arXiv subjects

Alessio Franci

Publications and source records attributed to Alessio Franci.

54 records · Page 3Linked to original sources

arXiv2018

Social decision-making driven by artistic explore-exploit tension

We studied social decision-making in the rule-based improvisational dance $There$ $Might$ $Be$ $Others$, where dancers make in-the-moment compositional choices. Rehearsals provided a natural test-bed with communication restricted to non-verbal cues. We observed a key artistic explore-exploit tension in which the dancers switched between exploitation of existing artistic opportunities and riskier exploration of new ones. We investigated how the rules influenced the dynamics using rehearsals together with a model generalized from evolutionary dynamics. We tuned the rules to heighten the tension and modeled nonlinear fitness and feedback dynamics for mutation rate to capture the observed temporal phasing of the dancers' exploration-versus-exploitation. Using bifurcation analysis, we identified key controls of the tension and showed how they could shape the decision-making dynamics of the model much like turning a "dial" in the instructions to the dancers could shape the dance. The investigation became an integral part of the development of the dance.

physics.soc-ph↗

arXiv2018

On-line detection of qualitative dynamical changes in nonlinear systems: the resting-oscillation case

Motivated by neuroscience applications, we introduce the concept of qualitative detection, that is, the problem of determining on-line the current qualitative dynamical behavior (e.g., resting, oscillating, bursting, spiking etc.) of a nonlinear system. The approach is thought for systems characterized by i) large parameter variability and redundancy, ii) a small number of possible robust, qualitatively different dynamical behaviors and, iii) the presence of sharply different characteristic timescales. These properties are omnipresent in neurosciences and hamper quantitative modeling and fitting of experimental data. As a result, novel control theoretical strategies are needed to face neuroscience challenges like on-line epileptic seizure detection. The proposed approach aims at detecting the current dynamical behavior of the system and whether a qualitative change is likely to occur without quantitatively fitting any model nor asymptotically estimating any parameter. We talk of qualitative detection. We rely on the qualitative properties of the system dynamics, extracted via singularity and singular perturbation theories, to design low dimensional qualitative detectors. We introduce this concept on a general class of singularly perturbed systems and then solve the problem for an analytically tractable class of two-dimensional systems with a single unknown sigmoidal nonlinearity and two sharply separated timescales. Numerical results are provided to show the performance of the designed qualitative detector.

math.OC↗

arXiv2018

Cellular switches orchestrate rhythmic circuits

Small inhibitory neuronal circuits have long been identified as key neuronal motifs to generate and modulate the coexisting rhythms of various motor functions. Our paper highlights the role of a cellular switching mechanism to orchestrate such circuits. The cellular switch makes the circuits reconfigurable, robust, adaptable, and externally controllable. Without this cellular mechanism, the circuits rhythms entirely rely on specific tunings of the synaptic connectivity, which makes them rigid, fragile, and difficult to control externally. We illustrate those properties on the much studied architecture of a small network controlling both the pyloric and gastric rhythms of crabs. The cellular switch is provided by a slow negative conductance often neglected in mathematical modeling of central pattern generators. We propose that this conductance is simple to model and key to computational studies of rhythmic circuit neuromodulation.

q-bio.NC↗

arXiv2018

Robust and tunable bursting requires slow positive feedback

We highlight that the robustness and tunability of a bursting model critically relies on currents that provide slow positive feedback to the membrane potential. Such currents have the ability of making the total conductance of the circuit negative in a time scale that is termed slow because intermediate between the fast time scale of the spike upstroke and the ultraslow time scale of even slower adaptation currents. We discuss how such currents can be assessed either in voltage-clamp experiments or in computational models. We show that, while frequent in the literature, mathematical and computational models of bursting that lack the slow negative conductance are fragile and rigid. Our results suggest that modeling the slow negative conductance of cellular models is important when studying the neuromodulation of rhythmic circuits at any broader scale.

q-bio.NC↗

arXiv2018

Multi-agent decision-making dynamics inspired by honeybees

When choosing between candidate nest sites, a honeybee swarm reliably chooses the most valuable site and even when faced with the choice between near-equal value sites, it makes highly efficient decisions. Value-sensitive decision-making is enabled by a distributed social effort among the honeybees, and it leads to decision-making dynamics of the swarm that are remarkably robust to perturbation and adaptive to change. To explore and generalize these features to other networks, we design distributed multi-agent network dynamics that exhibit a pitchfork bifurcation, ubiquitous in biological models of decision-making. Using tools of nonlinear dynamics we show how the designed agent-based dynamics recover the high performing value-sensitive decision-making of the honeybees and rigorously connect investigation of mechanisms of animal group decision-making to systematic, bio-inspired control of multi-agent network systems. We further present a distributed adaptive bifurcation control law and prove how it enhances the network decision-making performance beyond that observed in swarms.

math.OC↗

arXiv2017

A Realization Theory for Bio-inspired Collective Decision-Making

The collective decision-making exhibited by animal groups provides enormous inspiration for multi-agent control system design as it embodies several features that are desirable in engineered networks, including robustness and adaptability, low computational effort, and an intrinsically decentralized architecture. However, many of the mechanistic models for collective decision-making are described at the population-level abstraction and are challenging to implement in an engineered system. We develop simple and easy-to-implement models of opinion dynamics that realize the empirically observed collective decision-making behavior as well as the behavior predicted by existing models of animal groups. Using methods from Lyapunov analysis, singularity theory, and monotone dynamical systems, we rigorously investigate the steady-state decision-making behavior of our models.

math.OC↗

arXiv2017

Excitable behaviors

This chapter revisits the concept of excitability, a basic system property of neurons. The focus is on excitable systems regarded as behaviors rather than dynamical systems. By this we mean open systems modulated by specific interconnection properties rather than closed systems classified by their parameter ranges. Modeling, analysis, and synthesis questions can be formulated in the classical language of circuit theory. The input-output characterization of excitability is in terms of the local sensitivity of the current-voltage relationship. It suggests the formulation of novel questions for non-linear system theory, inspired by questions from experimental neurophysiology.

q-bio.NC↗

arXiv2016

Implementing robust neuromodulation in neuromorphic circuits

We introduce a methodology to implement the physiological transition {between distinct neuronal spiking modes} in electronic circuits composed of resistors, capacitors and transistors. The result is a simple neuromorphic device organized by the same geometry {and exhibiting the same input--output properties as} high-dimensional electrophysiological neuron models. {Preliminary} experimental results highlight the robustness of the approach in real-world applications.

math.OC↗

arXiv2016

A three-scale model of spatio-temporal bursting

We study spatio-temporal bursting in a three-scale reaction diffusion equation organized by the winged cusp singularity. For large time-scale separation the model exhibits traveling bursts, whereas for large space-scale separation the model exhibits standing bursts. Both behaviors exhibit a common singular skeleton, whose geometry is fully determined by persistent bifurcation diagrams of the winged cusp. The modulation of spatio-temporal bursting in such a model naturally translates into paths in the universal unfolding of the winged-cusp.

math.DS↗

arXiv2015

Singularly perturbed phase response curves

In this paper we propose a novel geometric method, based on singular perturbations, to approximate isochrones of relaxation oscillators and predict the qualitative shape of their (finite) phase response curve. This approach complements the infinitesimal phase response curve approach to relaxation oscillators and overcomes its limitations near the singular limit. We illustrate the power of the methodology by deriving semi-analytic formula for the (finite) phase response curve of generic planar relaxation oscillators to impulses and square pulses of finite duration and verify its goodness numerically on the FitzHugh-Nagumo model.

math.DS↗

arXiv2014

A positive feedback at the cellular level promotes robustness and modulation at the circuit level

The paper highlights the role of a positive feedback gating mechanism at the cellular level in the robust- ness and modulation properties of rhythmic activities at the circuit level. The results are presented in the context of half-center oscillators, which are simple rhythmic circuits composed of two reciprocally connected inhibitory neuronal populations. Specifically, we focus on rhythms that rely on a particu- lar excitability property, the post-inhibitory rebound, an intrinsic cellular property that elicits transient membrane depolarization when released from hyperpolarization. Two distinct ionic currents can evoke this transient depolarization: a hyperpolarization-activated cation current and a low-threshold T-type calcium current. The presence of a slow activation is specific to the T-type calcium current and provides a slow-positive feedback at the cellular level that is absent in the cation current. We show that this slow- positive feedback is necessary and sufficient to endow the network rhythm with physiological modulation and robustness properties. This study thereby identifies an essential cellular property to be retained at the network level in modeling network robustness and modulation.

q-bio.NC↗

arXiv2014

Realization of nonlinear behaviors from organizing centers

Borrowing the concept of organizing center from singularity theory, the paper proposes a methodology to realize nonlinear behaviors such as switches, relaxation oscillators, or bursters from core circuits that reveal the fundamental role of monotonicity and feedback in their robustness and modulation.

math.OC↗

arXiv2013

Modeling the modulation of neuronal bursting: a singularity theory approach

Exploiting the specific structure of neuron conductance-based models, the paper investigates the mathematical modeling of neuronal bursting modulation. The proposed approach combines singularity theory and geometric singular perturbations to capture the geometry of multiple time-scales attractors in the neighborhood of high-codimension singularities. We detect a three-time scale bursting attractor in the universal unfolding of the winged cusp singularity and discuss the physiological relevance of the bifurcation and unfolding parameters in determining a physiological modulation of bursting. The results suggest generality and simplicity in the organizing role of the winged cusp singularity for the global dynamics of conductance based models.

math.DS↗

arXiv2013

Modulation of beta oscillations during movement initiation: modeling the ionic basis of a functional switch

We use a computational model to propose a physiological mechanism by which transient control of beta oscillations in the indirect pathway of the basal ganglia is orchestrated at the cellular level. Our model includes a simple and robust mechanism by which a cellular switch (from bursting to tonic) almost instantaneously translates into a functional gating switch (from blocking to conducive) in an excitatory-inhibitory network. Applied to the control of beta oscillations in the basal ganglia, the model shows the modulation of beta activity under the action of a transient depolarization, for instance a dopamine signal. The model predicts, by analogy to the thalamocortical circuit, a novel gating function by which the transfer of cortical spikes through the indirect pathway is blocked under the inhibitory drive preceding movement but briefly released at the onset of movement execution.

q-bio.NC↗

arXiv2013

Modulation and Robustness of Endogenous Neuronal Spiking

Neuronal spiking exhibits an exquisite combination of modulation and robustness properties, rarely matched in artificial systems. We exploit the particular interconnection structure of conductance based models to investigate this remarkable property. We find that much of neuronal modulation and robustness can be explained by separating the total transmembrane current into three different components corresponding to the three time scales of neuronal bursting. Each equivalent current aggregates many ionic contributions into an equivalent voltage-dependent conductance, which defines a key modulation parameter. Plugging those equivalent feedback gains in a minimal abstract model recovers many experimental modulation scenarii as modulatory paths in elementary two-parameter charts. Likewise, robustness owes to the many possible physiological realizations of a same equivalent conductance, highlighting the role of equivalent conductances as prominent targets for neuromodulation and intrinsic homeostasis.

q-bio.NC↗

arXiv2013

A Balance Equation Determines a Switch in Neuronal Excitability

We use the qualitative insight of a planar neuronal phase portrait to detect an excitability switch in arbitrary conductance-based models from a simple mathematical condition. The condition expresses a balance between ion channels that provide a negative feedback at resting potential (restorative channels) and those that provide a positive feedback at resting potential (regenerative channels). Geometrically, the condition imposes a transcritical bifurcation that rules the switch of excitability through the variation of a single physiological parameter. Our analysis of six different published conductance based models always finds the transcritical bifurcation and the associated switch in excitability, which suggests that the mathematical predictions have a physiological relevance and that a same regulatory mechanism is potentially involved in the excitability and signaling of many neurons.

q-bio.NC↗

arXiv2012

An organizing center in a planar model of neuronal excitability

The paper studies the excitability properties of a generalized FitzHugh-Nagumo model. The model differs from the purely competitive FitzHugh-Nagumo model in that it accounts for the effect of cooperative gating variables such as activation of calcium currents. Excitability is explored by unfolding a pitchfork bifurcation that is shown to organize five different types of excitability. In addition to the three classical types of neuronal excitability, two novel types are described and distinctly associated to the presence of cooperative variables.

math.DS↗

arXiv2011

A Novel Phase Portrait to Understand Neuronal Excitability

Fifty years ago, Fitzugh introduced a phase portrait that became famous for a twofold reason: it captured in a physiological way the qualitative behavior of Hodgkin-Huxley model and it revealed the power of simple dynamical models to unfold complex firing patterns. To date, in spite of the enormous progresses in qualitative and quantitative neural modeling, this phase portrait has remained the core picture of neuronal excitability. Yet, a major difference between the neurophysiology of 1961 and of 2011 is the recognition of the prominent role of calcium channels in firing mechanisms. We show that including this extra current in Hodgkin-Huxley dynamics leads to a revision of Fitzugh-Nagumo phase portrait that affects in a fundamental way the reduced modeling of neural excitability. The revisited model considerably enlarges the modeling power of the original one. In particular, it captures essential electrophysiological signatures that otherwise require non-physiological alteration or considerable complexication of the classical model. As a basic illustration, the new model is shown to highlight a core dynamical mechanism by which the calcium conductance controls the two distinct firing modes of thalamocortical neurons.

math.DS↗