Structural identifiability analysis of linear reaction–advection–diffusion processes in mathematical biology

Effective application of mathematical models to interpret biological data and make accurate predictions often requires that model parameters are identifiable. Approaches to assess the so-called structural identifiability of models are well established for ordinary differential equation models, yet there are no commonly adopted approaches that can be applied to assess the structural identifiability of the partial differential equation (PDE) models that are requisite to capture spatial features inherent to many phenomena. The differential algebra approach to structural identifiability has recently been demonstrated to be applicable to several specific PDE models. In this brief article, we present general methodology for performing structural identifiability analysis on partially observed reaction–advection–diffusion PDE models that are linear in the unobserved quantities. We show that the differential algebra approach can always, in theory, be applied to such models. Moreover, despite the perceived complexity introduced by the addition of advection and diffusion terms, consideration of spatial analogues of non-spatial models cannot exacerbate structural identifiability. We conclude by discussing future possibilities and the computational cost of performing structural identifiability analysis on more general PDE models

Man of La Mancha Playbill

Providence College Department of Theater, Dance & Film The Friar\u27s Cell Man of La Mancha Tuesday-Friday, February 27-March 2 + Sunday, March 4, 1973, 8PM Saturday, March 3, 1973, 2:15PM + 8PM Director, R.L. Pelkington, O.P. Musical Director, J.L. Prest, O.P. Choreographer, R.L. Slavin Stage Manager, J.P. Garrity House Manager, R.P. Warner Cast: Captain of Guard - Fred Caiozzo, Don Quixote - Don Higgins, Sancho - Jim Hughes, Aldonza - Chris Mahoney, Padre (Governor) - Bill Dennis, Inn Keeper - Al Beaulieu, Dr. Carrasco - J. McDavitt, Antonia - Chris Altieri, Fermina - Denise Levesque, Housekeeper - Alex Tavares, Barber - Andy Bourgeois, Maria - Beth McHugh, Muleteers - Vince Clark, James Haag, Joseph Handly, Mike Lyons, Bob Butler, Joseph Coughlinhttps://digitalcommons.providence.edu/lamancha_pubs/1000/thumbnail.jp

Man of La Mancha Poster

Providence College Department of Theater, Dance & Film The Friar\u27s Cell Man of La Mancha Tuesday-Friday, February 27-March 2 + Sunday, March 4, 1973, 8PM Saturday, March 3, 1973, 2:15PM + 8PMhttps://digitalcommons.providence.edu/lamancha_pubs/1001/thumbnail.jp

Animal sentience research: Synthesis and proposals

Most commentaries on our target article broadly support our approach to evaluating evidence of animal sentience. In this Response, we clarify the framework’s purpose and address criticisms of our criteria. A recurring theme is that a framework to synthesise current evidence of sentience is not the same as an agenda for future directions in animal sentience research. Although future directions are valuable, our framework aims to evaluate existing evidence and inform animal welfare legislation

A FUSE Survey of Interstellar Molecular Hydrogen in the Small and Large Magellanic Clouds

We describe a moderate-resolution FUSE survey of H2 along 70 sight lines to the Small and Large Magellanic Clouds, using hot stars as background sources. FUSE spectra of 67% of observed Magellanic Cloud sources (52% of LMC and 92% of SMC) exhibit absorption lines from the H2 Lyman and Werner bands between 912 and 1120 A. Our survey is sensitive to N(H2) >= 10^14 cm^-2; the highest column densities are log N(H2) = 19.9 in the LMC and 20.6 in the SMC. We find reduced H2 abundances in the Magellanic Clouds relative to the Milky Way, with average molecular fractions = 0.010 (+0.005, -0.002) for the SMC and = 0.012 (+0.006, -0.003) for the LMC, compared with = 0.095 for the Galactic disk over a similar range of reddening. The dominant uncertainty in this measurement results from the systematic differences between 21 cm radio emission and Lya in pencil-beam sight lines as measures of N(HI). These results imply that the diffuse H2 masses of the LMC and SMC are 8 x 10^6 Msun and 2 x 10^6 Msun, respectively, 2% and 0.5% of the H I masses derived from 21 cm emission measurements. The LMC and SMC abundance patterns can be reproduced in ensembles of model clouds with a reduced H2 formation rate coefficient, R ~ 3 x 10^-18 cm^3 s^-1, and incident radiation fields ranging from 10 - 100 times the Galactic mean value. We find that these high-radiation, low-formation-rate models can also explain the enhanced N(4)/N(2) and N(5)/N(3) rotational excitation ratios in the Clouds. We use H2 column densities in low rotational states (J = 0 and 1) to derive a mean kinetic and/or rotational temperature = 82 +/- 21 K for clouds with N(H2) >= 10^16 cm^-2, similar to Galactic gas. We discuss the implications of this work for theories of star formation in low-metallicity environments. [Abstract abridged]Comment: 30 pages emulateapj, 14 figures (7 color), 7 tables, accepted for publication in the Astrophysical Journal, figures 11 and 12 compressed at slight loss of quality, see http://casa.colorado.edu/~tumlinso/h2/ for full version

SenseAI: Real-Time Inpainting for Electron Microscopy

Despite their proven success and broad applicability to Electron Microscopy (EM) data, joint dictionary-learning and sparse-coding based inpainting algorithms have so far remained impractical for real-time usage with an Electron Microscope. For many EM applications, the reconstruction time for a single frame is orders of magnitude longer than the data acquisition time, making it impossible to perform exclusively subsampled acquisition. This limitation has led to the development of SenseAI, a C++/CUDA library capable of extremely efficient dictionary-based inpainting. SenseAI provides N-dimensional dictionary learning, live reconstructions, dictionary transfer and visualization, as well as real-time plotting of statistics, parameters, and image quality metrics.Comment: Presented in ISCS2

Diffusion Distribution Model for Damage Mitigation in Scanning Transmission Electron Microscopy

Despite the widespread use of Scanning Transmission Electron Microscopy (STEM) for observing the structure of materials at the atomic scale, a detailed understanding of some relevant electron beam damage mechanisms is limited. Recent reports suggest that certain types of damage can be modeled as a diffusion process and that the accumulation effects of this process must be kept low in order to reduce damage. We therefore develop an explicit mathematical formulation of spatiotemporal diffusion processes in STEM that take into account both instrument and sample parameters. Furthermore, our framework can aid the design of Diffusion Controlled Sampling (DCS) strategies using optimally selected probe positions in STEM, that constrain the cumulative diffusion distribution. Numerical simulations highlight the variability of the cumulative diffusion distribution for different experimental STEM configurations. These analytical and numerical frameworks can subsequently be used for careful design of 2- and 4-dimensional STEM experiments where beam damage is minimised.Comment: Main document: 29 pages, 12 figures; Supplementary document: 18 pages, 5 figure

High‐speed 4‐dimensional scanning transmission electron microscopy using compressive sensing techniques

Here we show that compressive sensing allows 4‐dimensional (4‐D) STEM data to be obtained and accurately reconstructed with both high‐speed and reduced electron fluence. The methodology needed to achieve these results compared to conventional 4‐D approaches requires only that a random subset of probe locations is acquired from the typical regular scanning grid, which immediately generates both higher speed and the lower fluence experimentally. We also consider downsampling of the detector, showing that oversampling is inherent within convergent beam electron diffraction (CBED) patterns and that detector downsampling does not reduce precision but allows faster experimental data acquisition. Analysis of an experimental atomic resolution yttrium silicide dataset shows that it is possible to recover over 25 dB peak signal‐to‐noise ratio in the recovered phase using 0.3% of the total data. Lay abstract: Four‐dimensional scanning transmission electron microscopy (4‐D STEM) is a powerful technique for characterizing complex nanoscale structures. In this method, a convergent beam electron diffraction pattern (CBED) is acquired at each probe location during the scan of the sample. This means that a 2‐dimensional signal is acquired at each 2‐D probe location, equating to a 4‐D dataset. Despite the recent development of fast direct electron detectors, some capable of 100kHz frame rates, the limiting factor for 4‐D STEM is acquisition times in the majority of cases, where cameras will typically operate on the order of 2kHz. This means that a raster scan containing 256^2 probe locations can take on the order of 30s, approximately 100‐1000 times longer than a conventional STEM imaging technique using monolithic radial detectors. As a result, 4‐D STEM acquisitions can be subject to adverse effects such as drift, beam damage, and sample contamination. Recent advances in computational imaging techniques for STEM have allowed for faster acquisition speeds by way of acquiring only a random subset of probe locations from the field of view. By doing this, the acquisition time is significantly reduced, in some cases by a factor of 10‐100 times. The acquired data is then processed to fill‐in or inpaint the missing data, taking advantage of the inherently low‐complex signals which can be linearly combined to recover the information. In this work, similar methods are demonstrated for the acquisition of 4‐D STEM data, where only a random subset of CBED patterns are acquired over the raster scan. We simulate the compressive sensing acquisition method for 4‐D STEM and present our findings for a variety of analysis techniques such as ptychography and differential phase contrast. Our results show that acquisition times can be significantly reduced on the order of 100‐300 times, therefore improving existing frame rates, as well as further reducing the electron fluence beyond just using a faster camera