Search

In recent years, new and important perspectives were introduced in the field of neuroimaging with the emergence of the connectionist approach. In this new context, it is important to know not only which brain areas are activated by a particular stimulus but, mainly, how these areas are structurally and functionally connected, distributed, and organized in relation to other areas. Additionally, the arrangement of the network elements, i.e., its topology, and the dynamics they give rise to are also important. This new approach is called connectomics. It brings together a series of techniques and methodologies capable of systematizing, from the different types of signals and images of the nervous system, how neuronal units to brain areas are connected. Through this approach, the different patterns of connectivity can be graphically and mathematically represented by the so-called connectomes. The connectome uses quantitative metrics to evaluate structural and functional information from images of neural tracts and pathways or signals from the metabolic and/or electrophysiologic activity of cell populations or brain areas. Besides, with adequate treatment of this information, it is also possible to infer causal relationships. In this way, structural and functional evaluations are complementary descriptions which, together, represent the anatomic and physiologic neural properties, establishing a new paradigm for understanding how the brain functions by looking at brain connections. Here, we highlight five critical elements of a network that allows an integrative analysis, focusing mainly on a functional description. These elements include; (i) the properties of its nodes; (ii) the metrics for connectivity and coupling between nodes; (iii) the network topologies; (iv) the network dynamics and (v) the interconnections between different domains and scales of network representations., Comment: 39 pages, 14 figures and 4 tables

We continue the work of a series of previous studies of a mathematical model that describes the mean-field limit behavior of a homogeneous network of excitatory point spiking neurons. Contrary to other models, here noise is intrinsic to the neurons through a membrane-potential dependent spiking rate probability, that we assume to be given by a power law. This allows one to collapse several sources of neural noise into a single function, which aids for a more treatable mathematical and comptuational analysis. In particular, we give pseudo-analytical expressions for the invariant distributions of membrane potentials across the population and study their stability computationally. The neurons are assumed to be connected both by chemical and possibly electrical (gap junction) synapses and can also undergo a leakage of ions with the extracellular medium. The distributions are of compact support whenever leakage or gap junction rates are non-zero and an infinite discontinuity appears at the maximum potential in the population. This happens invariably for the leakage (with no gap junctions) and gap junction (without leakage) cases. However, these discontinuous distributions might only be stable for linear spiking rate functions. It was recently shown how the network can present highly synchronous states of global oscillations in its activity when leakage is not present and gap junctions are strong enough. Here we confirm how oscillations persist also when weak leakage is considered. Thus, these dendritic (rather than axonal) gap junctions could play a role in the high levels of neural synchrony necessary for the development of neural systems at young ages. The model, thus, presents a rich phenomenology and capability to reproduce several biological features of neural networks despite of its mathematical simplicity, hence presenting a powerful tool for high performance computing., Comment: 18 pages, 4 figures

We propose a new model based on the Ising model with the aim to study synaptic plasticity phenomena in neural networks. It is today well established in biology that the synapses or connections between certain types of neurons are strengthened when the neurons are co-active, a form of the so called synaptic plasticity. Such mechanism is believed to mediate the formation and maintenance of memories. The proposed model describes some features from that phenomenon. Together with the spin-flip dynamics, in our model the coupling constants are also subject to stochastic dynamics, so that they interact with each other. The evolution of the system is described by a continuous-time Markov jump process. Keyword Markov chain, Stochastic Ising model, synaptic plasticity, neural networks, transience

We show that the inductive coupling between the quantum mechanical motion of a superconducting microcantilever and a flux-dependent microwave quantum circuit can attain the strong single-photon nanomechanical coupling regime with feasible experimental parameters. We propose to use a superconducting strip, which is in the Meissner state, at the tip of a cantilever. A pick-up coil collects the flux generated by the sheet currents induced by an external quadrupole magnetic field centered at the strip location. The position-dependent magnetic response of the superconducting strip, enhanced by both diamagnetism and demagnetizing effects, leads to a strong magnetomechanical coupling to quantum circuits., Comment: Published Version. 8 pages (including supplementary material), 3 figures