Theoretical Formulation/Development of Signal Sampling with an Equal Arc Length Using the Frame Theorem

Non-uniform sampling with equal arc length intervals can be found in shape measurements with contact sensor arrays. In this study, the conditions of non-uniform spatial sampling with an equal arc length interval are derived from two frame theorems. First, for general non-uniform sampling, the condition is that the equal arc length interval of the sensors should be less than 1/4Ω. Second, for strictly increasing sampling, the condition is that the equal arc length interval of the sensors should be less than 1/2Ω. The Ω is the maximum frequency of the detected object. For the latter, if the sampling frequency is more twice than the sampling frequency required, the reconstruction error (RRMSE and MRE) is less than 5%. If the sampling frequency is more than 2.5 times, the reconstruction error is less than 3%. The simulation and the experiment are carried out and the results show that a sensor array with equal arc length interval can reconstruct the detected object with high accuracy.

Clustered sparsity and Poisson-gap sampling

Non-uniform sampling (NUS) is a popular way of reducing the amount of time taken by multidimensional NMR experiments. Among the various non-uniform sampling schemes that exist, the Poisson-gap (PG) schedules are particularly popular, especially when combined with compressed-sensing (CS) reconstruction of missing data points. However, the use of PG is based mainly on practical experience and has not, as yet, been explained in terms of CS theory. Moreover, an apparent contradiction exists between the reported effectiveness of PG and CS theory, which states that a “flat” pseudo-random generator is the best way to generate sampling schedules in order to reconstruct sparse spectra. In this paper we explain how, and in what situations, PG reveals its superior features in NMR spectroscopy. We support our theoretical considerations with simulations and analyses of experimental data from the Biological Magnetic Resonance Bank (BMRB). Our analyses reveal a previously unnoticed feature of many NMR spectra that explains the success of ”blue-noise” schedules, such as PG. We call this feature “clustered sparsity”. This refers to the fact that the peaks in NMR spectra are not just sparse but often form clusters in the indirect dimension, and PG is particularly suited to deal with such situations. Additionally, we discuss why denser sampling in the initial and final parts of the clustered signal may be useful.

Sketching and sampling approaches for fast and accurate long read classification

In modern sequencing experiments, identifying the sources of the reads is a crucial need. In metagenomics, where each read comes from one of potentially many members of a community, it can be important to identify the exact species the read is from. In other settings, it is important to distinguish which reads are from the targeted sample and which are from potential contaminants. In both cases, identification of the correct source of a read enables further investigation of relevant reads, while minimizing wasted work. This task is particularly challenging for long reads, which can have a substantial error rate that obscures the origins of each read. Existing tools for the read classification problem are often alignment or index-based, but such methods can have large time and/or space overheads. In this work, we investigate the effectiveness of several sampling and sketching-based approaches for read classification. In these approaches, a chosen sampling or sketching algorithm is used to generate a reduced representation (a "screen") of potential source genomes for a query readset before reads are streamed in and compared against this screen. Using a query read's similarity to the elements of the screen, the methods predict the source of the read. Such an approach requires limited pre-processing, stores and works with only a subset of the input data, and is able to perform classification with a high degree of accuracy. The sampling and sketching approaches investigated include uniform sampling, methods based on MinHash and its weighted and order variants, a minimizer-based technique, and a novel clustering-based sketching approach. We demonstrate the effectiveness of these techniques both in identifying the source microbial genomes for reads from a metagenomic long read sequencing experiment, and in distinguishing between long reads from organisms of interest and potential contaminant reads. We then compare these approaches to existing alignment, index and sketching-based tools for read classification, and demonstrate how such a method is a viable alternative for determining the source of query reads. Finally, we present a reference implementation of these approaches at https://github.com/arun96/sketching.

Problems of unification of fodder quality and nutritive value assessment systems

The article is devoted to the urgent need for improvement and unification of systems for the quality evaluation of feed and rations. Lack of uniform sampling methods, analysis methods, feed quality indicators; norms of the nutrient requirements depending on the physiological state of animals, a unified approach to balancing diets, and most importantly - the absence of an international standard system for assessing the energy nutritive value of feed and rations - complicates the mutual understanding of scientists and practitioners from different countries and the integration of scientific achievements into agricultural production.

A Coupled Sampling Design for Parameter Estimation in Microalgae Growth Experiment: Maximizing the Benefits of Uniform and Non-Uniform Sampling

As an important primary producer in aquatic ecosystems, the various parameters within the mathematical models are used to describe the growth of microalgae and need to be estimated by carefully designed experiments. Non-uniform sampling has proved to generate a deliberately optimized sampling temporal schedule that can benefit parameter estimation. However, the current non-uniform sampling method depends on prior knowledge of the nominal values of the model parameters. It also largely ignores the uncertainty associated with the nominal values, thus inducing unacceptable parameter estimates. This study focuses on the uncertainty problem and describes a new sampling design that couples the traditional uniform and non-uniform sampling schedules to benefit from the merits of both methods. Based on D-optimal design, we first derive the non-uniform optimal sampling points by maximizing the determinant of the Fisher information matrix. Then the confidence interval around the non-uniform sampling points is determined by Monte Carlo simulations based on the prior knowledge of parameter distribution. Finally, we wrap the non-uniform sampling points with the uniform sampling points within the confidence interval to obtain the ultimate optimal experimental design. Scenedesmus obliquus, whose growth curve follows a four-parameter model, was used as a case study. Compared with the traditional sampling design, the simulation results show that our proposed coupled sampling schedule can partly eliminate the uncertainty in parameter estimates caused by fixed systematic errors in observations. Our coupled sampling can also retain some advantages belonging to non-uniform sampling, in exploiting information maximization and managing the cost of sampling.

Retinal self-organization: a model of RGC and SAC mosaic formation

Individual retinal cell types exhibit semi-regular spatial patterns called retinal mosaics. These mosaics enable uniform sampling of visual information and are formed to varying degrees across cell types. Retinal ganglion cells (RGC) and amacrine cells (including starburst amacrine cells (SAC)) are notably known to exhibit such layouts. Mechanisms responsible for the formation of such organised structures and their requirements are still not well understood. Mosaic formation follows three main principles: (1) homotypic cells prevent nearby cells from adopting the same type, (2) cell tangential migration, with homotypic cell repulsion, (3) cell death (with RGCs exhibiting high rates of apoptosis).

Staring Spotlight SAR with Nonlinear Frequency Modulation Signal and Azimuth Non-Uniform Sampling for Low Sidelobe Imaging

In synthetic aperture radar (SAR) imaging, geometric resolution, sidelobe level (SLL) and signal-to-noise ratio (SNR) are the most important parameters for measuring the SAR image quality. The staring spotlight mode continuously transmits signals to a fixed area by steering the azimuth beam to acquire azimuth high geometric resolution, and its two-dimensional (2D) impulse response with the low SLL is usually obtained from the 2D weighted power spectral density (PSD) by the selected weighting window function. However, this results in the SNR reduction due to 2D amplitude window weighting. In this paper, the staring spotlight SAR with nonlinear frequency modulation (NLFM) signal and azimuth non-uniform sampling (ANUS) is proposed to obtain high geometric resolution SAR images with the low SLL and almost without any SNR reduction. The NLFM signal obtains non-equal interval frequency sampling points under uniform time sampling by adjusting the instantaneous chirp rate. Its corresponding PSD is similar to the weighting window function, and its pulse compression result without amplitude window weighting has low sidelobes. To obtain a similar Doppler frequency distribution for low sidelobe imaging in azimuth, the received SAR echoes are designed to be non-uniformly sampled in azimuth, in which the sampling sequence is dense in middle and sparse in both ends, and azimuth compression result with window weighting would also have low sidelobes. According to the echo model of the proposed imaging mode, both the back projection algorithm (BPA) and range migration algorithm (RMA) are modified and presented to handle the raw data of the proposed imaging mode. Both imaging results on simulated targets and experimental real SAR data processing results of a ground-based radar validate the proposed low sidelobe imaging mode.

Synchronization of Transmission Systems with ANS-DM Codecs

Adaptive Delta Modulation with Non-uniform Sampling (ANS-DM) is one of the waveform coding techniques, where a sampling instant and a quantization step size are adapted to the signal. The ANS-DM modulator produces an output binary stream, that carries information about the signal and includes necessary data of coder parameters (sampling instant and quantization step). In the demodulator, these values are recovered for proper signal reconstruction. The paper reports the problem of synchronizing clocks (transmitting and receiving) in the (ANS-DM) delta codecs systems. The original synchronization method, valuable in systems dedicated to the transmission of the bits with variable time duration was projected and experimentally verified. Performed measurements and observations have shown the elimination of the synchronization loss phenomenon.

Estimation of parameters of a sum of sinusoids sampled below the Nyquist rate with frequencies away from the grid

We are witnessing a growing interest in processing signals sampled below the Nyquist rate. The main limitation of current approaches considering estimation of multicomponent sinusoids parameters is the assumption of frequencies on the frequency grid. The sinusoids away from the frequency grid are considered in this paper. The proposed procedure has three stages. In the first two, a rough estimation of signal components is performed while in the third refinement in estimation is achieved in a component-by-component manner. We have tested the developed technique on an extended set of simulation examples showing excellent accuracy. Three scenarios are considered in experiments: missing samples, noisy environment, and non-uniform sampling below the Nyquist rate.