solo snare drumming has grown out of the strictly rudimental style and is now influenced by any number of traditional or modern techniques and styles. This requires the performer to be not only a master of rudimental and orchestral snare drum techniques, but to also be very familiar with world musical styles and to be open to new musical ideas being presented on the snare drum.The Nexus Portfolio for Snare Drum, containing five solo pieces for the snare drum, one by each member of the percussion ensemble Nexus, represents an excellent example of the variety of musical styles and technical requirements found in modern solo snare drum literature. Each solo is influenced by a different world musical style and reflects the interests and specialty of each individual composer. Additionally, the members of the group Nexus are considered by many to be some of the leading composers, performers and teachers of percussion and music for percussion, in the history of the art.The purpose of this lecture recital and research document is to prepare and perform the five snare dum solos in the Nexus Portfolio for Snare drum, focusing on the performance practice problems and a discussion of the compositional intent of the composers.The paper will delve into the background of the composers Bill Cahn, John Wyre, Robin Engelman, Bob Becker, and Russell Hartenberger, analysis of the five works, and comparison of the different styles of each solo. In addition, based on the analysis, performance problems inherent in each solo will be discussed and exercises to achieve maximum artistic expression will be included

Prehistoric dwelling : circular structures in north and central Britain c 2500 BC - AD 500

EThOS - Electronic Theses Online ServiceGBUnited Kingdo