44 research outputs found
Stream Distributed Coded Computing
The emerging large-scale and data-hungry algorithms require the computations
to be delegated from a central server to several worker nodes. One major
challenge in the distributed computations is to tackle delays and failures
caused by the stragglers. To address this challenge, introducing efficient
amount of redundant computations via distributed coded computation has received
significant attention. Recent approaches in this area have mainly focused on
introducing minimum computational redundancies to tolerate certain number of
stragglers. To the best of our knowledge, the current literature lacks a
unified end-to-end design in a heterogeneous setting where the workers can vary
in their computation and communication capabilities. The contribution of this
paper is to devise a novel framework for joint scheduling-coding, in a setting
where the workers and the arrival of stream computational jobs are based on
stochastic models. In our initial joint scheme, we propose a systematic
framework that illustrates how to select a set of workers and how to split the
computational load among the selected workers based on their differences in
order to minimize the average in-order job execution delay. Through
simulations, we demonstrate that the performance of our framework is
dramatically better than the performance of naive method that splits the
computational load uniformly among the workers, and it is close to the ideal
performance
Adaptive Causal Network Coding with Feedback for Multipath Multi-hop Communications
We propose a novel multipath multi-hop adaptive and causal random linear
network coding (AC-RLNC) algorithm with forward error correction. This
algorithm generalizes our joint optimization coding solution for point-to-point
communication with delayed feedback. AC-RLNC is adaptive to the estimated
channel condition, and is causal, as the coding adjusts the retransmission
rates using a priori and posteriori algorithms. In the multipath network, to
achieve the desired throughput and delay, we propose to incorporate an adaptive
packet allocation algorithm for retransmission, across the available resources
of the paths. This approach is based on a discrete water filling algorithm,
i.e., bit-filling, but, with two desired objectives, maximize throughput and
minimize the delay. In the multipath multi-hop setting, we propose a new
decentralized balancing optimization algorithm. This balancing algorithm
minimizes the throughput degradation, caused by the variations in the channel
quality of the paths at each hop. Furthermore, to increase the efficiency, in
terms of the desired objectives, we propose a new selective recoding method at
the intermediate nodes. We derive bounds on the throughput and the mean and
maximum in order delivery delay of AC-RLNC, both in the multipath and multipath
multi-hop case. In the multipath case, we prove that in the non-asymptotic
regime, the suggested code may achieve more than 90% of the channel capacity
with zero error probability. In the multipath multi-hop case, the balancing
procedure is proven to be optimal with regards to the achieved rate. Through
simulations, we demonstrate that the performance of our adaptive and causal
approach, compared to selective repeat (SR)-ARQ protocol, is capable of gains
up to a factor two in throughput and a factor of more than three in delay
A Kernel-based Approach to Diffusion Tensor and Fiber Clustering in the Human Skeletal Muscle
In this report, we present a kernel-based approach to the clustering of diffusion tensors in images of the human skeletal muscle. Based on the physical intuition of tensors as a means to represent the uncertainty of the position of water protons in the tissues, we propose a Mercer (i.e. positive definite) kernel over the tensor space where both spatial and diffusion information are taken into account. This kernel highlights implicitly the connectivity along fiber tracts. We show that using this kernel in a kernel-PCA setting compounded with a landmark-Isomap embedding and k-means clustering provides a tractable framework for tensor clustering. We extend this kernel to deal with fiber tracts as input using the multi-instance kernel by considering the fiber as set of tensors centered in the sampled points of the tract. The obtained kernel reflects not only interactions between points along fiber tracts, but also the interactions between diffusion tensors. We give an interpretation of the obtained kernel as a comparison of soft fiber representations and show that it amounts to a generalization of the Gaussian kernel Correlation. As in the tensor case, we use the kernel-PCA setting and k-means for grouping of fiber tracts. This unsupervised method is further extended by way of an atlas-based registration of diffusion-free images, followed by a classification of fibers based on non-linear kernel Support Vector Machines (SVMs) and kernel diffusion. The experimental results on a dataset of diffusion tensor images of the calf muscle of 25 patients (of which 5 affected by myopathies, i.e. neuromuscular diseases) show the potential of our method in segmenting the calf in anatomically relevant regions both at the tensor and fiber level