An Introduction To Compressive Sampling [A sensing/sampling paradigm that goes against the common knowledge in data acquisition]

This article surveys the theory of compressive sampling, also known as compressed sensing or CS, a novel sensing/sampling paradigm that goes against the common wisdom in data acquisition. CS theory asserts that one can recover certain signals and images from far fewer samples or measurements than traditional methods use. To make this possible, CS relies on two principles: sparsity, which pertains to the signals of interest, and incoherence, which pertains to the sensing modality. Our intent in this article is to overview the basic CS theory that emerged in the works [1]–[3], present the key mathematical ideas underlying this theory, and survey a couple of important results in the field. Our goal is to explain CS as plainly as possible, and so our article is mainly of a tutorial nature. One of the charms of this theory is that it draws from various subdisciplines within the applied mathematical sciences, most notably probability theory. In this review, we have decided to highlight this aspect and especially the fact that randomness can — perhaps surprisingly — lead to very effective sensing mechanisms. We will also discuss significant implications, explain why CS is a concrete protocol for sensing and compressing data simultaneously (thus the name), and conclude our tour by reviewing important applications

A Hybrid Adaptive Low-Mach-Number/Compressible Method: Euler Equations

Flows in which the primary features of interest do not rely on high-frequency acoustic effects, but in which long-wavelength acoustics play a nontrivial role, present a computational challenge. Integrating the entire domain with low-Mach-number methods would remove all acoustic wave propagation, while integrating the entire domain with the fully compressible equations can in some cases be prohibitively expensive due to the CFL time step constraint. For example, simulation of thermoacoustic instabilities might require fine resolution of the fluid/chemistry interaction but not require fine resolution of acoustic effects, yet one does not want to neglect the long-wavelength wave propagation and its interaction with the larger domain. The present paper introduces a new multi-level hybrid algorithm to address these types of phenomena. In this new approach, the fully compressible Euler equations are solved on the entire domain, potentially with local refinement, while their low-Mach-number counterparts are solved on subregions of the domain with higher spatial resolution. The finest of the compressible levels communicates inhomogeneous divergence constraints to the coarsest of the low-Mach-number levels, allowing the low-Mach-number levels to retain the long-wavelength acoustics. The performance of the hybrid method is shown for a series of test cases, including results from a simulation of the aeroacoustic propagation generated from a Kelvin-Helmholtz instability in low-Mach-number mixing layers. It is demonstrated that compared to a purely compressible approach, the hybrid method allows time-steps two orders of magnitude larger at the finest level, leading to an overall reduction of the computational time by a factor of 8

Normal Heat Conduction in a Chain with Weak Interparticle Anharmonic Potential

We analytically study heat conduction in a chain with interparticle interaction V(x)=lambda[1-cos(x)] and harmonic on-site potential. We start with each site of the system connected to a Langevin heat bath, and investigate the case of small coupling for the interior sites in order to understand the behavior of the system with thermal reservoirs at the boundaries only. We study, in a perturbative analysis, the heat current in the steady state of the one-dimensional system with weak interparticle potential. We obtain an expression for the thermal conductivity, compare the low and high temperature regimes, and show that, as we turn off the couplings with the interior heat baths, there is a "phase transition:'' the Fourier's law holds only at high temperatures

Number of fermion generations from a novel Grand Unified model

Electroweak interactions based on a gauge group $\rm SU(3)_L \times U(1)_X$, coupled to the QCD gauge group $\rm SU(3)_c$, can predict the number of generations to be multiples of three. We first try to unify these models within SU(N) groups, using antisymmetric tensor representations only. After examining why these attempts fail, we continue to search for an SU(N) GUT that can explain the number of fermion generations. We show that such a model can be found for $N=9$, with fermions in antisymmetric rank-1 and rank-3 representations only, and examine the constraints on various masses in the model coming from the requirement of unification.Comment: 17 pages, 1 eps figur

Too little too late : welfare impacts of rainfall shocks in rural Indonesia

The authors use regression analysis to assess the potential welfare impact of rainfall shocks in rural Indonesia. In particular, they consider two shocks: (i) a delay in the onset of monsoon and (ii) a significant shortfall in the amount of rain in the 90 day post-onset period. Focusing on households with family farm businesses, the analysis finds that a delay in the monsoon onset does not have a significant impact on the welfare of rice farmers. However, rice farm households located in areas exposed to low rainfall following the monsoon are negatively affected. Rice farm households appear to be able to protect their food expenditure in the face of weather shocks at the expense of lower nonfood expenditures per capita. The authors use propensity score matching to identify community programs that might moderate the welfare impact of this type of shock. Access to credit and public works projects in communities were among the programs with the strongest moderating effects. This is an important consideration for the design and implementation of adaptation strategies.Science of Climate Change,Climate Change Mitigation and Green House Gases,Housing&Human Habitats,Rural Poverty Reduction,Regional Economic Development

The Law of the Minimum and Sources of Nonzero Skewness for Crop Yield Distributions

Crop yields are not commonly found to be normally distributed, but the cause of the non-normal distribution is unclear. The non-normality might be due to weather variables and/or an underlying von Liebig law of the minimum (LoM) production function. Our objective is to determine the degree to which an underlying linear response stochastic plateau production function can explain the skewness of Oklahoma wheat yields at varied nitrogen rates. We use farm-level wheat data from a long-term experiment in Oklahoma, which is a unique data set to the literature. The Tembo et al. (2008) production function provides negative skewness at all levels of nitrogen with skewness near zero for both very high and very low levels of nitrogen. Observed skewness for wheat yields, however, is positive. The variation in the plateau by year shows positive skewness. Skewness in yield potential related to weather should be considered as a possible explanation of skewness.linear plateau model, non-normal distributions, skewness, wheat, yield distribution, Production Economics, Risk and Uncertainty, Q10,

Deep transfer learning for improving single-EEG arousal detection

Datasets in sleep science present challenges for machine learning algorithms due to differences in recording setups across clinics. We investigate two deep transfer learning strategies for overcoming the channel mismatch problem for cases where two datasets do not contain exactly the same setup leading to degraded performance in single-EEG models. Specifically, we train a baseline model on multivariate polysomnography data and subsequently replace the first two layers to prepare the architecture for single-channel electroencephalography data. Using a fine-tuning strategy, our model yields similar performance to the baseline model (F1=0.682 and F1=0.694, respectively), and was significantly better than a comparable single-channel model. Our results are promising for researchers working with small databases who wish to use deep learning models pre-trained on larger databases.Comment: Accepted for presentation at EMBC202