Compressive Inverse Scattering II. SISO Measurements with Born scatterers

Inverse scattering methods capable of compressive imaging are proposed and analyzed. The methods employ randomly and repeatedly (multiple-shot) the single-input-single-output (SISO) measurements in which the probe frequencies, the incident and the sampling directions are related in a precise way and are capable of recovering exactly scatterers of sufficiently low sparsity. For point targets, various sampling techniques are proposed to transform the scattering matrix into the random Fourier matrix. The results for point targets are then extended to the case of localized extended targets by interpolating from grid points. In particular, an explicit error bound is derived for the piece-wise constant interpolation which is shown to be a practical way of discretizing localized extended targets and enabling the compressed sensing techniques. For distributed extended targets, the Littlewood-Paley basis is used in analysis. A specially designed sampling scheme then transforms the scattering matrix into a block-diagonal matrix with each block being the random Fourier matrix corresponding to one of the multiple dyadic scales of the extended target. In other words by the Littlewood-Paley basis and the proposed sampling scheme the different dyadic scales of the target are decoupled and therefore can be reconstructed scale-by-scale by the proposed method. Moreover, with probes of any single frequency \om the coefficients in the Littlewood-Paley expansion for scales up to \om/(2\pi) can be exactly recovered.Comment: Add a new section (Section 3) on localized extended target

Lower Bounds for Structuring Unreliable Radio Networks

In this paper, we study lower bounds for randomized solutions to the maximal independent set (MIS) and connected dominating set (CDS) problems in the dual graph model of radio networks---a generalization of the standard graph-based model that now includes unreliable links controlled by an adversary. We begin by proving that a natural geographic constraint on the network topology is required to solve these problems efficiently (i.e., in time polylogarthmic in the network size). We then prove the importance of the assumption that nodes are provided advance knowledge of their reliable neighbors (i.e, neighbors connected by reliable links). Combined, these results answer an open question by proving that the efficient MIS and CDS algorithms from [Censor-Hillel, PODC 2011] are optimal with respect to their dual graph model assumptions. They also provide insight into what properties of an unreliable network enable efficient local computation.Comment: An extended abstract of this work appears in the 2014 proceedings of the International Symposium on Distributed Computing (DISC

Final Report: Efficient Databases for MPC Microdata

The purpose of this grant was to develop the theory and practice of high-performance databases for massive streamed datasets. Over the last three years, we have developed fast indexing technology, that is, technology for rapidly ingesting data and storing that data so that it can be efficiently queried and analyzed. During this project we developed the technology so that high-bandwidth data streams can be indexed and queried efficiently. Our technology has been proven to work data sets composed of tens of billions of rows when the data streams arrives at over 40,000 rows per second. We achieved these numbers even on a single disk driven by two cores. Our work comprised (1) new write-optimized data structures with better asymptotic complexity than traditional structures, (2) implementation, and (3) benchmarking. We furthermore developed a prototype of TokuFS, a middleware layer that can handle microdata I/O packaged up in an MPI-IO abstraction

On the Convergence of the Born Series in Optical Tomography with Diffuse Light

We provide a simple sufficient condition for convergence of Born series in the forward problem of optical diffusion tomography. The condition does not depend on the shape or spatial extent of the inhomogeneity but only on its amplitude.Comment: 23 pages, 7 figures, submitted to Inverse Problem

Convergence and Stability of the Inverse Scattering Series for Diffuse Waves

We analyze the inverse scattering series for diffuse waves in random media. In previous work the inverse series was used to develop fast, direct image reconstruction algorithms in optical tomography. Here we characterize the convergence, stability and approximation error of the serie

Don't Thrash: How to Cache Your Hash on Flash

This paper presents new alternatives to the well-known Bloom filter data structure. The Bloom filter, a compact data structure supporting set insertion and membership queries, has found wide application in databases, storage systems, and networks. Because the Bloom filter performs frequent random reads and writes, it is used almost exclusively in RAM, limiting the size of the sets it can represent. This paper first describes the quotient filter, which supports the basic operations of the Bloom filter, achieving roughly comparable performance in terms of space and time, but with better data locality. Operations on the quotient filter require only a small number of contiguous accesses. The quotient filter has other advantages over the Bloom filter: it supports deletions, it can be dynamically resized, and two quotient filters can be efficiently merged. The paper then gives two data structures, the buffered quotient filter and the cascade filter, which exploit the quotient filter advantages and thus serve as SSD-optimized alternatives to the Bloom filter. The cascade filter has better asymptotic I/O performance than the buffered quotient filter, but the buffered quotient filter outperforms the cascade filter on small to medium data sets. Both data structures significantly outperform recently-proposed SSD-optimized Bloom filter variants, such as the elevator Bloom filter, buffered Bloom filter, and forest-structured Bloom filter. In experiments, the cascade filter and buffered quotient filter performed insertions 8.6-11 times faster than the fastest Bloom filter variant and performed lookups 0.94-2.56 times faster.Comment: VLDB201

Multivariate MR Biomarkers Better Predict Cognitive Dysfunction in Mouse Models of Alzheimers Disease

To understand multifactorial conditions such as Alzheimers disease (AD) we need brain signatures that predict the impact of multiple pathologies and their interactions. To help uncover the relationships between brain circuits and cognitive markers we have used mouse models that represent, at least in part, the complex interactions altered in AD. In particular, we aimed to understand the relationship between vulnerable brain circuits and memory deficits measured in the Morris water maze, and we tested several predictive modeling approaches. We used in vivo manganese enhanced MRI voxel based analyses to reveal regional differences in volume (morphometry), signal intensity (activity), and magnetic susceptibility (iron deposition, demyelination). These regions included the hippocampus, olfactory areas, entorhinal cortex and cerebellum. The image based properties of these regions were used to predict spatial memory. We next used eigenanatomy, which reduces dimensionality to produce sets of regions that explain the variance in the data. For each imaging marker, eigenanatomy revealed networks underpinning a range of cognitive functions including memory, motor function, and associative learning. Finally, the integration of multivariate markers in a supervised sparse canonical correlation approach outperformed single predictor models and had significant correlates to spatial memory. Among a priori selected regions, the fornix also provided good predictors, raising the possibility of investigating how disease propagation within brain networks leads to cognitive deterioration. Our results support that modeling approaches integrating multivariate imaging markers provide sensitive predictors of AD-like behaviors. Such strategies for mapping brain circuits responsible for behaviors may help in the future predict disease progression, or response to interventions.Comment: 23 pages, 3 Tables, 6 Figures; submitted for publicatio

Prediction of the Onset of Disturbed Eating Behavior in Adolescent Girls With Type 1 Diabetes

OBJECTIVE—The purpose of this study was to identify predictors of the onset of disturbed eating behavior (DEB) in adolescent girls with type 1 diabetes

Adversarial Analyses of Window Backoff Strategies for Simple Multiple-Access Channels

Backoff strategies have typically been analyzed by making statistical assumptions on the distribution of problem inputs. Although these analyses have provided valuable insights into the efficacy of various backoff strategies, they leave open the question as to which backoff algorithms perform best in the worst case or on inputs, such as bursty inputs, that are not covered by the statistical models. This paper analyzes randomized backoff strategies using worst-case assumptions on the inputs. Specifically, we analyze algorithms for simple multiple-access channels, where the only feedback from each attempt to send a packet is a single bit indicating whether the transmission succeeded or the packet collided with another packet. We analyze a class of strategies, called window strategies, where each packet partitions time into a sequence (W₁, W₂,...) of windows. Within each window, the packet makes an access attempt during a single randomly selected slot. If its transmission is unsuccessful, it waits for its slot in the next window before retrying. We use delay-sequence arguments to show that for the batch problem, in which n packets all arrive at time 0, if every window has size W = Θ(n), then with high probability, all packets successfully transmit with makespan n lg lg n ± O(n). We use this result to analyze window backoff strategies with varying window sizes. Specifically, we show that the familiar binary exponential backoff algorithm, where Wk = Θ(2k), has makespan Θ(n lg n), and that more generally, for any constant r > 1, the r-exponential backoff algorithm in which Wk = Θ(rk) has makespan Θ(n lglg rn). We also show that for any constant r > 1, the r-polynomial backoff algorithm, in which Wk = Θ(kr), has makespan Θ((n/lg n)¹⁺¹/r). All of these batch strategies are monotonic, in the sense that the window size monotonically increases over time. We exhibit a monotonic backoff algorithm that achieves makespan Θ(n lg lg n/lg lg lg n). We prove that this algorithm, whose backoff is superpolynomial and subexponential, is optimal over all monotonic backoff schemes. In addition, we exhibit a simple backoff/backon algorithm, having window sizes that vary nonmonotonically according to a "sawtooth" pattern, that achieves the optimal makespan of Θ(n). We study the online setting using an adversarial queueing model. We define a (λ,T)-stream to be an input stream of packets in which at most n = λT packets arrive during any time interval of size T. In this model, to evaluate a given backoff algorithm (which does not know λ or T), we analyze the worst-case behavior of the algorithm over the class of (λ,T)-streams. Our results for the online setting focus on exponential backoff. We show that for any arrival rate λ, there exists a sufficiently large interval size T such that the throughput goes to 0 for some (λ,T)-stream. Moreover, there exists a sufficiently large constant c such that for any interval size T, if λ ⥠c lg lg n/lg n, the system is unstable in the sense that the arrival rate exceeds the throughput in the worst case. If, on the other hand, we have λ ⤠c/lg n for a sufficiently small constant c, then the system is stable. Surprisingly, the algorithms that guarantee smaller makespans in the batch setting require lower arrival rates to achieve stability than does exponential backoff, but when they are stable, they have better response times.Singapore-MIT Alliance (SMA

Thermoacoustic tomography with detectors on an open curve: an efficient reconstruction algorithm

Practical applications of thermoacoustic tomography require numerical inversion of the spherical mean Radon transform with the centers of integration spheres occupying an open surface. Solution of this problem is needed (both in 2-D and 3-D) because frequently the region of interest cannot be completely surrounded by the detectors, as it happens, for example, in breast imaging. We present an efficient numerical algorithm for solving this problem in 2-D (similar methods are applicable in the 3-D case). Our method is based on the numerical approximation of plane waves by certain single layer potentials related to the acquisition geometry. After the densities of these potentials have been precomputed, each subsequent image reconstruction has the complexity of the regular filtration backprojection algorithm for the classical Radon transform. The peformance of the method is demonstrated in several numerical examples: one can see that the algorithm produces very accurate reconstructions if the data are accurate and sufficiently well sampled, on the other hand, it is sufficiently stable with respect to noise in the data