Spike timing dependent plasticity (STDP) is believed to play an important role in shaping the structure of neural circuits. Here we show that STDP generates effective interactions between synapses of different neurons, which were neglected in previous theoretical treatments, and can be described as a sum over contributions from structural motifs. These interactions can have a pivotal influence on the connectivity patterns that emerge under the influence of STDP. In particular, we consider two highly ordered forms of structure: wide synfire chains, in which groups of neurons project to each other sequentially, and self connected assemblies. We show that high order synaptic interactions can enable the formation of both structures, depending on the form of the STDP function and the time course of synaptic currents. Furthermore, within a certain regime of biophysical parameters, emergence of the ordered connectivity occurs robustly and autonomously in a stochastic network of spiking neurons, without a need to expose the neural network to structured inputs during learning.

We expand the theory of Hawkes processes to the nonstationary case, in which the mutually exciting point processes receive time-dependent inputs. We derive an analytical expression for the time-dependent correlations, which can be applied to networks with arbitrary connectivity, and inputs with arbitrary statistics. The expression shows how the network correlations are determined by the interplay between the network topology, the transfer functions relating units within the network, and the pattern and statistics of the external inputs. We illustrate the correlation structure using several examples in which neural network dynamics are modeled as a Hawkes process. In particular, we focus on the interplay between internally and externally generated oscillations and their signatures in the spike and rate correlation functions.

Intensive care medicine is complex and resource-demanding. A critical and common challenge lies in inferring the underlying physiological state of a patient from partially observed data. Specifically for the cardiovascular system, clinicians use observables such as heart rate, arterial and venous blood pressures, as well as findings from the physical examination and ancillary tests to formulate a mental model and estimate hidden variables such as cardiac output, vascular resistance, filling pressures and volumes, and autonomic tone. Then, they use this mental model to derive the causes for instability and choose appropriate interventions. Not only this is a very hard problem due to the nature of the signals, but it also requires expertise and a clinician’s ongoing presence at the bedside. Clinical decision support tools based on mechanistic dynamical models offer an appealing solution due to their inherent explainability, corollaries to the clinical mental process, and predictive power. With a translational motivation in mind, we developed iCVS: a simple, with high explanatory power, dynamical mechanistic model to infer hidden cardiovascular states. Full model estimation requires no prior assumptions on physiological parameters except age and weight, and the only inputs are arterial and venous pressure waveforms. iCVS also considers autonomic and non-autonomic modulations. To gain more information without increasing model complexity, both slow and fast timescales of the blood pressure traces are exploited, while the main inference and dynamic evolution are at the longer, clinically relevant, timescale of minutes. iCVS is designed to allow bedside deployment at pediatric and adult intensive care units and for retrospective investigation of cardiovascular mechanisms underlying instability. In this paper, we describe iCVS and inference system in detail, and using a dataset of critically-ill children, we demonstrate its use and power to identify bleeding, distributive states, and cardiac dysfunction, in isolation and in combination.Author summaryA common challenge clinicians face across different disciplines is estimating the hidden physiological state of a patient based on partially observed data. Here we describe iCVS (inferring Cardio-Vascular States): a dynamical mechanistic model of the cardiovascular system. We developed iCVS with a translational goal in mind, showing high explanatory power, its inference relies only on routinely available signals, and enables the identification of various clinically important shock states. We demonstrate the use of the model on a dataset that was collected in a pediatric intensive care unit.