Many network problems are based on fundamental relationships involving time. Consider, for example, the problems of modeling the flow of information through a distributed network, studying the spread of a disease through a population, or analyzing the reachability properties of an airline timetable. In such settings, a natural model is that of a graph in which each edge is annotated with a time label specifying the time at which its endpoints “communicated. ” We will call such a graph a temporal network. To model the notion that information in such a network “flows ” only on paths whose labels respect the ordering of time, we call a path time-respecting if the time labels on its edges are non-decreasing. The central motivation for our work is the following question: how do the basic combinatorial and algorithmic properties of graphs change when we impose this additional temporal condition? The notion of a path is intrinsic to many of the most fundamental algorithmic problems on graphs; spanning trees, connectivity, flows, and cuts are some examples. When we focus on time-respecting paths in place of arbitrary paths, many of these problems acquire a character that is different from the

This paper presents a computational theory of developmental mental architectures for artificial and natural systems, motivated by neuroscience. The work is an attempt to approximately model biological mental architectures using mathematical tools. Six types of architecture are presented, beginning with the observation-driven Markov decision process as Type-1. From Type-1 to Type-6, the architecture progressively becomes more complete toward the necessary functions of autonomous mental development. Properties of each type are presented. Experiments are discussed with emphasis on their architectures. r 2007 Published by Elsevier B.V.

We present the first peer-to-peer data streaming application that guarantees predictable throughput and low latency in the BAR (Byzantine/Altruistic/Rational) model, in which nonaltruistic nodes can behave in ways that are self-serving (rational) or arbitrarily malicious (Byzantine). At the core of our solution is a BARtolerant version of gossip, a well-known technique for scalable and reliable data dissemination. BAR Gossip relies on verifiable pseudo-random partner selection to eliminate non-determinism that can be used to game the system while maintaining the robustness and rapid convergence of traditional gossip. A novel fair enough exchange primitive entices cooperation among selfish nodes on short timescales, avoiding the need for long-term node reputations. Our initial experience provides evidence for BAR Gossip’s robustness. Our BAR-tolerant streaming application provides over 99 % convergence for broadcast updates when all clients are selfish but not colluding, and over 95 % convergence when up to 40 % of clients collude while the rest follow the protocol. BAR Gossip also performs well when the client population consists of both selfish and Byzantine nodes, achieving over 93 % convergence even when 20 % of the nodes are Byzantine. 1

Abstract. A family of interpolating graphs C(S, ξ) of complexity ξ is constructed for a surface S and −2 ≤ ξ ≤ ξ(S). For ξ = −2, −1, ξ(S) − 1 these specialise to graphs quasi-isometric to the marking graph, the pants graph and the curve graph respectively. We generalise Theorems of Brock-Farb and Behrstock-Minsky to show that the rank of C(S, ξ) is rξ, the largest number of disjoint copies of subsurfaces of complexity greater than ξ that may be embedded in S. The interpolating graphs C(S, ξ) interpolate between the pants graph and the curve graph.