Bandwidth and density for block graphs

The bandwidth of a graph G is the minimum of the maximum difference between adjacent labels when the vertices have distinct integer labels. We provide a polynomial algorithm to produce an optimal bandwidth labeling for graphs in a special class of block graphs (graphs in which every block is a clique), namely those where deleting the vertices of degree one produces a path of cliques. The result is best possible in various ways. Furthermore, for two classes of graphs that are ``almost'' caterpillars, the bandwidth problem is NP-complete.Comment: 14 pages, 9 included figures. Note: figures did not appear in original upload; resubmission corrects thi

Microwave Inter-Connections and Switching by means of Carbon Nano-tubes

In this work, carbon nanotube (CNT) based interconnections and switches will be reviewed, discussing the possibility to use nanotubes as potential building blocks for signal routing in microwave networks. In particular, theoretical design of coplanar waveguide (CPW), micro‐strip single‐pole‐single‐throw (SPST) and single‐pole‐double‐throw (SPDT) devices has been performed to predict the electrical performances of CNT‐based RF switching configurations. Actually, by using the semiconductor‐conductor transition obtained by properly biasing the CNTs, an isolation better than 30 dB can be obtained between the ON and OFF states of the switch for very wide bandwidth applications. This happens owing to the shape deformation and consequent change in the band‐gap due to the external pressure caused by the electric field. State‐of‐art for other switching techniques based on CNTs and their use for RF nano‐interconnections is also discussed, together with current issues in measurement techniques

Harmonic Sums and Mellin Transforms up to two-loop Order

A systematic study is performed on the finite harmonic sums up to level four. These sums form the general basis for the Mellin transforms of all individual functions $f_i(x)$ of the momentum fraction $x$ emerging in the quantities of massless QED and QCD up to two--loop order, as the unpolarized and polarized splitting functions, coefficient functions, and hard scattering cross sections for space and time-like momentum transfer. The finite harmonic sums are calculated explicitly in the linear representation. Algebraic relations connecting these sums are derived to obtain representations based on a reduced set of basic functions. The Mellin transforms of all the corresponding Nielsen functions are calculated.Comment: 44 pages Latex, contract number adde

Rapid integrated assessment of food safety and nutrition related to pork consumption of regular consumers and mothers with young children in Vietnam

Pork is the most common and widely consumed meat product in Vietnam. The study aimed to assess nutrition and food safety risks and opportunities associated with pork value chains in Vietnam. Twenty-nine focus group discussions (FGD) were conducted in Hung Yen and Nghe An provinces with 164 participants who were both regular pork consumers and mothers with young children. In each province, three districts were selected, and in each district we selected one commune. To assess the quality of pork, we took 30 swab samples of pig carcasses at slaughterhouses, 90 pork samples at slaughterhouses and markets and analysed all samples for total bacterial count (TBC), coliforms, water holding capacity and pH. The results showed that pork was the main livestock product consumed and women are responsible for buying and preparing food for daily meals. Pork was the main animal sourced food (ASF) for Vietnamese consumers, for 50–60% of ASF. There was little knowledge of zoonotic diseases. The findings suggest further studies to address consumers’ concern on chemical contamination. Most market pork samples were not within the allowable range of limits standards of Vietnam for bacterial contamination: 90% of samples were above the official permissible limit for TBC and 98% did not meet standards for coliforms. Fifty percent of samples had acceptable pH but only 5% had acceptable water holding capacity. There were no significant differences in pork quality between intensifying Hung Yen and traditional Nghe An provinces, although there was a tendency for samples from Hung Yen to have better compliance. This rapid assessment revealed considerable interest and knowledge on pork nutrition and safety and found some behavioural but few quality and safety differences between traditional and intensifying systems. This indicated marketed pork is of low quality and safety, and a lack of support to consumers in making good choices

A unified convergence analysis for shuffling-type gradient methods

In this paper, we propose a unified convergence analysis for a class of generic shuffling-type gradient methods for solving finite-sum optimization problems. Our analysis works with any sampling without replacement strategy and covers many known variants such as randomized reshuffling, deterministic or randomized single permutation, and cyclic and incremental gradient schemes. We focus on two different settings: strongly convex and nonconvex problems, but also discuss the non-strongly convex case. Our main contribution consists of new non-asymptotic and asymptotic convergence rates for a wide class of shuffling-type gradient methods in both nonconvex and convex settings. We also study uniformly randomized shuffling variants with different learning rates and model assumptions. While our rate in the nonconvex case is new and significantly improved over existing works under standard assumptions, the rate on the strongly convex one matches the existing best-known rates prior to this paper up to a constant factor without imposing a bounded gradient condition. Finally, we empirically illustrate our theoretical results via two numerical examples: nonconvex logistic regression and neural network training examples. As byproducts, our results suggest some appropriate choices for diminishing learning rates in certain shuffling variants