π»
Self-Paced Training: Machine Learning with MATLAB
https://www.mathworks.com/training-schedule/machine-learning-with-matlab.html?s_tid=trg_mlml_mlacad_bod&class_format=Public%2BSelf%2BPaced
Self-Paced Training: Machine Learning with MATLAB
https://www.mathworks.com/training-schedule/machine-learning-with-matlab.html?s_tid=trg_mlml_mlacad_bod&class_format=Public%2BSelf%2BPaced
π Geometric structure and information change in phase transitions
Eun-jin Kim and Rainer Hollerbach
Phys. Rev. E 95, 062107 β Published 6 June 2017
π https://journals.aps.org/pre/abstract/10.1103/PhysRevE.95.062107
π ABSTRACT
We propose a toy model for a cyclic order-disorder transition and introduce a geometric methodology to understand stochastic processes involved in transitions. Specifically, our model consists of a pair of forward and backward processes (FPs and BPs) for the emergence and disappearance of a structure in a stochastic environment. We calculate time-dependent probability density functions (PDFs) and the information length L, which is the total number of different states that a system undergoes during the transition. Time-dependent PDFs during transient relaxation exhibit strikingly different behavior in FPs and BPs. In particular, FPs driven by instability undergo the broadening of the PDF with a large increase in fluctuations before the transition to the ordered state accompanied by narrowing the PDF width. During this stage, we identify an interesting geodesic solution accompanied by the self-regulation between the growth and nonlinear damping where the time scale Οof information change is constant in time, independent of the strength of the stochastic noise. In comparison, BPs are mainly driven by the macroscopic motion due to the movement of the PDF peak. The total information length L between initial and final states is much larger in BPs than in FPs, increasing linearly with the deviation Ξ³ of a control parameter from the critical state in BPs while increasing logarithmically with Ξ³ in FPs. L scales as |lnD| and Dβ1/2 in FPs and BPs, respectively, where D measures the strength of the stochastic forcing. These differing scalings with Ξ³ and D suggest a great utility of L in capturing different underlying processes, specifically, diffusion vs advection in phase transition by geometry. We discuss physical origins of these scalings and comment on implications of our results for bistable systems undergoing repeated order-disorder transitions (e.g., fitness).
https://journals.aps.org/pre/abstract/10.1103/PhysRevE.95.062107
Eun-jin Kim and Rainer Hollerbach
Phys. Rev. E 95, 062107 β Published 6 June 2017
π https://journals.aps.org/pre/abstract/10.1103/PhysRevE.95.062107
π ABSTRACT
We propose a toy model for a cyclic order-disorder transition and introduce a geometric methodology to understand stochastic processes involved in transitions. Specifically, our model consists of a pair of forward and backward processes (FPs and BPs) for the emergence and disappearance of a structure in a stochastic environment. We calculate time-dependent probability density functions (PDFs) and the information length L, which is the total number of different states that a system undergoes during the transition. Time-dependent PDFs during transient relaxation exhibit strikingly different behavior in FPs and BPs. In particular, FPs driven by instability undergo the broadening of the PDF with a large increase in fluctuations before the transition to the ordered state accompanied by narrowing the PDF width. During this stage, we identify an interesting geodesic solution accompanied by the self-regulation between the growth and nonlinear damping where the time scale Οof information change is constant in time, independent of the strength of the stochastic noise. In comparison, BPs are mainly driven by the macroscopic motion due to the movement of the PDF peak. The total information length L between initial and final states is much larger in BPs than in FPs, increasing linearly with the deviation Ξ³ of a control parameter from the critical state in BPs while increasing logarithmically with Ξ³ in FPs. L scales as |lnD| and Dβ1/2 in FPs and BPs, respectively, where D measures the strength of the stochastic forcing. These differing scalings with Ξ³ and D suggest a great utility of L in capturing different underlying processes, specifically, diffusion vs advection in phase transition by geometry. We discuss physical origins of these scalings and comment on implications of our results for bistable systems undergoing repeated order-disorder transitions (e.g., fitness).
https://journals.aps.org/pre/abstract/10.1103/PhysRevE.95.062107
Physical Review E
Geometric structure and information change in phase transitions
We propose a toy model for a cyclic order-disorder transition and introduce a geometric methodology to understand stochastic processes involved in transitions. Specifically, our model consists of a pair of forward and backward processes (FPs and BPs) forβ¦
πThe 2017 SIAM Conference on Applications of Dynamical Systems (DS17) was held in Sandy, Utah on May 21st - May 25th, 2017. The SIAM DS conference seeks to enable in-depth technical discussions on a wide variety of major computational efforts on large-scale problems in science and engineering, foster the interdisciplinary culture required to meet these large-scale challenges, and promote the training of the next generation of computational scientists.
Use the search box in the upper right to search for a speaker, talk title, or topic. Select "Content" to see the list of other SIAM meetings with presentations available for viewing.
π https://www.pathlms.com/siam/courses/4812
Use the search box in the upper right to search for a speaker, talk title, or topic. Select "Content" to see the list of other SIAM meetings with presentations available for viewing.
π https://www.pathlms.com/siam/courses/4812
Friends and enemies in the Middle East. Who is connected to whom? - interactive | News | The Guardian
https://www.theguardian.com/news/datablog/ng-interactive/2014/sep/24/friends-and-enemies-in-the-middle-east-who-is-connected-to-who-interactive
https://www.theguardian.com/news/datablog/ng-interactive/2014/sep/24/friends-and-enemies-in-the-middle-east-who-is-connected-to-who-interactive
the Guardian
Friends and enemies in the Middle East. Who is connected to whom? - interactive
As the US and UK are set to again commit to military involvement in the Middle East, this interactive visualises the intricate, complex and sometimes hidden relationships and alliances across the region
π₯ Gall's Law: "A complex system that works is invariably found to have evolved from a simple system that worked."
β John Gall (1975)
β John Gall (1975)
π https://motherboard.vice.com/en_us/article/we-are-programmed-to-die-early-and-thats-a-good-thing
Motherboard
We Are Programmed to Die Early, and Thatβs a Good Thing
Complex systems theorists have created a model that overturns longstanding assumptions about the relationship between death and natural selection.
Tutorials are short, self-paced βmini-coursesβ designed to introduce students to important techniques and to provide illustrations of their application in complex systems.
https://www.complexityexplorer.org/tutorials
https://www.complexityexplorer.org/tutorials
On some deep connections between computer science, statistical physics and information theory:
http://lptms.u-psud.fr/membres/mezard/edwards.pdf
http://lptms.u-psud.fr/membres/mezard/edwards.pdf
π Kindermann, Ross; Snell, J. Laurie (1980).
πΉ Markov Random Fields and Their Applications πΉ
(PDF): http://www.cmap.polytechnique.fr/~rama/ehess/mrfbook.pdf
πΉ Markov Random Fields and Their Applications πΉ
(PDF): http://www.cmap.polytechnique.fr/~rama/ehess/mrfbook.pdf
π Review:
"Statistical physics of inference: Thresholds and algorithms"
Lenka ZdeborovΓ‘, Florent Krzakala
(Submitted on 8 Nov 2015 (v1), last revised 28 Jul 2016 (this version, v4))
π https://arxiv.org/pdf/1511.02476
Many questions of fundamental interest in todays science can be formulated as inference problems: Some partial, or noisy, observations are performed over a set of variables and the goal is to recover, or infer, the values of the variables based on the indirect information contained in the measurements. For such problems, the central scientific questions are: Under what conditions is the information contained in the measurements sufficient for a satisfactory inference to be possible? What are the most efficient algorithms for this task? A growing body of work has shown that often we can understand and locate these fundamental barriers by thinking of them as phase transitions in the sense of statistical physics. Moreover, it turned out that we can use the gained physical insight to develop new promising algorithms. Connection between inference and statistical physics is currently witnessing an impressive renaissance and we review here the current state-of-the-art, with a pedagogical focus on the Ising model which formulated as an inference problem we call the planted spin glass. In terms of applications we review two classes of problems: (i) inference of clusters on graphs and networks, with community detection as a special case and (ii) estimating a signal from its noisy linear measurements, with compressed sensing as a case of sparse estimation. Our goal is to provide a pedagogical review for researchers in physics and other fields interested in this fascinating topic.
"Statistical physics of inference: Thresholds and algorithms"
Lenka ZdeborovΓ‘, Florent Krzakala
(Submitted on 8 Nov 2015 (v1), last revised 28 Jul 2016 (this version, v4))
π https://arxiv.org/pdf/1511.02476
Many questions of fundamental interest in todays science can be formulated as inference problems: Some partial, or noisy, observations are performed over a set of variables and the goal is to recover, or infer, the values of the variables based on the indirect information contained in the measurements. For such problems, the central scientific questions are: Under what conditions is the information contained in the measurements sufficient for a satisfactory inference to be possible? What are the most efficient algorithms for this task? A growing body of work has shown that often we can understand and locate these fundamental barriers by thinking of them as phase transitions in the sense of statistical physics. Moreover, it turned out that we can use the gained physical insight to develop new promising algorithms. Connection between inference and statistical physics is currently witnessing an impressive renaissance and we review here the current state-of-the-art, with a pedagogical focus on the Ising model which formulated as an inference problem we call the planted spin glass. In terms of applications we review two classes of problems: (i) inference of clusters on graphs and networks, with community detection as a special case and (ii) estimating a signal from its noisy linear measurements, with compressed sensing as a case of sparse estimation. Our goal is to provide a pedagogical review for researchers in physics and other fields interested in this fascinating topic.