The advent of the high-speed computer with its enormous storage capabilities enabled statisticians as well as researchers from the different topics of life sciences to apply mul tivariate statistical procedures to large data sets to explore ...
Author: Erhard Godehardt
Publisher: Springer Science & Business Media
The advent of the high-speed computer with its enormous storage capabilities enabled statisticians as well as researchers from the different topics of life sciences to apply mul tivariate statistical procedures to large data sets to explore their structures. More and more, methods of graphical representation and data analysis are used for investigations. These methods belong to a topic of growing popUlarity, known as "exploratory data analysis" or EDA. In many applications, there is reason to believe that a set of objects can be clus tered into subgroups that differ in meaningful ways. Extensive data sets, for example, are stored in clinical cancer registers. In large data sets like these, nobody would ex pect the objects to be homogeneous. The most commonly used terms for the class of procedures that seek to separate the component data into groups are "cluster analysis" or "numerical taxonomy". The origins of cluster analysis can be found in biology and anthropology at the beginning of the century. The first systematic investigations in cluster analysis are those of K. Pearson in 1894. The search for classifications or ty pologies of objects or persons, however, is indigenous not only to biology but to a wide variety of disciplines. Thus, in recent years, a growing interest in classification and related areas has taken place. Today, we see applications of cluster analysis not only to. biology but also to such diverse areas as psychology, regional analysis, marketing research, chemistry, archaeology and medicine.
The totality of these structural models aids in the collection as well as the interpretation of field data. The presentation is clear, precise and readily accessible to the nonmathematical reader.
Author: Per Hage
Publisher: Cambridge University Press
Category: Social Science
Hage and Harary present a comprehensive introduction to the use of graph theory in social and cultural anthropology. Using a wide range of empirical examples, the authors illustrate how graph theory can provide a language for expressing in a more exact fashion concepts and notions that can only be imperfectly rendered verbally. They show how graphs, digraphs and networks, together with their associated matrices and duality laws, facilitate the study of such diverse topics as mediation and power in exchange systems, reachability in social networks, efficiency in cognitive schemata, logic in kinship relations, and productivity in subsistence modes. The interaction between graphs and groups provides further means for the analysis of transformations in myths and permutations in symbolic systems. The totality of these structural models aids in the collection as well as the interpretation of field data. The presentation is clear, precise and readily accessible to the nonmathematical reader. It emphasizes the implicit presence of graph theory in much of anthropological thinking.
Abstract: "Structural equation modeling (SEM) has dominated causal analysis in the social and behavioral sciences since the 1960s.
Author: Judea Pearl
Category: Multivariate analysis
Abstract: "Structural equation modeling (SEM) has dominated causal analysis in the social and behavioral sciences since the 1960s. Currenly, many SEM practitioners are having difficulty articulating the causal content of SEM and are seeking foundational answers. Recent developments in the areas of graphical models and the logic of causality show potential for alleviating such difficulties and thus for revitalizing structural equations as the primary language of causal modeling. This paper summarizes several of these developments, including the prediction of vanishing partial correlations, model testing, model equivalence, parametric and nonparametric identifiability, control of confounding, and covariate selection. These developments clarify the causal and statistical components of structural equation models and the role of SEM in the empirical sciences."
Structure graph for FDI. An introduction to structural modeling and analysis can be found in  and the references therein. Because of the high level ...
Author: Michael Ungermann
Publisher: Logos Verlag Berlin GmbH
This work considers the problem of identifying the fault in a faulty dynamical system on the basis of the system's input and output signals only. For this purpose, a model-based method for the design of diagnostic tests which consist of specific input signals and appropriate residual generators is developed. The method extends the structure graph of dynamical systems in order to represent the couplings in a system which has been brought to a specific operating region. The resulting local structure graph is used to determine specific residual generators which can distinguish between faults on the basis of the system's input and output signals in the corresponding operating region. Algorithms to determine advantageous operating regions and input signals which drive the system into such operating regions are given. The application of the method to determine diagnostic tests is demonstrated using a typical automotive system, a throttle valve.
However, it is clear that this cannot be achieved for chain graphs: consider an ... These semi-graphoids can be shown to be structural models over N using ...
Author: Milan Studeny
Publisher: Springer Science & Business Media
Probabilistic Conditional Independence Structures provides the mathematical description of probabilistic conditional independence structures; the author uses non-graphical methods of their description, and takes an algebraic approach. The monograph presents the methods of structural imsets and supermodular functions, and deals with independence implication and equivalence of structural imsets. Motivation, mathematical foundations and areas of application are included, and a rough overview of graphical methods is also given. In particular, the author has been careful to use suitable terminology, and presents the work so that it will be understood by both statisticians, and by researchers in artificial intelligence. The necessary elementary mathematical notions are recalled in an appendix.
3.7 Graphs and Structures Since this thesis has been quite rabid in proposing graph models to represent networks of various macromolecular interactions, ...
Author: Robert Pilstål
Publisher: Linköping University Electronic Press
We are compounded entities, given life by a complex molecular machinery. When studying these molecules we have to make sense of a diverse set of dynamical nanostructures with wast and intricate patterns of interactions. Protein polymers is one of the major groups of building blocks of such nanostructures which fold up into more or less distinct three dimensional structures. Due to their shape, dynamics and chemical properties proteins are able to perform a plethora of specific functions essential to all known cellular lifeforms. The connection between protein sequence, translated into protein structure and in the continuation into protein function is well accepted but poorly understood. Malfunction in the process of protein folding is known to be implicated in natural aging, cancer and degenerative diseases such as Alzheimer's. Protein folds are described hierarchically by structural ontologies such as SCOP, CATH and Pfam all which has yet to succeed in deciphering the natural language of protein function. These paradigmatic views centered on protein structure fail to describe more mutable entities, such as intrinsically disordered proteins (IDPs) which lack a clear defined structure. As of 2012, about two thirds of cancer patients was predicted to survive past 5 years of diagnosis. Despite this, about a third do not survive and numerous of successfully treated patients suffer from secondary conditions due to chemotherapy, surgery and the like. In order to handle cancer more efficiently we have to better understand the underlying molecular mechanisms. Elusive to standard methods of investigation, IDPs have a central role in pathology; dysfunction in IDPs are key factors in cellular system failures such as cancer, as many IDPs are hub regulators for major cell functions. These IDPs carry short conserved functional boxes, that are not described by known ontologies, which suggests the existence of a smaller entity. In an investigation of a pair of such boxes of c-MYC, a plausible structural model of its interacting with Pin1 emerged, but such a model still leaves the observer with a puzzle of understanding the actual function of that interaction. If the protein is represented as a graph and modeled as the interaction patterns instead of as a structural entity, another picture emerges. As a graph, there is a parable from that of the boxes of IDPs, to that of sectors of allosterically connected residues and the theory of foldons and folding units. Such a description is also useful in deciphering the implications of specific mutations. In order to render a functional description feasible for both structured and disordered proteins, there is a need of a model separate from form and structure. Realized as protein primes, patterns of interaction, which has a specific function that can be defined as prime interactions and context. With function defined as interactions, it might be possible that the discussion of proteins and their mechanisms is thereby simplified to the point rendering protein structural determination merely supplementary to understanding protein function. Människan byggs upp av celler, de i sin tur består av än mindre beståndsdelar; livets molekyler. Dessa fungerar som mekaniska byggstenar, likt maskiner och robotar som sliter vid fabrikens band; envar utförandes en absolut nödvändig funktion för cellens, och hela kroppens, fortsatta överlevnad. De av livets molekyler som beskrivs centralt i den här avhandling är proteiner, vilka i sin tur består utav en lång kedja, med olika typer av länkar, som likt garn lindar upp sig i ett nystan av en (mer eller mindre...) bestämd struktur som avgör dess roll och funktion i cellen. Intrinsiellt oordnade proteiner (IDP) går emot denna enkla åskådning; de är proteiner som saknar struktur och beter sig mer likt spaghetti i vatten än en maskin. IDP är ändå funktionella och bär på centrala roller i cellens maskineri; exempel är oncoproteinet c-Myc som agerar "gaspedal" för cellen - fel i c-Myc's funktion leder till att cellerna löper amok, delar sig hejdlöst och vi får cancer. Man har upptäckt att c-Myc har en ombytlig struktur vi inte kan se; studier av punktvisa förändringar, mutationer, i kedjan av byggstenar hos c-Myc visar att många länkar har viktiga roller i funktionen. Detta ger oss bättre förståelse om cancer men samtidigt är laboratoriearbetet både komplicerat och dyrt; här kan evolutionen vägleda oss och avslöja hemligheterna snabbare. Molekylär evolution studeras genom att beräkna variation i proteinkedjan mellan besläktade arter som finns lagrade i databaser; detta visar snabbt, via nätverksanalys och grafteori, vilka delar av proteinet som är centrala och kopplade till varandra av nödvändighet för artens fortlevnad. På så vis hjälper evolutionen oss att förstå proteinfunktioner via modeller baserade på proteinernas interaktioner snarare än deras struktur. Samma modeller kan nyttjas för att förstå dynamiska förlopp och skillnader mellan normala och patologiska varianter av proteiner; mutationer kan uppstå i vår arvsmassa som kan leda till sjukdom. Genom analys av proteinernas kopplingsnätverk i grafmodellerna kan man bättre förutsäga vilka mutationer som är farligare än andra. Dessutom har det visat sig att en sådan representation kan ge bättre förståelse för den normala funktionen hos ett protein än vad en proteinstruktur kan. Här introduceras även konceptet proteinprimärer, vilket är en abstrakt representation av proteiner centrerad på deras interaktiva mönster, snarare än på partikulär form och struktur. Det är en förhoppning att en sådan representation skall förenkla diskussionen anbelangande proteinfunktion så till den grad att strukturbestämmelse av proteiner, som är en mycket kostsam och tidskrävande process, till viss mån kan anses vara sekundär i betydelse jämfört med funktionellt modellerande baserat på evolutionära data extraherade ur våra sekvensdatabaser.
Let the set X(S) contain all models that describe the system S structurally. ... The set XM (S) contains all mixed graphs derived from the structural models ...
Author: Boris Shishkov
Publisher: Springer Nature
This book constitutes the refereed proceedings of the 11th International Symposium on Business Modeling and Software Design, BMSD 2021, which took place in Sofia, Bulgaria, in July 2021. The 14 full and 13 short papers included in this book were carefully reviewed and selected from a total of 61 submissions. BMSD is a leading international forum that brings together researchers and practitioners interested in business modeling and its relation to software design. Particular areas of interest are: Business Processes and Enterprise Engineering; Business Models and Requirements; Business Models and Services; Business Models and Software; Information Systems Architectures and Paradigms; Data Aspects in Business Modeling and Software Development; Blockchain-Based Business Models and Information Systems; IoT and Implications for Enterprise Information Systems. The BMSD 2021 theme was: Towards Enterprises and Software that are Resilient against Disruptive Events.
[Giblin 1977] P.J. Giblin, Graphs, Surfaces and Homology, Chapman and Hall, London 1977. 135 [Godehardt 1988] E. Godehardt, Graphs as Structural Models, ...
Author: Ulrich Knauer
Publisher: Walter de Gruyter GmbH & Co KG
Graph models are extremely useful for a large number of applications as they play an important role as structuring tools. They allow to model net structures – like roads, computers, telephones, social networks – instances of abstract data structures – like lists, stacks, trees – and functional or object oriented programming. The focus of this highly self-contained book is on homomorphisms and endomorphisms, matrices and eigenvalues.
Random Structures Algorithms 5 , 627–648 . Bollobás , B. and O. Riordan ( 2000 ) . Constrained graph processes . Electron . J. Combin .
Author: D N Shanbhag
Publisher: Gulf Professional Publishing
This sequel to volume 19 of Handbook on Statistics on Stochastic Processes: Modelling and Simulation is concerned mainly with the theme of reviewing and, in some cases, unifying with new ideas the different lines of research and developments in stochastic processes of applied flavour. This volume consists of 23 chapters addressing various topics in stochastic processes. These include, among others, those on manufacturing systems, random graphs, reliability, epidemic modelling, self-similar processes, empirical processes, time series models, extreme value therapy, applications of Markov chains, modelling with Monte Carlo techniques, and stochastic processes in subjects such as engineering, telecommunications, biology, astronomy and chemistry. particular with modelling, simulation techniques and numerical methods concerned with stochastic processes. The scope of the project involving this volume as well as volume 19 is already clarified in the preface of volume 19. The present volume completes the aim of the project and should serve as an aid to students, teachers, researchers and practitioners interested in applied stochastic processes.
(A) (B) 6 Structural model Structural model: Equiv. random network ... Dashed lines in (A,B): equivalent random graphs of the full-scale structural model.
Author: Ivan Soltesz
Publisher: Academic Press
Epilepsy is a neurological disorder that affects millions of patients worldwide and arises from the concurrent action of multiple pathophysiological processes. The power of mathematical analysis and computational modeling is increasingly utilized in basic and clinical epilepsy research to better understand the relative importance of the multi-faceted, seizure-related changes taking place in the brain during an epileptic seizure. This groundbreaking book is designed to synthesize the current ideas and future directions of the emerging discipline of computational epilepsy research. Chapters address relevant basic questions (e.g., neuronal gain control) as well as long-standing, critically important clinical challenges (e.g., seizure prediction). Computational Neuroscience in Epilepsy should be of high interest to a wide range of readers, including undergraduate and graduate students, postdoctoral fellows and faculty working in the fields of basic or clinical neuroscience, epilepsy research, computational modeling and bioengineering. Covers a wide range of topics from molecular to seizure predictions and brain implants to control seizures Contributors are top experts at the forefront of computational epilepsy research Chapter contents are highly relevant to both basic and clinical epilepsy researchers
Frank , O. ( 1980 ) Sampling and inference in a population graph . ... D. ( 1965 ) Structural Models : An Introduction to the Theory of Directed Graphs .
Author: Peter J. Carrington
Publisher: Cambridge University Press
Category: Social Science
Models and Methods in Social Network Analysis, first published in 2005, presents the most important developments in quantitative models and methods for analyzing social network data that have appeared during the 1990s. Intended as a complement to Wasserman and Faust's Social Network Analysis: Methods and Applications, it is a collection of articles by leading methodologists reviewing advances in their particular areas of network methods. Reviewed are advances in network measurement, network sampling, the analysis of centrality, positional analysis or blockmodelling, the analysis of diffusion through networks, the analysis of affiliation or 'two-mode' networks, the theory of random graphs, dependence graphs, exponential families of random graphs, the analysis of longitudinal network data, graphical techniques for exploring network data, and software for the analysis of social networks.
Methods and Models Michael Kaufmann, Dorothea Wagner. Garg, A., and Tamassia, ... Graphs as Structural Models, Advances in System Analysis 4. Vieweg.
Author: Michael Kaufmann
Graph drawing comprises all aspects of visualizing structural relations between objects. The range of topics dealt with extends from graph theory, graph algorithms, geometry, and topology to visual languages, visual perception, and information visualization, and to computer-human interaction and graphics design. This monograph gives a systematic overview of graph drawing and introduces the reader gently to the state of the art in the area. The presentation concentrates on algorithmic aspects, with an emphasis on interesting visualization problems with elegant solutions. Much attention is paid to a uniform style of writing and presentation, consistent terminology, and complementary coverage of the relevant issues throughout the 10 chapters. This tutorial is ideally suited as an introduction for newcomers to graph drawing. Ambitioned practitioners and researchers active in the area will find it a valuable source of reference and information.