On cutting blocking sets and their codes

Let PG ⁡ ( r , q ) {\operatorname{PG}(r,q)} be the r-dimensional projective space over the finite field GF ⁡ ( q ) {\operatorname{GF}(q)} . A set 𝒳 {\mathcal{X}} of points of PG ⁡ ( r , q ) {\operatorname{PG}(r,q)} is a cutting blocking set if for each hyperplane Π of PG ⁡ ( r , q ) {\operatorname{PG}(r,q)} the set Π ∩ 𝒳 {\Pi\cap\mathcal{X}} spans Π. Cutting blocking sets give rise to saturating sets and minimal linear codes, and those having size as small as possible are of particular interest. We observe that from a cutting blocking set obtained in [20], by using a set of pairwise disjoint lines, there arises a minimal linear code whose length grows linearly with respect to its dimension. We also provide two distinct constructions: a cutting blocking set of PG ⁡ ( 3 , q 3 ) {\operatorname{PG}(3,q^{3})} of size 3 ⁢ ( q + 1 ) ⁢ ( q 2 + 1 ) {3(q+1)(q^{2}+1)} as a union of three pairwise disjoint q-order subgeometries, and a cutting blocking set of PG ⁡ ( 5 , q ) {\operatorname{PG}(5,q)} of size 7 ⁢ ( q + 1 ) {7(q+1)} from seven lines of a Desarguesian line spread of PG ⁡ ( 5 , q ) {\operatorname{PG}(5,q)} . In both cases, the cutting blocking sets obtained are smaller than the known ones. As a byproduct, we further improve on the upper bound of the smallest size of certain saturating sets and on the minimum length of a minimal q-ary linear code having dimension 4 and 6.

Sensory Profiling and External Preference Mapping of Pre-Thickened Water Products for Dysphagia

Dysphagia is a dysfunction of the swallowing system and thickened beverages are widely prescribed as a treatment. The objective of this study was to determine the sensory characteristics of pre-thickened water products and determine sensory drivers of liking for those types of products. Pre-thickened water products (two starch-based and two gum-based) were tested in both nectar and honey thick versions. Based on product availability, one product was neutral water, and the others were water with lemon flavoring added. The sensory characteristics of the products were evaluated with a highly trained descriptive panel, and the viscosity of the products was evaluated with both the Bostwick consistometer and the line spread test. Previously published consumer data was used to determine preference maps with the descriptive data. All lemon-flavored products had similar flavor characteristics, except the Thick & Easy Clear that had a less lemon-related flavor than the others. After excluding the lemon-related flavor characteristics, all pre-thickened products had similar “base flavor” notes, no matter whether the products were starch-based or gum-based. This contrasts with literature, which reports differences in flavor of thickened beverages prepared using thickening agents. The thickness of the products varied between nectar and honey thickness, but also varied among products that were stated to be at the same level of thickness. External preference mapping showed that both lemon-related flavor and a thinner beverage texture are potential drivers of consumers acceptance of the product, which was expected based on other studies. In conclusion, pre-thickened beverages are good alternatives for self-mixed thickening agents but a standard for thickness should be agreed on and used by manufacturers.

Stray-Light Correction Methodology for the Precision Solar Spectroradiometer

A stray-light correction methodology for the Precision Solar Spectroradiometer (PSR) is presented. The correction is based on laboratory-measured line spread functions also taking into account the radiation from the 2nd and 3rd grating orders. The efficiency of the correction is validated on solar and lamp measurement data. The results are compared to those obtained with a PSR equipped with an order-sorting filter and with a Precision Filter Radiometer.

Calibration of the Marshall Grazing Incidence X-Ray Spectrometer Experiment. II. Flight Instrument Calibration

The Marshall Grazing Incidence X-ray Spectrometer (MaGIXS) is a sounding rocket experiment that observes the soft X-ray spectrum of the Sun from 6.0–24 Å (0.5–2.0 keV), successfully launched on 2021 July 30. End-to-end alignment of the flight instrument and calibration experiments are carried out using the X-ray and Cryogenic Facility at NASA Marshall Space Flight Center. In this paper, we present the calibration experiments of MaGIXS, which include wavelength calibration, measurement of line spread function, and determination of effective area. Finally, we use the measured instrument response function to predict the expected count rates for MaGIXS flight observation looking at a typical solar active region.

Characterizations of the $G_2(4)$ and $L_3(4)$ Near Octagons

A triple $(\mathcal{S},S,\mathcal{Q})$ consisting of a near polygon $\mathcal{S}$, a line spread $S$ of $\mathcal{S}$ and a set $\mathcal{Q}$ of quads of $\mathcal{S}$ is called a polygonal triple if certain nice properties are satisfied, among which there is the requirement that the point-line geometry $\mathcal{S}'$ formed by the lines of $S$ and the quads of $\mathcal{Q}$ is itself also a near polygon. This paper addresses the problem of classifying all near polygons $\mathcal{S}$ that admit a polygonal triple $(\mathcal{S},S,\mathcal{Q})$ for which a given generalized polygon $\mathcal{S}'$ is the associated near polygon. We obtain several nonexistence results and show that the $G_2(4)$ and $L_3(4)$ near octagons are the unique near octagons that admit polygonal triples whose quads are isomorphic to the generalized quadrangle $W(2)$ and whose associated near polygons are respectively isomorphic to the dual split Cayley hexagon $H^D(4)$ and the unique generalized hexagon of order $(4,1)$.

Relationship between Syringe Flow Measurements and Viscosity of Nectar-Thick Beverages for Dysphagia Management

Commercial cold beverages thickened with a xanthan gum (XG)-based food thickener were examined at different thickness levels by using the simple, cost-effective syringe flow test (SFT) developed by the International Dysphagia Diet Standardization Initiative (IDDSI). We prepared cold thickened beverage (CTB) samples with different thickener concentrations and measured them by extrapolating the viscosity range (51–350 mPa·s) for nectar-like consistency. CTBs were also measured via the line-spread test (LST), and the flow distance value (cm) by LST and the volume remaining (mL) in the syringe by SFT was correlated with the apparent viscosity (ηa,50). Plots comparing ηa,50 with SFT or LST values showed good exponential relationships between the measurements. The SFT showed a better relationship (R2 = 0.928) than LST (R2 = 0.825), indicating that the former can predict the viscosity better in the range for nectar-like consistency. In particular, the SFT showed a significant difference (R2 = 0.964) compared to the LST (R2 = 0.709) for thickened protein-based beverages. These results suggest that the SFT using the IDDSI methodology is a more suitable instrument than the LST for accurately evaluating the viscosity of XG-based CTBs with nectar-like consistency.

Prediction of the layered ink layout for 3D printers considering a desired skin color and line spread function

We propose a layout estimation method for multi-layered ink using a measurement of the line spread function (LSF) and machine learning. The three-dimensional printing market for general consumers focuses on the reproduction of realistic appearance. In particular, for the reproduction of human skin, it is important to control translucency by adopting a multilayer structure. Traditionally, layer design has depended on the experience of designers. We, therefore, developed an efficient layout estimation to provide arbitrary skin color and translucency. In our method, we create multi-layered color patches of human skin and measure the LSF as a metric of translucency, and we employ a neural network trained with the data to estimate the layout. As an evaluation, we measured the LSF from the computer-graphics-created skin and fabricate skin using the estimated layout; evaluation with root-mean-square error showed that we can obtain color and translucency that are close to the target.