ON THE SOLUTIONS OF THE SCHWARTZ HOMOGENEOUS PROBLEM IN THE FORM OF VECTOR POLYNOMIALS OF THE SECOND DEGREE

This paper is devoted to introducing a nonlinear reconstruction operator, the piecewise polynomial harmonic (PPH), on nonuniform grids. We define this operator and we study its main properties, such as its reproduction of second-degree polynomials, approximation order, and conditions for convexity preservation. In particular, for σ quasi-uniform grids with σ≤4, we get a quasi C3 reconstruction that maintains the convexity properties of the initial data. We give some numerical experiments regarding the approximation order and the convexity preservation.

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A likelihood ratio approach for identifying three-quarter siblings in genetic databases

Heredity ◽

10.1038/s41437-020-00392-8 ◽

2021 ◽

Author(s):

Iván Galván-Femenía ◽

Carles Barceló-Vidal ◽

Lauro Sumoy ◽

Victor Moreno ◽

Rafael de Cid ◽

...

Keyword(s):

Likelihood Ratio ◽

Family Relationships ◽

Genetic Research ◽

Data Set ◽

Scientific Disciplines ◽

Genome Wide ◽

Standard Quality ◽

Control Procedures ◽

Identity By State ◽

Second Degree

AbstractThe detection of family relationships in genetic databases is of interest in various scientific disciplines such as genetic epidemiology, population and conservation genetics, forensic science, and genealogical research. Nowadays, screening genetic databases for related individuals forms an important aspect of standard quality control procedures. Relatedness research is usually based on an allele sharing analysis of identity by state (IBS) or identity by descent (IBD) alleles. Existing IBS/IBD methods mainly aim to identify first-degree relationships (parent–offspring or full siblings) and second degree (half-siblings, avuncular, or grandparent–grandchild) pairs. Little attention has been paid to the detection of in-between first and second-degree relationships such as three-quarter siblings (3/4S) who share fewer alleles than first-degree relationships but more alleles than second-degree relationships. With the progressively increasing sample sizes used in genetic research, it becomes more likely that such relationships are present in the database under study. In this paper, we extend existing likelihood ratio (LR) methodology to accurately infer the existence of 3/4S, distinguishing them from full siblings and second-degree relatives. We use bootstrap confidence intervals to express uncertainty in the LRs. Our proposal accounts for linkage disequilibrium (LD) by using marker pruning, and we validate our methodology with a pedigree-based simulation study accounting for both LD and recombination. An empirical genome-wide array data set from the GCAT Genomes for Life cohort project is used to illustrate the method.

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Author Correction to: Endemic Burkitt lymphoma in second-degree relatives in Northern Uganda: in-depth genome-wide analysis suggests clues about genetic susceptibility

Leukemia ◽

10.1038/s41375-021-01140-5 ◽

2021 ◽

Author(s):

Mateus H. Gouveia ◽

Isaac Otim ◽

Martin D. Ogwang ◽

Mingyi Wang ◽

Bin Zhu ◽

...

Keyword(s):

Genetic Susceptibility ◽

Burkitt Lymphoma ◽

Northern Uganda ◽

Genome Wide Analysis ◽

Genome Wide ◽

Second Degree

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1060 Does a second-degree relative with history of pre-eclampsia increase the risk of pre-eclampsia?

American Journal of Obstetrics and Gynecology ◽

10.1016/j.ajog.2020.12.1085 ◽

2021 ◽

Vol 224 (2) ◽

pp. S655-S656

Author(s):

Matthew A. Shanahan ◽

Alison N. Goulding ◽

Grace J. Johnson ◽

Kjersti M. Aagaard

Keyword(s):

Degree Relative ◽

History Of ◽

Second Degree

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The Use of Visible-Light Hyperspectral Imaging in Evaluating Burn Wounds: A Case Report

Journal of Burn Care & Research ◽

10.1093/jbcr/irab003 ◽

2021 ◽

Author(s):

Melissa McCarthy ◽

Victoria Irene Prete ◽

SeungJu Oh ◽

Garrick Gu ◽

Jorge Lujan-Hernandez ◽

...

Keyword(s):

Case Report ◽

Visible Light ◽

Hyperspectral Imaging ◽

Initial Evaluation ◽

Contrast Imaging ◽

Post Injury ◽

Irreversible Damage ◽

Thermal Burn ◽

Burn Depth ◽

Second Degree

Abstract Burn depth is a critical factor in determining the healing potential of a burn as the extent of injury ultimately guides overall treatment. Visible Light Hyperspectral Imaging is an FDA-approved, non-invasive, and non-contrast imaging technology that uses light waves within the visible spectrum to evaluate skin and superficial soft tissue perfusion. In this case report, Visible Light Hyperspectral Imaging was used to evaluate a 37-year-old male who presented to the Emergency Department with a thermal burn of the trunk, back, and right upper extremity. Images were taken at initial evaluation, 6-hours post-injury, and again during daily dressing changes until hospital day five when patient underwent surgical debridement. In this patient, operative treatment was postponed until 89.7-hours post-injury, at which point the clinical exam showed clear visual demarcation in regions of irreversible damage. Comparatively, Visible Light Hyperspectral Imaging analysis of the permanently injured tissue demonstrated acute but varying changes in both oxygenated hemoglobin and deoxygenated hemoglobin at the time of initial evaluation. The most dramatic change in tissue oxygenation occurred between 6.5 and 39.3 hours, demonstrating Visible Light Hyperspectral Imaging’s ability to detect significant differences in oxygenation values between areas of second-degree superficial burns and areas of second degree deep and third degree burns in the acute period. The data suggest that the utilization of Visible Light Hyperspectral Imaging in this 6.5-39.3-hour window may help predict final burn depth before clinical assessment, potentially allowing for surgical intervention within the first 48-hours following injury.

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