L-Visibility Drawings of IC-planar Graphs

An IC-plane graph is a topological graph where every edge is crossed at most once and no two crossed edges share a vertex. We show that every IC-plane graph has a visibility drawing where every vertex is an L-shape, and every edge is either a horizontal or vertical segment. As a byproduct of our drawing technique, we prove that an IC-plane graph has a RAC drawing in quadratic area with at most two bends per edge

Sodium content of restaurant dishes in China: a cross-sectional survey

BACKGROUND: Sodium intake in China is extremely high and eating in restaurants is increasingly popular. Little research has explored the sodium level of restaurant dishes. The present study aims to assess the content and sources of sodium in Chinese restaurants. METHODS: Cross-sectional data were obtained from the baseline survey of the Restaurant-based Intervention Study (RIS) in 2019. A total of 8131 best-selling restaurant dishes with detailed recipes from 192 restaurants in China were included. Sodium content per 100 g and per serving were calculated according to the Chinese Food Composition Table. The proportion of restaurant dishes exceeding the daily sodium reference intake level in a single serving and the major sources of sodium were determined. RESULTS: Median sodium content in restaurant dishes were 487.3 mg per 100 g, 3.4 mg per kcal, and 2543.7 mg per serving. For a single serving, 74.9% of the dishes exceeded the Chinese adults’ daily adequate intake for sodium (AI, 1500 mg per day), and 62.6% of dishes exceeded the proposed intake for preventing non-communicable chronic diseases (PI, 2000 mg per day). Cooking salt was the leading source of sodium in Chinese restaurant dishes (45.8%), followed by monosodium glutamate (17.5%), food ingredients (17.1%), soy sauce (9.4%), and other condiments/seasonings (10.2%). More types of salted condiments/seasonings use were related to higher sodium level. CONCLUSIONS: The sodium levels in Chinese restaurant dishes are extremely high and variable. In addition to cooking salt, other salted condiments/seasonings also contribute a large proportion of sodium. Coordinated sodium reduction initiatives targeting the main sources of sodium in restaurant dishes are urgently needed

Peroxisome proliferator-activated receptor α-independent peroxisome proliferation

Hepatic peroxisome proliferation, increases in the numerical and volume density of peroxisomes, is believed to be closely related to peroxisome proliferator-activated receptor α (PPARα) activation; however, it remains unknown whether peroxisome proliferation depends absolutely on this activation. To verify occurrence of PPARα-independent peroxisome proliferation, fenofibrate treatment was used, which was expected to significantly enhance PPARα dependence in the assay system. Surprisingly, a novel type of PPARα-independent peroxisome proliferation and enlargement was uncovered in PPARα-null mice. The increased expression of dynamin-like protein 1, but not peroxisome biogenesis factor 11α, might be associated with the PPARα-independent peroxisome proliferation at least in part.ArticleBIOCHEMICAL AND BIOPHYSICAL RESEARCH COMMUNICATIONS 346(4): 1307-1311(2006)journal articl

Perfect matchings of polyomino graphs

This paper gives necessary and sufficient conditions for a polyomino graph to have a perfect matching and to be elementary, respectively. As an application, we can decompose a non-elementary polyomino with perfect matchings into a number of elementary subpolyominoes so that the number of perfect matchings of the original non-elementary polyomino is equal to the product of those of the elementary subpolyominoes

Awareness and Use of Low-Sodium Salt Substitutes and Its Impact on 24-h Urinary Sodium and Potassium Excretion in China-A Cross-Sectional Study.

The use of low-sodium salt substitute (LSSS) has the potential to reduce sodium and increase potassium intake. LSSS has been available in the Chinese market for years. However, its real-world use and impact on sodium/potassium intake is unclear. Baseline data of 4000 adult individuals who participated in three similarly designed randomized controlled trials were pooled together for this analysis. Self-reported awareness and use of LSSS were collected using a standardized questionnaire, and the participants' 24-h urinary sodium and potassium excretion was used to estimate their dietary intake. Mixed-effects models were developed to assess the relationship between LSSS and 24-h urinary sodium and potassium excretion. 32.0% of the participants reported awareness of LSSS and 11.7% reported its current use. After adjusting for location, sex, age, and education, compared with the group of participants unaware of LSSS, participants who were aware of but not using LSSS and those who were using LSSS had a lower 24-h urinary sodium excretion by -356.1 (95% CI: -503.9, -205.9) mg/d and -490.6 (95% CI: -679.2, -293.7) mg/d, respectively (p 0.05). In conclusion, the findings of low usage of LSSS and the reduced urinary sodium excretion associated with the awareness and use of LSSS provide further support for the prometon of LSSS as a key salt reduction strategy in China

Direct electronic measurement of the spin Hall effect

The generation, manipulation and detection of spin-polarized electrons in nanostructures define the main challenges of spin-based electronics[1]. Amongst the different approaches for spin generation and manipulation, spin-orbit coupling, which couples the spin of an electron to its momentum, is attracting considerable interest. In a spin-orbit-coupled system, a nonzero spin-current is predicted in a direction perpendicular to the applied electric field, giving rise to a "spin Hall effect"[2-4]. Consistent with this effect, electrically-induced spin polarization was recently detected by optical techniques at the edges of a semiconductor channel[5] and in two-dimensional electron gases in semiconductor heterostructures[6,7]. Here we report electrical measurements of the spin-Hall effect in a diffusive metallic conductor, using a ferromagnetic electrode in combination with a tunnel barrier to inject a spin-polarized current. In our devices, we observe an induced voltage that results exclusively from the conversion of the injected spin current into charge imbalance through the spin Hall effect. Such a voltage is proportional to the component of the injected spins that is perpendicular to the plane defined by the spin current direction and the voltage probes. These experiments reveal opportunities for efficient spin detection without the need for magnetic materials, which could lead to useful spintronics devices that integrate information processing and data storage.Comment: 5 pages, 4 figures. Accepted for publication in Nature (pending format approval

Recognizing and Drawing IC-planar Graphs

IC-planar graphs are those graphs that admit a drawing where no two crossed edges share an end-vertex and each edge is crossed at most once. They are a proper subfamily of the 1-planar graphs. Given an embedded IC-planar graph $G$ with $n$ vertices, we present an $O(n)$-time algorithm that computes a straight-line drawing of $G$ in quadratic area, and an $O(n^3)$-time algorithm that computes a straight-line drawing of $G$ with right-angle crossings in exponential area. Both these area requirements are worst-case optimal. We also show that it is NP-complete to test IC-planarity both in the general case and in the case in which a rotation system is fixed for the input graph. Furthermore, we describe a polynomial-time algorithm to test whether a set of matching edges can be added to a triangulated planar graph such that the resulting graph is IC-planar

Limit points of eigenvalues of (di)graphs

The study on limit points of eigenvalues of undirected graphs was initiated by A. J. Hoffman in 1972. Now we extend the study to digraphs. We prove: 1. Every real number is a limit point of eigenvalues of graphs. Every complex number is a limit point of eigenvalues of digraphs. 2. For a digraph D, the set of limit points of eigenvalues of iterated subdivision digraphs of D is the unit circle in the complex plane if and only if D has a directed cycle. 3. Every limit point of eigenvalues of a set D of digraphs (graphs) is a limit point of eigenvalues of a set of bipartite digraphs (graphs), where consists of the double covers of the members in D. 4. Every limit point of eigenvalues of a set D of digraphs is a limit point of eigenvalues of line digraphs of the digraphs in D. 5. If M is a limit point of the largest eigenvalues of graphs, then -M is a limit point of the smallest eigenvalues of graphs

Interpolation theorem for a continuous function on orientations of a simple graph

Let G be a simple graph. A function f from the set of orientations of G to the set of Iron-negative integers is called a continuous function on orientations of G if, for any two orientations O-1 and O-2 of G, \f(O-1) - f(O-2)\ less than or equal to 1 whenever O-1 and O-2 differ in the orientation of exactly one edge of G. We show that any continuous function on orientations of a simple graph G has the interpolation property as follows: If there are two orientations O-1 and O-2 of G with f(O-1) = p and f(O-2) = q, where p < q, then for any integer k such that p < k < q, there are at least m orientations O of G satisfying f(O) = k, where m equals the number of edges of G. It follows that some useful invariants of digraphs including the connectivity, the arc-connectivity and the absorption number, etc., have the above interpolation property on the set of all orientations of G