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    Multi-stable perception balances stability and sensitivity  Open access

     Pastukhov, Alexander; Garcia Rodriguez, Pedro E.; Haenicke, Joachim; Guillamon Grabolosa, Antoni; Deco, Gustavo; Braun, Jochen
    Frontiers in Computational Neuroscience
    Date of publication: 2013
    Journal article

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    We report that multi-stable perception operates in a consistent, dynamical regime, balancing the conflicting goals of stability and sensitivity. When a multi-stable visual display is viewed continuously, its phenomenal appearance reverses spontaneously at irregular intervals. We characterized the perceptual dynamics of individual observers in terms of four statistical measures: the distribution of dominance times (mean and variance) and the novel, subtle dependence on prior history (correlation and time-constant). The dynamics of multi-stable perception is known to reflect several stabilizing and destabilizing factors. Phenomenologically, its main aspects are captured by a simplistic computational model with competition, adaptation, and noise. We identified small parameter volumes (~3% of the possible volume) in which the model reproduced both dominance distribution and history-dependence of each observer. For 21 of 24 data sets, the identified volumes clustered tightly (~15% of the possible volume), revealing a consistent "operating regime" of multi-stable perception. The "operating regime" turned out to be marginally stable or, equivalently, near the brink of an oscillatory instability. The chance probability of the observed clustering was <0.02. To understand the functional significance of this empirical "operating regime," we compared it to the theoretical "sweet spot" of the model. We computed this "sweet spot" as the intersection of the parameter volumes in which the model produced stable perceptual outcomes and in which it was sensitive to input modulations. Remarkably, the empirical "operating regime" proved to be largely coextensive with the theoretical "sweet spot." This demonstrated that perceptual dynamics was not merely consistent but also functionally optimized (in that it balances stability with sensitivity). Our results imply that multi-stable perception is not a laboratory curiosity, but reflects a functional optimization of perceptual dynamics for visual inference.

    We report that multi-stable perception operates in a consistent, dynamical regime, balancing the conflicting goals of stability and sensitivity. When a multi-stable visual display is viewed continuously, its phenomenal appearance reverses spontaneously at irregular intervals. We characterized the perceptual dynamics of individual observers in terms of four statistical measures: the distribution of dominance times (mean and variance) and the novel, subtle dependence on prior history (correlation and time-constant). The dynamics of multi-stable perception is known to reflect several stabilizing and destabilizing factors. Phenomenologically, its main aspects are captured by a simplistic computational model with competition, adaptation, and noise. We identified small parameter volumes (~3% of the possible volume) in which the model reproduced both dominance distribution and history-dependence of each observer. For 21 of 24 data sets, the identified volumes clustered tightly (~15% of the possible volume), revealing a consistent "operating regime" of multi-stable perception. The "operating regime" turned out to be marginally stable or, equivalently, near the brink of an oscillatory instability. The chance probability of the observed clustering was <0.02. To understand the functional significance of this empirical "operating regime," we compared it to the theoretical "sweet spot" of the model. We computed this "sweet spot" as the intersection of the parameter volumes in which the model produced stable perceptual outcomes and in which it was sensitive to input modulations. Remarkably, the empirical "operating regime" proved to be largely coextensive with the theoretical "sweet spot." This demonstrated that perceptual dynamics was not merely consistent but also functionally optimized (in that it balances stability with sensitivity). Our results imply that multi-stable perception is not a laboratory curiosity, but reflects a functional optimization of perceptual dynamics for visual inference.

  • Phase-amplitude response functions for transient-state stimuli

     Castejon i Company, Oriol; Guillamon Grabolosa, Antoni; Huguet Casades, Gemma
    Journal of Mathematical Neuroscience
    Date of publication: 2013-08
    Journal article

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    The phase response curve (PRC) is a powerful tool to study the effect of a perturbation on the phase of an oscillator, assuming that all the dynamics can be explained by the phase variable. However, factors like the rate of convergence to the oscillator, strong forcing or high stimulation frequency may invalidate the above assumption and raise the question of how is the phase variation away from an attractor. The concept of isochrons turns out to be crucial to answer this question; from it, we have built up Phase Response Functions (PRF) and, in the present paper, we complete the extension of advancement functions to the transient states by defining the Amplitude Response Function (ARF) to control changes in the transversal variables. Based on the knowledge of both the PRF and the ARF, we study the case of a pulse-train stimulus, and compare the predictions given by the PRC-approach (a 1D map) to those given by the PRF-ARF-approach (a 2D map); we observe differences up to two orders of magnitude in favor of the 2D predictions, especially when the stimulation frequency is high or the strength of the stimulus is large. We also explore the role of hyperbolicity of the limit cycle as well as geometric aspects of the isochrons. Summing up, we aim at enlightening the contribution of transient effects in predicting the phase response and showing the limits of the phase reduction approach to prevent from falling into wrong predictions in synchronization problems.

  • Synaptic depression and slow oscillatory activity in a biophysical network model of the cerebral cortex

     Benita, Jose M.; Guillamon Grabolosa, Antoni; Deco, Gustavo; Sánchez-Vives, Maria V.
    Frontiers in Computational Neuroscience
    Date of publication: 2012-08-28
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  • Mathematical models and multiscale simulations of cellular secretion processes  Open access

     González Vélez, Virginia
    Defense's date: 2011-07-26
    Department of Automatic Control, Universitat Politècnica de Catalunya
    Theses

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    Exocytosis is the cellular process whereby a product such as a hormone or a neurotransmitter is released as a response to stimulation. There are a lot of exocytotic cells in mammals, and each cell type has their specific subcellular mechanisms, needed to achieve the final substance release. Therefore, unveiling the role of subcellular mechanisms in secretion processes is highly relevant to understand disease evolution and possible therapies. The efficiency of the coupling between stimulus and secretion is mainly managed by an intracellular Ca2+ signal. In the present thesis, a modeling approach of Ca2+-triggered secretion is presented for some different cellular types. In particular, cells with different characteristic time scales were chosen in order to discuss about a multiscale approach for studying spatiotemporal features of secretion processes. The object of this piece of research ranges from a short temporal scale (fast secretion) up to a long temporal scale (slow secretion). The study also discuss the intermediate temporal scale, and the joining point between theoretical methodologies. Cellular Ca2+ and secretion dynamics have been studied in the abovementioned timescales for the calyx of Held presynaptic terminal, the pancreatic alpha cell, and the adrenal chromaffin cell, respectively. The aim of this work has been twofold: first, to develop mathematical models that follow actual sub-cellular mechanisms involved in secretion, and second, to make simulations on these models in order to reproduce the experimentally observed Ca2+ and secretory behaviour. The ultimate goal is to propose common methodologies and algorithms to support the theoretical approach for studying multiscale cellular processes.

    Exocitosis es el proceso celular por el cual un producto, sea una hormona o un neurotransmisor, es liberado en respuesta a un estímulo. Existen muchas células exocitóticas en los mamíferos y cada una de ellas posee sus mecanismos específicos para llevar a cabo esta función. Por esta razón, es de gran relevancia descubrir cuáles son los mecanismos intracelulares involucrados en el proceso de secreción para comprender la evolución y posibles terapias asociadas a las enfermedades. La eficiencia del acople entre el estímulo y la secreción celular es controlada por una señal de Ca2+ intracelular. En esta tesis se presenta una investigación teórica de modelado sobre la secreción controlada por Ca2+ para diferentes tipos celulares. En particular, se han escogido células con diferentes tiempos característicos para darle un enfoque multiescala al estudio. Cada tipo celular presenta características espacio-temporales específicas involucradas en la secreción. El estudio cubre desde una escala temporal corta (secreción rápida) hasta una escala temporal larga (secreción lenta), discutiendo también la escala intermedia que provee el punto de convergencia entre las metodologías empleadas. Para estudiar estas escalas temporales, se han escogido la terminal presináptica del cáliz de Held, la célula alfa de páncreas y la célula cromafin de glándulas suprarrenales, respectivamente. Los principales objetivos del trabajo han sido: Primero, proponer modelos matemáticos de los mecanismos intracelulares reales que participan en la secreción para cada tipo celular, y segundo, desarrollar simulaciones que logren reproducir el comportamiento fisiológico del Ca2+ y la secreción celulares. La perspectiva se orienta a proponer metodologías y algoritmos multiescala que puedan ser comunes para el estudio teórico de los procesos celulares.

  • Phase portraits of separable Hamiltonian systems

     Guillamon Grabolosa, Antoni; Pantazi, Chara
    Nonlinear analysis, theory, methods and applications
    Date of publication: 2011-08
    Journal article

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  • Ciudad de las Lenguas de Castellón

     Peñin Llobell, Alberto; Ferrater Lambarri, Carlos; Guillamon Grabolosa, Antoni
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  • DINAMICA ASOCIADA A CONEXIONES ENTRE OBJETOS INVARIANTES, ASTRODINÁMICA, NEUROCIENCIA Y OTRAS APLICACIONES

     Blazquez Sanz, David; Olive Farre, Maria del Carme; Gomez-Ullate Oteiza, David; Morales Ruiz, Juan Jose; Canalias Vila, Elisabet; Martinez-seara Alonso, Maria Teresa; Baldoma Barraca, Inmaculada Concepcion; Fedorov, Yury; Garcia Taberner, Laura; Guardia Munarriz, Marcel; Guillamon Grabolosa, Antoni; Gonchenko, Marina; Gutiérrez Serrés, Pere; Lazaro Ochoa, Jose Tomas; Luque Jiménez, Alejandro; Martin De La Torre, Pablo; Masdemont Soler, Josep Joaquim; Olle Torner, Maria Mercedes; Pacha Andujar, Juan Ramon; Pantazi, Chara; Puig Sadurni, Joaquim; Ramirez Ros, Rafael; Roldan Gonzalez, Pablo; Villanueva Castelltort, Jordi; Tamarit, Anna; Olivé Farré, Carme; Morales Ruíz, Juan José; Larreal Barreto, Oswaldo José; Huguet Casades, Gemma; Gómez-Ullate Oteiza, David; Acosta Humanez, Primitivo Belen; Benita Bordes, Jose Manuel; Basak, Inna; Blázquez Sanz, David; de la Llave Canosa, Rafael; de la Rosa Ibarra, Abraham; Delshams i Valdes, Amadeu
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  • The number of limit cycles in planar systems and generalized Abel equations with monotonous hyperbolicity

     Guillamon Grabolosa, Antoni; Sabatini, M
    Nonlinear analysis, theory, methods and applications
    Date of publication: 2009-09
    Journal article

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  • SISTEMES DINAMICS DE LA UPC

     Lazaro Ochoa, Jose Tomas; Roldan Gonzalez, Pablo; Olle Torner, Maria Mercedes; Gutiérrez Serrés, Pere; Masdemont Soler, Josep Joaquim; Gomez-Ullate Oteiza, David; Luque Jiménez, Alejandro; Larreal Barreto, Oswaldo José; Huguet Casades, Gemma; Pacha Andujar, Juan Ramon; Ramirez Ros, Rafael; Martinez-seara Alonso, Maria Teresa; Guillamon Grabolosa, Antoni; Martin De La Torre, Pablo; Canalias Vila, Elisabet; Puig Sadurni, Joaquim; Benita Bordes, Jose Manuel; Morales Ruiz, Juan Jose; Guardia Munarriz, Marcel; Olive Farre, Maria del Carme; de la Rosa Ibarra, Abraham; Baldoma Barraca, Inmaculada Concepcion; Blazquez Sanz, David; Fedorov, Yury; Acosta Humanez, Primitivo Belen; Gonchenko, Marina; Pantazi, Chara; de la Llave Canosa, Rafael; Villanueva Castelltort, Jordi; Delshams i Valdes, Amadeu
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    A computational and geometric approach to phase resetting curves and surfaces  Open access

     Guillamon Grabolosa, Antoni; Huguet Casades, Gemma
    SIAM journal on applied dynamical systems
    Date of publication: 2009
    Journal article

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  • Review of the paper: Uniqueness of limit cycles in the Duff and Levinson-type system. Auth.: Makoto Hayashi

     Guillamon Grabolosa, Antoni
    Mathematical reviews
    Date of publication: 2008-06
    Journal article

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  • The role of hyperbolic invariant objects: From Arnold diffusion to biological clocks  Open access

     Huguet Casades, Gemma
    Defense's date: 2008-10-16
    School of Mathematics and Statistics (FME), Universitat Politècnica de Catalunya
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    El marc d'aquesta tesi són els objectes invariants hiperbòlics (tors amb bigotis, cicles límit, NHIM,. . .), que constitueixen, per aquesta tesi, els objectes essencials per a l'estudi de diversos problemes des de la difusió d'Arnold fins als rellotges biològics. Treballem en tres temes diferents des d'un enfocament tant teòric com numèric, amb una especial atenció per a les aplicacions, especialment en neurobiologia:· Existència de difusió d'Arnold per a sistemes Hamiltonians a priori inestables· Algorismes numèrics ràpids per al càlcul de tors invariants i els "bigotis" associats, per a sistemes Hamiltonians utilitzant el mètode de la parametrització.· Càlcul d'isòcrones i corbes de resposta de fase (PRC) en sistemes neurobiològics usant el mètode de la parametrització.En la primera part de la tesi, hem considerat el cas d'un sistema Hamiltonià a priori inestable amb 2+1/2 graus de llibertat sotmès a una pertorbació de tipus general. "A priori inestable" significa que el sistema no pertorbat presenta un punt d'equilibri hiperbòlic amb una òrbita homoclínica associada. El resultat principal d'aquesta part de la tesi és que per a un conjunt genèric de pertorbacions prou regulars, el sistema presenta el fenòmen de la difusió d'Arnold, és a dir, existeixen trajectòries la variable acció de les quals experimenta un canvi d'ordre 1. La demostració es basa en un estudi detallat de les zones ressonants i els objectes invariants generats en elles, i ofereix una descripció completa de la geografia de les ressonàncies generades per una pertorbació genèrica.En la segona part d'aquest memòria, desenvolupem mètodes numèrics eficients que requereixen poca memòria i operacions per al càlcul de tors invariants i els "bigotis" associats en sistemes Hamiltonians (aplicacions simplèctiques i camps vectorials Hamiltonians).En particular, això inclou els objectes invariants involucrats en el mecanisme de la difusió d'Arnold, estudiat en el capítol anterior. Els algorismes es basen en el mètode de la parametrització i segueixen de prop demostracions recents del teorema KAM que no usen variables acció-angle. Donem detalls de la implementació numèrica que hem dut a terme i mostrem alguns exemples.En la darrera part de la tesi relacionem problemes de temps en sistemes biològics amb algunes eines conegudes de sistemes dinàmics. En particular, usem el mètode de la parametrització i les simetries de Lie per a calcular numèricament les isòcrones i les corbes de resposta de fase (PRC) associades a oscil·ladors i ho apliquem a diversos models biològics ben coneguts. A més a més, aconseguim estendre el càlcul de PRCs en un entorn de l'oscil·lador. Les PRCs són útils per a l'estudi de la sincronització d'oscil·ladors acoblats i una eina bàsica en biologia experimental (ritmes circadians, acoblament sinàptic i elèctric de neurones,. . . ).

  • Phase portraits of separable Hamiltonian systems

     Guillamon Grabolosa, Antoni; Pantazi, Chara
    Date: 2008-09
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  • Limit cycles and Lie symmetries

     Emilio, Freire; Armengol, Gasull; Guillamon Grabolosa, Antoni
    Bulletin des sciences mathématiques
    Date of publication: 2007-08
    Journal article

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  • aCteX: Autoaprenentatge científico-tècnic en xarxa

     Guillamon Grabolosa, Antoni
    Jornada de presentación de los resultados de los proyectos de mejora de la docencia, 2007
    Presentation's date: 2007-07-28
    Presentation of work at congresses

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  • "aCTeX": Autoaprenentatge científico-tècnic en xarxa

     Guillamon Grabolosa, Antoni; Ferrer Biosca, Alberto
    Date: 2007-01
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  • Geometric tools to determine the hyperbolicity of limit cycles

     Guillamon Grabolosa, Antoni; Sabatini, M
    Journal of mathematical analysis and applications
    Date of publication: 2007-07
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  • Limit cycles for generalized Abel equations

     Gasull, A; Guillamon Grabolosa, Antoni
    International journal of bifurcation and chaos
    Date of publication: 2006-12
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  • Paraules i nombres

     Guillamon Grabolosa, Antoni
    Materials matemàtics
    Date of publication: 2006-09
    Journal article

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  • Estimation of synaptic conductances

     Guillamon Grabolosa, Antoni; Mclaughlin, D W; Rinzel, J
    Journal of physiology-Paris
    Date of publication: 2006-07
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  • Mathematical problems arising in conductance estimation

     Guillamon Grabolosa, Antoni
    Workshop on Math. Aspects of Brain Functions. COmpositionality and Synchronization
    Presentation's date: 2006-10-09
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  • Dinámica Asociada a Conexiones entre Objetos Invariantes, Astrodinámica y otras aplicaciones (DACOBIA)

     Delshams i Valdes, Amadeu; Fedorov, Yury; Gonchenko, Marina; Pantazi, Chara; Sánchez Casas, José Pablo; Olle Torner, Maria Mercedes; Gutiérrez Serrés, Pere; Roldan Gonzalez, Pablo; Masdemont Soler, Josep Joaquim; Martinez-seara Alonso, Maria Teresa; Villanueva Castelltort, Jordi; Pacha Andujar, Juan Ramon; Guillamon Grabolosa, Antoni; Guardia Munarriz, Marcel; Larreal Barreto, Oswaldo José
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  • Els intersticis de la neuro... matemàtica

     Guillamon Grabolosa, Antoni
    Novena Trobada Matemàtica de la Societat Catalana de Matemàtiques
    Presentation's date: 2006-04-22
    Presentation of work at congresses

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  • Mathematical modeling in neuroscience with emphasis on questions related to cortical wiring and decisions

     Guillamon Grabolosa, Antoni
    Workshop on Behavioral Economics in the Light of Mathematics, Pxyxhology, Cognition and Bio Informatics
    Presentation's date: 2006-11-10
    Presentation of work at congresses

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  • La conjectura 3x+1

     Guillamon Grabolosa, Antoni
    Xerrada a alumnes de Secundària de l'Escola IES Valerià Pujol
    Presentation's date: 2005-02-02
    Presentation of work at congresses

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  • Estudio cualitativo de los sistemas dinámicos con énfasis en sus órbitas periódicas y sus bifurcaciones

     Guillamon Grabolosa, Antoni; Llibre Saló, Jaume
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  • Grup de recerca consolidat 2005. Sistemas Dinámicos de la UPC

     Delshams i Valdes, Amadeu; Pantazi, Chara; Gutiérrez Serrés, Pere; Roldan Gonzalez, Pablo; Baldoma Barraca, Inmaculada Concepcion; Lazaro Ochoa, Jose Tomas; Martinez-seara Alonso, Maria Teresa; Villanueva Castelltort, Jordi; Pacha Andujar, Juan Ramon; Guillamon Grabolosa, Antoni; Larreal Barreto, Oswaldo José
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  • Dues llaminadures matemàtiques

     Guillamon Grabolosa, Antoni
    Jornada de Portes Obertes FME
    Presentation's date: 2005-02-01
    Presentation of work at congresses

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  • A characterization of isochronous centres in terms of symmetries

     Freire, E; Gasull, A; Guillamon Grabolosa, Antoni
    Revista matemática iberoamericana
    Date of publication: 2004-06
    Journal article

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  • First derivate of the period function with applications

     Freire, E; Gasull, A; Guillamon Grabolosa, Antoni
    Journal of differential equations
    Date of publication: 2004-09
    Journal article

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  • The period function for second-order quadratic ODEs is monotone

     Gasull, A; Guillamon Grabolosa, Antoni; Villadelprat, A
    Qualitative theory of dynamical systems
    Date of publication: 2004-10
    Journal article

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  • Una introducció a les matemàtiques de l'activitat neuronal

     Guillamon Grabolosa, Antoni
    Butlletí de la Societat Catalana de Matemàtiques
    Date of publication: 2004-01
    Journal article

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  • Ajuts per a projectes de millora de la docència

     Bruguera Padro, Maria Montserrat; Guillamon Grabolosa, Antoni; Mitjana Riera, Margarida; Pañella Brustenga, Francisco de Asis; Rodriguez Jordana, Juan; Serrat Pie, Carles; Panyella, F; Juan-Pérez, Angel A.
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  • Ajuts per a projectes de millora de la docència

     Bruguera Padro, Maria Montserrat; Ferrer Biosca, Alberto; Guillamon Grabolosa, Antoni; Mitjana Riera, Margarida; Pañella Brustenga, Francisco de Asis; Rodriguez Jordana, Juan; Serrat Pie, Carles; Panyella, F; Pérez, R
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  • Traducció de: "Una actualització del Problema 3x+1 (de Marc Chamberland), d'anglès a català

     Guillamon Grabolosa, Antoni
    Butlletí de la Societat Catalana de Matemàtiques
    Date of publication: 2003-12
    Journal article

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  • aCTeX: Una eina telemàtica per a l'autoaprenentatge

     Guillamon Grabolosa, Antoni
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  • Les matemàtiques del cervell

     Guillamon Grabolosa, Antoni
    Jornada de Portes Obertes FME
    Presentation's date: 2003-02-01
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  • A pseudo-normal form for planar vector fields

     Delshams i Valdes, Amadeu; Guillamon Grabolosa, Antoni; Lazaro Ochoa, Jose Tomas
    Qualitative theory of dynamical systems
    Date of publication: 2002-03
    Journal article

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  • Period function for perturbed isochronous centres

     Freire, E; Gasull, A; Guillamon Grabolosa, Antoni
    Qualitative theory of dynamical systems
    Date of publication: 2002-02
    Journal article

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  • Grupo de sistemas dinámicos y teoría cualitativa de la UAB

     Guillamon Grabolosa, Antoni; Llibre Saló, Jaume
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  • Teoría cualitativa de los sistemas dinámicos con énfasis en sus bifurcaciones.

     Guillamon Grabolosa, Antoni; Llibre Saló, Jaume
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  • Periodic orbits and dynamical systems

     Guillamon Grabolosa, Antoni; Llibre Saló, Jaume
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  • Phase portrait of Hamiltonian systems with homogeneous nonlinearities

     Gasull, A; Guillamon Grabolosa, Antoni; Mañosa Fernández, Víctor
    Nonlinear analysis, theory, methods and applications
    Date of publication: 2000-08
    Journal article

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  • Grupo de sistemas dinámicos y teoría cualitativa de la UAB

     Guillamon Grabolosa, Antoni; Llibre Saló, Jaume
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  • An analytic-numerical method for computation of the Liaponov and period constants derived from their algebraic structure

     Gasull, A; Guillamon Grabolosa, Antoni; Mañosa Fernández, Víctor
    SIAM journal on numerical analysis
    Date of publication: 1999-05
    Journal article

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  • Teoría cualitativa de los sistemas dinámicos con énfasis en las órbitas periódicas

     Guillamon Grabolosa, Antoni; Llibre Saló, Jaume
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