arXiv subjects

Alessandro Torcini

Publications and source records attributed to Alessandro Torcini.

At least 55 records · Page 3Linked to original sources

arXiv2014

Stable chaos in fluctuation driven neural circuits

We study the dynamical stability of pulse coupled networks of leaky integrate-and-fire neurons against infinitesimal and finite perturbations. In particular, we compare current versus fluctuations driven networks, the former (latter) is realized by considering purely excitatory (inhibitory) sparse neural circuits. In the excitatory case the instabilities of the system can be completely captured by an usual linear stability (Lyapunov) analysis, on the other hand the inhibitory networks can display the coexistence of linear and nonlinear instabilities. The nonlinear effects are associated to finite amplitude instabilities, which have been characterized in terms of suitable indicators. For inhibitory coupling one observes a transition from chaotic to non chaotic dynamics by decreasing the pulse width. For sufficiently fast synapses the system, despite showing an erratic evolution, is linearly stable, thus representing a prototypical example of Stable Chaos.

cond-mat.dis-nn↗

arXiv2013

Linear stability in networks of pulse-coupled neurons

In a first step towards the comprehension of neural activity, one should focus on the stability of the various dynamical states. Even the characterization of idealized regimes, such as a perfectly periodic spiking activity, reveals unexpected difficulties. In this paper we discuss a general approach to linear stability of pulse-coupled neural networks for generic phase-response curves and post-synaptic response functions. In particular, we present: (i) a mean-field approach developed under the hypothesis of an infinite network and small synaptic conductances; (ii) a "microscopic" approach which applies to finite but large networks. As a result, we find that no matter how large is a neural network, its response to most of the perturbations depends on the system size. There exists, however, also a second class of perturbations, whose evolution typically covers an increasingly wide range of time scales. The analysis of perfectly regular, asynchronous, states reveals that their stability depends crucially on the smoothness of both the phase-response curve and the transmitted post-synaptic pulse. The general validity of this scenarion is confirmed by numerical simulations of systems that are not amenable to a perturbative approach.

cond-mat.dis-nn↗

arXiv2013

Emergence of slow collective oscillations in neural networks with spike timing dependent plasticity

The collective dynamics of excitatory pulse coupled neurons with spike timing dependent plasticity (STDP) is studied. The introduction of STDP induces persistent irregular oscillations between strongly and weakly synchronized states, reminiscent of brain activity during slow-wave sleep. We explain the oscillations by a mechanism, the Sisyphus Effect, caused by a continuous feedback between the synaptic adjustments and the coherence in the neural firing. Due to this effect, the synaptic weights have oscillating equilibrium values, and this prevents the system from relaxing into a stationary macroscopic state.

q-bio.NC↗

arXiv2012

Collective dynamics in sparse networks

The microscopic and macroscopic dynamics of random networks is investigated in the strong-dilution limit (i.e. for sparse networks). By simulating chaotic maps, Stuart-Landau oscillators, and leaky integrate-and-fire neurons, we show that a finite connectivity (of the order of a few tens) is able to sustain a nontrivial collective dynamics even in the thermodynamic limit. Although the network structure implies a non-additive dynamics, the microscopic evolution is extensive (i.e. the number of active degrees of freedom is proportional to the number of network elements).

cond-mat.dis-nn↗

arXiv2012

Chaos in the Hamiltonian mean field model

We study the dynamical properties of the canonical ordered phase of the Hamiltonian mean-field (HMF) model, in which $N$ particles, globally-coupled via pairwise attractive interactions, form a rotating cluster. Using a combination of numerical and analytical arguments, we first show that the largest Lyapunov exponent remains strictly positive in the infinite-size limit, converging to its asymptotic value with $1/\ln N$ corrections. We then elucidate the scaling laws ruling the behavior of this asymptotic value in the critical region separating the ordered, clustered phase and the disordered phase present at high energy densities. We also show that the full spectrum of Lyapunov exponents consists of a bulk component converging to the (zero) value taken by a test oscillator forced by the mean field, plus subextensive bands of ${\cal O}(\ln N)$ exponents taking finite values. We finally investigate the robustness of these results by studying a "2D" extension of the HMF model where each particle is endowed with 4 degrees of freedom, thus allowing the emergence of chaos at the level of single particle. Altogether, these results illustrate the subtle effects of global (or long-range) coupling, and the importance of the order in which the infinite-time and infinite-size limits are taken: for an infinite-size HMF system represented by the Vlasov equation, no chaos is present, while chaos exists and subsists for any finite system size.

nlin.CD↗

arXiv2012

Stability of the splay state in networks of pulse-coupled neurons

We analytically investigate the stability of {\it splay states} in networks of $N$ pulse-coupled phase-like models of neurons. By developing a perturbative technique, we find that, in the limit of large $N$, the Floquet spectrum scales as $1/N^2$ for generic discontinuous velocity fields. Moreover, the stability of the so-called short-wavelength component is determined by the sign of the jump at the discontinuity. Altogether, the form of the spectrum depends on the pulse shape but is independent of the velocity field.

cond-mat.dis-nn↗

arXiv2012

Convective Lyapunov Spectra

We generalize the concept of convective (or velocity-dependent) Lyapunov exponent $Λ(v)$ to an entire spectrum $Λ(v,n)$. Our results are supported by the consistency between the outcome of the chronotopic approach [{\it S. Lepri et al. J. Stat. Phys., 82 5/6 (1996) 1429}] and a more direct method. There exists a critical integrated density $n=n_c$, beyond which the convective exponent exhibits a discontinuous dependence on the velocity, which originates from the appearance of multiple branches. This phenomenon can be traced back to a change of concavity of the so-called {\it temporal} Lyapunov spectrum for $n>n_c$, which is therefore a dynamical invariant.

nlin.CD↗

arXiv2012

Splay states in finite pulse-coupled networks of excitable neurons

The emergence and stability of splay states is studied in fully coupled finite networks of N excitable quadratic integrate-and-fire neurons, connected via synapses modeled as pulses of finite amplitude and duration. For such synapses, by introducing two distinct types of synaptic events (pulse emission and termination), we were able to write down an exact event-driven map for the system and to evaluate the splay state solutions. For M overlapping post synaptic potentials the linear stability analysis of the splay state should take in account, besides the actual values of the membrane potentials, also the firing times associated to the M previous pulse emissions. As a matter of fact, it was possible, by introducing M complementary variables, to rephrase the evolution of the network as an event-driven map and to derive an analytic expression for the Floquet spectrum. We find that, independently of M, the splay state is marginally stable with N-2 neutral directions. Furthermore, we have identified a family of periodic solutions surrounding the splay state and sharing the same neutral stability directions. In the limit of $δ$-pulses, it is still possible to derive an event-driven formulation for the dynamics, however the number of neutrally stable directions, associated to the splay state, becomes N. Finally, we prove a link between the results for our system and a previous theory [Watanabe and Strogatz, Physica D, 74 (1994), pp. 197- 253] developed for networks of phase oscillators with sinusoidal coupling.

cond-mat.dis-nn↗

arXiv2011

Coherent periodic activity in excitatory Erdos-Renyi neural networks:The role of network connectivity

We consider an excitatory random network of leaky integrate-and-fire pulse coupled neurons. The neurons are connected as in a directed Erdös-Renyi graph with average connectivity $ $ scaling as a power law with the number of neurons in the network. The scaling is controlled by a parameter $γ$, which allows to pass from massively connected to sparse networks and therefore to modify the topology of the system. At a macroscopic level we observe two distinct dynamical phases: an Asynchronous State (AS) corresponding to a desynchronized dynamics of the neurons and a Partial Synchronization (PS) regime associated with a coherent periodic activity of the network. At low connectivity the system is in an AS, while PS emerges above a certain critical average connectivity $ _c$. For sufficiently large networks, $ _c$ saturates to a constant value suggesting that a minimal average connectivity is sufficient to observe coherent activity in systems of any size irrespectively of the kind of considered network: sparse or massively connected. However, this value depends on the nature of the synapses: reliable or unreliable. For unreliable synapses the critical value required to observe the onset of macroscopic behaviors is noticeably smaller than for reliable synaptic transmission. Due to the disorder present in the system, for finite number of neurons we have inhomogeneities in the neuronal behaviors, inducing a weak form of chaos, which vanishes in the thermodynamic limit. In such a limit the disordered systems exhibit regular (non chaotic) dynamics and their properties correspond to that of a homogeneous fully connected network for any $γ$-value. Apart for the peculiar exception of sparse networks, which remain intrinsically inhomogeneous at any system size.

cond-mat.dis-nn↗

arXiv2011

Extensive and Sub-Extensive Chaos in Globally-Coupled Dynamical Systems

Using a combination of analytical and numerical techniques, we show that chaos in globally-coupled identical dynamical systems, be they dissipative or Hamiltonian, is both extensive and sub-extensive: their spectrum of Lyapunov exponents is asymptotically flat (thus extensive) at the value $λ_0$ given by a single unit forced by the mean-field, but sandwiched between sub-extensive bands containing typically $\mathcal{O}(\log N)$ exponents whose values vary as $λ\simeq λ_\infty + c/\log N$ with $λ_\infty \neq λ_0$.

nlin.CD↗

arXiv2010

Collective chaos in pulse-coupled neural networks

We study the dynamics of two symmetrically coupled populations of identical leaky integrate-and-fire neurons characterized by an excitatory coupling. Upon varying the coupling strength, we find symmetry-breaking transitions that lead to the onset of various chimera states as well as to a new regime, where the two populations are characterized by a different degree of synchronization. Symmetric collective states of increasing dynamical complexity are also observed. The computation of the the finite-amplitude Lyapunov exponent allows us to establish the chaoticity of the (collective) dynamics in a finite region of the phase plane. The further numerical study of the standard Lyapunov spectrum reveals the presence of several positive exponents, indicating that the microscopic dynamics is high-dimensional.

cond-mat.dis-nn↗

arXiv2010

Collective oscillations in disordered neural networks

We investigate the onset of collective oscillations in a network of pulse-coupled leaky-integrate-and-fire neurons in the presence of quenched and annealed disorder. We find that the disorder induces a weak form of chaos that is analogous to that arising in the Kuramoto model for a finite number N of oscillators [O.V. Popovych at al., Phys. Rev. E 71} 065201(R) (2005)]. In fact, the maximum Lyapunov exponent turns out to scale to zero for N going to infinite, with an exponent that is different for the two types of disorder. In the thermodynamic limit, the random-network dynamics reduces to that of a fully homogenous system with a suitably scaled coupling strength. Moreover, we show that the Lyapunov spectrum of the periodically collective state scales to zero as 1/N^2, analogously to the scaling found for the `splay state'.

cond-mat.dis-nn↗

arXiv2009

Unfolding times for proteins in a force clamp

The escape process from the native valley for proteins subjected to a constant stretching force is examined using a model for a Beta-barrel. For a wide range of forces, the unfolding dynamics can be treated as one-dimensional diffusion, parametrized in terms of the end-to-end distance. In particular, the escape times can be evaluated as first passage times for a Brownian particle moving on the protein free-energy landscape, using the Smoluchowski equation. At strong forces, the unfolding process can be viewed as a diffusive drift away from the native state, while at weak forces thermal activation is the relevant mechanism. An escape-time analysis within this approach reveals a crossover from an exponential to an inverse Gaussian escape-time distribution upon passing from weak to strong forces. Moreover, a single expression valid at weak and strong forces can be devised both for the average unfolding time as well as for the corresponding variance. The analysis offers a possible explanation of recent experimental findings for ddFLN4 and ubiquitin.

cond-mat.stat-mech↗

arXiv2009

Stability of splay states in globally coupled rotators

The stability of dynamical states characterized by a uniform firing rate ({\it splay states}) is analyzed in a network of $N$ globally pulse-coupled rotators (neurons) subject to a generic velocity field. In particular, we analyse short-wavelength modes that were known to be marginally stable in the infinite $N$ limit and show that the corresponding Floquet exponent scale as $1/N^2$. Moreover, we find that the sign, and thereby the stability, of this spectral component is determined by the sign of the average derivative of the velocity field. For leaky-integrate-and-fire neurons, an analytic expression for the whole spectrum is obtained. In the intermediate case of continuous velocity fields, the Floquet exponents scale faster than $1/N^2$ (namely, as $1/N^4$) and we even find strictly neutral directions in a wider class than the sinusoidal velocity fields considered by Watanabe and Strogatz in {\it Physica D 74 (1994) 197-253}.

cond-mat.dis-nn↗

arXiv2009

Stable chaos

Stable chaos is a generalization of the chaotic behaviour exhibited by cellular automata to continuous-variable systems and it owes its name to an underlying irregular and yet linearly stable dynamics. In this review we discuss analogies and differences with the usual deterministic chaos and introduce several tools for its characterization. Some examples of transitions from ordered behavior to stable chaos are also analyzed to further clarify the underlying dynamical properties. Finally, two models are specifically discussed: the diatomic hard-point gas chain and a network of globally coupled neurons.

nlin.CD↗

arXiv2008

Changing the mechanical unfolding pathway of FnIII10 by tuning the pulling strength

We investigate the mechanical unfolding of the tenth type III domain from fibronectin, FnIII10, both at constant force and at constant pulling velocity, by all-atom Monte Carlo simulations. We observe both apparent two-state unfolding and several unfolding pathways involving one of three major, mutually exclusive intermediate states. All the three major intermediates lack two of seven native beta-strands, and share a quite similar extension. The unfolding behavior is found to depend strongly on the pulling conditions. In particular, we observe large variations in the relative frequencies of occurrence for the intermediates. At low constant force or low constant velocity, all the three major intermediates occur with a significant frequency. At high constant force or high constant velocity, one of them, with the N- and C-terminal beta-strands detached, dominates over the other two. Using the extended Jarzynski equality, we also estimate the equilibrium free-energy landscape, calculated as a function of chain extension. The application of a constant pulling force leads to a free-energy profile with three major local minima. Two of these correspond to the native and fully unfolded states, respectively, whereas the third one can be associated with the major unfolding intermediates.

q-bio.BM↗

arXiv2008

Free energy landscape of mechanically unfolded model proteins: extended Jarzinsky versus inherent structure reconstruction

The equilibrium free energy landscape of off-lattice model heteropolymers as a function of an internal coordinate, namely the end-to-end distance, is reconstructed from out-of-equilibrium steered molecular dynamics data. This task is accomplished via two independent methods: by employing an extended version of the Jarzynski equality (EJE) and the inherent structure (IS) formalism. A comparison of the free energies estimated with these two schemes with equilibrium results obtained via the umbrella sampling technique reveals a good quantitative agreement among all the approaches in a range of temperatures around the ``folding transition'' for the two examined sequences. In particular, for the sequence with good foldability properties, the mechanically induced structural transitions can be related to thermodynamical aspects of folding. Moreover, for the same sequence the knowledge of the landscape profile allows for a good estimation of the life times of the native configuration for temperatures ranging from the folding to the collapse temperature. For the random sequence, mechanical and thermal unfolding appear to follow different paths along the landscape.

cond-mat.stat-mech↗

arXiv2007

Reconstructing the free energy landscape of a mechanically unfolded model protein

The equilibrium free energy landscape of an off-lattice model protein as a function of an internal (reaction) coordinate is reconstructed from out-of-equilibrium mechanical unfolding manipulations. This task is accomplished via two independent methods: by employing an extended version of the Jarzynski equality (EJE) and the protein inherent structures (ISs). In a range of temperatures around the ``folding transition'' we find a good quantitative agreement between the free energies obtained via EJE and IS approaches. This indicates that the two methodologies are consistent and able to reproduce equilibrium properties of the examined system. Moreover, for the studied model the structural transitions induced by pulling can be related to thermodynamical aspects of folding.

cond-mat.stat-mech↗