Search

We study the problem of recovering the common $k$-sized support of a set of $n$ samples of dimension $d$, using $m$ noisy linear measurements per sample. Most prior work has focused on the case when $m$ exceeds $k$, in which case $n$ of the order $(k/m)\log(d/k)$ is both necessary and sufficient. Thus, in this regime, only the total number of measurements across the samples matter, and there is not much benefit in getting more than $k$ measurements per sample. In the measurement-constrained regime where we have access to fewer than $k$ measurements per sample, we show an upper bound of $O((k^{2}/m^{2})\log d)$ on the sample complexity for successful support recovery when $m\ge 2\log d$. Along with the lower bound from our previous work, this shows a phase transition for the sample complexity of this problem around $k/m=1$. In fact, our proposed algorithm is sample-optimal in both the regimes. It follows that, in the $m\ll k$ regime, multiple measurements from the same sample are more valuable than measurements from different samples.

In this work, we consider the controllability of a discrete-time linear dynamical system with sparse control inputs. Sparsity constraints on the input arises naturally in networked systems, where activating each input variable adds to the cost of control. We derive algebraic necessary and sufficient conditions for ensuring controllability of a system with an arbitrary transfer matrix. The derived conditions can be verified in polynomial time complexity, unlike the more traditional Kalman-type rank tests. Further, we characterize the minimum number of input vectors required to satisfy the derived conditions for controllability. Finally, we present a generalized Kalman decomposition-like procedure that separates the state-space into subspaces corresponding to sparse-controllable and sparse-uncontrollable parts. These results form a theoretical basis for designing networked linear control systems with sparse inputs., Comment: 11 pages

Data samples from $\mathbb{R}^{d}$ with a common support of size $k$ are accessed through $m$ random linear projections (measurements) per sample. It is well-known that roughly $k$ measurements from a single sample are sufficient to recover the support. In the multiple sample setting, do $k$ overall measurements still suffice when only $m$ measurements per sample are allowed, with $m

In this paper, we present a computationally efficient sparse signal recovery scheme using Deep Neural Networks (DNN). The architecture of the introduced neural network is inspired from sparse Bayesian learning (SBL) and named as Learned-SBL (L-SBL). We design a common architecture to recover sparse as well as block sparse vectors from single measurement vector (SMV) or multiple measurement vectors (MMV) depending on the nature of the training data. In the MMV model, the L-SBL network can be trained to learn any underlying sparsity pattern among the vectors including joint sparsity, block sparsity, etc. In particular, for block sparse recovery, learned-SBL does not require any prior knowledge of block boundaries. In each layer of the L-SBL, an estimate of the signal covariance matrix is obtained as the output of a neural network. Then a maximum a posteriori (MAP) estimator of the unknown sparse vector is implemented with non-trainable parameters. In many applications, the measurement matrix may be time-varying. The existing DNN based sparse signal recovery schemes demand the retraining of the neural network using current measurement matrix. The architecture of L-SBL allows it to accept the measurement matrix as an input to the network, and thereby avoids the need for retraining. We also evaluate the performance of Learned-SBL in the detection of an extended target using a multiple-input multiple-output (MIMO) radar. Simulation results illustrate that the proposed approach offers superior sparse recovery performance compared to the state-of-the-art methods., Comment: 13 pages, 22 figures

Clinical biosensors with low detection limit hold significant promise in the early diagnosis of debilitating diseases. Recent progress in sensor development has led to the demonstration of detection capable of detecting target molecules even down to single-molecule level. One crucial performance parameter which is not adequately discussed is the issue of measurement fidelity in such sensors. We define measurement fidelity based on the false positive rate of the system as we expect systems with higher sensitivity to concomitantly respond more to interfering molecules thus increasing the false-positive rates. We present a model which allows us to estimate the limit of detection of a biosensor system constrained by a specified false-positive rate. Two major results emerging from our model is that a) there is a lower bound to the detection limit for a target molecule determined by the variation in the concentration of background molecules interfering with the molecular recognition process and b) systems which use a secondary label, such as a fluorophore, can achieve lower detection limits for a given false positive rate. We also present data collected from literature to support our model. The insights from our model will be useful in the systematic design of future clinical biosensors to achieve relevant detection limits with assured fidelity., Comment: 12 pages, 4 figures

We investigate the conditions at which high-mode magnetohydrodynamic (MHD) waves propagating in a spinning solar macrospicule can become unstable with respect to the Kelvin--Helmholtz instability (KHI). We consider the macrospicule as a weakly twisted cylindrical magnetic flux tube moving along and rotating around its axis. Our study is based on the dispersion relation (in complex variables) of MHD waves obtained from the linearized MHD equations of an incompressible plasma for the macrospicule and cool ($\beta = 0$, rate of the plasma to the magnetic pressure) plasma for its environment. This dispersion equation is solved numerically at appropriate input parameters to find out an instability region or window that accommodates suitable unstable wavelengths on the order of the macro\-spicule width. It is established that an $m = 52$ MHD mode propagating in a macro\-spicule with width of $6$~Mm, axial velocity of $75$~km\,s$^{-1}$, and rotating one of $40$~km\,s$^{-1}$ can become unstable against the KHI with instability growth times of $2.2$ and $0.57$~min at $3$ and $5$~Mm unstable wavelengths, respectively. These growth times are much shorter than the macrospicule lifetime, which lasts about $15$~min. An increase or decease in the width of the jet would change the KHI growth times, which remain more or less on the same order when they are evaluated at wavelengths equal to the width or radius of the macrospicule. It is worth noting that the excited MHD modes are super-Alfv\'enic waves. A change in the background magnetic field can lead to another MHD mode number $m$ that ensures the required instability window., Comment: 21 pages, 4 figures, and 3 tables

Employing the projected-Hartree-Fock-Bogoliubov (PHFB) model in conjunction with four different parametrizations of pairing plus multipolar effective two body interaction and three different parametrizations of Jastrow short range correlations, nuclear transition matrix elements for the neutrinoless double-$\beta $ decay of $^{94,96}$Zr, $^{100}$Mo, $^{110}$Pd, $^{128,130}$Te and $^{150}$Nd isotopes are calculated within mechanisms involving light Majorana neutrino mass and right handed current. Statistically, model specific uncertainties in sets of twelve nuclear transition matrix elements are estimated by calculating the averages along with the standard deviations. For the considered nuclei, \ the most stringent extracted on-axis limits on the effective light Majorana neutrino mass $$, the effective weak coupling of right-handed leptonic current with right-handed hadronic current $<\lambda >$, and the effective weak coupling of right-handed leptonic current with left-handed hadronic current $<\eta >$ \ from the observed limit on half-life $T_{1/2}^{0\nu }$ of $^{130}$Te isotope are $0.33$ eV, $4.57\times 10^{-7}$ and $4.72\times 10^{-9}$, respectively.

A large filament composed principally of two sections erupted sequentially in the southern hemisphere on January 26 2016. The central, thick part of the northern section was first lifted up and lead to the eruption of the full filament. This event was observed in H-alpha with GONG and CLIMSO, and in ultraviolet (UV) with the AIA/SDO imager. The aim of the paper is to relate the photospheric motions below the filament and its environment to the eruption of the filament. An analysis of the photospheric motions using SDO/HMI continuum images with the coherent structure tracking (CST) algorithm developed to track granules, as well as large-scale photospheric flows, has been performed. The supergranule pattern is clearly visible outside the filament channel but difficult to detect inside because the modulus of the vector velocity is reduced in the filament channel, mainly in the magnetized areas. The horizontal photospheric flows are strong on the west side of the filament channel and oriented towards the filament. The ends of the filament sections are found in areas of concentration of corks. Whirled flows are found locally around the feet. The strong horizontal flows with an opposite direction to the differential rotation create strong shear and convergence along the magnetic polarity inversion line (PIL) in the filament channel. The filament has been destabilized by the converging flows, which initiate an ascent of the middle section of the filament until the filament reaches the critical height of the torus instability inducing, consequently, the eruption. The "n" decay index indicated an altitude of 60 Mm for the critical height. It is conjectured that the convergence along the PIL is due to the large-scale size cells of convection that transport the magnetic field to their borders., Comment: 10 pages, 9 figures

In this paper, we present the observations of two successive fast-mode extreme ultraviolet (EUV) wave events observed on 2016 July 23. Both fast-mode waves were observed by the Atmospheric Imaging Assembly (AIA) instrument on board the Solar Dynamics Observatory (SDO) satellite, with a traveling speed of ~ 675 and 640 km/s, respectively. These two wave events were associated with two filament eruptions and two GOES M-class solar flares from the NOAA active region 12565, which was located near the western limb. The EUV waves mainly move toward the south direction. We observed the interaction of the EUV waves with a helmet streamer further away in the south. When either or one of the EUV waves penetrates into the helmet streamer, a slowly propagating wave with a traveling speed of ~ 150 km/s is observed along the streamer. We suggest that the slowly-moving waves are slow-mode waves, and interpret this phenomenon as the magnetohydrodynamic (MHD) wave mode conversion from the fast mode to the slow mode. Besides, we observed several stationary fronts in the north and south of the source region., Comment: 17 pages, 9 figures, Accepted for publication in ApJ

Practical energy harvesting (EH) based communication systems typically use a battery to temporarily store the harvested energy prior to its use for communication. The batteries can be damaged when they are repeatedly charged (discharged) after being partially discharged (charged), overcharged or deeply discharged. This motivates the cycle constraint which says that a battery must be charged (discharged) only after it is sufficiently discharged (charged). We also assume Bernoulli energy arrivals, and a half-duplex constraint due to which the batteries are not charged and discharged simultaneously. In this context, we study EH communication systems with: (a) a single-battery with capacity 2B units and (b) dual-batteries, each having capacity of B units. The aim is to obtain the best possible long-term average throughputs and throughput regions in point-to-point (P2P) channels and multiple access channels (MAC), respectively. For the P2P channel, we obtain an analytical optimal solution in the single-battery case, and propose optimal and sub-optimal power allocation policies for the dual-battery case. We extend these policies to obtain achievable throughput regions in MACs by jointly allocating rates and powers. From numerical simulations, we find that the optimal throughput in the dual-battery case is significantly higher than that in the single-battery case, although the total storage capacity in both cases is 2B units. Further, in the proposed policies, the largest throughput region in the single-battery case is contained within that of the dual-battery case., Comment: A single battery case is added and its performance is compared with that of the dual-battery case, with additional simulation results