Related papers: Computation of amplification for systems arising f…
We study two measures of the complexity of heterogeneous extended systems, taking random Boolean networks as prototypical cases. A measure defined by Shalizi et al. for cellular automata, based on a criterion for optimal statistical…
For a closed-loop control system with a digital channel between the sensor and the controller, the notion of invariance entropy quantifies the smallest average rate of information transmission above which a given compact subset of the state…
Linear problems appear in a variety of disciplines and their application for the transmission matrix recovery is one of the most stimulating challenges in biomedical imaging. Its knowledge turns any random media into an optical tool that…
One of the most influential results in neural network theory is the universal approximation theorem [1, 2, 3] which states that continuous functions can be approximated to within arbitrary accuracy by single-hidden-layer feedforward neural…
Additive regression provides an extension of linear regression by modeling the signal of a response as a sum of functions of covariates of relatively low complexity. We study penalized estimation in high-dimensional nonparametric additive…
We examine the $\mathcal{H}_2$ norm of matrix-weighted leader-follower consensus on series-parallel networks. By using an extension of electrical network theory on matrix-valued resistances, voltages and currents, we show that the…
We describe a numerical technique to compute the equilibrium measure, in logarithmic potential theory, living on the attractor of Iterated Function Systems composed of one-dimensional affine maps. This measure is obtained as the limit of a…
In this paper, we investigate when system identification is statistically easy or hard, in the finite sample regime. Statistically easy to learn linear system classes have sample complexity that is polynomial with the system dimension. Most…
Varied sensory systems use noise in order to enhance detection of weak signals. It has been conjectured in the literature that this effect, known as stochastic resonance, may take place in central cognitive processes such as the memory…
In this paper, we study the statistical difficulty of learning to control linear systems. We focus on two standard benchmarks, the sample complexity of stabilization, and the regret of the online learning of the Linear Quadratic Regulator…
We study the $\mathcal{L}_p$ induced gain of discrete-time linear switching systems with graph-constrained switching sequences. We first prove that, for stable systems in a minimal realization, for every $p \geq 1$, the $\mathcal{L}_p$-gain…
This paper characterizes a new parametrization of nonlinear networked incrementally $L_2$-bounded operators in discrete time. The distinctive novelty is that our parametrization is \emph{free} -- that is, a sparse large-scale operator with…
This paper studies several aspects of signal reconstruction of sampled data in spaces of bandlimited functions. In the first part, signal spaces are characterized in which the classical sampling series uniformly converge, and we investigate…
We consider the problem of optimizing signal transmission through multi-channel noisy devices. We investigate an array of bithreshold noisy devices which are connected in parallel and convergent on a summing center. Utilizing the concept of…
This paper considers the problem of distributed estimation in an incremental network when the measurements taken by the node follow a widely linear model. The proposed algorithm which we refer to it as incremental augmented affine…
A key task in the field of modeling and analyzing nonlinear dynamical systems is the recovery of unknown governing equations from measurement data only. There is a wide range of application areas for this important instance of system…
We derive the ultimate bounds on the performance of nonlinear measurement schemes in the presence of noise. In particular, we investigate the precision of the second-order estimation scheme in the presence of the two most detrimental types…
In this paper, we propose an approach for computing invariant sets of discrete-time nonlinear systems by lifting the nonlinear dynamics into a higher dimensional linear model. In particular, we focus on the \emph{maximal admissible…
We introduce a simple method to estimate the system parameters in continuous dynamical systems from the time series. In this method, we construct a modified system by introducing some constants (controlling constants) into the given…
The amplitude of fluctuation-induced patterns might be expected to be proportional to the strength of the driving noise, suggesting that such patterns would be difficult to observe in nature. Here, we show that a large class of…