Related papers: Target formation on the circle by monotone system …
This paper investigates some aspects of a recently proposed nonlinear mathematical model of opinion dynamics. The main objective is to identify the network structures that maximize the average equilibrium opinion (HMO). We prove that…
We study the performance of discrete-time consensus protocols in the presence of additive noise. When the consensus dynamic corresponds to a reversible Markov chain, we give an exact expression for a weighted version of steady-state…
We discuss various ensembles of homogeneous complex networks and a Monte-Carlo method of generating graphs from these ensembles. The method is quite general and can be applied to simulate micro-canonical, canonical or grand-canonical…
There exist efficient algorithms to project a point onto the intersection of a convex cone and an affine subspace. Those conic projections are in turn the work-horse of a range of algorithms in conic optimization, having a variety of…
Positive $T$-martingales were developed as a general framework that extends the positive measure-valued martingales and are meant to model intermittent turbulence. We extend their scope by allowing the martingale to take complex values. We…
Converse optimality theory addresses an optimal control problem conversely where the system is unknown and the value function is chosen. Previous work treated this problem both in continuous and discrete time and non-extensively considered…
Linear response theory has found many applications in statistical physics. One of these is to compute minimal-work protocols that drive nonequilibrium systems between different thermodynamic states, which are useful for designing engineered…
This paper introduces several new algorithms for consensus over the special orthogonal group. By relying on a convex relaxation of the space of rotation matrices, consensus over rotation elements is reduced to solving a convex problem with…
Drawing inspiration from the theory of linear "decomposable systems", we provide a method, based on linear matrix inequalities (LMIs), which makes it possible to prove the convergence (or consensus) of a set of interacting agents with…
Reaching consensus -- a macroscopic state where the system constituents display the same microscopic state -- is a necessity in multiple complex socio-technical and techno-economic systems: their correct functioning ultimately depends on…
We study a continuous time Markov process whose state space consists of an assignment of +1 or -1 to each vertex of a graph G. The graphs that we treat are related to homogeneous trees of degree K $\geq$ 3, such as finite or infinite stacks…
Topic models are evaluated based on their ability to describe documents well (i.e. low perplexity) and to produce topics that carry coherent semantic meaning. In topic modeling so far, perplexity is a direct optimization target. However,…
We provide some on-off type criteria for recurrence and transience of regime-switching diffusion processes using the theory of M-matrix and the Perron-Frobenius theorem. State-independent and state-dependent regime-switching diffusion…
We present a method for fitting monotone curves using cubic B-splines, which is equivalent to putting a monotonicity constraint on the coefficients. We explore different ways of enforcing this constraint and analyze their theoretical and…
The methods of non-homogeneous random graphs calibration are developed for social networks simulation. The graphs are calibrated by the degree distributions of the vertices and the edges. The mathematical foundation of the methods is formed…
This paper introduces some tools from graph theory and distributed consensus algorithms to construct an optimal, yet robust, hierarchical information sharing structure for large-scale decision making and control problems. The proposed…
Distributed consensus algorithm over networks of quantum systems has been the focus of recent studies in the context of quantum computing and distributed control. Most of the progress in this category have been on the convergence conditions…
Cluster algorithms have been recently used to eliminate sign problems that plague Monte-Carlo methods in a variety of systems. In particular such algorithms can also be used to solve sign problems associated with the permutation of fermion…
Algorithms for community detection are usually stochastic, leading to different partitions for different choices of random seeds. Consensus clustering has proven to be an effective technique to derive more stable and accurate partitions…
A probability distribution over the Boolean cube is monotone if flipping the value of a coordinate from zero to one can only increase the probability of an element. Given samples of an unknown monotone distribution over the Boolean cube, we…