Interpolation and Extrapolation of Toeplitz Matrices via Optimal Mass Transport

In this work, we propose a novel method for quantifying distances between Toeplitz structured covariance matrices. By exploiting the spectral representation of Toeplitz matrices, the proposed distance measure is defined based on an optimal mass transport problem in the spectral domain. This may then be interpreted in the covariance domain, suggesting a natural way of interpolating and extrapolating Toeplitz matrices, such that the positive semi-definiteness and the Toeplitz structure of these matrices are preserved. The proposed distance measure is also shown to be contractive with respect to both additive and multiplicative noise, and thereby allows for a quantification of the decreased distance between signals when these are corrupted by noise. Finally, we illustrate how this approach can be used for several applications in signal processing. In particular, we consider interpolation and extrapolation of Toeplitz matrices, as well as clustering problems and tracking of slowly varying stochastic processes

Estimating Sparse Signals Using Integrated Wideband Dictionaries

In this paper, we introduce a wideband dictionary framework for estimating sparse signals. By formulating integrated dictionary elements spanning bands of the considered parameter space, one may efficiently find and discard large parts of the parameter space not active in the signal. After each iteration, the zero-valued parts of the dictionary may be discarded to allow a refined dictionary to be formed around the active elements, resulting in a zoomed dictionary to be used in the following iterations. Implementing this scheme allows for more accurate estimates, at a much lower computational cost, as compared to directly forming a larger dictionary spanning the whole parameter space or performing a zooming procedure using standard dictionary elements. Different from traditional dictionaries, the wideband dictionary allows for the use of dictionaries with fewer elements than the number of available samples without loss of resolution. The technique may be used on both one- and multi-dimensional signals, and may be exploited to refine several traditional sparse estimators, here illustrated with the LASSO and the SPICE estimators. Numerical examples illustrate the improved performance

Generalized Sparse Covariance-based Estimation

In this work, we extend the sparse iterative covariance-based estimator (SPICE), by generalizing the formulation to allow for different norm constraints on the signal and noise parameters in the covariance model. For a given norm, the resulting extended SPICE method enjoys the same benefits as the regular SPICE method, including being hyper-parameter free, although the choice of norms are shown to govern the sparsity in the resulting solution. Furthermore, we show that solving the extended SPICE method is equivalent to solving a penalized regression problem, which provides an alternative interpretation of the proposed method and a deeper insight on the differences in sparsity between the extended and the original SPICE formulation. We examine the performance of the method for different choices of norms, and compare the results to the original SPICE method, showing the benefits of using the extended formulation. We also provide two ways of solving the extended SPICE method; one grid-based method, for which an efficient implementation is given, and a gridless method for the sinusoidal case, which results in a semi-definite programming problem

Long Gamma-Ray Burst Host Galaxies and their Environments

In this book-chapter we first briefly discuss some basic observational issues related to what a GRB host galaxy is (whether they are operationally well defined as a class) and sample completeness. We then describe some of the early studies of GRB hosts starting with statistical studies of upper limits done prior to the first detections, the first host detection after the BeppoSAX breakthrough and leading up to the current Swift era. Finally, we discuss the status of efforts to construct a more complete sample of GRBs based on Swift and end with an outlook. We only consider the host galaxies of long-duration GRBs.Comment: 31 pages, 14 figures; Chapter 13 in "Gamma-Ray Bursts", eds. C. Kouveliotou, R. A. M. J. Wijers, S. E. Woosley, Cambridge University Press, 201

Sparse Semi-Parametric Chirp Estimator

In this work, we present a method for estimating the parameters detailing an unknown number of linear chirp signals, using an iterative sparse reconstruction framework. The proposed method is initiated by a re-weighted Lasso approach, and then use an iterative relaxation-based refining step to allow for high resolution estimates. The resulting estimates are found to be statistically efficient, achieving the Cramér-Rao lower bound. Numerical simulations illustrate the achievable performance, offering a notable improvement as compared to other recent approaches

Sparse Semi-Parametric Estimation of Harmonic Chirp Signals

In this work, we present a method for estimating the parameters detailing an unknown number of linear, possibly harmonically related, chirp signals, using an iterative sparse reconstruction framework. The proposed method is initiated by a re-weighted group-sparsity approach, followed by an iterative relaxation-based refining step, to allow for high resolution estimates. Numerical simulations illustrate the achievable performance, offering a notable improvement as compared to other recent approaches. The resulting estimates are found to be statistically efficient, achieving the corresponding Cram´er-Rao lower bound

Functional Studies of microRNAs in Neural Stem Cells: Problems and Perspectives

In adult mammals, neural stem cells (NSCs) are found in two niches of the brain; the subventricular zone by the lateral ventricles and the subgranular zone of the dentate gyrus in the hippocampus. Neurogenesis is a complex process that is tightly controlled on a molecular level. Recently, microRNAs (miRNAs) have been implicated to play a central role in the regulation of NCSs. miRNAs are small, endogenously expressed RNAs that regulate gene expression at the post-transcriptional level. However, functional studies of miRNAs are complicated due to current technical limitations. In this review we describe recent findings about miRNAs in NSCs looking closely at miR-124, miR-9, and let-7. In addition, we highlight technical strategies used to investigate miRNA function, accentuating limitations, and potentials

Effects of Different Types of Lower Body Resistance Exercise on Upper-body Strength in Men and Women, with Special Reference to Anabolic Hormones

International Journal of Exercise Science 14(3): 1052-1069, 2021. Resistance exercise has been shown to induce an acute hormonal response. The purpose of this study was to examine upper-body adaptations and the endocrine response to strength training in men and women when subjected to two different types of lower-body resistance training protocols. Nine males and eight females were assigned to either a Heavy Load (HL) (N = 10) or Mixed Load (ML) (N = 7) training routine three times per week for ten weeks. The HL-group executed low-volume, high-load resistance exercise for both lower and upper-body (4-6 reps at 80-90% of one repetition maximum (1-RM), three-minute inter-set rest). The ML-group performed the HL-protocol for the upper-body, but a high-volume, moderate-load protocol for the lower body (10-15 reps at 60-70% of 1-RM, one-minute inter-set rest). Volume load, 1-RM strength and hormonal measurements were analyzed by repeated-measures linear mixed models. Both groups increased their 1-RM in all assessments (p \u3c 0.01) with no significant difference between groups at any time. Growth hormone (GH), testosterone and bioavailable testosterone (T/SHBG) increased in both groups during a standardized exercise session (p \u3c 0.01) with ML having a greater increase in GH. The notion that acute elevations in anabolic hormones is important for muscle strength adaptation cannot be supported by the present study

GRBs as Probes of Massive Stars Near and Far

Long-duration gamma-ray bursts are the manifestations of massive stellar death. Due to the immense energy release they are detectable from most of the observable universe. In this way they allow us to study the deaths of single (or binary) massive stars possibly throughout the full timespan massive stars have existed in the Universe. GRBs provide a means to infer information about the environments and typical galaxies in which massive stars are formed. Two main obstacles remain to be crossed before the full potential of GRBs as probes of massive stars can be harvested: i) we need to build more complete and well understood samples in order not to be fooled by biases, and ii) we need to understand to which extent GRBs may be intrinsically biased in the sense that they are only formed by a limited subset of massive stars defined by most likely a restricted metallicity interval. We describe the status of an ongoing effort to build a more complete sample of long-duration GRBs with measured redshifts. Already now we can conclude that the environments of GRB progenitors are very diverse with metallicities ranging from solar to a hundredth solar and extinction ranging from none to A_V>5 mag. We have also identified a sightline with significant escape of Lyman continuum photons and another with a clear 2175AA extinction bump.Comment: Invited review - in "Massive Stars as Cosmic Engines", IAU Symp. 250 (Kauai), ed. F. Bresolin, P. A. Crowther, and J. Puls (Cambridge University Press), p. 443-456. Typos and refs correcte