Self-Stabilizing Repeated Balls-into-Bins

We study the following synchronous process that we call "repeated balls-into-bins". The process is started by assigning $n$ balls to $n$ bins in an arbitrary way. In every subsequent round, from each non-empty bin one ball is chosen according to some fixed strategy (random, FIFO, etc), and re-assigned to one of the $n$ bins uniformly at random. We define a configuration "legitimate" if its maximum load is $\mathcal{O}(\log n)$. We prove that, starting from any configuration, the process will converge to a legitimate configuration in linear time and then it will only take on legitimate configurations over a period of length bounded by any polynomial in $n$, with high probability (w.h.p.). This implies that the process is self-stabilizing and that every ball traverses all bins in $\mathcal{O}(n \log^2 n)$ rounds, w.h.p

Distributed Queuing in Dynamic Networks

We consider the problem of forming a distributed queue in the adversarial dynamic network model of Kuhn, Lynch, and Oshman (STOC 2010) in which the network topology changes from round to round but the network stays connected. This is a synchronous model in which network nodes are assumed to be fixed, the communication links for each round are chosen by an adversary, and nodes do not know who their neighbors are for the current round before they broadcast their messages. Queue requests may arrive over rounds at arbitrary nodes and the goal is to eventually enqueue them in a distributed queue. We present two algorithms that give a total distributed ordering of queue requests in this model. We measure the performance of our algorithms through round complexity, which is the total number of rounds needed to solve the distributed queuing problem. We show that in 1-interval connected graphs, where the communication links change arbitrarily between every round, it is possible to solve the distributed queueing problem in O(nk) rounds using O(log n) size messages, where n is the number of nodes in the network and k <= n is the number of queue requests. Further, we show that for more stable graphs, e.g. T-interval connected graphs where the communication links change in every T rounds, the distributed queuing problem can be solved in O(n+ (nk/min(alpha,T))) rounds using the same O(log n) size messages, where alpha > 0 is the concurrency level parameter that captures the minimum number of active queue requests in the system in any round. These results hold in any arbitrary (sequential, one-shot concurrent, or dynamic) arrival of k queue requests in the system. Moreover, our algorithms ensure correctness in the sense that each queue request is eventually enqueued in the distributed queue after it is issued and each queue request is enqueued exactly once. We also provide an impossibility result for this distributed queuing problem in this model. To the best of our knowledge, these are the first solutions to the distributed queuing problem in adversarial dynamic networks.Comment: In Proceedings FOMC 2013, arXiv:1310.459

Networked PID control design : a pseudo-probabilistic robust approach

Networked Control Systems (NCS) are feedback/feed-forward control systems where control components (sensors, actuators and controllers) are distributed across a common communication network. In NCS, there exist network-induced random delays in each channel. This paper proposes a method to compensate the effects of these delays for the design and tuning of PID controllers. The control design is formulated as a constrained optimization problem and the controller stability and robustness criteria are incorporated as design constraints. The design is based on a polytopic description of the system using a Poisson pdf distribution of the delay. Simulation results are presented to demonstrate the performance of the proposed method

Separation of Circulating Tokens

Self-stabilizing distributed control is often modeled by token abstractions. A system with a single token may implement mutual exclusion; a system with multiple tokens may ensure that immediate neighbors do not simultaneously enjoy a privilege. For a cyber-physical system, tokens may represent physical objects whose movement is controlled. The problem studied in this paper is to ensure that a synchronous system with m circulating tokens has at least d distance between tokens. This problem is first considered in a ring where d is given whilst m and the ring size n are unknown. The protocol solving this problem can be uniform, with all processes running the same program, or it can be non-uniform, with some processes acting only as token relays. The protocol for this first problem is simple, and can be expressed with Petri net formalism. A second problem is to maximize d when m is given, and n is unknown. For the second problem, the paper presents a non-uniform protocol with a single corrective process.Comment: 22 pages, 7 figures, epsf and pstricks in LaTe

Dynamic Analysis of the Arrow Distributed Protocol

Distributed queuing is a fundamental coordination problem that arises in a variety of applications, including distributed directories, totally ordered multicast, and distributed mutual exclusion. The arrow protocol is a solution to distributed queuing that is based on path reversal on a pre-selected spanning tree of the network. We present a novel and comprehensive competitive analysis of the arrow protocol. We consider the total cost of handling a finite number of queuing requests, which may or may not be issued concurrently, and show that the arrow protocol is $O(s\cdot \log D)$ -competitive to the optimal queuing protocol, where s and D are the stretch and the diameter, respectively, of the spanning tree. In addition, we show that our analysis is almost tight by proving that for every spanning tree chosen for execution, the arrow protocol is $\Omega(s \cdot \log(D/s)/{\log}\log(D/s))$ -competitive to the optimal queuing protocol. Our analysis reveals an intriguing connection between the arrow protocol and the nearest neighbor traveling salesperson tour on an appropriately defined grap

Towards a Unified Theory of Neocortex: Laminar Cortical Circuits for Vision and Cognition

A key goal of computational neuroscience is to link brain mechanisms to behavioral functions. The present article describes recent progress towards explaining how laminar neocortical circuits give rise to biological intelligence. These circuits embody two new and revolutionary computational paradigms: Complementary Computing and Laminar Computing. Circuit properties include a novel synthesis of feedforward and feedback processing, of digital and analog processing, and of pre-attentive and attentive processing. This synthesis clarifies the appeal of Bayesian approaches but has a far greater predictive range that naturally extends to self-organizing processes. Examples from vision and cognition are summarized. A LAMINART architecture unifies properties of visual development, learning, perceptual grouping, attention, and 3D vision. A key modeling theme is that the mechanisms which enable development and learning to occur in a stable way imply properties of adult behavior. It is noted how higher-order attentional constraints can influence multiple cortical regions, and how spatial and object attention work together to learn view-invariant object categories. In particular, a form-fitting spatial attentional shroud can allow an emerging view-invariant object category to remain active while multiple view categories are associated with it during sequences of saccadic eye movements. Finally, the chapter summarizes recent work on the LIST PARSE model of cognitive information processing by the laminar circuits of prefrontal cortex. LIST PARSE models the short-term storage of event sequences in working memory, their unitization through learning into sequence, or list, chunks, and their read-out in planned sequential performance that is under volitional control. LIST PARSE provides a laminar embodiment of Item and Order working memories, also called Competitive Queuing models, that have been supported by both psychophysical and neurobiological data. These examples show how variations of a common laminar cortical design can embody properties of visual and cognitive intelligence that seem, at least on the surface, to be mechanistically unrelated.National Science Foundation (SBE-0354378); Office of Naval Research (N00014-01-1-0624