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Effective Computability of Solutions of Ordinary Differential Equations The Thousand Monkeys Approach

Pieter Collins, Daniel S. Graça
2008 Electronical Notes in Theoretical Computer Science  
In this note we consider the computability of the solution of the initialvalue problem for ordinary differential equations with continuous righthand side.  ...  We present algorithms for the computation of the solution using the "thousand monkeys" approach, in which we generate all possible solution tubes, and then check which are valid.  ...  Additional support to DG was also provided by the Fundação Calouste Gulbenkian through the Programa Gulbenkian de Estímuloà Investigação.  ... 
doi:10.1016/j.entcs.2008.12.010 fatcat:4fnfeytmnzewdn4jbrjbc7yt7y

Using Evolutionary Algorithms to Search for Control Parameters in a Nonlinear Partial Differential Equation [chapter]

Rogene M. Eichler West, Erik De Schutter, George L. Wilcox
1999 IMA Volumes in Mathematics and its Applications  
Overview Many physical systems of interest to scientists and engineers can be modeled using a partial differential equation extended along the dimensions of time and space.  ...  Our objective was not to find the "best" solution, but rather we sought to produce the manifold of high fitness solutions that best accounts for biological variability.  ...  Sciences and Engineering at the University of Minnesota.  ... 
doi:10.1007/978-1-4612-1542-4_3 fatcat:r4fnzkplhzd2pduvmdc5cojbvi

Connectivity Inference from Neural Recording Data: Challenges, Mathematical Bases and Research Directions [article]

Ildefons Magrans de Abril, Junichiro Yoshimoto, Kenji Doya
2017 arXiv   pre-print
This article presents a review of computational methods for connectivity inference from neural activity data derived from multi-electrode recordings or fluorescence imaging.  ...  We first identify biophysical and technical challenges in connectivity inference along the data processing pipeline.  ...  and internal funding from the Okinawa Institute of Science and Technology Graduate University.  ... 
arXiv:1708.01888v2 fatcat:fezbmzuzenac7mqcnqhq5sveye

Dialysis culture of microorganisms: design, theory, and results

J S Schultz, P Gerhardt
1969 Bacteriological reviews  
ACKNOWLEDGMENTS We appreciatively acknowledge the library assistance of Lynn E. Sorensen and the resource of reference material accumulated in the theses of Elizabeth A.  ...  Tyrrell The experimental work by the authors and preparation of this article were supported by contracts from the Department of the Army, Fort Detrick, Frederick, Md., and by Public Health Service grants  ...  The equations for the batch situation can be handled best by computer simulation or by an approximating analytical approach.  ... 
pmid:4889148 pmcid:PMC378311 fatcat:egnzhnddjfbaris7n7cgjpev4q

Evolutionary algorithm optimization of biological learning parameters in a biomimetic neuroprosthesis

S. Dura-Bernal, S. A. Neymotin, C. C. Kerr, S. Sivagnanam, A. Majumdar, J. T. Francis, W. W. Lytton
2017 IBM Journal of Research and Development  
As model fidelity increases, so does the number of parameters and the complexity of finding appropriate parameter configurations.  ...  Biomimetic simulation permits neuroscientists to better understand the complex neuronal dynamics of the brain.  ...  Arm dynamics were calculated using an extended Hill-type muscle model [39] , comprising two ordinary differential equations, which accounts for the force-length-velocity properties of muscle fibers and  ... 
doi:10.1147/jrd.2017.2656758 pmid:29200477 pmcid:PMC5708558 fatcat:t2wpsrowwfgghkconkn5di6gym

Quantum mechanics in the brain

Christof Koch, Klaus Hepp
2006 Nature  
Therefore a well-founded understanding of these issues is desirable. The role of quantum mechanics for the photons received by the eye and for the molecules of life is not controversial.  ...  Arguments from biophysics and computational neuroscience make this unlikely.  ...  The time evolution from s to t is given by a 2-parameter family of unitary propagators U(t,s), the solution of a time-dependent Schrödinger equation.  ... 
doi:10.1038/440611a pmid:16572152 fatcat:czgo7ggs35ferce2bkxix327y4

Anomalous diffusion and the structure of human transportation networks

D. Brockmann
2008 The European Physical Journal Special Topics  
The dispersal of individuals of a species is the key driving force of various spatiotemporal phenomena which occur on geographical scales.  ...  The analysis shows that the distribution of travelling distances decays as a power law, indicating that the movement of bank notes is reminiscent of superdiffusive, scale free random walks known as Lèvy  ...  I(t) + S(t) = N ) and that disease transmission is more frequent than recovery (α > β) one obtains for the rescaled relative number of infecteds u(t) = αI(t)/N (α − β) a single ordinary differential equation  ... 
doi:10.1140/epjst/e2008-00640-0 fatcat:5mbagbl3cvdptjuujvc3hoxvoq

Evolution of intelligence

H.M. Hubey
2002 Kybernetes  
This paper uses differential/integral equations, fundamental ideas from the processing view of the brain-mind, multiple scale approximation via Taylor series, and basic reasoning some of which may be formulated  ...  dynamically e.g. in the form of a differential equation as done here, 7) concepts from AI, psychology, epistemology and physics coincide in many respects except for the terminology used, and these concepts  ...  In the case of a simple differential equation, a first order ordinary differential equation, given by 25) y′(t) + b(t) y(t) = f(t) has the solution 26) We note that for a constant b, it reduces to 27)  ... 
doi:10.1108/03684920210422557 fatcat:pc2dwhwmercfvcgqxb4v46caci

Deep sleep and its cognitive effects - Slow wave activity and the learning and sleep cycle

Elena Pastorelli
2021 Zenodo  
Despite the importance of the phenomenon in relation with the cognitive effects, a complete understanding of its functions and underlying mechanisms is still lacking.  ...  Among the contribution of this work, there is the building of fundamental instruments for the study of this phenomenon and of its interplay with learning, also thanks to the experimental context in which  ...  Acknowledgment This work was carried out with support from the European Union Horizon 2020  ... 
doi:10.5281/zenodo.5163097 fatcat:bpvpd4vkgnfwxpal4jsoz7rpqm

A tutorial on computational cognitive neuroscience: Modeling the neurodynamics of cognition

F. Gregory Ashby, Sebastien Helie
2011 Journal of Mathematical Psychology  
A variety of CCN solutions to these three problems are described. A real example of this approach is described, and some advantages and limitations of the CCN approach are discussed.  ...  Computational Cognitive Neuroscience (CCN) is a new field that lies at the intersection of computational neuroscience, machine learning, and neural network theory (i.e., connectionism).  ...  The classic solution is still the Hodgkin-Huxley model (1952) . This is a set of four coupled differential equations.  ... 
doi:10.1016/j.jmp.2011.04.003 pmid:21841845 pmcid:PMC3153062 fatcat:l2thzjqam5fedka3qrdlvssfmm

Quantifying the Number of Discriminable Coincident Dendritic Input Patterns through Dendritic Tree Morphology

Antonio G. Zippo, Gabriele E. M. Biella
2015 Scientific Reports  
This work investigates the discrimination capabilities of neurons through computational biophysical models to extract a predicting law for the dendritic input discrimination capability (M).  ...  Contextually, the synaptic clustering of inputs is the principal cellular strategy to separate groups of common correlated inputs.  ...  Della Rosa for the english proofreading of the manuscript.  ... 
doi:10.1038/srep11543 pmid:26100354 pmcid:PMC4482401 fatcat:rje7dphaj5c3bl74ahasw4mkge

Incomputability in Physics and Biology

GIUSEPPE LONGO
2012 Mathematical Structures in Computer Science  
Computability originated from Logic within the frame of the original path proposed by the founding fathers of the modern foundational analysis in Mathematics (Frege and Hilbert).  ...  Computability, in spite of the exact access to its own discrete data type, provides a unique tool for the investigation of "unpredictability", both in Physics and Biology, by its fine analysis of undecidability  ...  Moreover, Pour-El, Richards, Baverman, Yampolsky . . . were able to find unique (or only) non computable solutions of effective equational writing, .  ... 
doi:10.1017/s0960129511000569 fatcat:62nh3uyuwnfdhpntfqgnptnf3q

A quantitative account of mammalian rod phototransduction with PDE6 dimeric activation: responses to bright flashes

Trevor D. Lamb, Timothy W. Kraft
2020 Open Biology  
We simulate the stochastic nature of the activation and shut-off reactions to generate the predicted kinetics of the active molecular species on the disc membrane surfaces, and then we integrate the differential  ...  equations for the downstream cytoplasmic reactions to obtain the predicted electrical responses.  ...  We now derive the differential equations that underlie this approximate approach.  ... 
doi:10.1098/rsob.190241 pmid:31910741 fatcat:uzlnmd74tfbu5o7khlgqa5vvum

Dynamos of the Sun and Stars, and Associated Convection Zone Dynamics

Peter A. Gilman
1983 Symposium - International astronomical union  
For example, we do not allow ourselves the license to vary independently the convection and differential rotation, as is commonly done in kinematic dynamo calculations, because the laws of physics do not  ...  I like to view the model more as an analog to the solar or a stellar convection zone, rather than as an approximation—much as a laboratory rat or monkey is used as an analog to a human being in many medical  ...  I thank Ron Gilliland for reviewing the manuscript, Betsy Alves and Bobbie Morse for typing it, and Jack Miller and Mike Kuhn for programming the calculations.  ... 
doi:10.1017/s0074180900029910 fatcat:n7e6rg6ztne57ej44cbaqpx4me

Design and implementation of a biologically realistic olfactory cortex in analog VLSI

J.C. Principe, V.G. Tavares, J.G. Harris, W.J. Freeman
2001 Proceedings of the IEEE  
This analysis leads to a direct mixed-signal (analog amplitude/discrete time) implementation of the dynamical building block that simplifies the implementation of the interconnect.  ...  In this context, we motivate the use of nonconvergent dynamics for the signal to symbol translator.  ...  Equation (1) presages Grossberg's additive model [19] , and each PE is a second-order ordinary differential equation to take into consideration the independent dynamics of the wave density for the action  ... 
doi:10.1109/5.939813 fatcat:nrdbshn5u5eptnd33sc4n6vo3a
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