Sparsity and Parallel Acquisition: Optimal Uniform and Nonuniform Recovery Guarantees

The problem of multiple sensors simultaneously acquiring measurements of a single object can be found in many applications. In this paper, we present the optimal recovery guarantees for the recovery of compressible signals from multi-sensor measurements using compressed sensing. In the first half of the paper, we present both uniform and nonuniform recovery guarantees for the conventional sparse signal model in a so-called distinct sensing scenario. In the second half, using the so-called sparse and distributed signal model, we present nonuniform recovery guarantees which effectively broaden the class of sensing scenarios for which optimal recovery is possible, including to the so-called identical sampling scenario. To verify our recovery guarantees we provide several numerical results including phase transition curves and numerically-computed bounds.Comment: 13 pages and 3 figure

Sparse Multi-Response Tensor Regression for Alzheimer's Disease Study With Multivariate Clinical Assessments

Alzheimer's disease (AD) is a progressive and irreversible neurodegenerative disorder that has recently seen serious increase in the number of affected subjects. In the last decade, neuroimaging has been shown to be a useful tool to understand AD and its prodromal stage, amnestic mild cognitive impairment (MCI). The majority of AD/MCI studies have focused on disease diagnosis, by formulating the problem as classification with a binary outcome of AD/MCI or healthy controls. There have recently emerged studies that associate image scans with continuous clinical scores that are expected to contain richer information than a binary outcome. However, very few studies aim at modeling multiple clinical scores simultaneously, even though it is commonly conceived that multivariate outcomes provide correlated and complementary information about the disease pathology. In this article, we propose a sparse multi-response tensor regression method to model multiple outcomes jointly as well as to model multiple voxels of an image jointly. The proposed method is particularly useful to both infer clinical scores and thus disease diagnosis, and to identify brain subregions that are highly relevant to the disease outcomes. We conducted experiments on the Alzheimer's Disease Neuroimaging Initiative (ADNI) dataset, and showed that the proposed method enhances the performance and clearly outperforms the competing solutions

Rigidity−Stability Relationship in Interlocked Model Complexes Containing Phenylene-Ethynylene-Based Disubstituted Naphthalene and Benzene

Structural rigidity has been found to be advantageous for molecules if they are to find applications in functioning molecular devices. In the search for an understanding of the relationship between the rigidity and complex stability in mechanically interlocked compounds, the binding abilities of two π-electron-rich model compounds (2 and 4), where rigidity is introduced in the form of phenylacetylene units, toward the π-electron deficient tetracationic cyclophane, cyclobis(paraquat-p-phenylene) (CBPQT^(4+)), were investigated. 1,4-Bis(2-(2-methoxyethoxy)ethoxy)-2,5-bis(2-phenylethynyl)benzene 2 and 1,5-bis(2-(2-methoxyethoxy)ethoxy)- 2,6-bis(2-phenylethynyl)naphthalene 4 were synthesized, respectively, from the appropriate precursor dibromides 1 and 3 of benzene and naphthalene carrying two methoxyethoxyethoxy side chains. The rigid nature of the compounds 2 and 4 is reflected in the reduced stabilities of their 1:1 complexes with CBPQT^(4+). Binding constants for both 2 (100 M^(-1)) and 4 (140 M^(-1)) toward CBPQT^(4+) were obtained by isothermal titration microcalorimetry (ITC) in MeCN at 25 °C. Compounds 1-4 were characterized in the solid state by X-ray crystallography. The stabilization within and beyond these molecules is achieved by a combination of intra- and intermolecular [C-H· · · O], [C-H· · ·π], and [π-π] stacking interactions. The diethyleneglycol chains present in compounds 1-4 are folded as a consequence of both intra- and intermolecular hydrogen bonds. The preorganized structures in both precursors 1 and 3 are repeated in both model compounds 2 and 4. In the structures of compounds 2 and 4, the geometry of the rigid backbone is differentsthe two terminal phenyl groups are twisted with respect to the central benzenoid ring in compound 2 and roughly perpendicular to the plane central naphthalene core in compound 4. To understand the significantly decreased stabilities of these complexes toward rigid guest molecules, relative to more flexible systems, we performed density functional theory (DFT) calculations using the newly developed M06-suite of density functionals. We conclude that the reduced binding abilities are a consequence of electronic and not steric factors, originating from the extended delocalization of the aromatic system

Impact Compression Test on Concrete after High-Temperature Treatment and Numerical Simulation of All Feasible Loading Rates

Concrete materials are important in infrastructure and national defence construction. These materials inevitably bear complicated loads, which include static load, high temperature, and high strain rate. Therefore, the dynamic responses and fragmentation of concrete under high temperatures and loading rates should be investigated. However, the compressive properties of rock materials under ultrahigh loading rates (>20 m/s) are difficult to investigate using the split Hopkinson pressure bar. Impact compression tests were conducted on concrete specimens processed at different temperatures (20-800 °C) under three loading rates in this study to discuss the variation law of the impact compression strength of concrete materials after high-temperature treatment. On this basis, numerical simulation was conducted on impact compression test under all feasible loading rates (10-110 m/s). The results demonstrate that the peak stress of all concrete specimens increases linearly with loading rate before 21 m/s and gradually decreases after 21 m/s. Peak stress shows an inverted V-shaped variation law. Moreover, the temperature-induced weakening effect exceeds the strengthening effect caused by loading rate with the increase in temperature. The growth of peak stress decreases considerably, especially under an ultrahigh loading rate (>50 m/s). These conclusions can provide theoretical references for the design of the ultimate strength of concrete materials for practical applications, such as fire and explosion prevention