Compressive Sensing DNA Microarrays

Compressive sensing microarrays (CSMs) are DNA-based sensors that operate using group testing and compressive sensing (CS) principles. In contrast to conventional DNA microarrays, in which each genetic sensor is designed to respond to a single target, in a CSM, each sensor responds to a set of targets. We study the problem of designing CSMs that simultaneously account for both the constraints from CS theory and the biochemistry of probe-target DNA hybridization. An appropriate cross-hybridization model is proposed for CSMs, and several methods are developed for probe design and CS signal recovery based on the new model. Lab experiments suggest that in order to achieve accurate hybridization profiling, consensus probe sequences are required to have sequence homology of at least 80% with all targets to be detected. Furthermore, out-of-equilibrium datasets are usually as accurate as those obtained from equilibrium conditions. Consequently, one can use CSMs in applications in which only short hybridization times are allowed

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

Compressive Inverse Scattering I. High Frequency SIMO Measurements

Inverse scattering from discrete targets with the single-input-multiple-output (SIMO), multiple-input-single-output (MISO) or multiple-input-multiple-output (MIMO) measurements is analyzed by compressed sensing theory with and without the Born approximation. High frequency analysis of (probabilistic) recoverability by the $L^1$-based minimization/regularization principles is presented. In the absence of noise, it is shown that the $L^1$-based solution can recover exactly the target of sparsity up to the dimension of the data either with the MIMO measurement for the Born scattering or with the SIMO/MISO measurement for the exact scattering. The stability with respect to noisy data is proved for weak or widely separated scatterers. Reciprocity between the SIMO and MISO measurements is analyzed. Finally a coherence bound (and the resulting recoverability) is proved for diffraction tomography with high-frequency, few-view and limited-angle SIMO/MISO measurements.Comment: A new section on diffraction tomography added; typos fixed; new figures adde

Put “gender glasses” on the effects of phenolic compounds on cardiovascular function and diseases

Introduction: The influence of sex and gender is particularly relevant in cardiovascular diseases (CVD) as well as in several aspects of drug pharmacodynamics and pharmacokinetics. Anatomical and physiological differences between the sexes may influence the activity of many drugs, including the possibility of their interaction with other drugs, bioactive compounds, foods and beverages. Phenolic compounds could interact with our organism at organ, cellular, and molecular levels triggering a preventive action against chronic diseases, including CVD. Results: This article will review the role of sex on the activity of these bioactive molecules, considering the existence of sex differences in oxidative stress. It describes the pharmacokinetics of phenolic compounds, their effects on vessels, on cardiovascular system, and during development, including the role of nuclear receptors and microbiota. Conclusions: Although there is a large gap between the knowledge of the sex differences in the phenolic compounds’ activity and safety, and the urgent need for more research, available data underlie the possibility that plant-derived phenolic compounds could differently influence the health of male and female subjects