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Abstract This paper investigates the problem of recovering source terms in abstract initial value problems (IVP) commonly used to model various scientific phenomena in physics, chemistry, economics, and other fields. We consider source terms of the form$$F=h+\eta $$ $F=h+\eta$, where$$\eta $$ $\eta$is a Lipschitz continuous background source. The primary objective is to estimate the unknown parameters of non-instantaneous sources$$h(t)=\sum \limits _{j=0}^M h_je^{-\rho _j(t-t_j)}\chi _{[t_j,\infty )}(t)$$ $h\left(t\right)=\sum _{j=0}^M{h}_j{e}^{-{\rho }_j(t-t_j)}{\chi }_{[t_j,\infty )}\left(t\right)$, such as the decay rates, initial intensities and activation times. We present two novel recovery algorithms that employ distinct sampling methods of the solution of the IVP. Algorithm 1 combines discrete and weighted average measurements, whereas Algorithm 2 uses a different variant of weighted average measurements. We analyze the performance of these algorithms, providing upper bounds on the recovery errors of the model parameters. Our focus is on the structure of the dynamical samples used by the algorithms and on the error guarantees they yield. 

We extend the classical Kadec 1/4-theorem for systems of exponential functions on an interval to frames and atomic decompositions formed by sampling an orbit of a vector under an isometric group representation. 

Recent technological advances have enabled spatially resolved measurements of expression profiles for hundreds to thousands of genes in fixed tissues at single-cell resolution. However, scalable computational analysis methods able to take into consideration the inherent 3D spatial organization of cell types and nonuniform cellular densities within tissues are still lacking. To address this, we developed MERINGUE, a computational framework based on spatial autocorrelation and cross-correlation analysis to identify genes with spatially heterogeneous expression patterns, infer putative cell–cell communication, and perform spatially informed cell clustering in 2D and 3D in a density-agnostic manner using spatially resolved transcriptomic data. We applied MERINGUE to a variety of spatially resolved transcriptomic data sets including multiplexed error-robust fluorescence in situ hybridization (MERFISH), spatial transcriptomics, Slide-seq, and aligned in situ hybridization (ISH) data. We anticipate that such statistical analysis of spatially resolved transcriptomic data will facilitate our understanding of the interplay between cell state and spatial organization in tissue development and disease. 

The Arecibo Pisces Perseus Supercluster Survey (APPSS) is an HI survey measuring galaxy infall into the filament and clusters. Galaxies were selected for HI observations based on their location within the Pisces Perseus supercluster and SDSS and GALEX colors predictive of cold gas content. Most of the HI observations were conducted at Arecibo using the L Band Wide receiver, with some high-declination coverage provided by Green Bank. The observations provide increased sensitivity compared to ALFALFA blind survey data. For this project, we investigated a subset of 132 APPSS galaxies with declinations near 27 degrees. Using custom data reduction and analysis tools developed for the Undergraduate ALFALFA Team, we determined the following information for galaxies in our subset: systemic velocity, line width, integrated flux density, HI mass, and gas fraction (or corresponding limits for non-detections). We calculate our HI detection fraction and mean gas fraction as a function of stellar mass and compare to previous results. We investigate the distribution of systemic velocities for our galaxies with their location on the sky. Finally, we discuss several interesting sources from our subset of APPSS galaxies. This work has been supported by NSF grants AST-1211005, AST-1637299, and AST-1637339 

The Undergraduate ALFALFA Team (UAT) Groups project is a coordinated study of gas and star formation properties of galaxies in and around 36 nearby (z<0.03) groups and clusters of varied richness, morphological type mix, and X-ray luminosity. By studying a large range of environments and considering the spatial distributions of star formation, we probe mechanisms of gas depletion and morphological transformation. The project uses ALFALFA HI observations, optical observations, and digital databases like SDSS, and incorporates work undertaken by faculty and students at different institutions within the UAT. Here we present results from our wide area Hα and broadband R imaging project carried out with the WIYN 0.9m+MOSAIC/HDI at KPNO, including an analysis of radial star formation rates and extents of galaxies in the NGC 5846, Abell 779, NRGb331, and HCG 69 groups/clusters. This work has been supported by NSF grant AST-1211005 and AST-1637339. 

The Undergraduate ALFALFA Team (UAT) Groups project is a coordinated study of gas and star formation properties of galaxies in and around 36 nearby (z<0.03) groups and clusters of varied richness, morphological type mix, and X-ray luminosity. By studying a large range of environments and considering the spatial distributions of star formation, we probe mechanisms of gas depletion and morphological transformation. The project uses ALFALFA HI observations, optical observations, and digital databases like SDSS, and incorporates work undertaken by faculty and students at different institutions within the UAT. Here we present results from our wide area Hα and broadband R imaging project carried out with the WIYN 0.9m+MOSAIC/HDI at KPNO, including an analysis of radial star formation rates and extents of galaxies in the NGC 5846, Abell 779, NRGb331, and HCG 69 groups/clusters. This work has been supported by NSF grant AST-1211005 and AST-1637339.