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Water management is one of the most critical aspects of our society, together with population increase and climate change. Water scarcity requires a better characterization and monitoring of Water Distribution Networks (WDNs). This paper…

We prove results on mixing and mixing rates for toral extensions of nonuniformly expanding maps with subexponential decay of correlations. Both the finite and infinite measure settings are considered. Under a Dolgopyat-type condition on…

We study classes of dynamical systems that can be obtained by constructing recursive networks with monotone Boolean functions. Stack filters in nonlinear signal processing are special cases of such systems. We show an analytical connection…

In many systems consisting of interacting subsystems, the complex interactions between elements can be represented using multilayer networks. However percolation, key to understanding connectivity and robustness, is not trivially…

We consider the dynamics of a periodic chain of N coupled overdamped particles under the influence of noise. Each particle is subjected to a bistable local potential, to a linear coupling with its nearest neighbours, and to an independent…

Topological insulators in three dimensions are characterized by a Z2-valued topological invariant, which consists of a strong index and three weak indices. In the presence of disorder, only the strong index survives. This paper studies the…

In this work, we characterize a class of nonlinear monotone dynamical systems that have a certain translation invariance property which goes by the name of plus-homogeneity; usually called "topical" systems. Such systems need not be…

Band structures of topological insulators are characterized by non-local topological invariants. Consequently, proposals for the experimental detection using local probes are rare. A recent paper [Slager et al., Phys. Rev. B 92, 085126…

Topological insulators are typically characterized by particularly stable properties, such as global invariants, and can be identified by probing their robust surface states. A recently discovered novel form of band topology, delicate…

Multistability is a phenomenon prevalent in many natural systems. In climate, for example, it allows the possibility of irreversible consequences on planetary scale as a result of climate change. Indeed, a climate ``tipping element'' is a…

Balanced and swap-robust minimal trades, introduced in [1], are important for studying the balance and stability of server access request protocols under data popularity changes. Constructions of such trades have so far relied on paired…

There is a growing interest in discovery of internet topology at the interface level. A new generation of highly distributed measurement systems is currently being deployed. Unfortunately, the research community has not examined the problem…

The Survivable Network Design problem (SNDP) is a well-studied problem, motivated by the design of networks that are robust to faults under the assumption that any subset of edges up to a specific number can fail. We consider non-uniform…

The last years have witnessed rapid progress in the topological characterization of out-of-equilibrium systems. We report on robust signatures of a new type of topology -- the Euler class -- in such a dynamical setting. The enigmatic…

One of the hallmarks of topological insulators is the correspondence between the value of its bulk topological invariant and the number of topologically protected edge modes observed in a finite-sized sample. This bulk-boundary…

We discuss the nonlinear phenomena of irreversible tipping for non-autonomous systems where time-varying inputs correspond to a smooth "parameter shift" from one asymptotic value to another. We express tipping in terms of pullback…

We report the study of sudden transitions or tipping in a collection of systems induced due to multiplexing with another network of systems. The emergent dynamics of oscillators on one layer can undergo a sudden transition to steady state…

We find necessary and sufficient conditions for a dynamical system to be topologically conjugate to any given substitution minimal system, thus extending the results in [CKL] for the Morse and Toeplitz substitutions.

We show that for a non-trivial transitive dynamical system, it has a dense Mycielski invariant strongly scrambled set if and only if it has a fixed point, and it has a dense Mycielski invariant $\delta$-scrambled set for some $\delta>0$ if…

This paper studies distributed adaptive estimation over sensor networks with partially unknown source dynamics. We present parallel continuous-time and discrete-time designs in which each node runs a local adaptive observer and exchanges…