Yet Another Graph Partitioning Problem is NP-Hard

Recently a large number of graph separator problems have been proven to be \textsc{NP-Hard}. Amazingly we have found that $\alpha$-Subgraph-Balanced-Vertex-Separator, an important variant, has been overlooked. In this work ``Yet Another Graph Partitioning Problem is NP-Hard" we present the surprising result that $\alpha$-Subgraph-Balanced-Vertex-Separator is $NP$-Hard. This is despite the fact that the constraints of our new problem are harder to satisfy than the original problem

Topological & network theoretic approaches in hyperspectral remote sensing

Hyperspectral remote sensing is a valuable new technology that has numerous com- mercial and scientific applications. For example, it has been used to study crop health, mineral and soil composition, and pollution levels. Hyperspectral imaging also has im- portant military and intelligence applications such as the identification of man-made materials, and detection of chemical and biological plumes. The key mathematical challenges of hyperspectral imaging include image classification, anomaly detection, and target detection. Image classification is the process of grouping pixels into spec- trally similar clusters. This thesis describes a new topological and network-theoretic approach for classifying pixels in hyperspectral image data. Pixels in hyperspectral image data sets are thought of as constituting a point cloud in a high dimensional topological space, and a network structure is imposed on the data by considering the spectral distance between pairs of pixels. We use the tools of persistent homology to argue that the resulting network effectively models the com- plex nonlinear structures in the data. We then perform data clustering by applying a network based community detection algorithm called the method of maximum modu- larity. The method of maximum modularity is an unsupervised, deterministic method for detecting communities in networks where neither the number of communities nor their sizes needs to be specified in advance. Examples of real hyperspectral images that have been classified using the method of maximum modularity are provided in order to demonstrate the feasibility of the approach

There are no multiply-perfect Fibonacci numbers

Here, we show that no Fibonacci number (larger than 1) divides the sum of its divisors

Pool boiling on modified surfaces using R-123

This article has been made available through the Brunel Open Access Publishing Fund.Saturated pool boiling of R-123 was investigated for five horizontal copper surfaces modified by different treatments, namely, an emery-polished surface, a fine sandblasted surface, a rough sandblasted surface, an electron beam-enhanced surface, and a sintered surface. Each 40-mm-diameter heating surface formed the upper face of an oxygen-free copper block, electrically heated by embedded cartridge heaters. The experiments were performed from the natural convection regime through nucleate boiling up to the critical heat flux, with both increasing and decreasing heat flux, at 1.01 bar, and additionally at 2 bar and 4 bar for the emery-polished surface. Significant enhancement of heat transfer with increasing surface modification was demonstrated, particularly for the electron beam-enhanced and sintered surfaces. The emery-polished and sandblasted surface results are compared with nucleate boiling correlations and other published data. © 2014 Syed W. Ahmad, John S. Lewis, Ryan J. McGlen, and Tassos G. Karayiannis Published with license by Taylor & Francis

Autophagy, but Not Proteolysis, May Aid in Muscle Protein Synthesis

For muscle growth to occur, protein synthesis must be greater than protein degradation. However, up to this point, anabolic pathways have garnered the brunt of investigations examining anabolic capacity with little investigation into the connectedness of catabolic signaling on these anabolic targets. PURPOSE: The purpose of this study was to elucidate the contributions of proteasomal-dependent and autophagic-dependent catabolic pathways on anabolism via analysis of fractional synthetic rates (FSR) in L6 myotubes. METHODS: Differentiated, cultured L6 myoblasts were treated with media containing 4% deuterium oxide (stable isotope label) and a corresponding pharmacological treatment (NSC 185058 [autophagic inhibitor; 100 μM], MG-262 [proteasomal inhibitor; 0.01 μM] or DMSO control; n=3/group) during the final 24-hours of the differentiation period prior to harvest. The myofibrillar pellet of the processed samples was used to determine FSR via mass-spectrometry analysis. DMSO-treated myotubes served as controls, with a one-way analysis of variance and Tukey’s post-hoc test used to test for any differences among groups. RESULTS: Our results indicate that MG-262 had no impact on myofibrillar FSR when compared to DMSO control (MG-262 1.0993 %/day vs. control 1.239 %/day). However, NSC 185058 lowered myofibrillar FSR (NSC 185058 0.9009 %/day vs. control 1.239 %/day; P=0.0282). CONCLUSION: These data suggest that inhibition of autophagic machinery can impair anabolism. This may be due to autophagy’s role in increasing the amino acid pool within the cell. Further, the lack of inhibition seen from MG-262 suggests that there is a delineation of roles within the catabolic pathways in regard to their influence on anabolism in healthy, metabolically unchallenged myotubes

High-yield atmospheric water capture via bioinspired material segregation

Atmospheric water harvesting is urgently needed given increasing global water scarcity. Current sorbent-based devices that cycle between water capture and release have low harvesting rates. We envision a radically different multi-material architecture with segregated and simultaneous capture and release. This way, proven fast-release mechanisms that approach theoretical limits can be incorporated; however, no capture mechanism exists to supply liquid adequately for release. Inspired by tree frogs and airplants, our capture approach transports water through a hydrogel membrane ``skin'' into a liquid desiccant. We report an extraordinarily high capture rate of 5.50 $\text{kg}\,\text{m}^{-2}\,\text{d}^{-1}$ at a low humidity of 35%, limited by the convection of air to the device. At higher humidities, we demonstrate up to 16.9 $\text{kg}\,\text{m}^{-2}\,\text{d}^{-1}$, exceeding theoretical limits for release. Simulated performance of a hypothetical one-square-meter device shows that water could be supplied to two to three people in dry environments. This work is a significant step toward providing new resources to water-scarce regions.Comment: 22 pages, 23 figure