Generative Mixture of Networks

A generative model based on training deep architectures is proposed. The model consists of K networks that are trained together to learn the underlying distribution of a given data set. The process starts with dividing the input data into K clusters and feeding each of them into a separate network. After few iterations of training networks separately, we use an EM-like algorithm to train the networks together and update the clusters of the data. We call this model Mixture of Networks. The provided model is a platform that can be used for any deep structure and be trained by any conventional objective function for distribution modeling. As the components of the model are neural networks, it has high capability in characterizing complicated data distributions as well as clustering data. We apply the algorithm on MNIST hand-written digits and Yale face datasets. We also demonstrate the clustering ability of the model using some real-world and toy examples.Comment: 9 page

Holographic Two-Point Functions in Conformal Gravity

In this paper we compute the holographic two-point functions of four dimensional conformal gravity. Precisely we calculate the two-point functions for Energy- Momentum (EM) and Partially Massless Response (PMR) operators that have been identified as two response functions for two independent sources in the dual CFT. The correlation function of EM with PMR tensors turns out to be zero which is expected according to the conformal symmetry. The two-point function of EM is that of a transverse and traceless tensor, and the two-point function of PMR which is a traceless operator contains two distinct parts, one for a transverse-traceless tensor operator and another one for a vector field, both of which fulfill criteria of a CFT. We also discuss about the unitarity of the theory.Comment: 42 pages. Published version in JHE

Distributed k-ary System: Algorithms for Distributed Hash Tables

This dissertation presents algorithms for data structures called distributed hash tables (DHT) or structured overlay networks, which are used to build scalable self-managing distributed systems. The provided algorithms guarantee lookup consistency in the presence of dynamism: they guarantee consistent lookup results in the presence of nodes joining and leaving. Similarly, the algorithms guarantee that routing never fails while nodes join and leave. Previous algorithms for lookup consistency either suffer from starvation, do not work in the presence of failures, or lack proof of correctness. Several group communication algorithms for structured overlay networks are presented. We provide an overlay broadcast algorithm, which unlike previous algorithms avoids redundant messages, reaching all nodes in O(log n) time, while using O(n) messages, where n is the number of nodes in the system. The broadcast algorithm is used to build overlay multicast. We introduce bulk operation, which enables a node to efficiently make multiple lookups or send a message to all nodes in a specified set of identifiers. The algorithm ensures that all specified nodes are reached in O(log n) time, sending maximum O(log n) messages per node, regardless of the input size of the bulk operation. Moreover, the algorithm avoids sending redundant messages. Previous approaches required multiple lookups, which consume more messages and can render the initiator a bottleneck. Our algorithms are used in DHT-based storage systems, where nodes can do thousands of lookups to fetch large files. We use the bulk operation algorithm to construct a pseudo-reliable broadcast algorithm. Bulk operations can also be used to implement efficient range queries. Finally, we describe a novel way to place replicas in a DHT, called symmetric replication, that enables parallel recursive lookups. Parallel lookups are known to reduce latencies. However, costly iterative lookups have previously been used to do parallel lookups. Moreover, joins or leaves only require exchanging O(1) messages, while other schemes require at least log(f) messages for a replication degree of f. The algorithms have been implemented in a middleware called the Distributed k-ary System (DKS), which is briefly described

Handling Network Partitions and Mergers in Structured Overlay Networks

Structured overlay networks form a major class of peer-to-peer systems, which are touted for their abilities to scale, tolerate failures, and self-manage. Any long-lived Internet-scale distributed system is destined to face network partitions. Although the problem of network partitions and mergers is highly related to fault-tolerance and self-management in large-scale systems, it has hardly been studied in the context of structured peer-to-peer systems. These systems have mainly been studied under churn (frequent joins/failures), which as a side effect solves the problem of network partitions, as it is similar to massive node failures. Yet, the crucial aspect of network mergers has been ignored. In fact, it has been claimed that ring-based structured overlay networks, which constitute the majority of the structured overlays, are intrinsically ill-suited for merging rings. In this paper, we present an algorithm for merging multiple similar ring-based overlays when the underlying network merges. We examine the solution in dynamic conditions, showing how our solution is resilient to churn during the merger, something widely believed to be difficult or impossible. We evaluate the algorithm for various scenarios and show that even when falsely detecting a merger, the algorithm quickly terminates and does not clutter the network with many messages. The algorithm is flexible as the tradeoff between message complexity and time complexity can be adjusted by a parameter

Symmetric Replication for Structured Peer-to-Peer Systems

Structured peer-to-peer systems rely on replication as a basic means to provide fault-tolerance in presence of high churn. Most select replicas using either multiple hash functions, successor-lists, or leaf-sets. We show that all three alternatives have limitations. We present and provide full algorithmic speci¯cation for a generic replication scheme called symmetric replication which only needs O(1) message for every join and leave operation to maintain any replication degree. The scheme is applicable to all existing structured peer-to-peer systems, and can be implemented on-top of any DHT. The scheme has been implemented in our DKS system, and is used to do load-balancing, end-to-end fault-tolerance, and to increase the security by using distributed voting. We outline an extension to the scheme, implemented in DKS, which adds routing proximity to reduce latencies. The scheme is particularly suitable for use with erasure codes, as it can be used to fetch a random subset of the replicas for decoding