Resolving domination in graphs

summary:For an ordered set $W =\lbrace w_1, w_2, \cdots , w_k\rbrace$ of vertices and a vertex $v$ in a connected graph $G$, the (metric) representation of $v$ with respect to $W$ is the $k$-vector $r(v|W) = (d(v, w_1),d(v, w_2) ,\cdots , d(v, w_k))$, where $d(x,y)$ represents the distance between the vertices $x$ and $y$. The set $W$ is a resolving set for $G$ if distinct vertices of $G$ have distinct representations with respect to $W$. A resolving set of minimum cardinality is called a minimum resolving set or a basis and the cardinality of a basis for $G$ is its dimension $\dim G$. A set $S$ of vertices in $G$ is a dominating set for $G$ if every vertex of $G$ that is not in $S$ is adjacent to some vertex of $S$. The minimum cardinality of a dominating set is the domination number $\gamma (G)$. A set of vertices of a graph $G$ that is both resolving and dominating is a resolving dominating set. The minimum cardinality of a resolving dominating set is called the resolving domination number $\gamma _r(G)$. In this paper, we investigate the relationship among these three parameters

Powerful alliances in graphs

AbstractFor a graph G=(V,E), a non-empty set S⊆V is a defensive alliance if for every vertex v in S, v has at most one more neighbor in V−S than it has in S, and S is an offensive alliance if for every v∈V−S that has a neighbor in S, v has more neighbors in S than in V−S. A powerful alliance is both defensive and offensive. We initiate the study of powerful alliances in graphs

Computational Design Optimization of a Smart Material Shape Changing Building Skin Tile

The development and evaluation of a computational approach for optimal design of a smart material shape changing building skin is presented and numerically evaluated. Specifically, a unique shape-based approach is utilized to create an optimization approach to identify the activation and actuation mechanisms to minimize the difference between a desired shape and the estimated morphed shape. Three potential metrics of shape difference are considered and their capability to facilitate an efficient optimization process leading to accurate shape matching is evaluated. Details of the optimal design framework are presented, particularly focusing on the shape difference metrics as well as the strategy to parameterize the activation of the smart material. In particular, the parameterization strategy is a unique approach to easily integrate controllable localized activation within a smart material structure in a generally applicable way that does not limit the design search space. A series of numerical design examples are presented based on the concept of a smart material (e.g., shape memory polymer) shape changing tile that can be activated and actuated in a variety of ways to achieve desirable surface wrinkle patterns. These numerical design examples are applied to both 2D and 3D problems and consider a variety of parameterizations and target shapes. Results indicate that the shape-based approach can consistently determine the mechanisms of morphing needed to accurately match a target shape. Furthermore, it is shown that localized material activation can lead to not only a more accurate shape but also requires less energy and actuation devices to do so

Fast Fourier Optimization: Sparsity Matters

Many interesting and fundamentally practical optimization problems, ranging from optics, to signal processing, to radar and acoustics, involve constraints on the Fourier transform of a function. It is well-known that the {\em fast Fourier transform} (fft) is a recursive algorithm that can dramatically improve the efficiency for computing the discrete Fourier transform. However, because it is recursive, it is difficult to embed into a linear optimization problem. In this paper, we explain the main idea behind the fast Fourier transform and show how to adapt it in such a manner as to make it encodable as constraints in an optimization problem. We demonstrate a real-world problem from the field of high-contrast imaging. On this problem, dramatic improvements are translated to an ability to solve problems with a much finer grid of discretized points. As we shall show, in general, the "fast Fourier" version of the optimization constraints produces a larger but sparser constraint matrix and therefore one can think of the fast Fourier transform as a method of sparsifying the constraints in an optimization problem, which is usually a good thing.Comment: 16 pages, 8 figure

Challenging the obesity paradox: Extreme obesity and COPD mortality in the SUMMIT Trial

Populations with COPD demonstrate higher survival in overweight and obese compared with normal weight; the “obesity paradox”. Relationships in less-severe COPD are unclear, as is the impact of cardiovascular risk, and few studies include individuals at extremes of obesity.  We examined the relationship between body mass index (BMI; defined as underweight: 40 kg·m−2, suggesting that obesity may not remain protective at the extremes in this population

An integrated clinical program and crowdsourcing strategy for genomic sequencing and Mendelian disease gene discovery.

Despite major progress in defining the genetic basis of Mendelian disorders, the molecular etiology of many cases remains unknown. Patients with these undiagnosed disorders often have complex presentations and require treatment by multiple health care specialists. Here, we describe an integrated clinical diagnostic and research program using whole-exome and whole-genome sequencing (WES/WGS) for Mendelian disease gene discovery. This program employs specific case ascertainment parameters, a WES/WGS computational analysis pipeline that is optimized for Mendelian disease gene discovery with variant callers tuned to specific inheritance modes, an interdisciplinary crowdsourcing strategy for genomic sequence analysis, matchmaking for additional cases, and integration of the findings regarding gene causality with the clinical management plan. The interdisciplinary gene discovery team includes clinical, computational, and experimental biomedical specialists who interact to identify the genetic etiology of the disease, and when so warranted, to devise improved or novel treatments for affected patients. This program effectively integrates the clinical and research missions of an academic medical center and affords both diagnostic and therapeutic options for patients suffering from genetic disease. It may therefore be germane to other academic medical institutions engaged in implementing genomic medicine programs

Inhibitory Effects of Prior Low-dose X-irradiation on Ischemia-reperfusion Injury in Mouse Paw

We have reported that low-dose, unlike high-dose, irradiation enhanced antioxidation function and reduced oxidative damage. On the other hand, ischemia-reperfusion injury is induced by reactive oxygen species. In this study, we examined the inhibitory effects of prior low-dose X-irradiation on ischemia-reperfusion injury in mouse paw. BALB/c mice were irradiated by sham or 0.5 Gy of X-ray. At 4 hrs after irradiation, the left hind leg was bound 10 times with a rubber ring for 0.5, 1, or 2 hrs and the paw thickness was measured. Results show that the paw swelling thickness by ischemia for 0.5 hr was lower than that for 2 hrs. At 1 hr after reperfusion from ischemia for 1 hr, superoxide dismutase activity in serum was increased in those mice which received 0.5 Gy irradiation and in the case of the ischemia for 0.5 or 1 hr, the paw swelling thicknesses were inhibited by 0.5 Gy irradiation. In addition, interstitial edema in those mice which received 0.5 Gy irradiation was less than that in the mice which underwent by sham irradiation. These findings suggest that the ischemia-reperfusion injury is inhibited by the enhancement of antioxidation function by 0.5 Gy irradiation

The charcoal trap: Miombo forests and the energy needs of people

<p>Abstract</p> <p>Background</p> <p>This study evaluates the carbon dioxide and other greenhouse gas fluxes to the atmosphere resulting from charcoal production in Zambia. It combines new biomass and flux data from a study, that was conducted in a <it>miombo </it>woodland within the Kataba Forest Reserve in the Western Province of Zambia, with data from other studies.</p> <p>Results</p> <p>The measurements at Kataba compared protected area (3 plots) with a highly disturbed plot outside the forest reserve and showed considerably reduced biomass after logging for charcoal production. The average aboveground biomass content of the reserve (Plots 2-4) was around 150 t ha^-1, while the disturbed plot only contained 24 t ha^-1. Soil carbon was not reduced significantly in the disturbed plot. Two years of eddy covariance measurements resulted in net ecosystem exchange values of -17 ± 31 g C m^-2y^-1, in the first and 90 ± 16 g C m^-2in the second year. Thus, on the basis of these two years of measurement, there is no evidence that the <it>miombo </it>woodland at Kataba represents a present-day carbon sink. At the country level, it is likely that deforestation for charcoal production currently leads to a per capita emission rate of 2 - 3 t CO₂y^-1. This is due to poor forest regeneration, although the resilience of <it>miombo </it>woodlands is high. Better post-harvest management could change this situation.</p> <p>Conclusions</p> <p>We argue that protection of <it>miombo </it>woodlands has to account for the energy demands of the population. The production at national scale that we estimated converts into 10,000 - 15,000 GWh y^-1of energy in the charcoal. The term "Charcoal Trap" we introduce, describes the fact that this energy supply has to be substituted when woodlands are protected. One possible solution, a shift in energy supply from charcoal to electricity, would reduce the pressure of forests but requires high investments into grid and power generation. Since Zambia currently cannot generate this money by itself, the country will remain locked in the charcoal trap such as many other of its African neighbours. The question arises whether and how money and technology transfer to increase regenerative electrical power generation should become part of a post-Kyoto process. Furthermore, better inventory data are urgently required to improve knowledge about the current state of the woodland usage and recovery. Net greenhouse gas emissions could be reduced substantially by improving the post-harvest management, charcoal production technology and/or providing alternative energy supply.</p

Identifying a Window of Vulnerability during Fetal Development in a Maternal Iron Restriction Model

It is well acknowledged from observations in humans that iron deficiency during pregnancy can be associated with a number of developmental problems in the newborn and developing child. Due to the obvious limitations of human studies, the stage during gestation at which maternal iron deficiency causes an apparent impairment in the offspring remains elusive. In order to begin to understand the time window(s) during pregnancy that is/are especially susceptible to suboptimal iron levels, which may result in negative effects on the development of the fetus, we developed a rat model in which we were able to manipulate and monitor the dietary iron intake during specific stages of pregnancy and analyzed the developing fetuses. We established four different dietary-feeding protocols that were designed to render the fetuses iron deficient at different gestational stages. Based on a functional analysis that employed Auditory Brainstem Response measurements, we found that maternal iron restriction initiated prior to conception and during the first trimester were associated with profound changes in the developing fetus compared to iron restriction initiated later in pregnancy. We also showed that the presence of iron deficiency anemia, low body weight, and changes in core body temperature were not defining factors in the establishment of neural impairment in the rodent offspring

Genetic effects on gene expression across human tissues

Characterization of the molecular function of the human genome and its variation across individuals is essential for identifying the cellular mechanisms that underlie human genetic traits and diseases. The Genotype-Tissue Expression (GTEx) project aims to characterize variation in gene expression levels across individuals and diverse tissues of the human body, many of which are not easily accessible. Here we describe genetic effects on gene expression levels across 44 human tissues. We find that local genetic variation affects gene expression levels for the majority of genes, and we further identify inter-chromosomal genetic effects for 93 genes and 112 loci. On the basis of the identified genetic effects, we characterize patterns of tissue specificity, compare local and distal effects, and evaluate the functional properties of the genetic effects. We also demonstrate that multi-tissue, multi-individual data can be used to identify genes and pathways affected by human disease-associated variation, enabling a mechanistic interpretation of gene regulation and the genetic basis of diseas