Universal and Robust Distributed Network Codes

Random linear network codes can be designed and implemented in a distributed manner, with low computational complexity. However, these codes are classically implemented over finite fields whose size depends on some global network parameters (size of the network, the number of sinks) that may not be known prior to code design. Also, if new nodes join the entire network code may have to be redesigned. In this work, we present the first universal and robust distributed linear network coding schemes. Our schemes are universal since they are independent of all network parameters. They are robust since if nodes join or leave, the remaining nodes do not need to change their coding operations and the receivers can still decode. They are distributed since nodes need only have topological information about the part of the network upstream of them, which can be naturally streamed as part of the communication protocol. We present both probabilistic and deterministic schemes that are all asymptotically rate-optimal in the coding block-length, and have guarantees of correctness. Our probabilistic designs are computationally efficient, with order-optimal complexity. Our deterministic designs guarantee zero error decoding, albeit via codes with high computational complexity in general. Our coding schemes are based on network codes over ``scalable fields". Instead of choosing coding coefficients from one field at every node, each node uses linear coding operations over an ``effective field-size" that depends on the node's distance from the source node. The analysis of our schemes requires technical tools that may be of independent interest. In particular, we generalize the Schwartz-Zippel lemma by proving a non-uniform version, wherein variables are chosen from sets of possibly different sizes. We also provide a novel robust distributed algorithm to assign unique IDs to network nodes.Comment: 12 pages, 7 figures, 1 table, under submission to INFOCOM 201

Proposed shunt rounding technique for large-scale security constrained loss minimization

The official published version can be obtained from the link below - Copyright @ 2010 IEEE.Optimal reactive power flow applications often model large numbers of discrete shunt devices as continuous variables, which are rounded to their nearest discrete value at the final iteration. This can degrade optimality. This paper presents novel methods based on probabilistic and adaptive threshold approaches that can extend existing security constrained optimal reactive power flow methods to effectively solve large-scale network problems involving discrete shunt devices. Loss reduction solutions from the proposed techniques were compared to solutions from the mixed integer nonlinear mathematical programming algorithm (MINLP) using modified IEEE standard networks up to 118 buses. The proposed techniques were also applied to practical large-scale network models of Great Britain. The results show that the proposed techniques can achieve improved loss minimization solutions when compared to the standard rounding method.This work was supported in part by the National Grid and in part by the EPSRC. Paper no. TPWRS-00653-2009

Scalable Approach to Uncertainty Quantification and Robust Design of Interconnected Dynamical Systems

Development of robust dynamical systems and networks such as autonomous aircraft systems capable of accomplishing complex missions faces challenges due to the dynamically evolving uncertainties coming from model uncertainties, necessity to operate in a hostile cluttered urban environment, and the distributed and dynamic nature of the communication and computation resources. Model-based robust design is difficult because of the complexity of the hybrid dynamic models including continuous vehicle dynamics, the discrete models of computations and communications, and the size of the problem. We will overview recent advances in methodology and tools to model, analyze, and design robust autonomous aerospace systems operating in uncertain environment, with stress on efficient uncertainty quantification and robust design using the case studies of the mission including model-based target tracking and search, and trajectory planning in uncertain urban environment. To show that the methodology is generally applicable to uncertain dynamical systems, we will also show examples of application of the new methods to efficient uncertainty quantification of energy usage in buildings, and stability assessment of interconnected power networks

Improvements to Inference Compilation for Probabilistic Programming in Large-Scale Scientific Simulators

We consider the problem of Bayesian inference in the family of probabilistic models implicitly defined by stochastic generative models of data. In scientific fields ranging from population biology to cosmology, low-level mechanistic components are composed to create complex generative models. These models lead to intractable likelihoods and are typically non-differentiable, which poses challenges for traditional approaches to inference. We extend previous work in "inference compilation", which combines universal probabilistic programming and deep learning methods, to large-scale scientific simulators, and introduce a C++ based probabilistic programming library called CPProb. We successfully use CPProb to interface with SHERPA, a large code-base used in particle physics. Here we describe the technical innovations realized and planned for this library.Comment: 7 pages, 2 figure

Probability, Truth and Flow Graph

AbstractIn 1913 Jan Łukasiewicz proposed to use logic as mathematical foundations of probability. He claims that probability is “purely logical concept” and that his approach frees probability from its obscure philosophical connotation. He recommends to replace the concept of probability by the concept of a truth value, which can be regarded as a degree of truth, i.e., a number between 0 and 1, of propositional functions (called in his work indefinite propositions). Further he shows that all laws of probability can be obtained from a properly built logical calculus.In this paper we show that the idea of Łukasiewicz can be also expressed differently. Instead of using truth values in place of probability, stipulated by Łukasiewicz, we propose, in this paper, using of deterministic flow analysis in flow networks (graphs). In the proposed setting, flow is governed by some probabilistic rules (e.g., Bayes’ rule), or by the corresponding logical rules, proposed by Łukasiewicz, though, the formulas have entirely deterministic meaning, and need neither probabilistic nor logical interpretation. They simply describe flow distribution in flow graphs. However, flow graphs introduced here are different to those proposed by Ford and Fulkerson, for optimal flow analysis, because they model rather flow distribution in a plumbing network, then the optimal flow.The flow graphs considered in this paper can be also used as a description of a decision algorithms, where branches of the graph are interpreted as decision rules. This feature causes that flow networks can be also used as a new tool for data analysis, and knowledge representation