Wireless ad-hoc networks: Strategies and Scaling laws for the fixed SNR regime

This paper deals with throughput scaling laws for random ad-hoc wireless networks in a rich scattering environment. We develop schemes to optimize the ratio, $\rho(n)$ of achievable network sum capacity to the sum of the point-to-point capacities of source-destinations pairs operating in isolation. For fixed SNR networks, i.e., where the worst case SNR over the source-destination pairs is fixed independent of $n$, we show that collaborative strategies yield a scaling law of $\rho(n) = {\cal O}(\frac{1}{n^{1/3}})$ in contrast to multi-hop strategies which yield a scaling law of $\rho(n) = {\cal O}(\frac{1}{\sqrt{n}})$. While, networks where worst case SNR goes to zero, do not preclude the possibility of collaboration, multi-hop strategies achieve optimal throughput. The plausible reason is that the gains due to collaboration cannot offset the effect of vanishing receive SNR. This suggests that for fixed SNR networks, a network designer should look for network protocols that exploit collaboration. The fact that most current networks operate in a fixed SNR interference limited environment provides further motivation for considering this regime.Comment: 26 pages single column, submitted to Transactions on Information Theor

Robust Hydraulic Fracture Monitoring (HFM) of Multiple Time Overlapping Events Using a Generalized Discrete Radon Transform

In this work we propose a novel algorithm for multiple-event localization for Hydraulic Fracture Monitoring (HFM) through the exploitation of the sparsity of the observed seismic signal when represented in a basis consisting of space time propagators. We provide explicit construction of these propagators using a forward model for wave propagation which depends non-linearly on the problem parameters - the unknown source location and mechanism of fracture, time and extent of event, and the locations of the receivers. Under fairly general assumptions and an appropriate discretization of these parameters we first build an over-complete dictionary of generalized Radon propagators and assume that the data is well represented as a linear superposition of these propagators. Exploiting this structure we propose sparsity penalized algorithms and workflow for super-resolution extraction of time overlapping multiple seismic events from single well data

Methods for Large Scale Hydraulic Fracture Monitoring

In this paper we propose computationally efficient and robust methods for estimating the moment tensor and location of micro-seismic event(s) for large search volumes. Our contribution is two-fold. First, we propose a novel joint-complexity measure, namely the sum of nuclear norms which while imposing sparsity on the number of fractures (locations) over a large spatial volume, also captures the rank-1 nature of the induced wavefield pattern. This wavefield pattern is modeled as the outer-product of the source signature with the amplitude pattern across the receivers from a seismic source. A rank-1 factorization of the estimated wavefield pattern at each location can therefore be used to estimate the seismic moment tensor using the knowledge of the array geometry. In contrast to existing work this approach allows us to drop any other assumption on the source signature. Second, we exploit the recently proposed first-order incremental projection algorithms for a fast and efficient implementation of the resulting optimization problem and develop a hybrid stochastic & deterministic algorithm which results in significant computational savings.Comment: arXiv admin note: text overlap with arXiv:1305.006

Algorithms for item categorization based on ordinal ranking data

We present a new method for identifying the latent categorization of items based on their rankings. Complimenting a recent work that uses a Dirichlet prior on preference vectors and variational inference, we show that this problem can be effectively dealt with using existing community detection algorithms, with the communities corresponding to item categories. In particular we convert the bipartite ranking data to a unipartite graph of item affinities, and apply community detection algorithms. In this context we modify an existing algorithm - namely the label propagation algorithm to a variant that uses the distance between the nodes for weighting the label propagation - to identify the categories. We propose and analyze a synthetic ordinal ranking model and show its relation to the recently much studied stochastic block model. We test our algorithms on synthetic data and compare performance with several popular community detection algorithms. We also test the method on real data sets of movie categorization from the Movie Lens database. In all of the cases our algorithm is able to identify the categories for a suitable choice of tuning parameter.Comment: To appear in IEEE Allerton conference on computing, communications and control, 201