Stochastic Analysis of a Churn-Tolerant Structured Peer-to-Peer Scheme

We present and analyze a simple and general scheme to build a churn (fault)-tolerant structured Peer-to-Peer (P2P) network. Our scheme shows how to "convert" a static network into a dynamic distributed hash table(DHT)-based P2P network such that all the good properties of the static network are guaranteed with high probability (w.h.p). Applying our scheme to a cube-connected cycles network, for example, yields a $O(\log N)$ degree connected network, in which every search succeeds in $O(\log N)$ hops w.h.p., using $O(\log N)$ messages, where $N$ is the expected stable network size. Our scheme has an constant storage overhead (the number of nodes responsible for servicing a data item) and an $O(\log N)$ overhead (messages and time) per insertion and essentially no overhead for deletions. All these bounds are essentially optimal. While DHT schemes with similar guarantees are already known in the literature, this work is new in the following aspects: (1) It presents a rigorous mathematical analysis of the scheme under a general stochastic model of churn and shows the above guarantees; (2) The theoretical analysis is complemented by a simulation-based analysis that validates the asymptotic bounds even in moderately sized networks and also studies performance under changing stable network size; (3) The presented scheme seems especially suitable for maintaining dynamic structures under churn efficiently. In particular, we show that a spanning tree of low diameter can be efficiently maintained in constant time and logarithmic number of messages per insertion or deletion w.h.p. Keywords: P2P Network, DHT Scheme, Churn, Dynamic Spanning Tree, Stochastic Analysis

A Probabilistic Analysis of Kademlia Networks

Kademlia is currently the most widely used searching algorithm in P2P (peer-to-peer) networks. This work studies an essential question about Kademlia from a mathematical perspective: how long does it take to locate a node in the network? To answer it, we introduce a random graph K and study how many steps are needed to locate a given vertex in K using Kademlia's algorithm, which we call the routing time. Two slightly different versions of K are studied. In the first one, vertices of K are labelled with fixed IDs. In the second one, vertices are assumed to have randomly selected IDs. In both cases, we show that the routing time is about c*log(n), where n is the number of nodes in the network and c is an explicitly described constant.Comment: ISAAC 201

Investigation of How Neural Networks Learn From the Experiences of Peers Through Periodic Weight Averaging

We investigate a method, weighted average model fusion, that enables neural networks to learn from the experiences of other networks, as well as from their own experiences. This method is inspired by the the Social natural of humans, which has been shown to be one of the biggest factors in the development of our cognitive abilities. Modern machine learning has focuses predominantly on learning from direct training, and has largely ignored learning through Social engagement with peers, neural networks will the same topology. In order to explore learning through engagement with peers, we have created a way for neural networks to teach each other. Our method allows neural networks to exchange knowledge by combining their weights. It calculates a pairwise weighted average of the weights of two neural networks, and then replaces the existing weight with the new value. We find that weighted average model fusion successfully enables neural networks to learn from the experiences of their peers and combine it with the knowledge that is gained from its own individual experiences. Additionally, we explore the effects that several meta-parameters have on model fusion to provide deeper insights into how the behaves in a variety of scenarios

Quasirandom Load Balancing

We propose a simple distributed algorithm for balancing indivisible tokens on graphs. The algorithm is completely deterministic, though it tries to imitate (and enhance) a random algorithm by keeping the accumulated rounding errors as small as possible. Our new algorithm surprisingly closely approximates the idealized process (where the tokens are divisible) on important network topologies. On d-dimensional torus graphs with n nodes it deviates from the idealized process only by an additive constant. In contrast to that, the randomized rounding approach of Friedrich and Sauerwald (2009) can deviate up to Omega(polylog(n)) and the deterministic algorithm of Rabani, Sinclair and Wanka (1998) has a deviation of Omega(n^{1/d}). This makes our quasirandom algorithm the first known algorithm for this setting which is optimal both in time and achieved smoothness. We further show that also on the hypercube our algorithm has a smaller deviation from the idealized process than the previous algorithms.Comment: 25 page

Symmetry in Critical Random Boolean Network Dynamics

Using Boolean networks as prototypical examples, the role of symmetry in the dynamics of heterogeneous complex systems is explored. We show that symmetry of the dynamics, especially in critical states, is a controlling feature that can be used both to greatly simplify analysis and to characterize different types of dynamics. Symmetry in Boolean networks is found by determining the frequency at which the various Boolean output functions occur. There are classes of functions that consist of Boolean functions that behave similarly. These classes are orbits of the controlling symmetry group. We find that the symmetry that controls the critical random Boolean networks is expressed through the frequency by which output functions are utilized by nodes that remain active on dynamical attractors. This symmetry preserves canalization, a form of network robustness. We compare it to a different symmetry known to control the dynamics of an evolutionary process that allows Boolean networks to organize into a critical state. Our results demonstrate the usefulness and power of using the symmetry of the behavior of the nodes to characterize complex network dynamics, and introduce a novel approach to the analysis of heterogeneous complex systems

A general analytical model of adaptive wormhole routing in k-ary n-cubes

Several analytical models of fully adaptive routing have recently been proposed for k-ary n-cubes and hypercube networks under the uniform traffic pattern. Although,hypercube is a special case of k-ary n-cubes topology, the modeling approach for hypercube is more accurate than karyn-cubes due to its simpler structure. This paper proposes a general analytical model to predict message latency in wormhole-routed k-ary n-cubes with fully adaptive routing that uses a similar modeling approach to hypercube. The analysis focuses Duato's fully adaptive routing algorithm [12], which is widely accepted as the most general algorithm for achieving adaptivity in wormhole-routed networks while allowing for an efficient router implementation. The proposed model is general enough that it can be used for hypercube and other fully adaptive routing algorithms

A Neural Network Method for Classification of Sunlit and Shaded Components of Wheat Canopies in the Field Using High-Resolution Hyperspectral Imagery

(1) Background: Information rich hyperspectral sensing, together with robust image analysis, is providing new research pathways in plant phenotyping. This combination facilitates the acquisition of spectral signatures of individual plant organs as well as providing detailed information about the physiological status of plants. Despite the advances in hyperspectral technology in field-based plant phenotyping, little is known about the characteristic spectral signatures of shaded and sunlit components in wheat canopies. Non-imaging hyperspectral sensors cannot provide spatial information; thus, they are not able to distinguish the spectral reflectance differences between canopy components. On the other hand, the rapid development of high-resolution imaging spectroscopy sensors opens new opportunities to investigate the reflectance spectra of individual plant organs which lead to the understanding of canopy biophysical and chemical characteristics. (2) Method: This study reports the development of a computer vision pipeline to analyze ground-acquired imaging spectrometry with high spatial and spectral resolutions for plant phenotyping. The work focuses on the critical steps in the image analysis pipeline from pre-processing to the classification of hyperspectral images. In this paper, two convolutional neural networks (CNN) are employed to automatically map wheat canopy components in shaded and sunlit regions and to determine their specific spectral signatures. The first method uses pixel vectors of the full spectral features as inputs to the CNN model and the second method integrates the dimension reduction technique known as linear discriminate analysis (LDA) along with the CNN to increase the feature discrimination and improves computational efficiency. (3) Results: The proposed technique alleviates the limitations and lack of separability inherent in existing pre-defined hyperspectral classification methods. It optimizes the use of hyperspectral imaging and ensures that the data provide information about the spectral characteristics of the targeted plant organs, rather than the background. We demonstrated that high-resolution hyperspectral imagery along with the proposed CNN model can be powerful tools for characterizing sunlit and shaded components of wheat canopies in the field. The presented method will provide significant advances in the determination and relevance of spectral properties of shaded and sunlit canopy components under natural light conditions

A survey of statistical network models

Networks are ubiquitous in science and have become a focal point for discussion in everyday life. Formal statistical models for the analysis of network data have emerged as a major topic of interest in diverse areas of study, and most of these involve a form of graphical representation. Probability models on graphs date back to 1959. Along with empirical studies in social psychology and sociology from the 1960s, these early works generated an active network community and a substantial literature in the 1970s. This effort moved into the statistical literature in the late 1970s and 1980s, and the past decade has seen a burgeoning network literature in statistical physics and computer science. The growth of the World Wide Web and the emergence of online networking communities such as Facebook, MySpace, and LinkedIn, and a host of more specialized professional network communities has intensified interest in the study of networks and network data. Our goal in this review is to provide the reader with an entry point to this burgeoning literature. We begin with an overview of the historical development of statistical network modeling and then we introduce a number of examples that have been studied in the network literature. Our subsequent discussion focuses on a number of prominent static and dynamic network models and their interconnections. We emphasize formal model descriptions, and pay special attention to the interpretation of parameters and their estimation. We end with a description of some open problems and challenges for machine learning and statistics.Comment: 96 pages, 14 figures, 333 reference