Ji Liu | Yale University (original) (raw)

Papers by Ji Liu

Abstract: In times of normalcy, media help to shape a culture of common knowledge and predictabil... more Abstract: In times of normalcy, media help to shape a culture of common knowledge and predictability that is indispensable to social order. During volatile times, as the legitimacy and efficiency of common knowledge disappears, political mobilization is often constrained by limitations of local interaction networks. Learning processes shape the dynamics of diffusion initiated by a radical minority. Social media, in particular, provide long bridges that traverse across the confines of spatial mobilization.

Abstract The distributed averaging problem is to devise a protocol which will enable the members ... more Abstract The distributed averaging problem is to devise a protocol which will enable the members of a group of n> 1 agents to asymptotically determine in a decentralized manner, the average of the initial values of their scalar agreement variables. A typical averaging protocol can be modeled by a linear iterative equation whose update matrices are doubly stochastic.

Abstract For the purposes of this paper,“gossiping” is a distributed process whose purpose is to ... more Abstract For the purposes of this paper,“gossiping” is a distributed process whose purpose is to enable the members of a group of autonomous agents to asymptotically determine, in a decentralized manner, the average of the initial values of their scalar gossip variables. This paper discusses several different deterministic protocols for gossiping which avoid deadlocks and achieve consensus under different assumptions.

Summary. A sequence of allowable gossips between pairs of agents in a group is complete if the go... more Summary. A sequence of allowable gossips between pairs of agents in a group is complete if the gossip graph which the sequence generates contains a tree spanning the graph of all allowable gossip pairs. The stochastic matrix of a sequence of allowable gossips is shown to be a contraction for an appropriately defined Euclidian seminorm, if and only if the gossip sequence is complete. The significance of this result in determining the convergence rate of an infinite aperiodic sequence of gossips is explained.

Abstract: Gossiping is a well-studied distributed algorithm whose purpose is to enable the member... more Abstract: Gossiping is a well-studied distributed algorithm whose purpose is to enable the members of a group of autonomous agents to asymptotically determine in a decentralized manner, the average of their initial scalar-valued gossip variables. T-periodic gossiping is a gossiping protocol which stipulates that each agent must gossip with each of its neighbors exactly once every T time unit.

Many distributed control algorithms of current interest can be modeled by linear recursion equati... more Many distributed control algorithms of current interest can be modeled by linear recursion equations of the form x(t + 1) = M (t)x(t), t ≥ 1 where each M (t) is a realvalued "stochastic" or "doubly stochastic" matrix. Convergence of such recursions often reduces to deciding when the sequence of matrix products M (1), M (2)M (1), M (3)M (2)M ( , . . . converges. Certain types of stochastic and doubly stochastic matrices have the property that any sequence of products of such matrices of the form S1, S2S1, S3S2S1, . . . converges exponentially fast. We explicitly characterize the largest classes of stochastic and doubly stochastic matrices with positive diagonal entries which have these properties. The main goal of this paper is to find a "semi-norm" with respect to which matrices from these "convergability classes" are contractions. For any doubly stochastic matrix S such a semi-norm is identified and is shown to coincide with the second largest singular value of S.

Abstract This paper investigates accelerated gossip algorithms for distributed computations in ne... more Abstract This paper investigates accelerated gossip algorithms for distributed computations in networks where shift-registers are utilized at each node. By using tools from matrix analysis, we prove the existence of the desired acceleration and establish the fastest rate of convergence in expectation for two-register symmetric gossip. Some classes of networks with regular graph topologies are studied in detail to validate the analytical results by comparison with existing empirical data.

Abstract By the distributed averaging problem is meant the problem of computing the average value... more Abstract By the distributed averaging problem is meant the problem of computing the average value of a set of numbers possessed by the agents in a distributed network using only communication between neighboring agents. Gossiping is a well-known approach to the problem which seeks to iteratively arrive at a solution by allowing each agent to interchange information with at most one neighbor at each iterative step.

Distributed averaging deals with a network of n> 1 agents and the constraint that each agent is a... more Distributed averaging deals with a network of n> 1 agents and the constraint that each agent is able to communicate only with its neighbors. The purpose of the distributed averaging problem is to devise a protocol which will enable all n agents to asymptotically determine in a decentralized manner, the average of the initial values of their scalar agreement variables. Most distributed averaging protocols involve a linear iteration which depends only on the current estimates of the average.