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This work focuses on quantitative representation of transport in systems with quenched disorder. Explicit mapping of the quenched trap model to continuous time random walk is presented. Linear temporal transformation: $t\to…
In vivo and in vitro systems of cells and extra-cellular matrix (ECM) systems are well known to form ordered patterns of orientationally aligned fibers. Here, we interpret them as active analogs of the (disordered) isotropic to the…
A discrete rate theory for general multi-ion channels is presented, in which the continuous dynamics of ion diffusion is reduced to transitions between Markovian discrete states. In an open channel, the ion permeation process involves three…
Transport-dominated partial differential equation models have been used extensively over the past two decades to describe various collective migration phenomena in cell biology and ecology. To understand the behaviour of these models (and…
This paper presents a method to describe dynamics of an ion confined in a realistic finite range trap. We model this realistic potential with a solvable one and we obtain dynamical variables (raising and lowering operators) of this…
The promising performance increase offered by quantum computing has led to the idea of applying it to neural networks. Studies in this regard can be divided into two main categories: simulating quantum neural networks with the standard…
One way to model telecommunication networks are static Boolean models. However, dynamics such as node mobility have a significant impact on the performance evaluation of such networks. Consider a Boolean model in $\mathbb{R}^d$ and a random…
Flux of rigid or soft particles (such as drops, vesicles, red blood cells, etc.) in a channel is a complex function of particle concentration, which depends on the details of induced dissipation and suspension structure due to hydrodynamic…
We study numerically an electronic transport in strongly anisotropic weakly disorderd two-dimensional systems. We find that the conductance distribution is gaussian but the conductance fluctuations increase when anisotropy becomes stronger.…
We study the stability of coupled impedance passive regular linear systems under power-preserving interconnections. We present new conditions for strong, exponential, and non-uniform stability of the closed-loop system. We apply the…
We have developed a linearization method to investigate the subthreshold oscillatory behaviors in nonlinear autonomous systems. By considering firstly the neuronal system as an example, we show that this theoretical approach can predict…
This work addresses linear transport in turbulent media, with emphasis on neutral particle (atoms, molecules) transport in magnetized fusion plasmas. A stochastic model for turbulent plasmas, based upon a multivariate Gamma distribution, is…
We study the Monte Carlo dynamics of strongly correlated classical particles coupled to lattice degrees of freedom that exhibit the neutral-ionic transitions in one dimension, relevant to the organic compounds TTF-CA and TTF-BA. The…
Neural signals are characterized by rich temporal and spatiotemporal dynamics that reflect the organization of cortical networks. Theoretical research has shown how neural networks can operate at different dynamic ranges that correspond to…
Ionic transport within charged nanopores is commonly represented by resistor-capacitor transmission line circuits, where charging electrical double layers are modeled as capacitors, and the resistance to ionic current is modeled as…
The transport properties of a conduction junction model characterized by two mutually coupled channels that strongly differ in their couplings to the leads are investigated. Models of this type describe molecular redox junctions (where a…
Many transport processes on networks depend crucially on the underlying network geometry, although the exact relationship between the structure of the network and the properties of transport processes remain elusive. In this paper we…
This paper proposes a novel approach to improve the performance of distributed nonlinear control systems while preserving stability by leveraging Deep Neural Networks (DNNs). We build upon the Neural System Level Synthesis (Neur-SLS)…
We analyze Neural Ordinary Differential Equations (NODEs) from a control theoretical perspective to address some of the main properties and paradigms of Deep Learning (DL), in particular, data classification and universal approximation.…
Cortical neurons include many sub-cellular processes, operating at multiple timescales, which may affect their response to stimulation through non-linear and stochastic interaction with ion channels and ionic concentrations. Since new…