Fractional order differential equations and super diffusive systems

Super diffusive” systems, non-Markov processes…
Classically, (stochastic or deterministic) ODEs are “memoryless” in the sense that the current state (and not the history) of the system determines the future states/distribution of states.

One way you can destroy this is by using fractional derivatives in the formulation of the equation.
(Why this choice, as opposed to putting in explicit integrals over the history of the process, I have no idea. Perhaps it leads to more elegant paraterisation or solutions?)

I’ll make this precise later, but want to note some evocative similarities to other branching processes which I usually study in discrete index and/or state space.

Popoular in modelling Dengue and phamacokinetics, whatever that is.
Connections to to Lévy flights.

To learn: connection to long memory models.
Why not presume a state filter model and learn that?

AhEl07
Ahmed, E., & Elgazzar, A. S.(2007) On fractional order differential equations model for nonlocal epidemics. Physica A: Statistical Mechanics and Its Applications, 379(2), 607–614. DOI.
BeRT15
Bendahmane, M., Ruiz-Baier, R., & Tian, C. (2015) Turing pattern dynamics and adaptive discretization for a super-diffusive Lotka-Volterra model. Journal of Mathematical Biology, 72(6), 1441–1465. DOI.
HaSD11
Hanert, E., Schumacher, E., & Deleersnijder, E. (2011) Front dynamics in fractional-order epidemic models. Journal of Theoretical Biology, 279(1), 9–16. DOI.
PoRT11
Pooseh, S., Rodrigues, H. S., & Torres, D. F. M.(2011) Fractional derivatives in Dengue epidemics. arXiv:1108.1683 [Math, Q-Bio], 739–742. DOI.
SaRC15
Sardar, T., Rana, S., & Chattopadhyay, J. (2015) A mathematical model of dengue transmission with memory. Communications in Nonlinear Science and Numerical Simulation, 22(1–3), 511–525. DOI.

See original: The Living Thing / Notebooks Fractional order differential equations and super diffusive systems

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Conditional random fields

Er… Markov random fields… conditonal…. on something else?

AlSH04
Altun, Y., Smola, A. J., & Hofmann, T. (2004) Exponential Families for Conditional Random Fields. In Proceedings of the 20th Conference on Uncertainty in Artificial Intelligence (pp. 2–9). Arlington, Virginia, United States: AUAI Press
DeDL95
Della Pietra, S., Della Pietra, V., & Lafferty, J. (1995) Inducing Features of Random Fields. arXiv:cmp-lg/9506014.
Mcca12
McCallum, A. (2012) Efficiently Inducing Features of Conditional Random Fields. arXiv:1212.2504 [Cs, Stat].
SuMc10
Sutton, C., & McCallum, A. (2010) An Introduction to Conditional Random Fields. arXiv:1011.4088.

See original: The Living Thing / Notebooks Conditional random fields

Vivre la catastrophe

Le mot catastrophe a ceci d’intéressant et de pratique que l’on peut l’employer pour désigner un ensemble de situations hétéroclites, ayant pour point commun un caractère dit sensationnel, médiatiquement porteur et pour autant sans commune mesure. Une catastrophe pour les uns peut ne pas en être une pour les autres. On a ainsi pu lire dans la presse que le réchauffement climatique met en péril des populations entières que l’on nomme déjà les futurs « réfugiés climatiques » en rendant leur milieu trop hostile. Ce même réchauffement ouvre des voies navigables au nord de la Russie et permet à ce pays d’accéder à de nouvelles ressources naturelles dont l’exploitation serait sans doute financièrement rentable, mais non sans un impact probable sur l’environnement et les populations locales.

Image 10000000000001700000024512DAC584.jpg

Dirigé par Yoann Moreau, ce numéro 96 de la revue Communications mobilise plusieurs auteurs pour traiter de la catastrophe dans une approche pluridisciplinaire faisant écho aux recherches doctorales qu’...

See original: VertigO - la revue électronique en sciences de l'environnement Vivre la catastrophe

Le développement durable comme compromis

Corinne Gendron est titulaire de la Chaire de responsabilité sociale et de développement durable à l’Université du Québec à Montréal (UQAM). Professeure à l’école des sciences de la gestion de l’UQAM, elle a notamment écrit sur le développement durable, la responsabilité sociale de l’entreprise, la gestion environnementale et la norme ISO 14001. Dans le présent ouvrage, l’auteure propose un cadre d’analyse qui inclut dynamique sociale dans la transition vers une économie qui prenne en compte les externalités environnementales et donc moins dommageable pour l’environnement.

Image 10000000000000B800000111CBFBD0C1.jpg

En ouverture, le sociologue Alain Touraine, hautement cité par l’auteure, résume habilement l’œuvre de Corinne Gendron qu’il qualifie de provocante. À travers les yeux de Touraine, nous comprenons la profondeur, l’originalité et l’utilité de son travail à une époque où le Québec, moderne et industrialisé, laisse présager la possibilité d’une transformation socio-écologique.

Corinne Gendron poursuit, en guise d’intr...

See original: VertigO - la revue électronique en sciences de l'environnement Le développement durable comme compromis

Dynamical systems

Cool tricks in the mathematics of state space. A particular area of physics
often associated with chaos, statistical physics, and measure theory.

See also the weird end “nonlinear time series wizardy”, the boring end,
autoregressive time-series, and the state-space formulation, state filters.
Also “sync”. And
“Signal processing.”And “ergodic theory”.

I really need to work on this notebook.

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Ay, N., Der, R., & Prokopenko, M. (2010) Information Driven Self-Organization: The Dynamical System Approach to Autonomous Robot Behavior (No. 10-09-018). . Santa Fe Institute
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Ay, N., & Wennekers, T. (2003) Dynamical properties of strongly interacting Markov chains. Neural Networks, 16(10), 1483–1497. DOI.
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Badii, R., & Politi, A. (1999) Complexity: Hierarchical Structures and Scaling in Physics. . Cambridge University Press
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Chazottes, J.-R. (n.d.) An introduction to fluctuations of observables in chaotic dynamical systems.
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Kendall, B. E., Ellner, S. P., McCauley, E., Wood, S. N., Briggs, C. J., Murdoch, W. W., & Turchin, P. (2005) Population cycles in the pine looper moth: Dynamical tests of mechanistic hypotheses. Ecological Monographs, 75(2), 259–276.
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Marwan, N. (2008) A historical review of recurrence plots. The European Physical Journal Special Topics, 164(1), 3–12. DOI.
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See original: The Living Thing / Notebooks Dynamical systems

Practicing deliberately for excellence

Malcolm Gladwell had popularized the ‘10,000 hour’ rule to expertise in his popular book ‘Outliers’. As per his formulation, anyone who puts in 10,000 hours of effort could excel in a particular field. What one required was determination and raw effort. He had based these conclusions on the work [...]

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See original: The Mouse Trap Practicing deliberately for excellence