Related papers: A Sharp Bound on the $s$-Energy and Its Applicatio…
Many multi-agent systems evolve by repeatedly updating each state to a weighted average of its neighbors, a process known as averaging dynamics, whose behavior becomes difficult to analyze when the interaction network varies over time. In…
We introduce the "total s-energy" of a multiagent system with time-dependent links. This provides a new analytical lens on bidirectional agreement dynamics, which we use to bound the convergence rates of dynamical systems for…
The universal bound on specific entropy was originally inferred from black hole thermodynamics. We here show from classical thermodynamics alone that for a system at fixed volume or fixed pressure, the ratio of entropy to nonrelativistic…
The maximum entropy principle from statistical mechanics states that a closed system attains an equilibrium distribution that maximizes its entropy. We first show that for graphs with fixed number of edges one can define a stochastic edge…
We present methods for bounding infinite-time averages in dynamical systems governed by nonlinear PDEs. The methods rely on auxiliary functionals, which are similar to Lyapunov functionals but satisfy different inequalities. The…
Weighted-sum energy efficiency (WSEE) is a key performance metric in heterogeneous networks, where the nodes may have different energy efficiency (EE) requirements. Nevertheless, WSEE maximization is a challenging problem due to its…
This paper presents a consensus algorithm for a multi-agent system where each agent has access to its imperfect own state and neighboring state measurements. The measurements are subject to deterministic disturbances and the proposed…
Convergence of Extremum Seeking (ES) algorithms has been established in the limit of small gains. Using averaging theory and contraction analysis, we propose a framework for computing explicit bounds on the departure of the ES scheme from…
Wireless sensors can integrate rechargeable batteries and energy-harvesting (EH) devices to enable long-term, autonomous operation, thus requiring intelligent energy management to limit the adverse impact of energy outages. This work…
We consider a one-sided assignment market or exchange network with transferable utility and propose a model for the dynamics of bargaining in such a market. Our dynamical model is local, involving iterative updates of 'offers' based on…
In this paper, we show how to achieve close-to-optimal utility performance in energy harvesting networks with only finite capacity energy storage devices. In these networks, nodes are capable of harvesting energy from the environment. The…
The problem of finding an optimum using noisy evaluations of a smooth cost function arises in many contexts, including economics, business, medicine, experiment design, and foraging theory. We derive an asymptotic bound E[ (x_t - x*)^2 ] >=…
We derive a rigorous lower bound on the average local energy for the Ising model with quenched randomness. The result is that the lower bound is given by the average local energy calculated in the absence of all interactions other than the…
We establish upper and lower universal bounds for potentials of weighted designs on the sphere $\mathbb{S}^{n-1}$ that depend only on quadrature nodes and weights derived from the design structure. Our bounds hold for a large class of…
Performance of optimization on quadratic problems sensitively depends on the low-lying part of the spectrum. For large (effectively infinite-dimensional) problems, this part of the spectrum can often be naturally represented or approximated…
We consider power allocation algorithms for fixed-rate transmission over Nakagami-m non-ergodic block-fading channels with perfect transmitter and receiver channel state information and discrete input signal constellations, under both…
The Swendsen-Wang algorithm is a sophisticated, widely-used Markov chain for sampling from the Gibbs distribution for the ferromagnetic Ising and Potts models. This chain has proved difficult to analyze, due in part to the global nature of…
In systems described by the scattering theory, there is an upper bound, lower than Carnot, on the efficiency of steady-state heat to work conversion at a given output power. We show that interacting systems can overcome such bound and…
In this second part of our work, we study the steady state of the population and the social utility for the three dynamics SSD, NBRD and NRPM; which were introduced in the first part. We provide sufficient conditions on the network based on…
We consider repeated allocation of a shared resource via a non-monetary mechanism, wherein a single item must be allocated to one of multiple agents in each round. We assume that each agent has i.i.d. values for the item across rounds, and…