Hang-Hyun Jo leads a Junior Research Group called "Statistical Physics of Complex Dynamics" at the Asia Pacific Center for Theoretical Physics and Pohang University of Science and Technology in South Korea. The group includes two members and studies topics like interaction networks in many-body systems and temporal networks using statistical physics approaches. They analyze large digital datasets to characterize properties like bursts in interaction patterns and higher-order correlations between events.
1) The document discusses analyzing social networks using mobile phone call and SMS data. It finds communities have core strong ties within and weak ties between, and weak ties help spread information.
2) Dynamics show bursty communication patterns. Bursts remain even after removing weekly patterns, suggesting multiple reasons for bursts.
3) Social interactions are contextual. Events happen in overlapping communities and bursty patterns differ by communication context. Understanding both topology and dynamics provides a "Social Connectome" of comprehensive social interaction mapping.
The document summarizes a study that mapped the rich-club organization of hub regions in the human connectome (structural brain network). Researchers used diffusion tensor imaging data from 21 subjects to reconstruct whole-brain structural networks and examine their connectivity profiles. They identified a group of 12 strongly interconnected bihemispheric hub regions, including the precuneus, frontal and parietal cortices, hippocampus, putamen, and thalamus. Importantly, these hub regions were found to be more densely interconnected than expected based on their degree alone, together forming a rich club in the human connectome.
The high mass_stelar_initial_mass_function_in_m31_clustersSérgio Sacani
Em uma pesquisa feita com o Telescópio Espacial Hubble da NASA, analisando imagens de 2753 jovens, aglomerados estelares azuis, na vizinha galáxia de Andrômeda, a M31, os astrônomos descobriram que a M31 e a nossa própria galáxia, possuem uma porcentagem similar de estrelas recém-nascidas, com base na massa estudada.
Identificando qual porcentagem de estrelas tem uma massa particular, dentro de um aglomerado, ou sua Função de Massa Inicial, IMF, os cientistas podem interpretar melhor a luz de galáxias distantes e entender a história de formação das estrelas no universo.
A intensa pesquisa, agrupou 414 mosaicos fotográficos feitos pelo Hubble da M31, uma colaboração única feita entre astrônomos, cientistas cidadãos, voluntários que forneceram uma ajuda valiosa em analisar a montanha de dados do Hubble.
“Dada a quantidade de imagens do Hubble, nosso estudo da IMF, não seria possível sem a ajuda dos cientistas cidadãos”, disse Daniel Weisz, da Universidade de Washington em Seatle. Weisz, é o principal autor do artigo que foi publicado no dia 20 de Junho no The Astrophysical Journal.
Michael Farina presented on establishing new upper bounds for the k-distance domination numbers of grid graphs by generalizing an existing construction of dominating sets to k-distance dominating sets. Armando Grez examined a method for constructing fullerene patches with 4 pentagonal faces and produced an exact process for drawing them. Darleen Perez-Lavin partitioned the set of permutations with a peak set into subsets ending with an ascent or descent and provided formulas to enumerate these subsets for Coxeter groups of types B and D.
Spreading processes on temporal networksPetter Holme
This document discusses temporal networks and how temporal structures can impact dynamical processes on networks. It begins by describing different types of temporal networks including person-to-person communication, information dissemination, physical proximity, and cellular biology networks. It then discusses methods for analyzing temporal network structures like inter-event times and how bursty or heavy-tailed distributions can slow spreading compared to memory-less processes. The document also presents examples of how neutralizing temporal structures like inter-event times or beginning/end times can impact spreading simulations. Finally, it discusses how different temporal network datasets exhibit diverse temporal structures.
My talk at the 2017 SIAM "Snowbird" conference on applications of dynamical systems (#SIAMDS17).
I spoke in a session on topological data analysis (TDA). My talk concerned persistent homology and its application to Brexit data (including voting data) and "functional networks" from coupled time series from both experiments and output of dynamical systems.
Eventually, a version of these slides that is synchronized with the audio of my talk is supposed to be posted online.
Networks in Space: Granular Force Networks and BeyondMason Porter
This is my talk for the Network Geometry Workshop (http://ginestra-bianconi-6flt.squarespace.com) at QMUL on 16 July 2015.
(A few of the slides are adapted from slides by my coauthors Dani Bassett and Karen Daniels.)
Temporal Networks of Human InteractionPetter Holme
Temporal networks provide a framework for modeling systems of interactions that occur between nodes over time. These networks capture both the topological structure of connections as well as the timing of interactions. Three key aspects of temporal networks discussed in the document are:
1) Temporal networks can be represented using contact sequences that capture when interactions occur between nodes, unlike static networks which only represent connections.
2) The temporal structure of interactions, such as patterns in the timing of contacts, can impact dynamical processes unfolding on the network like information or disease spreading.
3) Randomizing the timing of contacts in empirical temporal network data can alter dynamical processes, highlighting the importance of temporal structure beyond just topology.
1) The document discusses analyzing social networks using mobile phone call and SMS data. It finds communities have core strong ties within and weak ties between, and weak ties help spread information.
2) Dynamics show bursty communication patterns. Bursts remain even after removing weekly patterns, suggesting multiple reasons for bursts.
3) Social interactions are contextual. Events happen in overlapping communities and bursty patterns differ by communication context. Understanding both topology and dynamics provides a "Social Connectome" of comprehensive social interaction mapping.
The document summarizes a study that mapped the rich-club organization of hub regions in the human connectome (structural brain network). Researchers used diffusion tensor imaging data from 21 subjects to reconstruct whole-brain structural networks and examine their connectivity profiles. They identified a group of 12 strongly interconnected bihemispheric hub regions, including the precuneus, frontal and parietal cortices, hippocampus, putamen, and thalamus. Importantly, these hub regions were found to be more densely interconnected than expected based on their degree alone, together forming a rich club in the human connectome.
The high mass_stelar_initial_mass_function_in_m31_clustersSérgio Sacani
Em uma pesquisa feita com o Telescópio Espacial Hubble da NASA, analisando imagens de 2753 jovens, aglomerados estelares azuis, na vizinha galáxia de Andrômeda, a M31, os astrônomos descobriram que a M31 e a nossa própria galáxia, possuem uma porcentagem similar de estrelas recém-nascidas, com base na massa estudada.
Identificando qual porcentagem de estrelas tem uma massa particular, dentro de um aglomerado, ou sua Função de Massa Inicial, IMF, os cientistas podem interpretar melhor a luz de galáxias distantes e entender a história de formação das estrelas no universo.
A intensa pesquisa, agrupou 414 mosaicos fotográficos feitos pelo Hubble da M31, uma colaboração única feita entre astrônomos, cientistas cidadãos, voluntários que forneceram uma ajuda valiosa em analisar a montanha de dados do Hubble.
“Dada a quantidade de imagens do Hubble, nosso estudo da IMF, não seria possível sem a ajuda dos cientistas cidadãos”, disse Daniel Weisz, da Universidade de Washington em Seatle. Weisz, é o principal autor do artigo que foi publicado no dia 20 de Junho no The Astrophysical Journal.
Michael Farina presented on establishing new upper bounds for the k-distance domination numbers of grid graphs by generalizing an existing construction of dominating sets to k-distance dominating sets. Armando Grez examined a method for constructing fullerene patches with 4 pentagonal faces and produced an exact process for drawing them. Darleen Perez-Lavin partitioned the set of permutations with a peak set into subsets ending with an ascent or descent and provided formulas to enumerate these subsets for Coxeter groups of types B and D.
Spreading processes on temporal networksPetter Holme
This document discusses temporal networks and how temporal structures can impact dynamical processes on networks. It begins by describing different types of temporal networks including person-to-person communication, information dissemination, physical proximity, and cellular biology networks. It then discusses methods for analyzing temporal network structures like inter-event times and how bursty or heavy-tailed distributions can slow spreading compared to memory-less processes. The document also presents examples of how neutralizing temporal structures like inter-event times or beginning/end times can impact spreading simulations. Finally, it discusses how different temporal network datasets exhibit diverse temporal structures.
My talk at the 2017 SIAM "Snowbird" conference on applications of dynamical systems (#SIAMDS17).
I spoke in a session on topological data analysis (TDA). My talk concerned persistent homology and its application to Brexit data (including voting data) and "functional networks" from coupled time series from both experiments and output of dynamical systems.
Eventually, a version of these slides that is synchronized with the audio of my talk is supposed to be posted online.
Networks in Space: Granular Force Networks and BeyondMason Porter
This is my talk for the Network Geometry Workshop (http://ginestra-bianconi-6flt.squarespace.com) at QMUL on 16 July 2015.
(A few of the slides are adapted from slides by my coauthors Dani Bassett and Karen Daniels.)
Temporal Networks of Human InteractionPetter Holme
Temporal networks provide a framework for modeling systems of interactions that occur between nodes over time. These networks capture both the topological structure of connections as well as the timing of interactions. Three key aspects of temporal networks discussed in the document are:
1) Temporal networks can be represented using contact sequences that capture when interactions occur between nodes, unlike static networks which only represent connections.
2) The temporal structure of interactions, such as patterns in the timing of contacts, can impact dynamical processes unfolding on the network like information or disease spreading.
3) Randomizing the timing of contacts in empirical temporal network data can alter dynamical processes, highlighting the importance of temporal structure beyond just topology.
Community search is the problem of finding a good community for a given set of query vertices.
In this work we propose a novel method that it is in general more efficient and effective than state-of-the art, it can handle multiple query vertices, it yields optimal communities, and it is parameter free.
This document summarizes a study that models electromagnetic wave propagation through crowds of people at GSM frequencies. The crowd is modeled as randomly oriented dielectric cylinders of varying sizes to represent humans. Simulations are run to determine the attenuation of electromagnetic radiation for different crowd densities, frequencies, and polarizations. The results show that crowds can significantly attenuate electromagnetic waves through absorption and scattering. Modeling crowds as discrete scatterers provides insights into how human presence affects wireless signal propagation.
The Algorithms of Life - Scientific Computing for Systems Biologyinside-BigData.com
In this deck from ISC 2019, Ivo Sbalzarini from TU Dresden presents: The Algorithms of Life - Scientific Computing for Systems Biology. In his talk, Sbalzarini mainly discussed the rapidly growing importance and influence in the life sciences for scientific high-performance computing.
"Scientific high-performance computing is of rapidly growing importance and influence in the life sciences. Thanks to the increasing knowledge about the molecular foundations of life, recent advances in biomedical data science, and the availability of predictive biophysical theories that can be numerically simulated, mechanistic understanding of the emergence of life comes within reach. Computing is playing a pivotal and catalytic role in this scientific revolution, both as a tool of investigation and hypothesis testing, but also as a school of thought and systems model. This is because a developing tissue, embryo, or organ can itself be seen as a massively parallel distributed computing system that collectively self-organizes to bring about behavior we call life. In any multicellular organism, every cell constantly takes decisions about growth, division, and migration based on local information, with cells communicating with each other via chemical, mechanical, and electrical signals across length scales from nanometers to meters. Each cell can therefore be understood as a mechano-chemical processing element in a complexly interconnected million- or billion-core computing system. Mechanistically understanding and reprogramming this system is a grand challenge. While the “hardware” (proteins, lipids, etc.) and the “source code” (genetic code) are increasingly known, we known virtually nothing about the algorithms that this code implements on this hardware. Our vision is to contribute to this challenge by developing computational methods and software systems for high-performance data analysis, inference, and numerical simulation of computer models of biological tissues, incorporating the known biochemistry and biophysics in 3D-space and time, in order to understand biological processes on an algorithmic basis. This ranges from real-time approaches to biomedical image analysis, to novel simulation languages for parallel high-performance computing, to virtual reality and machine learning for 3D microscopy and numerical simulations of coupled biochemical-biomechanical models. The cooperative, interdisciplinary effort to develop and advance our understanding of life using computational approaches not only places high-performance computing center stage, but also provides stimulating impulses for the future development of this field."
Watch the video: https://wp.me/p3RLHQ-kBB
Learn more: https://www.isc-hpc.com/
Sign up for our insideHPC Newsletter: http://insidehpc.com/newsletter
This document describes a new method for detecting community structure in complex networks based on node similarity. The method works as follows:
1. It calculates the similarity between all node pairs using a local node similarity metric.
2. It treats each node as its own community initially. Then it iteratively incorporates the community of the current node with the communities containing its most similar nodes.
3. It selects the most similar uncovered node as the next current node, and repeats the process until all nodes have been incorporated into communities.
The method requires only local network information and has a computational complexity of O(nk) for a network with n nodes and average degree k. It is evaluated on real and computer-generated networks, demonstrating
Some key models of social network generation are discussed, including random graph models, Watts-Strogatz models, and scale-free networks. Scale-free networks can generate networks with few components, small diameters, and heavy-tailed degree distributions, but do not capture high clustering. Biological networks like metabolic and protein interaction networks also tend to be scale-free.
A Technique for Partially Solving a Family of Diffusion Problemsijtsrd
Our aim in this paper is to expose the interesting role played by differ integral specifically, semi derivatives and semi integrals in solving certain diffusion problems. Along with the wave equation and Laplace equation, the diffusion equation is one of the three fundamental partial differential equation of mathematical physics. I will not discuss convential solutions of the diffusion equation at all. These range from closed form solutions for very simple model problems to computer methods for approximating the concentration of the diffusing substance on a network of points. Such solutions are described extensively in the literature .My purpose, rather, is to expose a technique for partially solving a family of diffusion problems, a technique that leads to a compact equation which is first order partially and half order temporally. I shall show that, for semi finite systems initially at equilibrium, our semi differential equation leads to a relationship between the intensive variable and the flux at the boundary. Use of this relationship then obviates the need to solve the original diffusion equation in those problems for which this behavior at the boundary is of primary importance. I shall, in fact, freely make use of the general properties established for differ integral operators as if all my functions were differ integrable. Dr. Ayaz Ahmad "A Technique for Partially Solving a Family of Diffusion Problems" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-2 | Issue-6 , October 2018, URL: http://www.ijtsrd.com/papers/ijtsrd18576.pdf
1) Mature dendritic cells project dendrite-like protrusions that allow them to scan a larger area than their cell body.
2) Upon initial contact with a T cell via a dendrite, dendritic cells project numerous mobile membrane extensions and migrate their cell body toward the T cell to tightly entangle it.
3) Using time-lapse microscopy and two-photon imaging of lymph nodes, the study observed dendritic cells polarizing membrane extensions and migrating toward T cells after initial dendrite-mediated contact, before tight conjugation.
1. The document discusses using call detail record (CDR) data to study how mobile phone users manage their social contacts over time and characterize or predict social turnover.
2. By detecting new and old social relationships from CDRs that show communication patterns and frequencies between users, the author aims to analyze how users' social networks evolve and change.
3. The author proposes studying properties like the distribution of inter-event times between calls to the same contact and how this distribution depends on relationship longevity to provide insights into social turnover.
This document summarizes research on creating an isotropic photonic band gap in a 2D disordered dielectric structure. Key points:
- Researchers designed a hyperuniform disordered network of dielectric cylinders and walls that combines advantages of disorder (isotropy) and controlled scattering properties (hyperuniformity and uniform local topology).
- Experiments realized this structure using alumina cylinders and walls and observed a complete photonic band gap in the microwave region, matching theoretical simulations.
- The intrinsic isotropy of this material enables arbitrary waveguide bending, unlike photonic crystals which are anisotropic due to periodicity. This demonstrates potential for precise photon manipulation in planar optical circuits.
These are slides for my tutorial talk on network dynamics. (The colors are fine in the downloaded version, though there seem to be color issues if you view the slides directly in slideshare.)
This document summarizes research on direct non-linear inversion of 1D acoustic media using the inverse scattering series. Key points:
- A method is derived for directly inverting 1D acoustic media with varying velocity and density, without requiring an estimate of properties above reflectors or assuming linear relationships between property changes and reflection data.
- Testing on a single reflector case showed improved estimates of property changes beyond the reflector compared to linear methods, for a wider range of angles.
- A special parameter related to velocity change was identified that has the correct sign in the linear inversion and is not affected by issues like "leakage" that complicate inversions.
The document discusses issues with computational scientific software and proposes a solution called Digital Scientific Notations. Current scientific software is difficult to test and validate due to a lack of specifications and documentation. This makes the software results unverifiable and prevents comparison of different models. The proposed Digital Scientific Notations would embed computational models and methods into scholarly documents using a formal programming language. This would allow models to be precisely defined, validated, and compared, addressing current verification and reproducibility problems in computational science.
This document summarizes a presentation on machine learning of epidemic processes in networks. It discusses using machine learning to predict epidemic spreading from network structure. Specifically, it covers using features like degree, clustering, and centrality measures as inputs to algorithms like random forests and neural networks to predict the fraction of infected nodes. The best approach uses a combination of network measures, not a single measure. This allows machine learning to help identify influential spreaders and understand how network structure influences epidemic dynamics.
Abstracts Of The Emerging Scholars Program Research Projects Fall 2010 Suppor...Claire Webber
This document provides abstracts summarizing 18 undergraduate research projects supported by CUNY Compact funds in Spring 2008. The projects covered a diverse range of topics across various departments including physics, biology, mathematics, engineering, architecture and chemistry. For each project, the abstract lists the student researcher, faculty mentor, department, and provides a brief 3 sentence summary of the project title, aims, methods, and results or conclusions.
THE ISSUE OF UNCERTAINTY FOR HYDROLOGIC EVENTS IN THE MISSOURI RIVER WATERSHE...Boris Shmagin
1. The document discusses a paradigm shift in science and methodology due to computers, with concepts moving from a simple to complex world. Pattern recognition problems in cognitive science helped develop new methods.
2. The new paradigm introduces direct search for solutions, emphasis on decision making, and a unity of technical and holistic languages for pattern description. This leads to a convergence of exact science and humanities.
3. The main difference between the new and old paradigms is a focus on controlling algorithm complexity rather than function complexity to guarantee inference success. Low complexity algorithms can create complex functions that generalize well.
A@kash Physics NCERT Maps.pdf physics short notes physics short notes physics...FahadAlam52
Physics short notes physics short notes physics short notes physics short notes physics short notes physics short notes physics short notes physics short notes physics short notes physics short notes physics short notes physics short notes physics short notes physics short notes physics short notes physics short notes physics short notes physics short notes physics short notes physics short notes physics short notes physics short notes physics short notes physics short notes physics short notes physics short notes physics short notes physics short notes physics short notes physics short notes physics short notes physics short notes physics short notes physics short notes physics short notes physics short notes physics short notes physics short notes
The document summarizes recent progress in developing a "cosmological bootstrap" approach to predicting cosmological correlations directly from fundamental physical principles like locality, causality and unitarity, without relying on explicit models of inflation or particle physics. Key points include:
- Cosmological correlators can be understood through their singularities as energies are conserved, similar to how scattering amplitudes are understood through their singularities.
- Symmetries of de Sitter space constrain how these singularities are connected in the physical regime.
- Unitarity constraints like the optical theorem provide additional restrictions on the form of correlators.
- Oscillatory features in certain correlators can encode information about particle production during inflation,
The document outlines a seminar on how quantum events may play a role in coherent biomolecular systems. It discusses several topics: (1) introducing motivations around reconciling quantum mechanics and relativity in biological systems; (2) exploring quantum network dynamics and structures like solitons that could provide stability; and (3) investigating chiral and tensegrity-stable solitons in higher dimensions that may model quantum networks sustaining topological identities. The goal is to better understand intracellular control and signaling at the quantum scale.
Evidence of Jet Activity from the Secondary Black Hole in the OJ 287 Binary S...Sérgio Sacani
Wereport the study of a huge optical intraday flare on 2021 November 12 at 2 a.m. UT in the blazar OJ287. In the binary black hole model, it is associated with an impact of the secondary black hole on the accretion disk of the primary. Our multifrequency observing campaign was set up to search for such a signature of the impact based on a prediction made 8 yr earlier. The first I-band results of the flare have already been reported by Kishore et al. (2024). Here we combine these data with our monitoring in the R-band. There is a big change in the R–I spectral index by 1.0 ±0.1 between the normal background and the flare, suggesting a new component of radiation. The polarization variation during the rise of the flare suggests the same. The limits on the source size place it most reasonably in the jet of the secondary BH. We then ask why we have not seen this phenomenon before. We show that OJ287 was never before observed with sufficient sensitivity on the night when the flare should have happened according to the binary model. We also study the probability that this flare is just an oversized example of intraday variability using the Krakow data set of intense monitoring between 2015 and 2023. We find that the occurrence of a flare of this size and rapidity is unlikely. In machine-readable Tables 1 and 2, we give the full orbit-linked historical light curve of OJ287 as well as the dense monitoring sample of Krakow.
Compositions of iron-meteorite parent bodies constrainthe structure of the pr...Sérgio Sacani
Magmatic iron-meteorite parent bodies are the earliest planetesimals in the Solar System,and they preserve information about conditions and planet-forming processes in thesolar nebula. In this study, we include comprehensive elemental compositions andfractional-crystallization modeling for iron meteorites from the cores of five differenti-ated asteroids from the inner Solar System. Together with previous results of metalliccores from the outer Solar System, we conclude that asteroidal cores from the outerSolar System have smaller sizes, elevated siderophile-element abundances, and simplercrystallization processes than those from the inner Solar System. These differences arerelated to the formation locations of the parent asteroids because the solar protoplane-tary disk varied in redox conditions, elemental distributions, and dynamics at differentheliocentric distances. Using highly siderophile-element data from iron meteorites, wereconstruct the distribution of calcium-aluminum-rich inclusions (CAIs) across theprotoplanetary disk within the first million years of Solar-System history. CAIs, the firstsolids to condense in the Solar System, formed close to the Sun. They were, however,concentrated within the outer disk and depleted within the inner disk. Future modelsof the structure and evolution of the protoplanetary disk should account for this dis-tribution pattern of CAIs.
Contenu connexe
Similaire à Statistical Physics of Complex Dynamics
Community search is the problem of finding a good community for a given set of query vertices.
In this work we propose a novel method that it is in general more efficient and effective than state-of-the art, it can handle multiple query vertices, it yields optimal communities, and it is parameter free.
This document summarizes a study that models electromagnetic wave propagation through crowds of people at GSM frequencies. The crowd is modeled as randomly oriented dielectric cylinders of varying sizes to represent humans. Simulations are run to determine the attenuation of electromagnetic radiation for different crowd densities, frequencies, and polarizations. The results show that crowds can significantly attenuate electromagnetic waves through absorption and scattering. Modeling crowds as discrete scatterers provides insights into how human presence affects wireless signal propagation.
The Algorithms of Life - Scientific Computing for Systems Biologyinside-BigData.com
In this deck from ISC 2019, Ivo Sbalzarini from TU Dresden presents: The Algorithms of Life - Scientific Computing for Systems Biology. In his talk, Sbalzarini mainly discussed the rapidly growing importance and influence in the life sciences for scientific high-performance computing.
"Scientific high-performance computing is of rapidly growing importance and influence in the life sciences. Thanks to the increasing knowledge about the molecular foundations of life, recent advances in biomedical data science, and the availability of predictive biophysical theories that can be numerically simulated, mechanistic understanding of the emergence of life comes within reach. Computing is playing a pivotal and catalytic role in this scientific revolution, both as a tool of investigation and hypothesis testing, but also as a school of thought and systems model. This is because a developing tissue, embryo, or organ can itself be seen as a massively parallel distributed computing system that collectively self-organizes to bring about behavior we call life. In any multicellular organism, every cell constantly takes decisions about growth, division, and migration based on local information, with cells communicating with each other via chemical, mechanical, and electrical signals across length scales from nanometers to meters. Each cell can therefore be understood as a mechano-chemical processing element in a complexly interconnected million- or billion-core computing system. Mechanistically understanding and reprogramming this system is a grand challenge. While the “hardware” (proteins, lipids, etc.) and the “source code” (genetic code) are increasingly known, we known virtually nothing about the algorithms that this code implements on this hardware. Our vision is to contribute to this challenge by developing computational methods and software systems for high-performance data analysis, inference, and numerical simulation of computer models of biological tissues, incorporating the known biochemistry and biophysics in 3D-space and time, in order to understand biological processes on an algorithmic basis. This ranges from real-time approaches to biomedical image analysis, to novel simulation languages for parallel high-performance computing, to virtual reality and machine learning for 3D microscopy and numerical simulations of coupled biochemical-biomechanical models. The cooperative, interdisciplinary effort to develop and advance our understanding of life using computational approaches not only places high-performance computing center stage, but also provides stimulating impulses for the future development of this field."
Watch the video: https://wp.me/p3RLHQ-kBB
Learn more: https://www.isc-hpc.com/
Sign up for our insideHPC Newsletter: http://insidehpc.com/newsletter
This document describes a new method for detecting community structure in complex networks based on node similarity. The method works as follows:
1. It calculates the similarity between all node pairs using a local node similarity metric.
2. It treats each node as its own community initially. Then it iteratively incorporates the community of the current node with the communities containing its most similar nodes.
3. It selects the most similar uncovered node as the next current node, and repeats the process until all nodes have been incorporated into communities.
The method requires only local network information and has a computational complexity of O(nk) for a network with n nodes and average degree k. It is evaluated on real and computer-generated networks, demonstrating
Some key models of social network generation are discussed, including random graph models, Watts-Strogatz models, and scale-free networks. Scale-free networks can generate networks with few components, small diameters, and heavy-tailed degree distributions, but do not capture high clustering. Biological networks like metabolic and protein interaction networks also tend to be scale-free.
A Technique for Partially Solving a Family of Diffusion Problemsijtsrd
Our aim in this paper is to expose the interesting role played by differ integral specifically, semi derivatives and semi integrals in solving certain diffusion problems. Along with the wave equation and Laplace equation, the diffusion equation is one of the three fundamental partial differential equation of mathematical physics. I will not discuss convential solutions of the diffusion equation at all. These range from closed form solutions for very simple model problems to computer methods for approximating the concentration of the diffusing substance on a network of points. Such solutions are described extensively in the literature .My purpose, rather, is to expose a technique for partially solving a family of diffusion problems, a technique that leads to a compact equation which is first order partially and half order temporally. I shall show that, for semi finite systems initially at equilibrium, our semi differential equation leads to a relationship between the intensive variable and the flux at the boundary. Use of this relationship then obviates the need to solve the original diffusion equation in those problems for which this behavior at the boundary is of primary importance. I shall, in fact, freely make use of the general properties established for differ integral operators as if all my functions were differ integrable. Dr. Ayaz Ahmad "A Technique for Partially Solving a Family of Diffusion Problems" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-2 | Issue-6 , October 2018, URL: http://www.ijtsrd.com/papers/ijtsrd18576.pdf
1) Mature dendritic cells project dendrite-like protrusions that allow them to scan a larger area than their cell body.
2) Upon initial contact with a T cell via a dendrite, dendritic cells project numerous mobile membrane extensions and migrate their cell body toward the T cell to tightly entangle it.
3) Using time-lapse microscopy and two-photon imaging of lymph nodes, the study observed dendritic cells polarizing membrane extensions and migrating toward T cells after initial dendrite-mediated contact, before tight conjugation.
1. The document discusses using call detail record (CDR) data to study how mobile phone users manage their social contacts over time and characterize or predict social turnover.
2. By detecting new and old social relationships from CDRs that show communication patterns and frequencies between users, the author aims to analyze how users' social networks evolve and change.
3. The author proposes studying properties like the distribution of inter-event times between calls to the same contact and how this distribution depends on relationship longevity to provide insights into social turnover.
This document summarizes research on creating an isotropic photonic band gap in a 2D disordered dielectric structure. Key points:
- Researchers designed a hyperuniform disordered network of dielectric cylinders and walls that combines advantages of disorder (isotropy) and controlled scattering properties (hyperuniformity and uniform local topology).
- Experiments realized this structure using alumina cylinders and walls and observed a complete photonic band gap in the microwave region, matching theoretical simulations.
- The intrinsic isotropy of this material enables arbitrary waveguide bending, unlike photonic crystals which are anisotropic due to periodicity. This demonstrates potential for precise photon manipulation in planar optical circuits.
These are slides for my tutorial talk on network dynamics. (The colors are fine in the downloaded version, though there seem to be color issues if you view the slides directly in slideshare.)
This document summarizes research on direct non-linear inversion of 1D acoustic media using the inverse scattering series. Key points:
- A method is derived for directly inverting 1D acoustic media with varying velocity and density, without requiring an estimate of properties above reflectors or assuming linear relationships between property changes and reflection data.
- Testing on a single reflector case showed improved estimates of property changes beyond the reflector compared to linear methods, for a wider range of angles.
- A special parameter related to velocity change was identified that has the correct sign in the linear inversion and is not affected by issues like "leakage" that complicate inversions.
The document discusses issues with computational scientific software and proposes a solution called Digital Scientific Notations. Current scientific software is difficult to test and validate due to a lack of specifications and documentation. This makes the software results unverifiable and prevents comparison of different models. The proposed Digital Scientific Notations would embed computational models and methods into scholarly documents using a formal programming language. This would allow models to be precisely defined, validated, and compared, addressing current verification and reproducibility problems in computational science.
This document summarizes a presentation on machine learning of epidemic processes in networks. It discusses using machine learning to predict epidemic spreading from network structure. Specifically, it covers using features like degree, clustering, and centrality measures as inputs to algorithms like random forests and neural networks to predict the fraction of infected nodes. The best approach uses a combination of network measures, not a single measure. This allows machine learning to help identify influential spreaders and understand how network structure influences epidemic dynamics.
Abstracts Of The Emerging Scholars Program Research Projects Fall 2010 Suppor...Claire Webber
This document provides abstracts summarizing 18 undergraduate research projects supported by CUNY Compact funds in Spring 2008. The projects covered a diverse range of topics across various departments including physics, biology, mathematics, engineering, architecture and chemistry. For each project, the abstract lists the student researcher, faculty mentor, department, and provides a brief 3 sentence summary of the project title, aims, methods, and results or conclusions.
THE ISSUE OF UNCERTAINTY FOR HYDROLOGIC EVENTS IN THE MISSOURI RIVER WATERSHE...Boris Shmagin
1. The document discusses a paradigm shift in science and methodology due to computers, with concepts moving from a simple to complex world. Pattern recognition problems in cognitive science helped develop new methods.
2. The new paradigm introduces direct search for solutions, emphasis on decision making, and a unity of technical and holistic languages for pattern description. This leads to a convergence of exact science and humanities.
3. The main difference between the new and old paradigms is a focus on controlling algorithm complexity rather than function complexity to guarantee inference success. Low complexity algorithms can create complex functions that generalize well.
A@kash Physics NCERT Maps.pdf physics short notes physics short notes physics...FahadAlam52
Physics short notes physics short notes physics short notes physics short notes physics short notes physics short notes physics short notes physics short notes physics short notes physics short notes physics short notes physics short notes physics short notes physics short notes physics short notes physics short notes physics short notes physics short notes physics short notes physics short notes physics short notes physics short notes physics short notes physics short notes physics short notes physics short notes physics short notes physics short notes physics short notes physics short notes physics short notes physics short notes physics short notes physics short notes physics short notes physics short notes physics short notes physics short notes
The document summarizes recent progress in developing a "cosmological bootstrap" approach to predicting cosmological correlations directly from fundamental physical principles like locality, causality and unitarity, without relying on explicit models of inflation or particle physics. Key points include:
- Cosmological correlators can be understood through their singularities as energies are conserved, similar to how scattering amplitudes are understood through their singularities.
- Symmetries of de Sitter space constrain how these singularities are connected in the physical regime.
- Unitarity constraints like the optical theorem provide additional restrictions on the form of correlators.
- Oscillatory features in certain correlators can encode information about particle production during inflation,
The document outlines a seminar on how quantum events may play a role in coherent biomolecular systems. It discusses several topics: (1) introducing motivations around reconciling quantum mechanics and relativity in biological systems; (2) exploring quantum network dynamics and structures like solitons that could provide stability; and (3) investigating chiral and tensegrity-stable solitons in higher dimensions that may model quantum networks sustaining topological identities. The goal is to better understand intracellular control and signaling at the quantum scale.
Similaire à Statistical Physics of Complex Dynamics (20)
Evidence of Jet Activity from the Secondary Black Hole in the OJ 287 Binary S...Sérgio Sacani
Wereport the study of a huge optical intraday flare on 2021 November 12 at 2 a.m. UT in the blazar OJ287. In the binary black hole model, it is associated with an impact of the secondary black hole on the accretion disk of the primary. Our multifrequency observing campaign was set up to search for such a signature of the impact based on a prediction made 8 yr earlier. The first I-band results of the flare have already been reported by Kishore et al. (2024). Here we combine these data with our monitoring in the R-band. There is a big change in the R–I spectral index by 1.0 ±0.1 between the normal background and the flare, suggesting a new component of radiation. The polarization variation during the rise of the flare suggests the same. The limits on the source size place it most reasonably in the jet of the secondary BH. We then ask why we have not seen this phenomenon before. We show that OJ287 was never before observed with sufficient sensitivity on the night when the flare should have happened according to the binary model. We also study the probability that this flare is just an oversized example of intraday variability using the Krakow data set of intense monitoring between 2015 and 2023. We find that the occurrence of a flare of this size and rapidity is unlikely. In machine-readable Tables 1 and 2, we give the full orbit-linked historical light curve of OJ287 as well as the dense monitoring sample of Krakow.
Compositions of iron-meteorite parent bodies constrainthe structure of the pr...Sérgio Sacani
Magmatic iron-meteorite parent bodies are the earliest planetesimals in the Solar System,and they preserve information about conditions and planet-forming processes in thesolar nebula. In this study, we include comprehensive elemental compositions andfractional-crystallization modeling for iron meteorites from the cores of five differenti-ated asteroids from the inner Solar System. Together with previous results of metalliccores from the outer Solar System, we conclude that asteroidal cores from the outerSolar System have smaller sizes, elevated siderophile-element abundances, and simplercrystallization processes than those from the inner Solar System. These differences arerelated to the formation locations of the parent asteroids because the solar protoplane-tary disk varied in redox conditions, elemental distributions, and dynamics at differentheliocentric distances. Using highly siderophile-element data from iron meteorites, wereconstruct the distribution of calcium-aluminum-rich inclusions (CAIs) across theprotoplanetary disk within the first million years of Solar-System history. CAIs, the firstsolids to condense in the Solar System, formed close to the Sun. They were, however,concentrated within the outer disk and depleted within the inner disk. Future modelsof the structure and evolution of the protoplanetary disk should account for this dis-tribution pattern of CAIs.
The cost of acquiring information by natural selectionCarl Bergstrom
This is a short talk that I gave at the Banff International Research Station workshop on Modeling and Theory in Population Biology. The idea is to try to understand how the burden of natural selection relates to the amount of information that selection puts into the genome.
It's based on the first part of this research paper:
The cost of information acquisition by natural selection
Ryan Seamus McGee, Olivia Kosterlitz, Artem Kaznatcheev, Benjamin Kerr, Carl T. Bergstrom
bioRxiv 2022.07.02.498577; doi: https://doi.org/10.1101/2022.07.02.498577
Mending Clothing to Support Sustainable Fashion_CIMaR 2024.pdfSelcen Ozturkcan
Ozturkcan, S., Berndt, A., & Angelakis, A. (2024). Mending clothing to support sustainable fashion. Presented at the 31st Annual Conference by the Consortium for International Marketing Research (CIMaR), 10-13 Jun 2024, University of Gävle, Sweden.
Embracing Deep Variability For Reproducibility and Replicability
Abstract: Reproducibility (aka determinism in some cases) constitutes a fundamental aspect in various fields of computer science, such as floating-point computations in numerical analysis and simulation, concurrency models in parallelism, reproducible builds for third parties integration and packaging, and containerization for execution environments. These concepts, while pervasive across diverse concerns, often exhibit intricate inter-dependencies, making it challenging to achieve a comprehensive understanding. In this short and vision paper we delve into the application of software engineering techniques, specifically variability management, to systematically identify and explicit points of variability that may give rise to reproducibility issues (eg language, libraries, compiler, virtual machine, OS, environment variables, etc). The primary objectives are: i) gaining insights into the variability layers and their possible interactions, ii) capturing and documenting configurations for the sake of reproducibility, and iii) exploring diverse configurations to replicate, and hence validate and ensure the robustness of results. By adopting these methodologies, we aim to address the complexities associated with reproducibility and replicability in modern software systems and environments, facilitating a more comprehensive and nuanced perspective on these critical aspects.
https://hal.science/hal-04582287
Mechanisms and Applications of Antiviral Neutralizing Antibodies - Creative B...Creative-Biolabs
Neutralizing antibodies, pivotal in immune defense, specifically bind and inhibit viral pathogens, thereby playing a crucial role in protecting against and mitigating infectious diseases. In this slide, we will introduce what antibodies and neutralizing antibodies are, the production and regulation of neutralizing antibodies, their mechanisms of action, classification and applications, as well as the challenges they face.
Microbial interaction
Microorganisms interacts with each other and can be physically associated with another organisms in a variety of ways.
One organism can be located on the surface of another organism as an ectobiont or located within another organism as endobiont.
Microbial interaction may be positive such as mutualism, proto-cooperation, commensalism or may be negative such as parasitism, predation or competition
Types of microbial interaction
Positive interaction: mutualism, proto-cooperation, commensalism
Negative interaction: Ammensalism (antagonism), parasitism, predation, competition
I. Mutualism:
It is defined as the relationship in which each organism in interaction gets benefits from association. It is an obligatory relationship in which mutualist and host are metabolically dependent on each other.
Mutualistic relationship is very specific where one member of association cannot be replaced by another species.
Mutualism require close physical contact between interacting organisms.
Relationship of mutualism allows organisms to exist in habitat that could not occupied by either species alone.
Mutualistic relationship between organisms allows them to act as a single organism.
Examples of mutualism:
i. Lichens:
Lichens are excellent example of mutualism.
They are the association of specific fungi and certain genus of algae. In lichen, fungal partner is called mycobiont and algal partner is called
II. Syntrophism:
It is an association in which the growth of one organism either depends on or improved by the substrate provided by another organism.
In syntrophism both organism in association gets benefits.
Compound A
Utilized by population 1
Compound B
Utilized by population 2
Compound C
utilized by both Population 1+2
Products
In this theoretical example of syntrophism, population 1 is able to utilize and metabolize compound A, forming compound B but cannot metabolize beyond compound B without co-operation of population 2. Population 2is unable to utilize compound A but it can metabolize compound B forming compound C. Then both population 1 and 2 are able to carry out metabolic reaction which leads to formation of end product that neither population could produce alone.
Examples of syntrophism:
i. Methanogenic ecosystem in sludge digester
Methane produced by methanogenic bacteria depends upon interspecies hydrogen transfer by other fermentative bacteria.
Anaerobic fermentative bacteria generate CO2 and H2 utilizing carbohydrates which is then utilized by methanogenic bacteria (Methanobacter) to produce methane.
ii. Lactobacillus arobinosus and Enterococcus faecalis:
In the minimal media, Lactobacillus arobinosus and Enterococcus faecalis are able to grow together but not alone.
The synergistic relationship between E. faecalis and L. arobinosus occurs in which E. faecalis require folic acid
Immunotherapy presentation from clinical immunology
Statistical Physics of Complex Dynamics
1. Hang-Hyun Jo
Asia Pacific Center for Theoretical Physics, Republic of Korea
Dept. of Physics, Pohang University of Science and Technology, Republic of Korea
Statistical Physics of
Complex Dynamics
2. Junior Research Group
• Title: Statistical Physics of Complex Dynamics (CoDy)
• Period: May 1, 2017—April 30, 2022
• Members: Hang-Hyun Jo (leader),
Byoung-Hwa Lee (PhD student),
Takayuki Hiraoka (postdoc, since July)
6. Real world networks
10
0
10
1
10
2
10
10
6
10
4
10
2
10
0
100 102 104 106 108
10
10 12
10 10
10 8
10 6
10 4
10 2
vi vj
Oij=0 Oij=1/3
Oij=1Oij=2/3
A B
<O>
w
,<O>
b
0 0.2 0.4 0.6 0.8 1
0
0.05
0.1
0.15
0.2
P
cum
(w), P
cum
(b)
C D
Degree k Link weight w (s)
P(k)
P(w)
Fig. 1. Characterizing the large-scale structure and the tie strengths of the
mobile call graph. (A and B) Vertex degree (A) and tie strength distribution (B).
Each distribution was fitted with P(x) ϭ a(x ϩ x0)Ϫx exp(Ϫx/xc), shown as a blue
A
B
1
100
10
Internet by K. C. Claffy
Protein-protein interaction
by H. Jeong
Mobile phone user network
by J.-P. Onnela
Thanks to the large-scale digital datasets or “Big Data”
7. • Node: elements in a system
• Link: interaction between elements
8. Local property Global property
Topological
property
Heterogeneous degree
Assortativity
Local clustering
etc.
Small-world effect
Community structure
etc.
Intensity-related
property
Heterogeneous weight
and strength
Neighborhood overlap
etc.
“Strength of weak tie”
hypothesis
etc.
Network properties
9. 3
TABLE I. Stylized facts derived from various datasets with the expected behaviors for the whole social network [20, 21].
The symbol % (&) implies that the overall trend is monotonically increasing (decreasing). The initially increasing and then
decreasing behavior is denoted by %&. For the Granovetterian community structure, see the main text for the details.
Category Property or measure Stylized fact (expectation)
Topological Degree distribution, P(k) & (%&)
Average degree of neighbors as a function of degree, knn(k) %
Local clustering coe cient as a function of degree, c(k) &
Community size distribution, P(g) &
Intensity-related Strength distribution, P(s) & (%&)
Weight distribution, P(w) &
Strength as a function of degree, s(k) %
Neighborhood overlap as a function of weight, o(w) %
Granovetterian community structure, fc > 0
corresponding to ⇠ k2
i in Eq. (3), is typically stronger
than that of finding new links between neighbors, in re-
lation to ei in Eq. (3). For example, if every new neighbor
of a node i creates a new link to one of node i’s existing
neighbors, then ei ⇠ ki, leading to c(k) ⇠ k 1
. This be-
havior can be measured in terms of the PCC between ci
and ki, which is denoted hereafter as ⇢ck.
The intensities are correlated with topological proper-
ties, which can be called intensity-topology correlation
or weight-topology correlation as used in [9]. A link-
level consequence of intensity-topology correlation can be
measured by the average neighborhood overlap for links
with weight w, denoted by o(w). The neighborhood over-
lap of a link is the fraction of common neighbors of neigh-
Stylized facts in social networks
Jo et al., arXiv:1611.03664 (2016)
11. Why temporal networks?
• Directionality due to the time asymmetry
• Speed of collective dynamics depends on the
interaction activity.
P. Holme, J. Saramäki / Physics Reports 519 (2012) 97–125 99
the reachability issue and the intransitivity of temporal networks (more specifically a contact sequence). In (a), the times of the
ces A–D are indicated on the edges. Assume that, for example, a disease starts spreading at vertex A and spreads further as soon
e dashed lines and vertices show this spreading process for four different times. The spreading will not continue further than what
1 picture, i.e. D cannot get infected. However, if the spreading started at vertex D, the entire set of vertices would eventually be
he edges into one static graph cannot capture this effect that arises from the time ordering of contacts. Panel (b) visualizes the same
he temporal dimension explicitly. The colors of the lines in (b) match the vertex colors in (a).
e time evolution of the network structure in these windows. Such an approach does not cover all aspects
ructure of contact patterns. For example, the edges between vertices of temporal networks need not be
networks, whether directed or not, if A is directly connected to B and B is directly connected to C, then A
Holme, Saramaki,
Physics Reports (2012)
Information from D reaches A, but not the other way around!
12. event
time
burst
communitiesindividuals
Threshold, t = 0.20
t = 0.27
0.4
D
0.6 0.8 1
Largest
subcommunity
Remaining
hierarchy
t
0 0.2 0.4 0.6 0.8
Word association
2 0.4 0.6 0.8
drogram threshold, t
Metabolic
Largest
community
Second
largest
Third largest
Ahnetal.,Nature(2010)
Jo (in preparation)
22. Cyclic “Poisson” process
Malmgren et al., PNAS (2008)
time-varying rate with weekly cycle for e-mail usage
heavy tail of inter-event time distribution
Are weekly cycles the ONLY reason for bursts?
23. De-seasoning cycles?
Jo et al., NJP (2012)
mobile call sequence of one user
: weekly cycle (T=7 days)⇢(t)
: no cyclic patterns⇢⇤
(t⇤
) = 1
de-seasoned by weekly cycle
B7 = 0.146
B0 = 0.224
B =
h⌧i
+ h⌧i
24. Bursts are robust!
Burstiness remains finite after
de-seasoning weekly cycles.
burstiness
de-seasoning period (days)
different activity groupGolden moles have a blue-green sheen to their
coats that is a rare example of iridescence in
mammals, report Matthew Shawkey at the
University of Akron in Ohio and his colleagues.
The group conducted the first detailed study of
iridescent outer hairs and non-iridescent downy
hairs from four species of golden mole. Iridescent
hairs were highly flattened with much smaller
scales than their less eye-catching counterparts.
The scales form multiple layers, which alternate
in colour between light and dark, and probably
produce colour as light passes between layers in a
phenomenon called thin-film interference.
All four mole species are blind, so it is unlikely
that the hairs evolved as sexual ornamentation.
The authors suggest that the iridescence of
these burrowing animals is a by-product of
adaptations for durable, low-friction pelts.
Biol. Lett. http://dx.doi.org/10.1098/rsbl.2011.1168
(2012)
EVOLUTION
Glad rags for a blind mole
cannot currently be cultured,
their genomes may soon be
accessible.
Until now, metagenomic
analyses have been able
to identify only dominant
members of a microbial
community or those sequenced
previously. Virginia Armbrust
and her group at the University
of Washington in Seattle
developed computational
tools to tame the massive
amount of data produced by
next-generation sequencers.
The method successfully
sequenced two of 14 candidate
genomes identified in samples
from Puget Sound, most
notably a microbe of low
abundance but great interest
— a representative of the
mysterious, as yet uncultured
organisms known as marine
group II Euryarchaeota.
Researchers now have a way
to peer into the secret lives of
the uncultured majority.
Science 335, 587–590 (2012)
CANCER DRUGS
Chemo spans
generations
Some commonly used cancer
drugs not only generate
mutations in treated mice,
but scar the genomes of their
NETWORKS
Patchy
communication
People tend to communicate
with each other in bursts,
exchanging clusters of
messages over short time
periods, and following
these up with longer gaps in
communication. But are these
patterns simply the result of a
tendency to talk more during
the day and the working week?
Hang-Hyun Jo of Aalto
University in Finland and
his colleagues found that
these temporal cycles are not
sufficient to explain the bursts.
They analysed 322 million
mobile-phone calls between
more than 5 million users
over 119 days in 2007. After
removing the effects of the
day–night and working-week
cycles, the bursts remained.
The authors suggest that
the patterns reflect something
fundamental in the way that
people communicate.
N. J. Phys. 14, 013055 (2012)
P
C.PFEIFFER&P.HALEY
MATERIALS
Printing tiny
coiled antennas
Typically, the largest circuit
component in wireless
electronic devices such as
mobile phones is the antenna,
which sends and receives
electromagnetic waves. The
tiniest antennas available are
made up of wires twisted into
three-dimensional coils to save
on space while maintaining
high radiation efficiency and
wide bandwidth. But bending
wires is cumbersome and
expensive.
Stephen Forrest and
Anthony Grbic at the
University of Michigan in Ann
Arbor and their colleagues
report a way to rapidly transfer
metallic patterns directly onto
a curved polymer, which can
be pre-moulded to a desired
shape. Stamping the pattern
onto a hemispherical polymer,
for instance, produces
miniature high-performance
antennas curled in spherical
helices (pictured).
Adv. Mater. http://dx.doi.org/10.
1002/adma/201104290 (2012)
Nature (2012)
26. Memory coefficient
⌧⌧
time
Goh & Barabási, EPL (2008)
M =
h(⌧i h⌧i)(⌧i+1 h⌧i)i
2
K.-I. Goh and A. L. Barab´asi
-1
-0.75
-0.5
-0.25
0
0.25
0.5
0.75
1
-1 -0.75 -0.5 -0.25 0 0.25 0.5 0.75 1
B
M
a
heartbeat
-0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4
-0.1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
B
M
b
human
activities
texts
natural
phenomena
Fig. 4: (Color online) (a) The (M, B) phase diagram. Human activities (red) are captured by activity patte
email (⋆) [5], library loans (◦) [7], and printing ( ) [28] of individuals in Universities, call center record at an
( ) [29], and phone initiation record from a mobile phone company (⋄). Data for natural phenomena (black
records in Japan (•) [26] and daily precipitation records in New Mexico, USA ( ) [27]. Data for written tex
27. Bursty train size distribution
E = 1E = 5 E = 4E = 2 E = 1 E = 2
time
t
P t(E) ⇠ E
Karsai et al., Sci. Rep. (2012)
P t(E) ⇠ e E/Ec
for uncorrelated inter-event times
for highly correlated inter-event times
: correlated bursts
29. Figure 2.1: Schematic diagramme of an event sequence, where each vertical line
indicates the timing of the event. (a) The inter-event time ⌧ is the time interval
between two consecutive events. The residual time ⌧r is the time interval from
a random moment (e.g., the timing annotated by the vertical arrow) to the next
event. (b) For a given time window t, a bursty train is determined by a set
of events separated by ⌧ t, while events in di↵erent trains are separated by
⌧ > t. The number of events in each train, i.e., burst size, is denoted by E. In
most empirical datasets, both distributions of ⌧ and E are heavy-tailed.
for i = 1, · · · , n 1. From this we construct the sequence of inter-event times, i.e.,
{⌧1, · · · , ⌧n 1}. By ignoring the order of inter-event times, we obtain the inter-
event time distribution P(⌧). For the completely regular time series, all inter-event
times are the same as the mean inter-event time denoted by h⌧i. The inter-event
time distribution then reads P(⌧) = (⌧ h⌧i), where (·) denotes the Dirac delta
function. Here the standard deviation of inter-event times, denoted by , is zero.
P(⌧) ⇠ ⌧ ↵
A(td) ⇠ tdP t(E) ⇠ E
⇠ td for 0 < < 1, then one finds the scaling
f) ⇠ f ⌘
with
⌘ = 1 . (4)
n the interevent times are i.i.d. random variables
P(⌧) ⇠ ⌧ ↵
, implying no interdependency between
event times, the power-law exponent ⌘ is obtained
unction of ↵ as follows [11, 12]:
⌘ =
8
<
:
↵ 1 for 1 < ↵ 2,
3 ↵ for 2 < ↵ 3,
0 for ↵ > 3.
(5)
bining Eqs. (4) and (5), we have
↵ + = 2 for 1 < ↵ 2, (6)
↵ = 2 for 2 < ↵ 3. (7)
e power-law exponents can also be related via Hurst
nent H, i.e., = 2 2H [13] or ⌘ = 2H 1 [12, 14].
for uncorrelated inter-event times
What if inter-event times are correlated?
31. Other result: Exponential P(E)
Two-state Markov-chain Poisson nature of individual cellphone call statistics
Jiang et al., J. Stat. Mech. (2016)
32. PHYSICAL REVIEW E 94, 032311 (2016)
Measuring burstiness for finite event sequences
Eun-Kyeong Kim1
and Hang-Hyun Jo2,3,*
1
GeoVISTA Center, Department of Geography, Pennsylvania State University, PA 16802, USA
2
BK21plus Physics Division and Department of Physics, Pohang University of Science and Technology, Pohang 37673, Republic of Korea
3
Department of Computer Science, Aalto University School of Science, P. O. Box 15500, Espoo, Finland
(Received 4 April 2016; published 15 September 2016)
Characterizing inhomogeneous temporal patterns in natural and social phenomena is important to understand
underlying mechanisms behind such complex systems and, hence, even to predict and control them. Temporal
inhomogeneities in event sequences have been described in terms of bursts that are rapidly occurring events in
short time periods alternating with long inactive periods. The bursts can be quantified by a simple measure, called
the burstiness parameter, which was introduced by Goh and Barab´asi [Europhys. Lett. 81, 48002 (2008)]. The
burstiness parameter has been widely used due to its simplicity, which, however, turns out to be strongly affected
by the finite number of events in the time series. As the finite-size effects on burstiness parameter have been
largely ignored, we analytically investigate the finite-size effects of the burstiness parameter. Then we suggest
an alternative definition of burstiness that is free from finite-size effects and yet simple. Using our alternative
burstiness measure, one can distinguish the finite-size effects from the intrinsic bursty properties in the time
series. We also demonstrate the advantages of our burstiness measure by analyzing empirical data sets.
DOI: 10.1103/PhysRevE.94.032311
I. INTRODUCTION spatiotemporal organization of aftershocks in seismology [23].
In addition, higher-order correlations between interevent times
Novel burstiness measure
33. Burstiness parameter
• regular time series:
• Poisson or random time series:
• bursty time series:
r = 0, B = 1
r = 1, B = 0
r ! 1, B ! 1
B =
µ
+ µ
=
r 1
r + 1
r =
µ
: coefficient of variation (CV)
➜ only when # of events is infinite!
(µ = h⌧i)
34. Motivation
• # of events = n
• All empirical datasets have finite n.
• Elements of small n have been arbitrarily ignored.
• How to isolate finite-size effects from intrinsic
bursty dynamics?
35. Single burst model
t1 tn
n events
: total period
: lower bound of inter-event time
inter-event times under
periodic boundary condition:
we conclude
n events, each
time interval
ings, and the
i = 1, · · · , n.
condition in
oundary con-
ent times are
(2)
ime distribu-
= 1
FIG. 1. Schematic diagram of the localized model: n events
are localized in the period beginning at t0 in [0, T), and
they are separated from each other at least by ⌧0.
B. Localized model
We now consider the general case that all events are
localized in the interval [t0, t0 + ) with t0 0 and
t0+ < T, indicating that events do not take place in the
intervals [0, t0) and [t0 + , T), as depicted in Fig. 1. A
similar model has been studied in a di↵erent context [27].
The localization parameter is introduced to simulate
the bursty limit for ⌧ T. Since we use periodic bound-
ary condition, t0 can be ignored. In addition, the lower
bound of interevent time, ⌧0, is introduced, implying that
events must be separated from each other at least by ⌧0.
Accordingly, it is assumed that
(n 1)⌧0 T ⌧0, (8)
leading to ⌧0 T
n . If ⌧0 = T
n , one gets the regular time
series.
⌧i =
(
T tn + t1 if i = 1
ti ti 1 if i = 2, · · · , n
36. Order statistics analysis
placed by ⌘ (n 1)⌧0 to define interevent times
as
⌧i ⌘
⇢
⌧1, + T if i = 1
⌧i, + ⌧0 if i 6= 1.
(9)
Using Eq. (3), we get
h⌧ii =
⇢
T n 1
n+1 ( + 2⌧0) if i = 1
+2⌧0
n+1 if i 6= 1,
(10)
and
h⌧2
i i =
(
6 2
(n+1)(n+2) + 4(T )
n+1 + (T )2
if i = 1
2 2
(n+1)(n+2) + 2⌧0
n+1 + ⌧2
0 if i 6= 1.
(11)
Then we calculate the mean µn and the variance 2
n of
interevent times to get the coe cient of variation rn =
n
µn
:
µn = 1
n [h⌧1i + (n 1)h⌧i6=1i], (12)
2
n = 1
n [h⌧2
1 i + (n 1)h⌧2
i6=1i] µ2
n, (13)
rn(x, y) =
q
(n 1)[1+n(1 x)2
+n(n+1)y2
2n(2 x)y]
n+1 .(14)
Here we have defined
(4)
(5)
(6)
each
tisfy
erage
(7)
tion.
as
⌧i ⌘
⇢
⌧1, + T if i = 1
⌧i, + ⌧0 if i 6= 1.
(9)
Using Eq. (3), we get
h⌧ii =
⇢
T n 1
n+1 ( + 2⌧0) if i = 1
+2⌧0
n+1 if i 6= 1,
(10)
and
h⌧2
i i =
(
6 2
(n+1)(n+2) + 4(T )
n+1 + (T )2
if i = 1
2 2
(n+1)(n+2) + 2⌧0
n+1 + ⌧2
0 if i 6= 1.
(11)
Then we calculate the mean µn and the variance 2
n of
interevent times to get the coe cient of variation rn =
n
µn
:
µn = 1
n [h⌧1i + (n 1)h⌧i6=1i], (12)
2
n = 1
n [h⌧2
1 i + (n 1)h⌧2
i6=1i] µ2
n, (13)
rn(x, y) =
q
(n 1)[1+n(1 x)2
+n(n+1)y2
2n(2 x)y]
n+1 .(14)
Here we have defined
x ⌘ T , y ⌘ ⌧0
T , (15)
discussed in Appendix A. Interevent times are
s
⌧i,d ⌘
⇢
d tn + t1 if i = 1
ti ti 1 if i 6= 1.
(2)
rder statistics [25, 26], interevent time distribu-
written as follows:
P(⌧i,d) =
8
<
:
(⌧1,d/d)(1 ⌧1,d/d)n 2
B(2,n 1)d if i = 1
(1 ⌧i,d/d)n 1
B(1,n)d if i 6= 1,
(3)
(n, m) denotes the beta function,
m) =
Z 1
0
zn 1
(1 z)m 1
dz = (n 1)!(m 1)!
(n+m 1)! . (4)
ion values of ⌧i,d and ⌧2
i,d are obtained as
h⌧i,di =
⇢ 2d
n+1 if i = 1
d
n+1 if i 6= 1,
(5)
(
the bursty limit for ⌧ T. Since we us
ary condition, t0 can be ignored. In ad
bound of interevent time, ⌧0, is introduc
events must be separated from each oth
Accordingly, it is assumed that
(n 1)⌧0 T ⌧0
leading to ⌧0 T
n . If ⌧0 = T
n , one gets
series.
Then, we use definitions in Eq. (2)
placed by ⌘ (n 1)⌧0 to define
as
⌧i ⌘
⇢
⌧1, + T if i =
⌧i, + ⌧0 if i 6=
Using Eq. (3), we get
h⌧ii =
⇢
T n 1
n+1 ( + 2⌧0) if
+2⌧0
n+1 if
and
h⌧2
i i =
(
6 2
(n+1)(n+2) + 4(T )
n+1 + (T
2 2
+ 2⌧0
+ ⌧2
0
Using Eq. (3), we get
h⌧ii =
⇢
T n 1
n+1 ( + 2⌧0) if i = 1
+2⌧0
n+1 if i 6= 1,
(10)
and
h⌧2
i i =
(
6 2
(n+1)(n+2) + 4(T )
n+1 + (T )2
if i = 1
2 2
(n+1)(n+2) + 2⌧0
n+1 + ⌧2
0 if i 6= 1.
(11)
Then we calculate the mean µn and the variance 2
n of
interevent times to get the coe cient of variation rn =
n
µn
:
µn = 1
n [h⌧1i + (n 1)h⌧i6=1i], (12)
2
n = 1
n [h⌧2
1 i + (n 1)h⌧2
i6=1i] µ2
n, (13)
rn(x, y) =
q
(n 1)[1+n(1 x)2
+n(n+1)y2
2n(2 x)y]
n+1 .(14)
Here we have defined
x ⌘ T , y ⌘ ⌧0
T , (15)
!
. (4)
s
(5)
(6)
of each
satisfy
average
(7)
ection.
Using Eq. (3), we get
h⌧ii =
⇢
T n 1
n+1 ( + 2⌧0) if i = 1
+2⌧0
n+1 if i 6= 1,
(10)
and
h⌧2
i i =
(
6 2
(n+1)(n+2) + 4(T )
n+1 + (T )2
if i = 1
2 2
(n+1)(n+2) + 2⌧0
n+1 + ⌧2
0 if i 6= 1.
(11)
Then we calculate the mean µn and the variance 2
n of
interevent times to get the coe cient of variation rn =
n
µn
:
µn = 1
n [h⌧1i + (n 1)h⌧i6=1i], (12)
2
n = 1
n [h⌧2
1 i + (n 1)h⌧2
i6=1i] µ2
n, (13)
rn(x, y) =
q
(n 1)[1+n(1 x)2
+n(n+1)y2
2n(2 x)y]
n+1 .(14)
Here we have defined
x ⌘ T , y ⌘ ⌧0
T , (15)
CV:
h⌧i,di =
⇢ 2d
n+1 if i = 1
d
n+1 if i 6= 1,
(5)
di =
(
6d2
(n+1)(n+2) if i = 1
2d2
(n+1)(n+2) if i 6= 1.
(6)
ed that ⌧i,ds are independent of each
they are not independent but to satisfy
n
i=1 ⌧i,d = d. Instead we find on average
i = h⌧1,di + (n 1)h⌧i6=1,di = d. (7)
e discussed later in the next Subsection.
i +2⌧0
n+1 if i 6= 1
and
h⌧2
i i =
(
6 2
(n+1)(n+2) + 4(T )
n+1 + (T )2
2 2
(n+1)(n+2) + 2⌧0
n+1 + ⌧2
0
Then we calculate the mean µn and the var
interevent times to get the coe cient of var
n
µn
:
µn = 1
n [h⌧1i + (n 1)h⌧i6=1i],
2
n = 1
n [h⌧2
1 i + (n 1)h⌧2
i6=1i] µ2
n,
rn(x, y) =
q
(n 1)[1+n(1 x)2
+n(n+1)y2
2n
n+1
Here we have defined
x ⌘ T , y ⌘ ⌧0
T ,
satisfying the conditions that
(n 1)y x 1 y, y 1
n . (16)
It is straightforward to show that rn(x, y) is a non-
increasing function of x and y, respectively.
In order to study the strong bias due to the finite size
of event sequences, we define the burstiness parameter
using x and y as follows:
Bn(x, y) ⌘ rn(x,y) 1
rn(x,y)+1 . (17)
satisfying the conditions that
(n 1)y x 1 y, y 1
n .
It is straightforward to show that rn(x, y) i
increasing function of x and y, respectively.
In order to study the strong bias due to the
of event sequences, we define the burstiness p
37. Reference cases
• regular time series:
• random time series:
• extremely bursty time series:
hat ⌧i,ds are independent of each
are not independent but to satisfy
i,d = d. Instead we find on average
⌧1,di + (n 1)h⌧i6=1,di = d. (7)
cussed later in the next Subsection.
n
µn
:
µn = 1
n [h⌧1i + (n 1)h⌧i6=1i],
2
n = 1
n [h⌧2
1 i + (n 1)h⌧2
i6=1i] µ2
n,
rn(x, y) =
q
(n 1)[1+n(1 x)2
+n(n+1)y2
2n(2 x)
n+1
Here we have defined
x ⌘ T , y ⌘ ⌧0
T ,
(n 1)y x 1 y, y 1
n . (16)
It is straightforward to show that rn(x, y) is a non-
increasing function of x and y, respectively.
In order to study the strong bias due to the finite size
of event sequences, we define the burstiness parameter
using x and y as follows:
Bn(x, y) ⌘ rn(x,y) 1
rn(x,y)+1 . (17)
We discuss three reference cases. Firstly, the regular time
series means that all interevent times are the same as
µn, implying that x = 1 1
n and y = 1
n . Since rn = 0
independent of n, we get
Bn(1 1
n , 1
n ) = 1. (18)
Secondly, the Poissonian or random time series corre-
sponds to the case with = T and ⌧0 = 0, i.e., x = 1
and y = 0, leading to rn =
q
n 1
n+1 . We get
Bn(1, 0) =
p
n 1
p
n+1p
n 1+
p
n+1
. (19)
Note that B1(1, 0) = 1 and that Bn(1, 0) is always nega-
tive but approaches 0 as n increases, i.e., Bn(1, 0) ⇡ 1
2n
for large n, as shown in Fig. 2(a). Since this result
FIG. 2. (Color onlin
three reference cases:
for random time serie
merical results for the
to the analytic result
ness parameter An(r
parameter B(r) in Eq
plot of B(r) for indivi
but using Twitter dat
C. Novel defi
increasing function of x and y, respectively.
In order to study the strong bias due to the finite size
of event sequences, we define the burstiness parameter
using x and y as follows:
Bn(x, y) ⌘ rn(x,y) 1
rn(x,y)+1 . (17)
We discuss three reference cases. Firstly, the regular time
series means that all interevent times are the same as
µn, implying that x = 1 1
n and y = 1
n . Since rn = 0
independent of n, we get
Bn(1 1
n , 1
n ) = 1. (18)
Secondly, the Poissonian or random time series corre-
sponds to the case with = T and ⌧0 = 0, i.e., x = 1
and y = 0, leading to rn =
q
n 1
n+1 . We get
Bn(1, 0) =
p
n 1
p
n+1p
n 1+
p
n+1
. (19)
Note that B1(1, 0) = 1 and that Bn(1, 0) is always nega-
tive but approaches 0 as n increases, i.e., Bn(1, 0) ⇡ 1
2n
for large n, as shown in Fig. 2(a). Since this result
is based on the assumption of independence of ⌧is, we
test our result by comparing it to numerical values of
burstiness parameter. For this, we generate 105
event se-
quences for each n to obtain the burstiness parameter as
FIG. 2. (Color on
three reference case
for random time ser
merical results for th
to the analytic resu
ness parameter An
parameter B(r) in E
plot of B(r) for indi
but using Twitter d
C. Novel de
In order to fix
rameter due to th
a novel definition
by An(r), where i
Bn(1 1
n , 1
n ) = 1. (18)
Secondly, the Poissonian or random time series corre-
sponds to the case with = T and ⌧0 = 0, i.e., x = 1
and y = 0, leading to rn =
q
n 1
n+1 . We get
Bn(1, 0) =
p
n 1
p
n+1p
n 1+
p
n+1
. (19)
Note that B1(1, 0) = 1 and that Bn(1, 0) is always nega-
tive but approaches 0 as n increases, i.e., Bn(1, 0) ⇡ 1
2n
for large n, as shown in Fig. 2(a). Since this result
is based on the assumption of independence of ⌧is, we
test our result by comparing it to numerical values of
burstiness parameter. For this, we generate 105
event se-
quences for each n to obtain the burstiness parameter as
depicted in Fig. 2(a). We find that the deviation of our
analytic results from the simulations is negligible.
Finally, the extremely bursty time series corresponds
to the case that all events occur asymptotically at the
same time, i.e., x = y = 0, leading to rn =
p
n 1. Thus
one gets
Bn(0, 0) =
p
n 1 1p
n 1+1
. (20)
Note that B1(0, 0) = 1 and B2(0, 0) = 0. Bn(0, 0) be-
comes positive for n 3, and then approaches 1 as n
FIG. 2. (Color onlin
three reference cases:
for random time serie
merical results for the
to the analytic result
ness parameter An(r
parameter B(r) in Eq
plot of B(r) for indivi
but using Twitter dat
C. Novel defi
In order to fix th
rameter due to the
a novel definition o
by An(r), where it
r = n
µn
. Then An(
tions:
A
A
which correspond t
extremely bursty ti
was originally defin
An(r) = anr bn
r+cn
wit
ying the conditions that
(n 1)y x 1 y, y 1
n . (16)
straightforward to show that rn(x, y) is a non-
sing function of x and y, respectively.
order to study the strong bias due to the finite size
nt sequences, we define the burstiness parameter
x and y as follows:
rn(x,y) 1
38. Novel burstiness measure
which correspond to the cases of regular, random, and
extremely bursty time series, respectively. Since B(r)
was originally defined as r 1
r+1 , we similarly assume that
An(r) = anr bn
r+cn
with coe cients an, bn, and cn. Using a
general formula of Eq. (B2) in Appendix B, we get
An(r) =
p
n+1r
p
n 1
(
p
n+1 2)r+
p
n 1
(22)
for 0 r
p
n 1. Our novel burstiness parameter
An has no longer a upper bound due to the finite n, as
depicted in Fig. 2(b), where the curves for di↵erent ns
are described by
An(r) =
p
n+1
p
n 1+(
p
n+1+
p
n 1)B(r)
p
n+1+
p
n 1 2+(
p
n+1
p
n 1 2)B(r)
. (23)
Then let us consider two event sequences with the same
value of r but with di↵erent ns. The original burstiness
nce cases: Eq. (18) for regular time series, Eq. (19)
time series, and Eq. (20) for the bursty limit. Nu-
ults for the random case are plotted for comparison
ytic results. (b) Comparison of the novel bursti-
eter An(r) in Eq. (22) to the original burstiness
B(r) in Eq. (1) for several values of n. (c) Scatter
) for individual Twitter users. (d) The same as (b)
Twitter dataset.
Novel definition of burstiness parameter
to fix the bias in the original burstiness pa-
ue to the finite number of events, we suggest
finition of the burstiness parameter, denoted
where it is assumed to be a function of only
Then An(r) must satisfy the following condi-
An(0) = 1,
An
⇣q
n 1
n+1
⌘
= 0, (21)
An
p
n 1 = 1,
respond to the cases of regular, random, and
bursty time series, respectively. Since B(r)
ally defined as r 1
r+1 , we similarly assume that
nr bn
r+cn
with coe cients an, bn, and cn. Using a
mula of Eq. (B2) in Appendix B, we get
p p
: regular time series
: random time series
: bursty time series
3
(16)
non-
e size
meter
39. Correlated bursts
PHYSICAL REVIEW E 92, 022814 (2015)
Correlated bursts and the role of memory range
Hang-Hyun Jo,1,2
Juan I. Perotti,2,3
Kimmo Kaski,2
and J´anos Kert´esz2,4
1
BK21plus Physics Division and Department of Physics, Pohang University of Science and Technology, Pohang 790-784, Republic of Korea
2
Department of Computer Science, School of Science, Aalto University, P.O. Box 15500, Espoo, Finland
3
IMT Institute for Advanced Studies Lucca, Piazza San Francesco 19, I-55100 Lucca, Italy
4
Center for Network Science, Central European University, N´ador utca 9, H-1051 Budapest, Hungary
(Received 8 May 2015; published 20 August 2015)
Inhomogeneous temporal processes in natural and social phenomena have been described by bursts that are
rapidly occurring events within short time periods alternating with long periods of low activity. In addition to the
analysis of heavy-tailed interevent time distributions, higher-order correlations between interevent times, called
correlated bursts, have been studied only recently. As the underlying mechanism behind such correlated bursts is
far from being fully understood, we devise a simple model for correlated bursts using a self-exciting point process
with a variable range of memory. Whether a new event occurs is stochastically determined by a memory function
that is the sum of decaying memories of past events. In order to incorporate the noise and/or limited memory
capacity of systems, we apply two memory loss mechanisms: a fixed number or a variable number of memories.
By analysis and numerical simulations, we find that too much memory effect may lead to a Poissonian process,
implying that there exists an intermediate range of memory effect to generate correlated bursts comparable to
empirical findings. Our conclusions provide a deeper understanding of how long-range memory affects correlated
bursts.
DOI: 10.1103/PhysRevE.92.022814 PACS number(s): 89.75.Da, 05.40.−a, 89.20.−a
I. INTRODUCTION
Many natural phenomena and human activities are ex-
M and the burstiness parameter B, defined as
B =
σ − ⟨τ⟩
. (3)
40. Self-exciting point process
• Memory function = sum of memory kernel of the past
events
• cf.) Epidemic Type Aftershock Sequence (ETAS)
models for earthquakes
t1 tn
m(t) =
nX
i=1
1
t ti
for t > tn p[m(t)] = 1 e µm(t) ✏
: prob. of a new event in time t
41. • Memory loss due to the limited capacity, noise, etc.
• Sequential memory loss: fixed L
• Preferential memory loss: variable L
Memory loss mechanism
µ = 0.1, ✏ = 10 6
, ✏L = 10 6
: memory initialization probability whenever
an event occurs
m(t) =
nX
i=n L+1
1
t ti
m(t) =
nX
i=n L+1
1
t ti
42. ~ event rate
→ approaching Poisson process?
Sequential case: m(t)
m(t) =
nX
i=n L+1
1
t ti
43. L events new event
Sequential case: P(τ)
⌧L 1 · · · ⌧2 ⌧1 t
P(⌧|{⌧i}) =
"⌧ 1Y
t=1
e µm(t|{⌧i}) ✏
#
h
1 e µm(⌧|{⌧i}) ✏
i
p[m(t)] = 1 e µm(t) ✏
48. Contextual bursts
PHYSICAL REVIEW E 87, 062131 (2013)
Contextual analysis framework for bursty dynamics
Hang-Hyun Jo,*
Raj Kumar Pan, Juan I. Perotti, and Kimmo Kaski
Department of Biomedical Engineering and Computational Science, Aalto University School of Science, P. O. Box 12200, Espoo, Finland
(Received 20 March 2013; published 20 June 2013)
To understand the origin of bursty dynamics in natural and social processes we provide a general analysis
framework in which the temporal process is decomposed into subprocesses and then the bursts in subprocesses,
called contextual bursts, are combined to collective bursts in the original process. For the combination of
subprocesses, it is required to consider the distribution of different contexts over the original process. Based on
minimal assumptions for interevent time statistics, we present a theoretical analysis for the relationship between
contextual and collective interevent time distributions. Our analysis framework helps to exploit contextual
information available in decomposable bursty dynamics.
DOI: 10.1103/PhysRevE.87.062131 PACS number(s): 05.40.−a, 89.75.Da, 89.20.−a
I. INTRODUCTION
In a wide range of natural and social phenomena, inho-
mogeneous or non-Poissonian temporal processes have been
observed. They are described in terms of 1/f noise [1,2], or in
terms of bursts that are rapidly occurring events within short
time periods alternating with long periods of low activity [3–5].
In studies of inhomogeneous temporal processes one finds a
crucial for the process than their real timings or when the real
timings are not available, such as the sequence of words in the
text [21]. In addition, the origin of bursts can be explored more
explicitly as the effect of any intrinsic temporal patterns, such
as circadian and weekly cycles of humans [22], is excluded.
Moreover, the human bursty dynamics has often been modeled
in terms of the ordinal time frame by ignoring the real time
50. collective real inter-event time
P(l) ⇠ l ↵
contextual real inter-event time
P(⌧) ⇠ ⌧ ↵0
contextual ordinal inter-event time
P(n) ⇠ n
irrelevant context
irrelevant time-frame
⌧ =
nX
i=1
li ↵0
= min{(↵ 1)( 1) + 1, ↵, }
51. Overview of analysis
→ probability of making one τ
from n collective inter-event times
⌧ =
nX
i=1
li P(⌧) =
1X
n=1
P(n)Fn(⌧)
Fn(⌧) =
nY
i=1
Z 1
l0
dliP(li) ⌧
nX
i=1
li
!
P(l) ⇠ l ↵
P(n) ⇠ n
↵0
= min{(↵ 1)( 1) + 1, ↵, }
52. Numerical confirmation
with αc ≡ (α − 1)(β − 1) + 1 and crossovers n× and x× =
(τ − n×l0)n−ν
× . For derivation, (τ − nl0)n−ν
has been replaced
by x and then approximated as x ≈ τn−ν
. While the first term
in the parentheses is independent of τ, the second term is
obtained as ταc−α
− xαc−α
× , leading to
P(τ) ∝ c1τ−αc
+ c2τ−α
, (7)
with coefficients c1 and c2. Thus, we obtain
α′
= min{αc,α} if 1 < α < 2. (8)
The condition for αc = α is β = 2, when the second term in
Eq. (6) gives the logarithmic correction as ln τ. That is, if the
tail of P(n) is sufficiently small, α′
= α is obtained, implying
that contextual bursts in a real time frame are determined only
by collective bursts. In any case, we get α′
< β, implying that
contextual bursts in a real time frame are stronger than those
in an ordinal time frame due to large fluctuations of collective
interevent times.
Figures 3(a) and 3(b) show that our analysis is confirmed
by the numerical simulations (to be described later) for α = 3
2
and l0 = 1. We find that the numerically obtained Fn(τ) for
different ns collapse into one curve corresponding to g−
1 (x)
for x < x× and g+
1 (x) for x > x×. Then, based on the simple
scaling form P(τ) ∼ τ−α′
, we estimate the value of α′
, which
10-8
10
-6
10
-4
10-2
10
0
10
-2
10
-1
10
0
10
1
10
2
10
3
10
4
Fn(τ)n
2
(τ-n)n
-2
(a)
n=10
20
40
80
160
320
10
-6
10
-4
10
-2
10
0
100
101
102
103
104
P(τ)
τ
(b)
β=1.1
2
3
1
1.5
1 2 3 4
β
α’
10
-6
10
-4
10
-2
10
0
0 20 40 60 80 100
Fn(τ)n2/3
(τ-τc)n-2/3
-x0
(c)
n=10
20
40
80
160
320
10-6
10-4
10-2
10
0
10
0
10
1
10
2
10
3
P(τ)
τ
(d)
β=1.1
2.5
4
1
2
2.5
1 2 3 4
β
α’
100(e) 100(f)
↵ = 3/2
↵ = 5/2
Fn(⌧) P(⌧)
53. Relation to transport models
→ partition function of mass transport models
Majumdar et al., PRL (2005)
al Review R199
Particle:
Site:
u(1)
u(2)
u(3)
u(1)u(3) u(2)
1 2 3 4
1 2 3 4
5
5
(a)
(b)
Figure 1. Mapping between the zero-range process and the asymmetric exclusion process.
ZRP with a corresponding configuration of particles in an exclusion model. (The mapping
Evans, Hanney, JPA (2005)
Fn(⌧) =
nY
i=1
Z 1
l0
dliP(li) ⌧
nX
i=1
li
!
54. Effect of bursts on spreading
Analytically Solvable Model of Spreading Dynamics with Non-Poissonian Processes
Hang-Hyun Jo,1,*
Juan I. Perotti,1
Kimmo Kaski,1
and János Kertész2,1
1
BECS, Aalto University School of Science, FI-00076 Espoo, Finland
2
Center for Network Science, Central European University, H-1051 Budapest, Hungary
(Received 22 November 2013; revised manuscript received 5 February 2014; published 17 March 2014)
Non-Poissonian bursty processes are ubiquitous in natural and social phenomena, yet little is known
about their effects on the large-scale spreading dynamics. In order to characterize these effects, we devise
an analytically solvable model of susceptible-infected spreading dynamics in infinite systems for arbitrary
inter-event time distributions and for the whole time range. Our model is stationary from the beginning, and
the role of the lower bound of inter-event times is explicitly considered. The exact solution shows that for
early and intermediate times, the burstiness accelerates the spreading as compared to a Poisson-like process
with the same mean and same lower bound of inter-event times. Such behavior is opposite for late-time
dynamics in finite systems, where the power-law distribution of inter-event times results in a slower and
algebraic convergence to a fully infected state in contrast to the exponential decay of the Poisson-like
process. We also provide an intuitive argument for the exponent characterizing algebraic convergence.
DOI: 10.1103/PhysRevX.4.011041 Subject Areas: Complex Systems
I. INTRODUCTION
Events of the dynamical processes of various complex
systems are often not distributed homogeneously in time
but have intermittent or bursty character. This is ubiqui-
by model calculations [8,14,20–22]. In those studies, the
bursty character of an event sequence was found to slow
down the late-time dynamics of spreading, evidenced also
by a heavy tail in the inter-event time distribution.
PHYSICAL REVIEW X 4, 011041 (2014)
57. Conflicting results
Spreading on the mobile
phone network
Karsai et al., PRE (2011)
Spreading on the sexual
network
Rocha et al., PLOS CB (2011)
slower
faster
vs.
58. Susceptible-Infected (SI)
spreading dynamics
P(w) =
1
µ
Z 1
w
P(l)dl, µ = hli
l0
w
w0
w00
l00
l
l
S
I
S
S
S
: # infected nodes in time t
branching process
l = inter-event time
w = residual time
P(l) ! n(t)
59. Exact solution for an infinite
system
˜n(s) =
1
s
+
˜P(s)
(s µ 1)[1 ˜P(s)]
P(l) =
l↵ 1
c
(1 ↵, l0
lc
)
l ↵
e l/lc
✓(l l0)
for arbitrary inter-event time distribution
and for the entire range of time
Laplace transform
x ⌘
l0
µ
, y ⌘
l0
lc
,
x
y
=
(1 ↵, y)
(2 ↵, y)
C(x, y, ↵) ⌘ µ
dn(t)
dt t=l+
0
=
y1 ↵
e y
x (1 ↵, y)
C(x, y, 0)
Bursts speed up the initial spreading!
60. Bursts speed up initial spreading
but slow down at final stage!
a
t
i
a
w
e
α
t
d
100
101
10
2
103
0 1 2 3 4
n0(t)
t
(a)
power law
power law + cutoff
shifted Poisson
0.0
0.2
0.4
0.6
0.8
1.0
0 5 10 15 20
n0(t)/N
t
(b)
10
-2
10
-1
(c)
α=2.001
2.2
2.4 1.6
1.8(d)
estimated
β=α-1
ANALYTICALLY SOLVABLE MODEL OF SPREADING …P(l) =
l↵ 1
c
(1 ↵, l0
lc
)
l ↵
e l/lc
✓(l l0)
All cases with the same mean and lower bound of inter-event times
61. Future works
• How to characterize correlated contextual bursts
(CCB)?
• Effects of CCB on collective dynamics (avalanche,
diffusion, etc.) on temporal networks?
• Interplay between bursts and network topology?
• e.g., Jo et al., PLOS ONE (2011)
• Origin of bursts and temporal scale-invariance?