Joaquín J Torres

• Doctor
• Professor (Associate) at University of Granada

Triadic interactions in the brain are general mechanisms by which a node, e.g. a neuron or a glia cell such as the astrocyte, can regulate directly the link, e.g. synapse between other two nodes. The regulation takes place in a familiar way by either depressing or facilitating synaptic transmission. Such interactions are ubiquitous in neural system...

Triadic interactions are general mechanisms by which a node or neuron can regulate directly the link or synapse between other two neurons. The regulation takes place in a familiar way by either depressing or facilitating synaptic transmission. Such interactions are ubiquitous in neural systems, accounting for axo-axonic synapses and tripartite syna...

Triadic interactions are higher-order interactions which occur when a set of nodes affects the interaction between two other nodes. Examples of triadic interactions are present in the brain when glia modulate the synaptic signals among neuron pairs or when interneuron axo-axonic synapses enable presynaptic inhibition and facilitation, and in ecosys...

Balanced neural networks, in which excitatory and inhibitory inputs compensate each other on average, give rise to a dynamical phase dominated by fluctuations called an asynchronous state, crucial for brain functioning. However, structural disorder, which is inherent to random networks, can hinder such an excitation-inhibition balance. Indeed, stru...

A continuously growing body of evidence indicates that astrocytes, which is the most abundant sub-type of glial cells in the nervous system, not only provide structural and metabolic support to neurons, but also they are essential sentinels and dynamic modulators of neuronal and synaptic functions. However, the potential constructive role of astroc...

Topological signals defined on nodes, links and higher dimensional simplices define the dynamical state of a network or of a simplicial complex. As such, topological signals are attracting increasing attention in network theory, dynamical systems, signal processing and machine learning. Topological signals defined on the nodes are typically studied...

The last decade has witnessed a remarkable progress in our understanding of the brain. This has mainly been based on the scrutiny and modeling of the transmission of activity among neurons across lively synapses. A main conclusion, thus far, is that essential features of the mind rely on collective phenomena that emerge from a willful interaction o...

Simplicial synchronization reveals the role that topology and geometry have in determining the dynamical properties of simplicial complexes. Simplicial network geometry and topology are naturally encoded in the spectral properties of the graph Laplacian and of the higher-order Laplacians of simplicial complexes. Here we show how the geometry of sim...

The interplay between structure and function affects the emerging properties of many natural systems. Here we use an adaptive neural network model that couples activity and topological dynamics and reproduces the experimental temporal profiles of synaptic density observed in the brain. We prove that the existence of a transient period of relatively...

We here study a network of synaptic relations mingling excitatory and inhibitory neuron nodes that displays oscillations quite similar to electroencephalogram (EEG) brain waves, and identify abrupt variations brought about by swift synaptic mediations. We thus conclude that corresponding changes in EEG series surely come from the slowdown of the ac...

Topological signals defined on nodes, links and higher dimensional simplices define the dynamical state of a network or of a simplicial complex. As such, topological signals are attracting increasing attention in network theory, dynamical systems, signal processing and machine learning. Topological signals defined on the nodes are typically studied...

Simplicial complexes capture the underlying network topology and geometry of complex systems ranging from the brain to social networks. Here we show that algebraic topology is a fundamental tool to capture the higher-order dynamics of simplicial complexes. In particular we consider topological signals, i.e., dynamical signals defined on simplices o...

Simplicial synchronization reveals the role that topology and geometry have in determining the dynamical properties of simplicial complexes. Simplicial network geometry and topology are naturally encoded in the spectral properties of the graph Laplacian and of the higher-order Laplacians of simplicial complexes. Here we show how the geometry of sim...

Phase Transitions in Grey Matter: Brain Architecture and Mind Dynamics relates the complex systems that we know as ‘mind’ and ‘brain’ to simple concepts in physics such as ‘phase transition’ and ‘criticality’ and establishes a close mathematical link between them. A serious review of live issues in science – from interaction and correlation to emer...

DESCRIPTION The cooperation between networked neurons fostered by, say, synaptic mechanisms has been revealed as essential in determining mind dynamics. Following this track, it has been laid out in previous chapters how the concept of phase transitions may be relevant for improving our understanding of the brain phenomena we are interested in. The...

DESCRIPTION The evolution of physics and related fields over the last little more than a century, leading to the formidable technological development of which we are witnesses, has confirmed that accurate and verifiable observation is the unsurpassed method for optimizing the generation of knowledge and progress. An objective of this essay is to sh...

DESCRIPTION Scientists continue to delve on sure grounds into the secrets of the mind and, finishing this essay, we return to consider a few significant novel observations. These advances steered us to assemble and refine the image we have been sketching, then confirmed how the result is a perfectly consistent and useful theoretical framework, from...

DESCRIPTION There are concepts, ideas, perspectives, and nuances in physics that, after appearing or becoming widely celebrated, have then affected, to a greater or lesser extent, the development of other fields of science. This extrapolation process is not without its difficulties. Imagine Galileo Galilei trying to convince theologians that the pl...

Phase Transitions in Grey Matter: Brain Architecture and Mind Dynamics relates the complex systems that we know as ‘mind’ and ‘brain’ to simple concepts in physics such as ‘phase transition’ and ‘criticality’ and establishes a close mathematical link between them. A serious review of live issues in science – from interaction and correlation to emer...

DESCRIPTION The neuron is a cell, the smallest significant component of the nervous system, that has aroused considerable interest by itself and even more so in conjunction with its surrounding components. Santiago Ramón y Cajal revealed its existence more than a century ago, and it soon attracted so much the curiosity of researchers that this cell...

DESCRIPTION Phase Transitions in Grey Matter: Brain Architecture and Mind Dynamics relates the complex systems that we know as ‘mind’ and ‘brain’ to simple concepts in physics such as ‘phase transition’ and ‘criticality’ and establishes a close mathematical link between them. A serious review of live issues in science – from interaction and correla...

DESCRIPTION The Byzantine Empire—center through a millennium for commerce, culture, and data in the world—was a fertile setup in which bestiaries spread [Kalof and Resl, A Cultural History of Animals in the Medieval Age (1000–1400) (Berg Publishers, Oxford, 2007 Kalof, L., and Resl, B., A Cultural History of Animals in the Medieval Age (Berg Publis...

Simplicial complexes capture the underlying network topology and geometry of complex systems ranging from the brain to social networks. Representing complex systems as simplicial complexes opens the possibility to use the powerful tools of algebraic topology to characterize their structure. Here we show that algebraic topology can also be a fundame...

The interaction between synaptic and intrinsic dynamics can efficiently shape neuronal input-output relationships in response to temporally structured spike trains. We use a neuron model with subthreshold oscillations receiving inputs through a synapse with short-term depression and facilitation to show that the combination of intrinsic subthreshol...

Simplicial complexes constitute the underlying topology of interacting complex systems including among the others brain and social interaction networks. They are generalized network structures that allow to go beyond the framework of pairwise interactions and to capture the many-body interactions between two or more nodes strongly affecting dynamic...

The higher-order interactions of complex systems, such as the brain, are captured by their simplicial complex structure and have a significant effect on dynamics. However, the existing dynamical models defined on simplicial complexes make the strong assumption that the dynamics resides exclusively on the nodes. Here we formulate the higher-order Ku...

Here we study the emergence of chimera states, a recently reported phenomenon referring to the coexistence of synchronized and unsynchronized dynamical units, in a population of Morris-Lecar neurons which are coupled by both electrical and chemical synapses, constituting a hybrid synaptic architecture, as in actual brain connectivity. This scheme c...

Here we study the emergence of chimera states, a recently reported phenomenon referring to the coexistence of synchronized and unsynchronized dynamical units, in a population of Morris-Lecar neurons which are coupled by both electrical and chemical synapses, constituting a hybrid synaptic architecture, as in actual brain connectivity. This scheme c...

Simplicial complexes constitute the underlying topology of interacting complex systems including among the others brain and social interaction networks. They are generalized network structures that allow to go beyond the framework of pairwise interactions and to capture the many-body interactions between two or more nodes strongly affecting dynamic...

The higher-order interactions of complex systems, such as the brain, are captured by their simplicial complex structure and have a significant effect on dynamics. However the existing dynamical models defined on simplicial complexes make the strong assumption that the dynamics resides exclusively on the nodes. Here we formulate the higher-order Kur...

Electroencephalography (EEG) monitors —by either intrusive or noninvasive electrodes— time and frequency variations and spectral content of voltage fluctuations or waves, known as brain rhythms, which in some way uncover activity during both rest periods and specific events in which the subject is under stimulus. This is a useful tool to explore br...

The interaction between synaptic and intrinsic dynamics can efficiently shape neuronal input-output relationships in response to temporally structured spike trains. We use a neuron model with subthreshold oscillations receiving inputs through a synapse with short-term depression and facilitation to show that the combination of intrinsic subthreshol...

The inverse stochastic resonance (ISR) phenomenon consists of an unexpected depression in the response of a system under external noise, e.g., as observed in the mean firing rate in some pacemaker neurons subject to moderate values of noise. A possible cause for such unexpected reaction is the occurrence of a bistable regime controlling these neuro...

Nature exhibits countless examples of adaptive networks, whose topology evolves constantly coupled with the activity due to its function. The brain is an illustrative example of a system in which a dynamic complex network develops by the generation and pruning of synaptic contacts between neurons while memories are acquired and consolidated. Here,...

Electroencephalography (EEG) monitors ---by either intrusive or noninvasive electrodes--- time and frequency variations and spectral content of voltage fluctuations or waves, known as brain rhythms, which in some way uncover activity during both rest periods and specific events in which the subject is under stimulus. This is a useful tool to explor...

Recently there is a surge of interest in network geometry and topology. Here we show that the spectral dimension plays a fundamental role in establishing a clear relation between the topological and geometrical properties of a network and its dynamics. Specifically we explore the role of the spectral dimension in determining the synchronization pro...

Recently there is a surge of interest in network geometry and topology. Here we show that the spectral dimension plays a fundamental role in establishing a clear relation between the topological and geometrical properties of a network and its dynamics. Specifically we explore the role of the spectral dimension in determining the synchronization pro...

We observe and study a self-organized phenomenon whereby the activity in a network of spiking neurons spontaneously terminates. We consider different types of populations, consisting of bistable model neurons connected electrically by gap junctions, or by either excitatory or inhibitory synapses, in a scale-free connection topology. We find that st...

The inverse stochastic resonance (ISR) phenomenon consists in an unexpected depression in the response of a system under external noise, e.g., as observed in the behavior of the mean-firing rate in some pacemaker neurons in the presence of moderate values of noise. A possible requirement for such behavior is the existence of a bistable regime in th...

The dynamics of networks of neuronal cultures has been recently shown to be strongly dependent on the network geometry and in particular on their dimensionality. However, this phenomenon has been so far mostly unexplored from the theoretical point of view. Here we reveal the rich interplay between network geometry and synchronization of coupled osc...

We observe and study a self-organized phenomenon whereby the activity in a network of spiking neurons spontaneously terminates. We consider different types of populations, consisting of bistable model neurons connected electrically by gap junctions, or by either excitatory or inhibitory synapses, in a scale-free connection topology. We find that st...

A fundamental question in neuroscience is how structure and function of neural systems are related. We study this interplay by combining a familiar auto-associative neural network with an evolving mechanism for the birth and death of synapses. A feedback loop then arises leading to two qualitatively different behaviours. In one, the network structu...

The interplay between structure and function is critical in determining the behavior of several systems. Here we propose an adaptive network model inspired in synaptic pruning that couples activity and topological dynamics. The coupling creates a discontinuous phase transition between an ordered memory phase and a disordered one as a function of th...

The dynamics of networks of neuronal cultures has been recently shown to be strongly dependent on the network geometry and in particular on their dimensionality. However, this phenomenon has been so far mostly unexplored from the theoretical point of view. Here we reveal the rich interplay between network geometry and synchronization of coupled osc...

Inverse Stochastic Resonance (ISR) is a phenomenon in which the average spiking rate of a neuron exhibits a minimum with respect to noise. ISR has been studied in individual neurons, but here, we investigate ISR in scale-free networks, where the average spiking rate is calculated over the neuronal population. We use Hodgkin-Huxley model neurons wit...

A fundamental question in neuroscience is how structure and function of neural systems are related. We study this interplay by combining a familiar auto-associative neural network with an evolving mechanism for the birth and death of synapses. A feedback loop then arises leading to two qualitatively different types of behaviour. In one, the network...

We investigate the behavior of a model neuron that receives a biophysically-realistic noisy post-synaptic current based on uncorrelated spiking activity from a large number of afferents. We show that, with static synapses, such noise can give rise to inverse stochastic resonance (ISR) as a function of the presynaptic firing rate. We compare this to...

We investigate the behavior of a model neuron that receives a biophysically-realistic noisy post-synaptic current based on uncorrelated spiking activity from a large number of afferents. We show that, with static synapses, such noise can give rise to inverse stochastic resonance (ISR) as a function of the presynaptic firing rate. We compare this to...

We study emerging phenomena in binary neural networks where, with a probability c synaptic intensities are chosen according with a Hebbian prescription, and with probability (1-c) there is an extra random contribution to synaptic weights. This new term, randomly taken from a Gaussian bimodal distribution, balances the synaptic population in the net...

We study emerging phenomena in binary neural networks where, with a probability c synaptic intensities are chosen according with a Hebbian prescription, and with probability (1-c) there is an extra random contribution to synaptic weights. This new term, randomly taken from a Gaussian bimodal distribution, balances the synaptic population in the net...

Presentation on "25th Annual Computational Neuroscience Meeting: CNS-2016 " BMC Neuroscience 17, 112-113 (2016).

In the last years, network scientists have directed their interest to the multi-layer character of real-world systems, and explicitly considered the structural and dynamical organization of graphs made of diverse layers between its constituents. Most complex systems include multiple subsystems and layers of connectivity and, in many cases, the inte...

In this paper we analyze the interplay between the subthreshold oscillations of a single neuron conductance-based model and the short-term plasticity of a dynamic synapse with a depressing mechanism. In previous research, the computational properties of subthreshold oscillations and dynamic synapses have been studied separately. Our results show th...

Time series corresponding to the power spectra shown in Fig 12 in the main text (color code is the same in both figures). Panel A: The incoming stimulus consists of 8-spike bursts with a spiking frequency equal to 25Hz received through a dynamic synapse where gd = 0.5mS and U=0.15. Each time series correspond to a different depression level: τrec =...

The interaction between intrinsic oscillations and synaptically modulated input can lead to complex preferred input/output relations. The figure shows the different response of a neuron to the same input delivered through a dynamic synapse with gd = 0.5mS and U=0.15 as a function of the depression level as given by τrec. The incoming stimulus consi...

Signal-to-noise ratio (SNR) at 18Hz when the neuron receives a tonic input at this frequency through a weak static synapse under the modulatory effect of different depressing inputs. The SNR is estimated as the ratio of input signal power (in this case 18Hz) to the mean spectral density power around the input frequency (18 ± 1.5Hz). Left panel: The...

Time series corresponding to the power spectra shown in Fig 11 in the main text (color code is the same in both figures). Panel A: Only the dynamic channel is active with gd = 0.5mS and U=0.35. The incoming stimulus consists of bursts with 8 spikes with a spiking frequency equal to 30Hz. Each time series correspond to a different depression level:...

Short-term synaptic plasticity mechanisms in the proposed synaptic model. The figure shows the evolving dynamics of the fraction of bound receptors in the synaptic cleft, r(t), when two tonic spiking stimuli at different frequencies (20Hz and 35Hz in panels A and B, respectively) are transmitted through a static—i.e., a synapse with no dynamical sy...

ICGenealogy: towards a common topology of neuronal ion channel function and genealogy in model and experiment Ion channels are fundamental constituents determining the function of single neurons and neuronal circuits. To understand their complex interactions, the field of computational modeling has proven essential: since its emergence, thousands...

Noise-delayed decay (NDD) phenomenon emerges when the first-spike latency of a periodically forced stochastic neuron exhibits a maximum for a particular range of noise intensity. Here, we investigate the latency response dynamics of a single Hodgkin-Huxley neuron that is subject to both a suprathreshold periodic stimulus and a background activity a...

We here illustrate how a well-founded study of the brain may originate in assuming analogies with phase-transition phenomena. Analyzing to what extent a weak signal endures in noisy environments, we identify the underlying mechanisms, and it results a description of how the excitability associated to (non-equilibrium) phase changes and criticality...

We investigate the efficient transmission and processing of weak signals (subthreshold) in a realistic neural medium in the presence of different levels of the underlying noise. Assuming Hebbian weights for maximal synaptic conductances - that naturally balances the network with excitatory and inhibitory synapses - and considering short-term synapt...

SynonymsAttractor neural network; Binary neural network; Equilibrium neural network; Recurrent neural networkDefinitionHopfield model was originally introduced as the representation of a physical system, whose state in a given time is defined by a vector X(t) = {X1(t), … , XN (t)}, with a large number of locally stable states in its phase space, na...

SynonymsLearning in feed-forward neural networksDefinitionThe perceptron is a neural network based in the nonlinear McCulloch-Pitts neuron model. It is composed of a single layer of N neurons (presynaptic) that are connected by means of unidirectional or feed-forward connections, or synapses, to a unique (postsynaptic) neuron (see Fig. 1). This “si...

In this paper we review our research on the effect and computational role of dynamical synapses on feed-forward and recurrent neural networks. Among others, we report on the appearance of a new class of dynamical memories which result from the destabilization of learned memory attractors. This has important consequences for dynamic information proc...

Short-term memory in the brain cannot in general be explained the way long-term memory can - as a gradual modification of synaptic weights - since it takes place too quickly. Theories based on some form of cellular bistability, however, do not seem able to account for the fact that noisy neurons can collectively store information in a robust manner...

This is a short review of recent studies in our group on how weak signals may ef¿ciently propagate in a system with noise-induced excitation-inhibition competition which adapts to the activity at short-time scales and thus induces excitable conditions. Our numerical results on simple mathematical models should hold for many complex networks in natu...

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We review some recent results on neural dynamics and information processing which arise when considering several biophysical factors of interest, in particular, short-term synaptic plasticity and neural heterogeneity. The inclusion of short-term synaptic plasticity leads to enhanced long-term memory capacities, a higher robustness of memory to nois...

Here we numerically study the emergence of stochastic resonance as a mild phenomenon and how this transforms into an amazing enhancement of the signal-to-noise ratio at several levels of a disturbing ambient noise. The setting is a cooperative, interacting complex system modelled as an Ising-Hopfield network in which the intensity of mutual interac...

We studied, both analytically and numerically, complex excitable networks, in which connections are time dependent and some of the nodes remain silent at each time step. More specifically, (a) there is a heterogenous distribution of connection weights and, depending on the current degree of order, some connections are reinforced/weakened with stren...

We study the signatures of phase transitions in the time evolution of wave-packets by analyzing two simple model systems: a graphene quantum dot model in a magnetic field and a Dirac oscillator in a magnetic field. We have characterized the phase transitions using the autocorrelation function. Our work also reveals that the description in terms of...

Short-term synaptic depression and facilitation have been found to greatly influence the performance of autoassociative neural networks. However, only partial results, focused for instance on the computation of the maximum storage capacity at zero temperature, have been obtained to date. In this work, we extended the study of the effect of these sy...

In recent years, many new experimental studies on emerging phenomena in neural systems have been reported. The high efficiency of living neural systems to encode, process, and learn information has stimulated an increased interest among theoreticians in developing mathematical approaches and tools to model biological neural networks. In this chapte...

We present a general theory which allows one to study the effects on emergent, cooperative behavior of a complex interplay between different dynamic processes that occur in actual systems at the neuron, synapse and network levels. We consider synaptic changes at different time scales from less than the millisecond to the scale of learning, and the...

This thesis is a compendium of research which brings together ideas from the fields of Complex Networks and Computational Neuroscience to address two questions regarding neural systems: 1) How the activity of neurons, via synaptic changes, can shape the topology of the network they form part of, and 2) How the resulting network structure, in its tu...

We theoretically describe how weak signals may be efficiently transmitted throughout more than one frequency range in noisy excitable media by kind of stochastic multiresonance. This serves us here to reinterpret recent experiments in neuroscience, and to suggest that many other systems in nature might be able to exhibit several resonances. In fact...

In this work we study the detection of weak stimuli by spiking (integrate-and-fire) neurons in the presence of certain level of noisy background neural activity. Our study has focused in the realistic assumption that the synapses in the network present activity-dependent processes, such as short-term synaptic depression and facilitation. Employing...

Theoretical derivations. In this supplementary text we derive an analytical approximation of the input-ouput correlation function defined in the main text, which is used together with numerical simulations to show the behavior of the system under study. (PDF)

The behaviour of many complex dynamical systems has been found to depend crucially on the structure of the underlying networks of interactions. An intriguing feature of empirical networks is their assortativity—i.e., the extent to which the degrees of neighbouring nodes are correlated. However, until very recently it was difficult to take this prop...

A wide range of empirical networks whether biological, technological, information-related or linguistic generically exhibit important degree-degree anticorrelations (i.e., they are disassortative), the only exceptions being social ones, which tend to be positively correlated (assortative). Using an information-theory approach, we show that the equi...

The performance of attractor neural networks has been shown to depend crucially on the heterogeneity of the underlying topology. We take this analysis a step further by examining the effect of degree-degree correlations -- or assortativity -- on neural-network behavior. We make use of a method recently put forward for studying correlated networks a...