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Effective Computability of Solutions of Ordinary Differential Equations The Thousand Monkeys Approach
2008
Electronical Notes in Theoretical Computer Science
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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]
1999
IMA Volumes in Mathematics and its Applications
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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]
2017
arXiv
pre-print
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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
1969
Bacteriological reviews
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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
2017
IBM Journal of Research and Development
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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
2006
Nature
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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
2008
The European Physical Journal Special Topics
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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
2002
Kybernetes
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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
2021
Zenodo
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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
2011
Journal of Mathematical Psychology
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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
2015
Scientific Reports
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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
2012
Mathematical Structures in Computer Science
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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
2020
Open Biology
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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
1983
Symposium - International astronomical union
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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
2001
Proceedings of the IEEE
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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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