A short constructive proof of A.R. Rao’s characterization of potentially Kr+1-graphic sequences

AbstractLet Kr+1 be the complete graph on r+1 vertices. Rao proved that a non-increasing sequence (d1,d2,…,dn) of nonnegative integers with dr+1≥r has a realization containing Kr+1 as a subgraph if and only if ∑i=1ndi is even and ∑i=1sdi+∑i=1tdr+1+i≤(s+t)(s+t−1)+∑i=s+1r+1min{s+t,di−r+s}+∑i=r+t+2nmin{s+t,di} for all s and t with 0≤s≤r+1 and 0≤t≤n−r−1. In this paper, we give a short constructive proof of this characterization that can be implemented as an algorithm to construct a realization containing Kr+1

Stress-Strain Behaviour of Completely Decomposed Granite in Both Triaxial and Plane Strain Conditions

Most of the field problems in geotechnical engineering are in three dimensional state or close to a plane strain condition. Strength and deformation properties of soils in plane strain condition are considerably different from those in an axisymmetric condition. Many researchers have investigated the behaviour of soils under a plane strain condition. However, most of the previous studies have concentrated on sedimentary type of soils like sand and clay. Our understanding on the plane strain behaviour for residual soils is less than that for sedimentary soils. A true triaxial system with four sliding rigid-plates and real time feedback control has been used to test specimens of a completely decomposed granite (CDG) soil (a residual soil) under plane strain condition. The setup of the true-triaxial rigid plates is briefly introduced first. The preparation of soil specimens and testing procedures are described. The basic properties of the CDG are presented. The stressstrain and strength behaviour of the soil obtained under plane strain condition was investigated and compared to the behaviour obtained under axisymmetric loading conditions. The results revealed that the critical state line in q-p′ space obtained under plane strain condition is the same as that obtained under axisymmetric condition. However, the critical state line in e- ln p′ space obtained under undrained plane strain condition is different from that obtained under axisymmetric condition. The peak friction angle for plane strain tests is higher than that from axisymmetric loadings. It is also found that shear bands occur only in drained plane strain compression. Defuse bulging is the mode of failure for undrained plane strain as well as triaxial loading

A variation of a classical Turán-type extremal problem

AbstractA variation of a classical Turán-type extremal problem (Erdős on Graphs: His Legacy of Unsolved Problems (1998) p. 36) is considered as follows: determine the smallest even integer σ(Kr,s,n) such that every n-term graphic non-increasing sequence π=(d1,d2,…,dn) with term sum σ(π)=d1+d2+⋯+dn≥σ(Kr,s,n) has a realization G containing Kr,s as a subgraph, where Kr,s is a r×s complete bipartite graph. In this paper, we determine σ(Kr,s,n) exactly for every fixed s≥r≥3 when n≥n0(r,s), where m=[(r+s+1)24] andn0(r,s)=m+3s2−2s−6,ifs≤2randsis even,m+3s2+2s−8,ifs≤2randsis odd,m+2s2+(2r−6)s+4r−8,ifs≥2r+1

Expression, purification and structural analysis of functional GABA transporter 1 using the baculovirus expression system

The γ-aminobutyric acid (GABA) transporter 1 (GAT1) belongs to a family of Na+ and Cl−-coupled transport proteins and possesses 12 putative transmembrane domains. To perform structural analyses of the GAT1 protein, the GAT1/green fluorescent protein (GFP) fusion protein was functionally expressed in insect Sf9 cells by the BAC-TO-BAC® baculovirus expression system. A two-step procedure to purify the GAT1/GFP fusion protein from insect Sf9 cells has been established and involves immunoaffinity chromatography using self-prepared anti-GFP antibodies and size-exclusion fast protein liquid chromatography (SE- FPLC). A yield of 200–300 μg of the GAT1/GFP protein could be purified from 400–600 mL of infected Sf9 cells. The purified protein was analyzed by transmission electron microscopy (TEM), which revealed that the GAT1/GFP fusion protein was isolated in its monomeric form

CsACO4, an ACC oxidase gene regulating male differentiation in cucumber

Ethylene has been implicated as a sex-determining hormone in cucumber: Its exogenous application increases femaleness and gynoecious genotypes were reported to produce more ethylene. 1- aminocyclopropane-1-carboxylate (ACC) oxidase (ACO) is the key enzyme in ethylene biosynthesis. In this study, a 1,188 base pair (bp) fragment was amplified from cucumber (Jinyan-4) genome with degenerated primers derived from the ACO amino acid consensus sequence among different plant species. The putative new gene was analyzed by bioinformatic tools. Phylogenic analysis result of the new gene (CsACO4, GenBank accession number AY450356) was in accordance with the evolution relationship of genetics among various plant species. The result of BLAST showed the sequence presented a very high match with the ACO genes from other plants; the homologue was from 80 to 99%. Using the sequence, a RNA interference (RNAi) transformation vector was constructed through the way of BP cloning. Eleven transgenic plants were obtained. The transgene integrated into cucumber genome was proved with PCR and southern blotting. The morphological exploration showed that the inserted RNAi target fragments could inhibit the endogenous CsACO4 gene expression and that it could regulate male differentiation in the lower nodes in cucumber.Keywords: Cucumber, ACC oxidase gene, RNAi, male differentiatio

Observation of fractional topological numbers at photonic edges and corners

Topological phases of matter are featured with exotic edge states. However, the fractional topological numbers at edges, though predicted long ago by Jackiw and Rebbi, remain elusive in topological photonic systems. Here, we report on the observation of fractional topological numbers at the topological edges and corners in one- and two-dimensional photonic crystals. The fractional topological numbers are determined via the measurements of the photonic local density-of-states. In one-dimensional photonic crystals, we witness a rapid change of the fractional topological number at the edges rising from 0 to 1/2 when the photonic band gap experiences a topological transition, confirming the well-known prediction of Jackiw and Rebbi. In two-dimensional systems, we discover that the fractional topological number in the corner region varies from 0 to 1/2 and 1/4 in different photonic band gap phases. Our study paves the way toward topological manipulation of fractional quantum numbers in photonics.Comment: All comments are welcom

Observation of quantum fingerprinting beating the classical limit

Quantum communication has historically been at the forefront of advancements, from fundamental tests of quantum physics to utilizing the quantum-mechanical properties of physical systems for practical applications. In the field of communication complexity, quantum communication allows the advantage of an exponential reduction in the information transmitted over classical communication to accomplish distributed computational tasks. However, to date, demonstrating this advantage in a practical setting continues to be a central challenge. Here, we report an experimental demonstration of a quantum fingerprinting protocol that for the first time surpasses the ultimate classical limit to transmitted information. Ultra-low noise superconducting single-photon detectors and a stable fibre-based Sagnac interferometer are used to implement a quantum fingerprinting system that is capable of transmitting less information than the classical proven lower bound over 20 km standard telecom fibre for input sizes of up to two Gbits. The results pave the way for experimentally exploring the advanced features of quantum communication and open a new window of opportunity for research in communication complexity and testing the foundations of physics.Comment: 19 pages, 4 figure