The distribution of time intervals between successive spikes generated by a neuronal cell --the interspike intervals (ISI)-- may reveal interesting features of the underlying dynamics. In this study we analyze the ISI sequence --the spike train-- generated by a simple network of neurons whose output activity is modeled by a jump-diffusion process. We prove that, when specific ranges of the involved parameters are chosen, it is possible to observe multimodal ISI distributions which reveal that the modeled network fires with more than one single preferred time interval. Furthermore, the system exhibits resonance behavior, with modulation of the spike timings by the noise intensity. We also show that inhibition helps the signal transmission between the units of the simple network.

A new, non–parametric and binless estimator for the mutual information of a d–dimensional random vector is proposed. First of all, an equation that links the mutual information to the entropy of a suitable random vector with uniformly distributed components is deduced. When d = 2 this equation reduces to the well known connection between mutual information and entropy of the copula function associated to the original random variables. Hence, the problem of estimating the mutual information of the original random vector is reduced to the estimation of the entropy of a random vector obtained through a multidimensional transformation. The estimator we propose is a two–step method: first estimate the transformation and obtain the transformed sample, then estimate its entropy. The properties of the new estimator are discussed through simulation examples and its performances are compared to those of the best estimators in the literature. The precision of the estimator converges to values of the same order of magnitude of the best estimator tested. However, the new estimator is unbiased even for larger dimensions and smaller sample sizes, while the other tested estimators show a bias in these cases.

We study the estimation of the input parameters in a Feller neuronal model from a trajectory of the membrane potential sampled at discrete times. These input parameters are identified with the drift and the infinitesimal variance of the underlying stochastic diffusion process with multiplicative noise. The state space of the process is restricted from below by an inaccessible boundary. Further, the model is characterized by the presence of an absorbing threshold, the first hitting of which determines the length of each trajectory and which constrains the state space from above. We compare, both in the presence and in the absence of the absorbing threshold, the efficiency of different known estimators. In addition, we propose an estimator for the drift term, which is proved to be more efficient than the others, at least in the explored range of the parameters. The presence of the threshold makes the estimates of the drift term biased, and two methods to correct it are proposed.

Estimation of the input parameters of stochastic (leaky) integrate-and-fire neuronal models is studied. It is shown that the presence of a firing threshold brings a systematic error to the estimation procedure. Analytical formulas for the bias are given for two models, the randomized random walk and the perfect integrator. For the third model considered, the leaky integrate-and-fire model, the study is performed by using Monte Carlo simulated trajectories. The bias is compared with other errors appearing during the estimation, and it is documented that the effect of the bias has to be taken into account in experimental studies.

Computational models are at the forefront of the pursuit of personalized medicine thanks to their descriptive and predictive abilities. In the presence of complex and heterogeneous data, patient stratification is a prerequisite for effective precision medicine, since disease development is often driven by individual variability and unpredictable environmental events. Herein, we present GreatNectorworkflow as a valuable tool for (i) the analysis and clustering of patient-derived longitudinal data, and (ii) the simulation of the resulting model of patient-specific disease dynamics. GreatNectoris designed by combining an analytic strategy composed of CONNECTOR, a data-driven framework for the inspection of longitudinal data, and an unsupervised methodology to stratify the subjects with GreatMod, a quantitative modeling framework based on the Petri Net formalism and its generalizations. To illustrate GreatNectorcapabilities, we exploited longitudinal data of four immune cell populations collected from Multiple Sclerosis patients. Our main results report that the T-cell dynamics after alemtuzumab treatment separate non-responders versus responders patients, and the patients in the non-responders group are characterized by an increase of the Th17 concentration around 36 months. GreatNectoranalysis was able to stratify individual patients into three model meta-patients whose dynamics suggested insight into patient-tailored interventions.