Search results for: graphs-as-structural-models

Graphs as Structural Models

Author : Erhard Godehardt
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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.

Graphs as Structural Models

Author : Erhard Godehardt
File Size : 49.75 MB
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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.

Structural Models

Author : Frank Harary
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P graphs for Process Systems Engineering

Author : Ferenc Friedler
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This book discusses the P-graph framework for developing and understanding effective design tools for process systems engineering, and addresses the current state of its theory and applications. The book details the new philosophy of the axioms-based mathematical modelling of processing systems, the basic algorithms, areas of application, future directions, and the proofs of theorems and algorithms. Because of the rigorous foundation of the theory, the framework provides a firm basis for future research in mathematical modelling, optimization, and design of complex engineering systems. The various P-graph applications discussed include process network synthesis, reliability engineering, and systems resilience. The framework opens new avenues for research in complex systems including redundant operations for critical infrastructure, systems sustainability, and modelling tools for disaster engineering. Demonstration software is provided to facilitate the understanding of the theory. The book will be of interest to institutions, companies, and individuals performing research and R&D in process systems engineering.

Test Signal Generation for Service Diagnosis Based on Local Structure Graphs

Author : Michael Ungermann
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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.

Probabilistic Conditional Independence Structures

Author : Milan Studeny
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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.

On protein structure function and modularity from an evolutionary perspective

Author : Robert Pilstål
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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.

Business Modeling and Software Design

Author : Boris Shishkov
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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.

Control Reconfiguration of Dynamical Systems

Author : Thomas Steffen
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Reconfiguration, an approach for fault-tolerant control, involves changing the control structure in response to the fault. This monograph extends this idea to actuator faults and studies in detail the so-called virtual actuator approach. "Control Reconfiguration of Dynamical Systems" also introduces structural analysis as a tool for reconfiguration. Because a fault changes the structure of the system, the reconfiguration solution is sought on a structural level. Novel algorithms are presented to test for reconfigurability and to find a reconfiguration solution. A MATLAB toolbox is supplied, which contains the main algorithms and examples. The book addresses advanced engineering students, developers and researchers that have a specific interest in control reconfiguration.

Models and Methods in Social Network Analysis

Author : Peter J. Carrington
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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.