Exploiting the Synergy Between Gossiping and Structured Overlays

In this position paper we argue for exploiting the synergy between gossip-based algorithms and structured overlay networks (SON). These two strands of research have both aimed at building fault-tolerant, dynamic, self-managing, and large-scale distributed systems. Despite the common goals, the two areas have, however, been relatively isolated. We focus on three problem domains where there is an untapped potential of using gossiping combined with SONs. We argue for applying gossip-based membership for ring-based SONs---such as Chord and Bamboo---to make them handle partition mergers and loopy networks. We argue that small world SONs---such as Accordion and Mercury---are specifically well-suited for gossip-based membership management. The benefits would be better graph-theoretic properties. Finally, we argue that gossip-based algorithms could use the overlay constructed by SONs. For example, many unreliable broadcast algorithms for SONs could be augmented with anti-entropy protocols. Similarly, gossip-based aggregation could be used in SONs for network size estimation and load-balancing purposes

On the equivalence between graph isomorphism testing and function approximation with GNNs

Graph neural networks (GNNs) have achieved lots of success on graph-structured data. In the light of this, there has been increasing interest in studying their representation power. One line of work focuses on the universal approximation of permutation-invariant functions by certain classes of GNNs, and another demonstrates the limitation of GNNs via graph isomorphism tests. Our work connects these two perspectives and proves their equivalence. We further develop a framework of the representation power of GNNs with the language of sigma-algebra, which incorporates both viewpoints. Using this framework, we compare the expressive power of different classes of GNNs as well as other methods on graphs. In particular, we prove that order-2 Graph G-invariant networks fail to distinguish non-isomorphic regular graphs with the same degree. We then extend them to a new architecture, Ring-GNNs, which succeeds on distinguishing these graphs and provides improvements on real-world social network datasets

Improving Surgical Training Phantoms by Hyperrealism: Deep Unpaired Image-to-Image Translation from Real Surgeries

Current `dry lab' surgical phantom simulators are a valuable tool for surgeons which allows them to improve their dexterity and skill with surgical instruments. These phantoms mimic the haptic and shape of organs of interest, but lack a realistic visual appearance. In this work, we present an innovative application in which representations learned from real intraoperative endoscopic sequences are transferred to a surgical phantom scenario. The term hyperrealism is introduced in this field, which we regard as a novel subform of surgical augmented reality for approaches that involve real-time object transfigurations. For related tasks in the computer vision community, unpaired cycle-consistent Generative Adversarial Networks (GANs) have shown excellent results on still RGB images. Though, application of this approach to continuous video frames can result in flickering, which turned out to be especially prominent for this application. Therefore, we propose an extension of cycle-consistent GANs, named tempCycleGAN, to improve temporal consistency.The novel method is evaluated on captures of a silicone phantom for training endoscopic reconstructive mitral valve procedures. Synthesized videos show highly realistic results with regard to 1) replacement of the silicone appearance of the phantom valve by intraoperative tissue texture, while 2) explicitly keeping crucial features in the scene, such as instruments, sutures and prostheses. Compared to the original CycleGAN approach, tempCycleGAN efficiently removes flickering between frames. The overall approach is expected to change the future design of surgical training simulators since the generated sequences clearly demonstrate the feasibility to enable a considerably more realistic training experience for minimally-invasive procedures.Comment: 8 pages, accepted at MICCAI 2018, supplemental material at https://youtu.be/qugAYpK-Z4

Image Augmentation using Radial Transform for Training Deep Neural Networks

Deep learning models have a large number of free parameters that must be estimated by efficient training of the models on a large number of training data samples to increase their generalization performance. In real-world applications, the data available to train these networks is often limited or imbalanced. We propose a sampling method based on the radial transform in a polar coordinate system for image augmentation to facilitate the training of deep learning models from limited source data. This pixel-wise transform provides representations of the original image in the polar coordinate system by generating a new image from each pixel. This technique can generate radial transformed images up to the number of pixels in the original image to increase the diversity of poorly represented image classes. Our experiments show improved generalization performance in training deep convolutional neural networks with radial transformed images.Comment: This paper is accepted for presentation at IEEE International Conference on Acoustics, Speech and Signal Processing (IEEE ICASSP), 201

Tight Lower Bounds for Greedy Routing in Higher-Dimensional Small-World Grids

We consider Kleinberg's celebrated small world graph model (Kleinberg, 2000), in which a D-dimensional grid {0,...,n-1}^D is augmented with a constant number of additional unidirectional edges leaving each node. These long range edges are determined at random according to a probability distribution (the augmenting distribution), which is the same for each node. Kleinberg suggested using the inverse D-th power distribution, in which node v is the long range contact of node u with a probability proportional to ||u-v||^(-D). He showed that such an augmenting distribution allows to route a message efficiently in the resulting random graph: The greedy algorithm, where in each intermediate node the message travels over a link that brings the message closest to the target w.r.t. the Manhattan distance, finds a path of expected length O(log^2 n) between any two nodes. In this paper we prove that greedy routing does not perform asymptotically better for any uniform and isotropic augmenting distribution, i.e., the probability that node u has a particular long range contact v is independent of the labels of u and v and only a function of ||u-v||. In order to obtain the result, we introduce a novel proof technique: We define a budget game, in which a token travels over a game board, while the player manages a "probability budget". In each round, the player bets part of her remaining probability budget on step sizes. A step size is chosen at random according to a probability distribution of the player's bet. The token then makes progress as determined by the chosen step size, while some of the player's bet is removed from her probability budget. We prove a tight lower bound for such a budget game, and then obtain a lower bound for greedy routing in the D-dimensional grid by a reduction