Sampling Theorem and Discrete Fourier Transform on the Riemann Sphere

Using coherent-state techniques, we prove a sampling theorem for Majorana's (holomorphic) functions on the Riemann sphere and we provide an exact reconstruction formula as a convolution product of $N$ samples and a given reconstruction kernel (a sinc-type function). We also discuss the effect of over- and under-sampling. Sample points are roots of unity, a fact which allows explicit inversion formulas for resolution and overlapping kernel operators through the theory of Circulant Matrices and Rectangular Fourier Matrices. The case of band-limited functions on the Riemann sphere, with spins up to $J$, is also considered. The connection with the standard Euler angle picture, in terms of spherical harmonics, is established through a discrete Bargmann transform.Comment: 26 latex pages. Final version published in J. Fourier Anal. App

Crowd-sourcing of structure-from-motion data for terrain modelling in a real-world disaster scenario:a proof of concept

Structure-from-motion (SfM) photogrammetry techniques are now widely available to generate digital terrain models (DTMs) from optical imagery, providing an alternative to costlier options such as LiDAR or satellite surveys. SfM could be a useful tool in hazard studies because its minimal cost makes it accessible even in developing regions and its speed of use can provide updated data rapidly in hazard-prone regions. Our study is designed to assess whether crowd-sourced SfM data is comparable to an industry standard LiDAR dataset, demonstrating potential real-world use of SfM if employed for disaster risk reduction purposes. Three groups with variable SfM knowledge utilized 16 different camera models, including four camera phones, to collect 1001 total photos in one hour of data collection. Datasets collected by each group were processed using VisualSFM, and the point densities, accuracies and distributions of points in the resultant point clouds (DTM skeletons) were compared. Our results show that the point clouds are resilient to inconsistency in users’ SfM knowledge: crowd-sourced data collected by a moderately informed general public yields topography results comparable in data density and accuracy to those produced with data collected by highly-informed SfM users or experts using LiDAR. This means that in a real-world scenario involving participants with a diverse range of expertise, topography models could be produced from crowd-sourced data quite rapidly and to a very high standard. This could be beneficial to disaster risk reduction as a relatively quick, simple and low-cost method to attain rapidly updated knowledge of terrain attributes, useful for the prediction and mitigation of many natural hazards

Fourteen Months into the Covid-19 Pandemic: What We Miss the Most

As the U.S. continues to emerge from the deadliest pandemic in over one hundred years, vaccination rates among Americans have steadily risen, and public health guidelines that have been in place for over a year are increasingly relaxed. In short, Americans are readjusting to a “new normal.” But what this “new normal” looks like for many Americans remains unclear. To better understand what Americans are most looking forward to, the National Center for Disaster Preparedness (NCDP) at Columbia University’s Earth Institute partnered with the Marist Institute for Public Opinion to survey Americans and better understand what they are most looking forward to doing – or what getting back to ‘normal’ means to them

Three-Dimensional Imaging-Based Web Application for Predicting Tracheal Tube Depth in Preterm Neonates

BACKGROUND: Positioning a tracheal tube (TT) to the correct depth in preterm infants is challenging. Currently, there is no reliable single-predictor model for neonates applicable to the whole range of size or age. OBJECTIVE: In this study, we used post-mortem magnetic resonance imaging (PMMRI) of preterm infants to measure tracheal dimensions and to develop a clinical guide for TT positioning. METHODS: We measured tracheal length (TL) and tracheal diameter (TD) in a cohort of normal neonates and foetuses that underwent PMMRI (cause of death unexplained). The distance between the lips and the mid-tracheal point, i.e., the mid-tracheal length (mid-TL), and the TD measurement were obtained. We produced univariate prediction models of mid-TL and TD, using gestational age (GA), foot length (FL), crown-rump length (CRL) and body weight (BW) as potential predictors, as well as multiple prediction models for mid-TL. RESULTS: Tracheal measurements were performed in 117 cases, with a mean GA of 28.8 weeks (range 14-42 weeks). The best linear association was between mid-TL and FL (mid-TL = FL × 0.914 + 1.859; R2 = 0.94), but was improved by multivariate regression models. We developed a prediction tool using only GA and BW (R2 = 0.92), and all four predictors (GA, BW, FL and CRL; R2 = 0.94) which is now available as a web-based application via the Internet. CONCLUSION: Post-mortem imaging data provide estimates of TT insertion depth. Our prediction tool based on age and BW can be used at the bedside and is ready to be tested in clinical practice

Wnt11/Fzd7 signaling compartmentalizes AKAP2/PKA to regulate L-type Ca2+ channel

Calcium influx through the voltage-gated L-type calcium channels (LTCC) mediates a wide range of physiological processes from contraction to secretion. Despite extensive research on regulation of LTCC conductance by PKA phosphorylation in response to β-adrenergic stimulation, the science remains incomplete. Here, we show that Wnt11, a non-canonical Wnt ligand, through its G protein-coupled receptor (GPCR) Fzd7 attenuates the LTCC conductance by preventing the proteolytic processing of its C terminus. This is mediated across species by protein kinase A (PKA), which is compartmentalized by A-kinase anchoring proteins (AKAP). Systematic analysis of all AKAP family members revealed AKAP2 anchoring of PKA is central to the Wnt11-dependent regulation of the channel. The identified Wnt11/AKAP2/PKA signalosome is required for heart development, controlling the intercellular electrical coupling in the developing zebrafish heart. Altogether, our data revealed Wnt11/Fzd7 signaling via AKAP2/PKA as a conserved alternative GPCR system regulating Ca(2+) homeostasis

RCRC Issue Briefs: Why Children Should Be the #1 Disaster Priority

The Resilient Children/Resilient Communities Initiative (RCRC) Issue Briefs, in this document, are designed to be used by the RCRC communities and all other communities who are seeking to elevate children’s disaster resilience to the attention of local, state, and federal legislators or other decision-makers. These reports can also be used by legislators and decision–makers at all levels of government as informative briefs to better understand the issues faced by communities in disasters within the context of COVID-19 and other disasters. Readers are encouraged to explore topics and voices that most resonate with their own community. To access an online and interactive version of RCRC Issue Briefs, please visit https://rcrctoolbox.org/rcrc-issue-briefs

Informes Temáticos RCRC: Porqué los Niños Deben Ser la Prioridad #1 en Desastres

Los Informes Temáticos RCRC, en este documento, están diseñados para ser utilizados por las comunidades de la iniciativa RCRC y todas las otras comunidades que buscan elevar la resiliencia de los niños ante desastres a la atención de legisladores locales, estatales y federales u otros responsables de la toma de decisiones. Estos informes también pueden ser utilizados por legisladores y responsables de la toma de decisiones en todos los niveles de gobierno como documentos informativos para comprender mejor los problemas que enfrentan las comunidades en desastres en el contexto de COVID-19 y otros desastres. Se anima a los lectores a explorar los temas y mensajes que más resuenan con su propia comunidad. Para acceder a una versión online e interactiva de los Informes Temáticos RCRC, visite https://rcrctoolbox.org/rcrc-issue-briefs-es/

Processing Ordinality and Quantity: The Case of Developmental Dyscalculia

In contrast to quantity processing, up to date, the nature of ordinality has received little attention from researchers despite the fact that both quantity and ordinality are embodied in numerical information. Here we ask if there are two separate core systems that lie at the foundations of numerical cognition: (1) the traditionally and well accepted numerical magnitude system but also (2) core system for representing ordinal information. We report two novel experiments of ordinal processing that explored the relation between ordinal and numerical information processing in typically developing adults and adults with developmental dyscalculia (DD). Participants made “ordered” or “non-ordered” judgments about 3 groups of dots (non-symbolic numerical stimuli; in Experiment 1) and 3 numbers (symbolic task: Experiment 2). In contrast to previous findings and arguments about quantity deficit in DD participants, when quantity and ordinality are dissociated (as in the current tasks), DD participants exhibited a normal ratio effect in the non-symbolic ordinal task. They did not show, however, the ordinality effect. Ordinality effect in DD appeared only when area and density were randomized, but only in the descending direction. In the symbolic task, the ordinality effect was modulated by ratio and direction in both groups. These findings suggest that there might be two separate cognitive representations of ordinal and quantity information and that linguistic knowledge may facilitate estimation of ordinal information