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Author: Olle Abrahamsson
Publisher: Linköping University Electronic Press
ISBN: 9180755992
Category :
Languages : en
Pages : 156
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Book Description
This thesis studies two problems defined on complex networks, of which the first explores a conceivable extension of structural balance theory and the other concerns convergence issues in opinion dynamics. In the first half of the thesis we discuss possible definitions of structural balance conditions in a network with preference orderings as node attributes. The main result is that for the case with three alternatives (A, B, C) we reduce the (3!)3 = 216 possible configurations of triangles to 10 equivalence classes, and use these as measures of balance of a triangle towards possible extensions of structural balance theory. Moreover, we derive a general formula for the number of equivalent classes for preferences on n alternatives. Finally, we analyze a real-world data set and compare its empirical distribution of triangle equivalence classes to a null hypothesis in which preferences are randomly assigned to the nodes. The second half of the thesis concerns an opinion dynamics model in which each agent takes a random Bernoulli distributed action whose probability is updated at each discrete time step, and we prove that this model converges almost surely to consensus. We also provide a detailed critique of a claimed proof of this result in the literature. We generalize the result by proving that the assumption of irreducibility in the original model is not necessary. Furthermore, we prove as a corollary of the generalized result that the almost sure convergence to consensus holds also in the presence of a fully stubborn agent which never changes its opinion. In addition, we show that the model, in both the original and generalized cases, converges to consensus also in rth moment. Avhandlingen studerar två problem definierade på komplexa nätverk, varav det första utforskar en tänkbar utökning av strukturell balansteori och det andra behandlar konvergensfrågor inom opinionsdynamik. I avhandlingens första hälft diskuteras möjliga definitioner på villkor för strukturell balans i ett nätverk med preferensordningar som nodattribut. Huvudresultatet är att för fallet med tre alternativ (A, B, C) så kan de (3!)3 = 216 möjliga konfigurationerna av trianglar reduceras till 10 ekvivalensklasser, vilka används som mått på en triangels balans som ett steg mot möjliga utökningar av strukturell balansteori. Vi härleder även en generell formel för antalet ekvivalensklasser för preferensordningar med n alternativ. Slutligen analyseras en empirisk datamängd och dess empiriska sannolikhetsfördelning av triangel-ekvivalensklasser jämförs med en nollhypotes i vilken preferenser tilldelas noderna slumpmässigt. Den andra hälften av avhandlingen rör en opinionsdynamikmodell där varje agent agerar slumpmässigt enligt en Bernoullifördelning vars sannolikhet uppdateras vid varje diskret tidssteg, och vi bevisar att denna modell konvergerar nästan säkert till konsensus. Vi ger också en detaljerad kritik av ett påstått bevis av detta resultat i litteraturen. Vi generaliserar resultatet genom att visa att antagandet om irreducibilitet i den ursprungliga modellen inte är nödvändigt. Vidare visar vi, som följdsats av det generaliserade resultatet, att den nästan säkra konvergensen till konsensus även håller om en agent är fullständigt envis och aldrig byter åsikt. I tillägg till detta visar vi att modellen, både i det ursprungliga och i det generaliserade fallet, konvergerar till konsensus även i r:te ordningens moment.
Author: Olle Abrahamsson
Publisher: Linköping University Electronic Press
ISBN: 9180755992
Category :
Languages : en
Pages : 156
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Book Description
This thesis studies two problems defined on complex networks, of which the first explores a conceivable extension of structural balance theory and the other concerns convergence issues in opinion dynamics. In the first half of the thesis we discuss possible definitions of structural balance conditions in a network with preference orderings as node attributes. The main result is that for the case with three alternatives (A, B, C) we reduce the (3!)3 = 216 possible configurations of triangles to 10 equivalence classes, and use these as measures of balance of a triangle towards possible extensions of structural balance theory. Moreover, we derive a general formula for the number of equivalent classes for preferences on n alternatives. Finally, we analyze a real-world data set and compare its empirical distribution of triangle equivalence classes to a null hypothesis in which preferences are randomly assigned to the nodes. The second half of the thesis concerns an opinion dynamics model in which each agent takes a random Bernoulli distributed action whose probability is updated at each discrete time step, and we prove that this model converges almost surely to consensus. We also provide a detailed critique of a claimed proof of this result in the literature. We generalize the result by proving that the assumption of irreducibility in the original model is not necessary. Furthermore, we prove as a corollary of the generalized result that the almost sure convergence to consensus holds also in the presence of a fully stubborn agent which never changes its opinion. In addition, we show that the model, in both the original and generalized cases, converges to consensus also in rth moment. Avhandlingen studerar två problem definierade på komplexa nätverk, varav det första utforskar en tänkbar utökning av strukturell balansteori och det andra behandlar konvergensfrågor inom opinionsdynamik. I avhandlingens första hälft diskuteras möjliga definitioner på villkor för strukturell balans i ett nätverk med preferensordningar som nodattribut. Huvudresultatet är att för fallet med tre alternativ (A, B, C) så kan de (3!)3 = 216 möjliga konfigurationerna av trianglar reduceras till 10 ekvivalensklasser, vilka används som mått på en triangels balans som ett steg mot möjliga utökningar av strukturell balansteori. Vi härleder även en generell formel för antalet ekvivalensklasser för preferensordningar med n alternativ. Slutligen analyseras en empirisk datamängd och dess empiriska sannolikhetsfördelning av triangel-ekvivalensklasser jämförs med en nollhypotes i vilken preferenser tilldelas noderna slumpmässigt. Den andra hälften av avhandlingen rör en opinionsdynamikmodell där varje agent agerar slumpmässigt enligt en Bernoullifördelning vars sannolikhet uppdateras vid varje diskret tidssteg, och vi bevisar att denna modell konvergerar nästan säkert till konsensus. Vi ger också en detaljerad kritik av ett påstått bevis av detta resultat i litteraturen. Vi generaliserar resultatet genom att visa att antagandet om irreducibilitet i den ursprungliga modellen inte är nödvändigt. Vidare visar vi, som följdsats av det generaliserade resultatet, att den nästan säkra konvergensen till konsensus även håller om en agent är fullständigt envis och aldrig byter åsikt. I tillägg till detta visar vi att modellen, både i det ursprungliga och i det generaliserade fallet, konvergerar till konsensus även i r:te ordningens moment.
Author: Pasquale Commendatore
Publisher: Springer
ISBN: 3319408038
Category : Business & Economics
Languages : en
Pages : 363
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Book Description
This volume sheds light on the current state of complex networks and nonlinear dynamics applied to the understanding of economic and social phenomena ranging from geographical economics to macroeconomics and finance, and its purpose is to give readers an overview of several interesting topics for research at an intermediate level. Three different and interdisciplinary, but complementary, aspects of networks are put together in a single piece, namely: (i) complex networks theory, (ii) applied network analysis to social and economic interrelations, and (iii) dynamical evolution of systems and networks. The volume includes contributions from excellent scholars in economics and social sciences as well as leading experts in the fields of complex networks and nonlinear dynamics.
Author: Renaud Lambiotte
Publisher: Cambridge University Press
ISBN: 1108808654
Category : Science
Languages : en
Pages : 102
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Book Description
Complex networks are typically not homogeneous, as they tend to display an array of structures at different scales. A feature that has attracted a lot of research is their modular organisation, i.e., networks may often be considered as being composed of certain building blocks, or modules. In this Element, the authors discuss a number of ways in which this idea of modularity can be conceptualised, focusing specifically on the interplay between modular network structure and dynamics taking place on a network. They discuss, in particular, how modular structure and symmetries may impact on network dynamics and, vice versa, how observations of such dynamics may be used to infer the modular structure. They also revisit several other notions of modularity that have been proposed for complex networks and show how these can be related to and interpreted from the point of view of dynamical processes on networks.
Author: Fakhteh Ghanbarnejad
Publisher: Springer
ISBN: 3030146839
Category : Science
Languages : en
Pages : 246
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Book Description
This book bridges the gap between advances in the communities of computer science and physics--namely machine learning and statistical physics. It contains diverse but relevant topics in statistical physics, complex systems, network theory, and machine learning. Examples of such topics are: predicting missing links, higher-order generative modeling of networks, inferring network structure by tracking the evolution and dynamics of digital traces, recommender systems, and diffusion processes. The book contains extended versions of high-quality submissions received at the workshop, Dynamics On and Of Complex Networks (doocn.org), together with new invited contributions. The chapters will benefit a diverse community of researchers. The book is suitable for graduate students, postdoctoral researchers and professors of various disciplines including sociology, physics, mathematics, and computer science.
Author: Maximilien Gadouleau
Publisher: Springer Nature
ISBN: 3031658876
Category :
Languages : en
Pages : 165
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Book Description
Author: Alain Barrat
Publisher: Cambridge University Press
ISBN: 9781107626256
Category : Science
Languages : en
Pages : 361
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Book Description
The availability of large data sets have allowed researchers to uncover complex properties such as large scale fluctuations and heterogeneities in many networks which have lead to the breakdown of standard theoretical frameworks and models. Until recently these systems were considered as haphazard sets of points and connections. Recent advances have generated a vigorous research effort in understanding the effect of complex connectivity patterns on dynamical phenomena. For example, a vast number of everyday systems, from the brain to ecosystems, power grids and the Internet, can be represented as large complex networks. This new and recent account presents a comprehensive explanation of these effects.
Author: Oksana Moryakova
Publisher: Linköping University Electronic Press
ISBN: 9180757715
Category :
Languages : en
Pages : 74
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Book Description
Complexity reduction is one of the main issues of digital signal processing (DSP) algorithms, especially in communication systems where each new generation brings new requirements towards increasing data rates and improved accuracy positioning, leading to the growth of power consumption and chip area. To meet these requirements and at the same time find a trade-off between high performance and low implementation cost, more sophisticated DSP algorithms need to be developed. Recent communication standards require flexible, adaptive systems capable of real-time frequency-domain tuning. Variable digital filters (VDFs) address these needs by enabling "on-the-fly" frequency response adjustments without the need for online filter design. The key feature of VDFs is that they require only an adjustment of one or a few parameters to change their characteristics, without the need for extensive additional computations. Most VDF coefficients remain fixed after the initial design, allowing for efficient hardware implementation. This makes VDFs essential for modern adaptive communication technologies. This thesis primarily focuses on the design and low-complexity implementation techniques of VDFs and presents three main contributions. Firstly, it proposes three VDF realizations for simultaneous lowpass filtering and equalization using polynomial channel models, with systematic design procedures based on minimax optimization for all the proposed structures. In addition, a fast design method for the VDFs with several variable parameters, which can substantially decrease the design time, is presented. Secondly, it introduces frequency-domain implementations of VDFs using the overlap-save technique. Based on the assumption that these filters have been designed using a common design approach based on optimizing the impulse response coefficients, the filter DFT coefficients are proposed to be implemented as fixed, hybrid, or variable weights. Lastly, the thesis presents an efficient design approach for a variable-bandwidth digital filter implemented in the frequency domain using the overlap-save method. The proposed approach is based on a hybrid of frequency sampling and optimization, allowing for direct optimization of the DFT coefficients considering the filter frequency-domain implementation and thereby noticeably reducing the cost of implementation and an online update of the DFT filter coefficients when the bandwidth is varied. Reduktion av komplexitet är en av huvudfrågorna för digital signalbehandling (DSP) algoritmer, särskilt i kommunikationssystem där varje ny generation ställer nya krav på att öka datahastigheter och förbättrad noggrannhet positionering, vilket leder till en ökning av strömförbrukningen och kretsytan. För att möta dessa krav och samtidigt hitta en avvägning mellan hög prestanda och låg implementeringskostnad behöver mer sofistikerade DSP-algoritmer utvecklas. Senaste kommunikationsstandarder kräver flexibla, adaptiva system som kan frekvensdomäninställning i realtid. Variabla digitala filter (VDF) tillgodoser dessa behov genom att möjliggöra "on-the-fly" frekvenssvarsjusteringar utan behov av onlinefilterdesign. Nyckelegenskapen hos VDF:er är att de bara kräver en justering av en eller ett fåtal parametrar för att ändra deras egenskaper, utan behov av omfattande ytterligare beräkningar. De flesta VDF-koefficienter förblir fixerade efter den ursprungliga designen, vilket möjliggör effektiv hårdvaruimplementering. Detta gör VDF:er väsentliga för modern adaptiv kommunikationsteknik. Den här avhandlingen fokuserar främst på design och implementeringstekniker med låg komplexitet för VDF:er och presenterar tre huvudsakliga bidrag. För det första föreslår den tre VDF-realiseringar för samtidig lågpassfiltrering och utjämning med användning av polynomkanalmodeller, med systematiska designprocedurer baserade på minimax optimering för alla föreslagna strukturer. Dessutom presenteras en snabb designmetod för VDF:erna med flera variabla parametrar, som avsevärt kan minska designtiden. För det andra introducerar den frekvensdomänimplementationer av VDF:er med överlappningssparateknik. Baserat på antagandet att dessa filter har utformats med användning av en gemensam designmetod baserad på optimering av impulssvarskoefficienterna, föreslås filtrets DFT-koefficienter implementeras som fasta, hybrida eller variabla vikter. Slutligen presenterar avhandlingen en effektiv designansats för ett digitalt filter med variabel bandbredd implementerat i frekvensdomänen med användning av överlappningssparametoden. Det föreslagna tillvägagångssättet är baserat på en hybrid av frekvenssampling och optimering, vilket möjliggör direkt optimering av DFT-koefficienterna med tanke på implementeringen av filterfrekvensdomänen och därigenom märkbart minska kostnaden för implementering och en onlineuppdatering av DFT-filterkoefficienterna när bandbredden är varierande.
Author: Rosa Maria Benito
Publisher: Springer Nature
ISBN: 3030934136
Category : Technology & Engineering
Languages : en
Pages : 833
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Book Description
This book highlights cutting-edge research in the field of network science, offering scientists, researchers, students, and practitioners a unique update on the latest advances in theory and a multitude of applications. It presents the peer-reviewed proceedings of the X International Conference on Complex Networks and their Applications (COMPLEX NETWORKS 2021). The carefully selected papers cover a wide range of theoretical topics such as network models and measures; community structure, network dynamics; diffusion, epidemics and spreading processes; resilience and control as well as all the main network applications, including social and political networks; networks in finance and economics; biological and neuroscience networks, and technological networks.
Author: Sven Banisch
Publisher: Springer
ISBN: 3319248774
Category : Science
Languages : en
Pages : 205
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Book Description
This self-contained text develops a Markov chain approach that makes the rigorous analysis of a class of microscopic models that specify the dynamics of complex systems at the individual level possible. It presents a general framework of aggregation in agent-based and related computational models, one which makes use of lumpability and information theory in order to link the micro and macro levels of observation. The starting point is a microscopic Markov chain description of the dynamical process in complete correspondence with the dynamical behavior of the agent-based model (ABM), which is obtained by considering the set of all possible agent configurations as the state space of a huge Markov chain. An explicit formal representation of a resulting “micro-chain” including microscopic transition rates is derived for a class of models by using the random mapping representation of a Markov process. The type of probability distribution used to implement the stochastic part of the model, which defines the updating rule and governs the dynamics at a Markovian level, plays a crucial part in the analysis of “voter-like” models used in population genetics, evolutionary game theory and social dynamics. The book demonstrates that the problem of aggregation in ABMs - and the lumpability conditions in particular - can be embedded into a more general framework that employs information theory in order to identify different levels and relevant scales in complex dynamical systems
Author: Luca Maria Aiello
Publisher: Springer
ISBN: 303005411X
Category : Technology & Engineering
Languages : en
Pages : 906
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Book Description
This book highlights cutting-edge research in the field of network science, offering scientists, researchers, students and practitioners a unique update on the latest advances in theory, together with a wealth of applications. It presents the peer-reviewed proceedings of the VII International Conference on Complex Networks and their Applications (COMPLEX NETWORKS 2018), which was held in Cambridge on December 11–13, 2018. The carefully selected papers cover a wide range of theoretical topics such as network models and measures; community structure and network dynamics; diffusion, epidemics and spreading processes; and resilience and control; as well as all the main network applications, including social and political networks; networks in finance and economics; biological and neuroscience networks; and technological networks.
