**5** Publications

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Entropy (Basel) 2019 May 14;21(5). Epub 2019 May 14.

Department of Philosophy, Logic and Philosophy of Science, Faculty of Philosophy, University of Seville, 41018 Seville, Spain.

Informational Structures (IS) and Informational Fields (IF) have been recently introduced to deal with a continuous dynamical systems-based approach to Integrated Information Theory (IIT). IS and IF contain all the geometrical and topological constraints in the phase space. This allows one to characterize all the past and future dynamical scenarios for a system in any particular state. In this paper, we develop further steps in this direction, describing a proper continuous framework for an abstract formulation, which could serve as a prototype of the IIT postulates.

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http://dx.doi.org/10.3390/e21050493 | DOI Listing |

http://www.ncbi.nlm.nih.gov/pmc/articles/PMC7514983 | PMC |

May 2019

Appl Math Optim 2015;71(3):379-410

Institute of Computer Science, Faculty of Mathematics and Computer Science, Jagiellonian University, ul. Łojasiewicza 6, 30-348 Kraków, Poland.

In this paper the sensitivity of optimal solutions to control problems described by second order evolution subdifferential inclusions under perturbations of state relations and of cost functionals is investigated. First we establish a new existence result for a class of such inclusions. Then, based on the theory of sequential [Formula: see text]-convergence we recall the abstract scheme concerning convergence of minimal values and minimizers. The abstract scheme works provided we can establish two properties: the Kuratowski convergence of solution sets for the state relations and some complementary [Formula: see text]-convergence of the cost functionals. Then these two properties are implemented in the considered case.

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http://dx.doi.org/10.1007/s00245-014-9262-4 | DOI Listing |

http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4469275 | PMC |

January 2015

Biol Cybern 2010 Jun 21;102(6):489-502. Epub 2010 Apr 21.

Institute of Computer Science, Jagiellonian University, Łojasiewicza 6, 30-348, Kraków, Poland.

Neurotransmitters in the terminal bouton of a presynaptic neuron are stored in vesicles, which diffuse in the cytoplasm and, after a stimulation signal is received, fuse with the membrane and release its contents into the synaptic cleft. It is commonly assumed that vesicles belong to three pools whose content is gradually exploited during the stimulation. This article presents a model that relies on the assumption that the release ability is associated with the vesicle location in the bouton. As a modeling tool, partial differential equations are chosen as they allow one to express the continuous dependence of the unknown vesicle concentration on both the time and space variables. The model represents the synthesis, concentration-gradient-driven diffusion, and accumulation of vesicles as well as the release of neuroactive substances into the cleft. An initial and boundary value problem is numerically solved using the finite element method (FEM) and the simulation results are presented and discussed. Simulations were run for various assumptions concerning the parameters that govern the synthesis and diffusion processes. The obtained results are shown to be consistent with those obtained for a compartment model based on ordinary differential equations. Such studies can be helpful in gaining a deeper understanding of synaptic processes including physiological pathologies. Furthermore, such mathematical models can be useful for estimating the biological parameters that are included in a model and are hard or impossible to measure directly.

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http://dx.doi.org/10.1007/s00422-010-0380-z | DOI Listing |

June 2010

Biol Cybern 2008 Dec 20;99(6):443-58. Epub 2008 Sep 20.

Institute of Computer Science, Jagiellonian University, Nawojki 11, 30-072, Kraków, Poland.

In this paper a mathematical description of a presynaptic episode of slow synaptic neuropeptide transport is proposed. Two interrelated mathematical models, one based on a system of reaction diffusion partial differential equations and another one, a compartment type, based on a system of ordinary differential equations (ODE) are formulated. Processes of inflow, calcium triggered activation, diffusion and release of neuropeptide from large dense core vesicles (LDCV) as well as inflow and diffusion of ionic calcium are represented. The models assume the space constraints on the motion of inactive LDCVs and free diffusion of activated ones and ions of calcium. Numerical simulations for the ODE model are presented as well. Additionally, an electronic circuit, reflecting the functional properties of the mathematically modelled presynaptic slow transport processes, is introduced.

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http://dx.doi.org/10.1007/s00422-008-0250-0 | DOI Listing |

December 2008

J Math Biol 2008 Apr 9;56(4):559-76. Epub 2007 Oct 9.

Institute of Computer Science, Jagiellonian University, Nawojki 11, 30-072 Kraków, Poland.

In this paper a methodology of mathematical description of the synthesis, storage and release of the neurotransmitter during the fast synaptic transport is presented. The proposed model is based on the initial and boundary value problem for a parabolic nonlinear partial differential equation (PDE). Presented approach enables to express space and time dependences in the process: rate of vesicular replenishment, gradients of vesicular concentration and, through the boundary conditions, the location of docking and release sites. The model should be a good starting point for future numerical simulations since it is based on thoroughly studied parabolic equation. In the article classical and variational formulation of the problem is presented and the unique solution is shown to exist. The model is referred to the model based on ordinary differential equations (ODEs), created by Aristizabal and Glavinovic (AG model). It is shown that, under some assumptions, AG model is a special case of the introduced one.

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http://dx.doi.org/10.1007/s00285-007-0131-5 | DOI Listing |

April 2008