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Permutation entropy measures the complexity of deterministic time series via a data symbolic quantization consisting of rank vectors called ordinal patterns or just permutations. The reasons for the increasing popularity of this entropy in…
We address the problem of applying the Kolmogorov-Sinai method of entropic analysis, expressed in a generalized non-extensive form, to the dynamics of the logistic map at the chaotic threshold, which is known to be characterized by a power…
This paper proposes a simple adaptive sensing and group testing algorithm for sparse signal recovery. The algorithm, termed Compressive Adaptive Sense and Search (CASS), is shown to be near-optimal in that it succeeds at the lowest possible…
Driven by physical questions pertaining to quantifying particle dynamics, microscopy can now resolve complex systems at the single particle level, from cellular organisms to individual ions. Yet, available analysis techniques face…
Constant-time programming is a widely deployed approach to harden cryptographic programs against side channel attacks. However, modern processors often violate the underlying assumptions of standard constant-time policies by transiently…
Detection with high dimensional multimodal data is a challenging problem when there are complex inter- and intra- modal dependencies. While several approaches have been proposed for dependent data fusion (e.g., based on copula theory),…
Optical systems which measure independent random projections of a scene according to compressed sensing (CS) theory face a myriad of practical challenges related to the size of the physical platform, photon efficiency, the need for high…
In this review article, we discuss connections between the physics of disordered systems, phase transitions in inference problems, and computational hardness. We introduce two models representing the behavior of glassy systems, the spiked…
The recent development of compressed sensing has led to spectacular advances in the understanding of sparse linear estimation problems as well as in algorithms to solve them. It has also triggered a new wave of developments in the related…
We present methods that can provide an exponential savings in the resources required to perform dynamic parameter estimation using quantum systems. The key idea is to merge classical compressive sensing techniques with quantum control…
The problem of defining and studying complexity of a time series has interested people for years. In the context of dynamical systems, Grassberger has suggested that a slow approach of the entropy to its extensive asymptotic limit is a sign…
Collective behavior, both in real biological systems as well as in theoretical models, often displays a rich combination of different kinds of order. A clear-cut and unique definition of "phase" based on the standard concept of order…
It is generally believed that the dynamics of simple fluids can be considered to be chaotic, at least to the extent that they can be modeled as classical systems of particles interacting with short range, repulsive forces. Here we give a…
Information theory on a time-discrete setting in the framework of time series analysis is generalized to the time-continuous case. Considerations of the Roessler and Lorenz dynamics as well as the Ornstein-Uhlenbeck process yield for…
Choosing the optimal observable to model dynamical systems for which we do not know the driving equations is nearly always an ad hoc art. Takens' Delay Embedding Theorem guarantees a diffeomorphism between delay-coordinate vectors built…
A central concept in the connection between physics and information theory is entropy, which represents the amount of information extracted from the system by the observer performing measurements in an experiment. Indeed, Jaynes' principle…
In deep learning inference, model parameters are pruned and quantized to reduce the model size. Compression methods and common subexpression (CSE) elimination algorithms are applied on sparse constant matrices to deploy the models on…
Contraction theory is a recently developed dynamic analysis and nonlinear control system design tool based on an exact differential analysis of convergence. This paper extends contraction theory to local and global stability analysis of…
Data compression algorithms are generally perceived as being of interest for data communication and storage purposes only. However, their use in the field of data classification and analysis is also of equal importance. Automatic data…
In this paper we prove estimates on the behaviour of the Kolmogorov-Sinai entropy relative to a partition for randomly perturbed dynamical systems. Our estimates use the entropy for the unperturbed system and are obtained using the notion…