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We consider the problem of approximating flow functions of continuous-time dynamical systems with inputs. It is well-known that continuous-time recurrent neural networks are universal approximators of this type of system. In this paper, we…
We present a simple one-dimensional trapping model prompted by the problem of ion current across biological membranes. The trap is modeled mimicking the ionic channel membrane behaviour. Such voltage-sensitive channels are open or closed…
A probabilistic model describes a system in its observational state. In many situations, however, we are interested in the system's response under interventions. The class of structural causal models provides a language that allows us to…
There has been an increasing interest in modeling continuous-time dynamics of temporal graph data. Previous methods encode time-evolving relational information into a low-dimensional representation by specifying discrete layers of neural…
Enabling robots to perform complex dynamic tasks such as picking up an object in one sweeping motion or pushing off a wall to quickly turn a corner is a challenging problem. The dynamic interactions implicit in these tasks are critical…
We present a neuronal network model inspired by the Ising model, where each neuron is a binary spin ($s_i = \pm1$) interacting with its neighbors on a 2D lattice. Updates are asynchronous and follow Metropolis dynamics, with a…
Networks observed in real world like social networks, collaboration networks etc., exhibit temporal dynamics, i.e. nodes and edges appear and/or disappear over time. In this paper, we propose a generative, latent space based, statistical…
We propose a discrete time dynamical system (a map) as phenomenological model of excitable and spiking-bursting neurons. The model is a discontinuous two-dimensional map. We find condition under which this map has an invariant region on the…
Recurrent neural networks (RNNs) are powerful dynamical models, widely used in machine learning (ML) and neuroscience. Prior theoretical work has focused on RNNs with additive interactions. However, gating - i.e. multiplicative -…
We describe a simple conductance-based model neuron that includes intra- and extra-cellular ion concentration dynamics and show that this model exhibits periodic bursting. The bursting arises as the fast spiking behavior of the neuron is…
Current robot architectures for modeling interaction behavior are not well suited to the dual task of sequencing discrete actions and incorporating information instantly. Additionally, for communication based on body motion, actions also…
This paper is a preliminary work to address the problem of dynamical systems with parameters varying in time. An idea to predict their behaviour is proposed. These systems are called \emph{transient systems}, and are distinguished from…
This study investigates how dynamical systems may be learned and modelled with a neuromorphic network which is itself a dynamical system. The neuromorphic network used in this study is based on a complex electrical circuit comprised of…
The identification and modeling of time-varying systems is a fundamental challenge in signal processing and system identification. To address this challenge, we propose a class of time-varying state-space model (SSM) based neural networks…
A central challenge in neuroscience is understanding how neural system implements computation through its dynamics. We propose a nonlinear time series model aimed at characterizing interpretable dynamics from neural trajectories. Our model…
This article proposes a dynamical system modeling approach for the analysis of longitudinal data of self-regulated systems experiencing multiple excitations. The aim of such an approach is to focus on the evolution of a signal (e.g., heart…
We develop a dynamical systems approach to prioritizing and selecting multiple recurring tasks with the aim of conferring a degree of deliberative goal selection to a mobile robot confronted with competing objectives. We take navigation as…
Dynamic gene-regulatory networks are complex since the number of potential components involved in the system is very large. Estimating dynamic networks is an important task because they compromise valuable information about interactions…
Many biological systems can sense periodical variations in a stimulus input and produce well-timed, anticipatory responses after the input is removed. Such systems show memory effects for retaining timing information in the stimulus and…
We propose and study a model of hypothetical magnetosensitive ionic channels which are long thought to be a possible candidate to explain the influence of weak magnetic fields on living organisms ranging from magnetotactic bacteria to…