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On the Distribution and Convergence of Feature Space in Self-Organizing Maps

Hujun Yin, Nigel M. Allinson
1995 Neural Computation  
Self-organizing maps: Sta- tionary states, metastability and convergence rate. Biol. Cybernet. 67, 35-45. Kohonen, T. 1984. Self-Organization and Associative Memory. Springer-Verlag, London.  ...  Ritter, H., and Schulten, K. 1986. On the stationary states of Kohonen’s self- organizing sensory mapping. Biol. Cybernet. 54, 99-106. Ritter, H., and Schulten, K. 1988.  ... 
doi:10.1162/neco.1995.7.6.1178 pmid:7584896 fatcat:5ryv4mwk4bgcledxvfhgkqqc7a

Spatiotemporal Self-Organization of Fluctuating Bacterial Colonies

Tobias Grafke, Michael E. Cates, Eric Vanden-Eijnden
2017 Physical Review Letters  
Adding fluctuations, we find that static colonies are now metastable, moving between spatial locations via rare and strongly nonequilibrium pathways, whereas the limit cycle becomes almost periodic such  ...  Without noise, the system shows both static phase separation and a limit cycle, in which a rising global population causes a dense bacterial colony to form, which then declines by local cell death, before  ...  Schäfer for his help with the numerical scheme and A. Donev, O. Hirschberg, and C. Nardini for interesting discussions. MEC is funded by the  ... 
doi:10.1103/physrevlett.119.188003 pmid:29219541 fatcat:rg4grsj7qffthk6e3hshdlygke

The Self-Organized Critical Multiverse [article]

Guram Kartvelishvili, Justin Khoury, Anushrut Sharma
2020 arXiv   pre-print
We focus on a finite region of the landscape, which exchanges volume with the rest of the landscape and as such acts as an open system.  ...  Through a change of variables the master equation governing the comoving volume of de Sitter vacua is mapped to a stochastic equation for coupled overdamped stochastic oscillators – the well-known Ornstein-Uhlenbeck  ...  This has motivated the tantalizing idea of self-organizing criticality [33] [34] [35] .  ... 
arXiv:2003.12594v1 fatcat:vwqw6gwnjvckpae4326swezlsq

Quenches across the self-organization transition in multimode cavities

Tim Keller, Valentin Torggler, Simon B Jäger, Stefan Schütz, Helmut Ritsch, Giovanna Morigi
2018 New Journal of Physics  
Numerical simulations for different ramp protocols predict that the system exhibits long-lived metastable states, whose occurrence strongly depends on initial temperature, ramp speed, and number of atoms  ...  or slowly ramped across the self-ordering transition.  ...  Acknowledgments The authors thank Tobias Donner, Sebastian Krämer, and Francesco Rosati for stimulating and helpful discussions.  ... 
doi:10.1088/1367-2630/aaa161 fatcat:vxekjwny3vevjdugwmoeovqm7q

Self-Organized Escape Processes of Linear Chains in Nonlinear Potentials [chapter]

Torsten Gross, Dirk Hennig, Lutz Schimansky-Geier
2014 First-Passage Phenomena and Their Applications  
We study a spatially one dimensional set-up consisting of a linearly coupled oscillator chain of N mass-points situated in a metastable nonlinear potential.  ...  Compared to a chain system with linear damping and thermal fluctuations the breathers help the chain to overcome the barriers faster in the case of low damping.  ...  It casts the stationary equation into a two-dimensional map and links the localized lattice solutions to its homoclinic orbits.  ... 
doi:10.1142/9789814590297_0022 fatcat:cz3nctnnfnaghkn4dpxbnf2oue

Self-organized control for musculoskeletal robots [article]

Ralf Der, Georg Martius
2016 arXiv   pre-print
This paper advocates for a new paradigm of self-organized control.  ...  When applying this controller to a muscle-tendon driven arm-shoulder system from the Myorobotics toolkit, we observe a vast variety of self-organized behavior patterns: when left alone, the arm realizes  ...  RD thanks for the hospitality at the Max-Planck-Institute and for helpful discussions with Nihat Ay and Keyan Zahedi.  ... 
arXiv:1602.02990v2 fatcat:peafbej4j5fbpadldx6pxgl3ai

Introduction: Self-organization in nonequilibrium chemical systems

Irving R. Epstein, John A. Pojman, Oliver Steinbock
2006 Chaos  
The field of self-organization in nonequilibrium chemical systems comprises the study of dynamical phenomena in chemically reacting systems far from equilibrium.  ...  The articles in this Focus Issue provide an overview of the development and current state of the field.  ...  In this Focus Issue we highlight the dynamics of chemically reacting systems far from equilibrium with emphasis on such systems' ability to self-organize.  ... 
doi:10.1063/1.2354477 pmid:17014235 fatcat:cman2jcklnhrld2fdf2lywrjwy

Self-Organized Behavior Generation for Musculoskeletal Robots

Ralf Der, Georg Martius
2017 Frontiers in Neurorobotics  
Reasons are the expected scalability, robustness, and resilience of self-organizing systems.  ...  Besides converging toward one of these attractors, variate behavior is also arising from a self-induced attractor morphing driven by the learning rule.  ...  Special thanks go also to Rafael Hostettler for helping us with the robot and control framework.  ... 
doi:10.3389/fnbot.2017.00008 pmid:28360852 pmcid:PMC5352682 fatcat:asizufjnlvbmrlpqqp4a56mi4e

Avalanches, transport, and local equilibrium in self-organized criticality

Afshin Montakhab, J. M. Carlson
1998 Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics  
In particular, we construct a mapping between the open and closed system avalanche size distributions which accounts for finite size fluctuations in the density and the critical point.  ...  The rate of convergence is obtained self consistently by assuming the average density is of the form c Ϫ ϳ 1 N b . ͑10͒ The exponent b is determined by balancing the time scale associated with addition  ...  In particular, analogies between self-organized criticality ͑SOC͒ ͓10͔ and the more traditional criticality which underlies dynamical phase transitions ͓11,12͔ have shown that local equilibrium can apply  ... 
doi:10.1103/physreve.58.5608 fatcat:ggizeg76zvaphmsy4ts2eomomi

Pathways to self-organization: Crystallization via nucleation and growth

S. Jungblut, C. Dellago
2016 The European Physical Journal E : Soft matter  
Crystallization, a prototypical self-organization process during which a disordered state spontaneously transforms into a crystal characterized by a regular arrangement of its building blocks, usually  ...  More specifically, we will address the rare event problem arising in the simulation of nucleation processes and explain how to calculate nucleation rates accurately.  ...  rates of metastable states.  ... 
doi:10.1140/epje/i2016-16077-6 pmid:27498980 fatcat:ybuwb4fsibclbchwvntc344z44

Synaptic balance due to homeostatically self-organized quasicritical dynamics

Mauricio Girardi-Schappo, Ludmila Brochini, Ariadne A. Costa, Tawan T. A. Carvalho, Osame Kinouchi
2020 Physical Review Research  
This homeostatically self-organized quasi-critical (SOqC) dynamics generates E/I synaptic current cancellation in fast time scales, causing fluctuation-driven asynchronous-irregular (AI) firing.  ...  Our model thus unifies two different perspectives on cortical spontaneous activity: both critical avalanches and fluctuation-driven AI firing arise from SOqC homeostatic adaptation, and are indeed two  ...  to drive networks towards the so-called Self-Organized quasi-Critical state (SOqC as defined by Bonachela & Muñoz [10, 17] ).  ... 
doi:10.1103/physrevresearch.2.012042 fatcat:k77mzh422rbidka67jn74npbce

A principle of natural self-organization

Manfred Eigen, Peter Schuster
1977 Die Naturwissenschaften  
The self-organizing properties of hypercycles are elucidated, using analytical as well as numerical techniques.  ...  This paper is the first part of a trilogy, which comprises a detailed study of a special type of functional organization and demonstrates its relevance with respect to the origin and evolution of life.  ...  Only when the population variables xk(t) become stationary, will E(O reach a constant steady-state value which is metastable since it depends on the population of the spectrum of mutants.  ... 
doi:10.1007/bf00450633 pmid:593400 fatcat:nvbiufpdqvfs7jvub6ivib3mrq

Order out of Randomness: Self-Organization Processes in Astrophysics

Markus J. Aschwanden, Felix Scholkmann, William Béthune, Werner Schmutz, Valentina Abramenko, Mark C. M. Cheung, Daniel Müller, Arnold Benz, Guennadi Chernov, Alexei G. Kritsuk, Jeffrey D. Scargle, Andrew Melatos (+3 others)
2018 Space Science Reviews  
Self-organization is a property of dissipative nonlinear processes that are governed by an internal driver and a positive feedback mechanism, which creates regular geometric and/or temporal patterns and  ...  Self-organizing systems create spontaneous order out of chaos, during the evolution from an initially disordered system to an ordered stationary system, via quasi-periodic limit-cycle dynamics, harmonic  ...  Acknowledgements The author acknowledges the hospitality and partial support for two workshops on "Self-Organized Criticality and Turbulence" at the International Space Science Institute (ISSI) at Bern  ... 
doi:10.1007/s11214-018-0489-2 fatcat:5rn4notrafg6vpfrnnc7g6m5wy

A Non-Genetic Basis for Cancer Progression and Metastasis: Self-Organizing Attractors in Cell Regulatory Networks

Sui Huang, Donald E. Ingber, Lalage Wakefield, Kent Hunter
2007 Breast Disease  
The concepts of gene expression state space and attractors are introduced which provide a mathematical and molecular basis for an "epigenetic landscape".  ...  The implications of this concept for a new integrative understanding of tumor formation and metastatic progression are discussed.  ...  All genes were used for the hierarchal clustering (on the left) and the self-organizing maps (SOM) which are displayed as GEDI maps (on the right).  ... 
doi:10.3233/bd-2007-26104 fatcat:kxwudkomyfekdo5otsc3fpnyvi

25 Years of Self-Organized Criticality: Solar and Astrophysics

Markus J. Aschwanden, Norma B. Crosby, Michaila Dimitropoulou, Manolis K. Georgoulis, Stefan Hergarten, James McAteer, Alexander V. Milovanov, Shin Mineshige, Laura Morales, Naoto Nishizuka, Gunnar Pruessner, Raul Sanchez (+3 others)
2014 Space Science Reviews  
Shortly after the seminal paper "Self-Organized Criticality: An explanation of 1/f noise" by Bak, Tang, and Wiesenfeld (1987), the idea has been applied to solar physics, in "Avalanches and the Distribution  ...  , and boson clouds.  ...  Acknowledgements The author team acknowledges the hospitality and partial support for two workshops on "Self-Organized Criticality and Turbulence" at the International Space Science Institute (ISSI) at  ... 
doi:10.1007/s11214-014-0054-6 fatcat:cykffsdfvneoddyjq2dplijgji
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