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Power grid, communications, computer and product reticulation networks are frequently layered or subdivided by design. The layering divides responsibilities and can be driven by operational, commercial, regulatory and privacy concerns. From…
In this paper, we consider a stabilization problem of an uncertain system in a networked control setting. Due to the network, the measurements are quantized to finite-bit signals and may be randomly lost in the communication. We study…
In this paper, we consider decentralized optimization problems where agents have individual cost functions to minimize subject to subspace constraints that require the minimizers across the network to lie in low-dimensional subspaces. This…
The notion of symmetry is shown to be at the heart of all error correction/avoidance strategies for preserving quantum coherence of an open quantum system S e.g., a quantum computer. The existence of a non-trivial group of symmetries of the…
Agents learn about a changing state using private signals and their neighbors' past estimates of the state. We present a model in which Bayesian agents in equilibrium use neighbors' estimates simply by taking weighted sums with…
Acquisition of data is a difficult task in many applications of machine learning, and it is only natural that one hopes and expects the population risk to decrease (better performance) monotonically with increasing data points. It turns…
In this article, we consider the problem of stabilizing stochastic processes, which are constrained to a bounded Euclidean domain or a compact smooth manifold, to a given target probability density. Most existing works on modeling and…
Localized wave fronts are a fundamental feature of biological systems from cell biology to ecology. Here, we study a broad class of bistable models subject to self-activation, degradation and spatially inhomogeneous activating agents. We…
We address the self-stabilizing bit-dissemination problem, designed to capture the challenges of spreading information and reaching consensus among entities with minimal cognitive and communication capacities. Specifically, a group of $n$…
Self-stabilizing algorithms are an important because of their robustness and guaranteed convergence. Starting from any arbitrary state, a self-stabilizing algorithm is guaranteed to converge to a legitimate state.Those algorithms are not…
Vector clock algorithms are basic wait-free building blocks that facilitate causal ordering of events. As wait-free algorithms, they are guaranteed to complete their operations within a finite number of steps. Stabilizing algorithms allow…
Synchronous Counting is the task of reaching agreement on a common round counter in a synchronous system of $n$ nodes with up to $t$ Byzantine faults in a self-stabilizing manner. That is, after transient faults may have arbitrarily…
We present results on the last topic we collaborate with our late friend, Professor Ajoy Kumar Datta (1958-2019). In this work, we shed new light on a self-stabilizing wave algorithm proposed by Colette Johnen in 1997. This algorithm…
We present a scheme to convert self-stabilizing algorithms that use randomization during and following convergence to self-stabilizing algorithms that use randomization only during convergence. We thus reduce the number of random bits from…
Consider a network whose nodes have some initial values, and it is desired to design an algorithm that builds on neighbor to neighbor interactions with the ultimate goal of convergence to the average of all initial node values or to some…
We propose an asynchronous, decentralized algorithm for consensus optimization. The algorithm runs over a network in which the agents communicate with their neighbors and perform local computation. In the proposed algorithm, each agent can…
Consider the execution of a sequential algorithm that requires the program to converge to an optimal state, and then terminate/stutter. To design such an algorithm, we need to ensure that the state space that it traverses forms a directed…
A crucial challenge in decentralized systems is state estimation in the presence of unknown inputs, particularly within heterogeneous sensor networks with dynamic topologies. While numerous consensus algorithms have been introduced, they…
We present a self-stabilizing leader election algorithm for arbitrary networks, with space-complexity $O(\max\{\log \Delta, \log \log n\})$ bits per node in $n$-node networks with maximum degree~$\Delta$. This space complexity is…
A theory for stabilization of quantum resonances by a mechanism similar to one leading to classical resonances in nonlinear systems is presented. It explains recent surprising experimental results, obtained for cold Cesium atoms when driven…