Linear inequalities among graph invariants: Using GraPHedron to uncover optimal relationships

Optimality of a linear inequality in finitely many graph invariants is defined through a geometric approach. For a fixed number of graph vertices, consider all the tuples of values taken by the invariants on a selected class of graphs. Then form the polytope which is the convex hull of all these tuples. By definition, the optimal linear inequalities correspond to the facets of this polytope. They are finite in number, are logically independent, and generate precisely all the linear inequalities valid on the class of graphs. The computer system GraPHedron, developed by some of the authors, is able to produce experimental data about such inequalities for a "small" number of vertices. It greatly helps in conjecturing optimal linear inequalities, which are then hopefully proved for any number of vertices. Two examples are investigated here for the class of connected graphs. First, all the optimal linear inequalities for the stability number and the number of edges are obtained. To this aim, a problem of Ore (1962) related to the Turán Theorem (1941) is solved. Second, several optimal inequalities are established for three invariants: the maximum degree, the irregularity, and the diameter. © 2008 Wiley Periodicals, Inc

Exploring the context of sedentary behaviour in older adults (what, where, why, when and with whom)

BACKGROUND: Older adults are the most sedentary segment of the population. Little information is available about the context of sedentary behaviour to inform guidelines and intervention. There is a dearth of information about when, where to intervene and which specific behaviours intervention should target. The aim of this exploratory study was to obtain objective information about what older adults do when sedentary, where and when they are sedentary and in what social context. METHODS: The study was a cross-sectional data collection. Older adults (Mean age = 73.25, SD ± 5.48, median = 72, IQR = 11) volunteers wore activPAL monitors and a Vicon Revue timelapse camera between 1 and 7 days. Periods of sedentary behaviour were identified using the activPAL and the context extracted from the pictures taken during these periods. Analysis of context was conducted using the Sedentary Behaviour International Taxonomy classification system. RESULTS: In total, 52 days from 36 participants were available for analysis. Participants spent 70.1 % of sedentary time at home, 56.9 % of sedentary time on their own and 46.8 % occurred in the afternoon. Seated social activities were infrequent (6.9 % of sedentary bouts) but prolonged (18 % of sedentary time). Participants appeared to frequently have vacant sitting time (41 % of non-screen sedentary time) and screen sitting was prevalent (36 % of total sedentary time). CONCLUSIONS: This study provides valuable information to inform future interventions to reduce sedentary behaviour. Interventions should consider targeting the home environment and focus on the afternoon sitting time, though this needs confirmation in a larger study. Tackling social isolation may also be a target to reduce sedentary time

In vivo imaging of systemic transport and elimination of xenobiotics and endogenous molecules in mice

We describe a two-photon microscopy-based method to evaluate the in vivo systemic transport of compounds. This method comprises imaging of the intact liver, kidney and intestine, the main organs responsible for uptake and elimination of xenobiotics and endogenous molecules. The image quality of the acquired movies was sufficient to distinguish subcellular structures like organelles and vesicles. Quantification of the movement of fluorescent dextran and fluorescent cholic acid derivatives in different organs and their sub-compartments over time revealed significant dynamic differences. Calculated half-lives were similar in the capillaries of all investigated organs but differed in the specific sub-compartments, such as parenchymal cells and bile canaliculi of the liver, glomeruli, proximal and distal tubules of the kidney and lymph vessels (lacteals) of the small intestine. Moreover, tools to image immune cells, which can influence transport processes in inflamed tissues, are described. This powerful approach provides new possibilities for the analysis of compound transport in multiple organs and can support physiologically based pharmacokinetic modeling, in order to obtain more precise predictions at the whole body scale

Bayesian data fusion applied to water table spatial mapping

Water table elevations are usually sampled in space using piezometric measurements that are unfortunately expensive to obtain and are thus scarce over space. Most of the time, piezometric data are sparsely distributed over large areas, thus providing limited direct information about the level of the corresponding water table. As a consequence, there is a real need for approaches that are able at the same time to (1) provide spatial predictions at unsampled locations and (2) enable the user to account for all potentially available secondary information sources that are in some way related to water table elevations. In this paper, a recently developed Bayesian data fusion (BDF) framework is applied to the problem of water table spatial mapping. After a brief presentation of the underlying theory, specific assumptions are made and discussed to account for a digital elevation model and for the geometry of a corresponding river network. On the basis of a data set for the Dijle basin in the north part of Belgium, the suggested model is then implemented and results are compared to those of standard techniques such as ordinary kriging and cokriging. Respective accuracies and precisions of these estimators are finally evaluated using a ‘‘leave-one-out’’ cross-validation procedure. Although the BDF methodology was illustrated here for the integration of only two secondary information sources (namely, a digital elevation model and the geometry of a river network), the method can be applied for incorporating an arbitrary number of secondary information sources, thus opening new avenues for the important topic of data integration in a spatial mapping context

Support-based Implementation of Bayesian Data Fusion for Spatial Enhancement : Applications to ASTER Thermal Images

In this letter, a general Bayesian data fusion (BDF) approach is proposed and applied to the spatial enhancement of ASTER thermal images. This method fuses information coming from the visible or near-infrared bands (15 x 15 m pixels) with the thermal infrared bands (90 x 90 m pixels) by explicitly accounting for the change of support. By relying on linear multivariate regression assumptions, differences of support size for input images can be explicitly accounted for. Due to the use of locally varying variances, it also avoids producing artifacts on the fused images. Based on a set of ASTER images over the region of Lausanne, Switzerland, the advantages of this support-based approach are assessed and compared to the downscaling cokriging approach recently proposed in the literature. Results show that improvements are substantial with respect to both visual and quantitative criteria. Although the method is illustrated here with a specific case study, it is versatile enough to be applied to the spatial enhancement problem in general. It thus opens new avenues in the context of remotely sensed images