On inversions and Doob hh-transforms of linear diffusions

Let $X$ be a regular linear diffusion whose state space is an open interval $E\subseteq\mathbb{R}$. We consider a diffusion $X^*$ which probability law is obtained as a Doob $h$-transform of the law of $X$, where $h$ is a positive harmonic function for the infinitesimal generator of $X$ on $E$. This is the dual of $X$ with respect to $h(x)m(dx)$ where $m(dx)$ is the speed measure of $X$. Examples include the case where $X^*$ is $X$ conditioned to stay above some fixed level. We provide a construction of $X^*$ as a deterministic inversion of $X$, time changed with some random clock. The study involves the construction of some inversions which generalize the Euclidean inversions. Brownian motion with drift and Bessel processes are considered in details.Comment: 19 page

Isotropic Conductivity of Two-Dimensional Three-Component Symmetric Composites

The effective dc-conductivity problem of isotropic, two-dimensional (2D), three-component, symmetric, regular composites is considered. A simple cubic equation with one free parameter for $\sigma_{e}(\sigma_1,\sigma_2,\sigma_3)$ is suggested whose solutions automatically have all the exactly known properties of that function. Numerical calculations on four different symmetric, isotropic, 2D, three-component, regular structures show a non-universal behavior of $\sigma_{e}(\sigma_1,\sigma_2,\sigma_3)$ with an essential dependence on micro-structural details, in contrast with the analogous two-component problem. The applicability of the cubic equation to these structures is discussed. An extension of that equation to the description of other types of 2D three-component structures is suggested, including the case of random structures. Pacs: 72.15.Eb, 72.80.Tm, 61.50.AhComment: 8 pages (two columns), 8 figures. J. Phys. A - submitte

Four problems with global carbon markets: a critical review

This article offers a critique of global carbon markets and trading, with a special focus on the Clean Development Mechanism of the Kyoto Protocol. It explores problems with the use of tradable permits to address climate change revolving around four areas: homogeneity, justice, gaming, and information. Homogeneity problems arise from the non-linear nature of climate change and sensitivity of emissions, which complicate attempts to calculate carbon offsets. Justice problems involve issues of dependency and the concentration of wealth among the rich, meaning carbon trading often counteracts attempts to reduce poverty. Gaming problems include pressures to promote high-volume, least-cost projects and the consequences of emissions leakage. Information problems encompass transaction costs related to carbon trading and market participation and the comparatively weak institutional capacity of project evaluators

Representations of time in human frontoparietal cortex

Precise time estimation is crucial in perception, action and social interaction. Previous neuroimaging studies in humans indicate that perceptual timing tasks involve multiple brain regions; however, whether the representation of time is localized or distributed in the brain remains elusive. Using ultra-high-field functional magnetic resonance imaging combined with multivariate pattern analyses, we show that duration information is decoded in multiple brain areas, including the bilateral parietal cortex, right inferior frontal gyrus and, albeit less clearly, the medial frontal cortex. Individual differences in the duration judgment accuracy were positively correlated with the decoding accuracy of duration in the right parietal cortex, suggesting that individuals with a better timing performance represent duration information in a more distinctive manner. Our study demonstrates that although time representation is widely distributed across frontoparietal regions, neural populations in the right parietal cortex play a crucial role in time estimation

GTI-space : the space of generalized topological indices

A new extension of the generalized topological indices (GTI) approach is carried out torepresent 'simple' and 'composite' topological indices (TIs) in an unified way. Thisapproach defines a GTI-space from which both simple and composite TIs represent particular subspaces. Accordingly, simple TIs such as Wiener, Balaban, Zagreb, Harary and Randićconnectivity indices are expressed by means of the same GTI representation introduced for composite TIs such as hyper-Wiener, molecular topological index (MTI), Gutman index andreverse MTI. Using GTI-space approach we easily identify mathematical relations between some composite and simple indices, such as the relationship between hyper-Wiener and Wiener index and the relation between MTI and first Zagreb index. The relation of the GTI space with the sub-structural cluster expansion of property/activity is also analysed and some routes for the applications of this approach to QSPR/QSAR are also given

Resistance distance, information centrality, node vulnerability and vibrations in complex networks

We discuss three seemingly unrelated quantities that have been introduced in different fields of science for complex networks. The three quantities are the resistance distance, the information centrality and the node displacement. We first prove various relations among them. Then we focus on the node displacement, showing its usefulness as an index of node vulnerability.We argue that the node displacement has a better resolution as a measure of node vulnerability than the degree and the information centrality

Loss of bacterial diversity during antibiotic treatment of intubated patients colonized with Pseudomonas aeruginosa

Management of airway infections caused by Pseudomonas aeruginosa is a serious clinical challenge, but little is known about the microbial ecology of airway infections in intubated patients. We analyzed bacterial diversity in endotracheal aspirates obtained from intubated patients colonized by P. aeruginosa by using 16S rRNA clone libraries and microarrays (PhyloChip) to determine changes in bacterial community compositions during antibiotic treatment. Bacterial 16S rRNA genes were absent from aspirates obtained from patients briefly intubated for elective surgery but were detected by PCR in samples from all patients intubated for longer periods. Sequencing of 16S rRNA clone libraries demonstrated the presence of many orally, nasally, and gastrointestinally associated bacteria, including known pathogens, in the lungs of patients colonized with P. aeruginosa. PhyloChip analysis detected the same organisms and many additional bacterial groups present at low abundance that were not detected in clone libraries. For each patient, both culture-independent methods showed that bacterial diversity decreased following the administration of antibiotics, and communities became dominated by a pulmonary pathogen. P. aeruginosa became the dominant species in six of seven patients studied, despite treatment of five of these six with antibiotics to which it was sensitive in vitro. Our data demonstrate that the loss of bacterial diversity under antibiotic selection is highly associated with the development of pneumonia in ventilated patients colonized with P. aeruginosa. Interestingly, PhyloChip analysis demonstrated reciprocal changes in abundance between P. aeruginosa and the class Bacilli, suggesting that these groups may compete for a similar ecological niche and suggesting possible mechanisms through which the loss of microbial diversity may directly contribute to pathogen selection and persistence

Route planning with transportation network maps: an eye-tracking study.

Planning routes using transportation network maps is a common task that has received little attention in the literature. Here, we present a novel eye-tracking paradigm to investigate psychological processes and mechanisms involved in such a route planning. In the experiment, participants were first presented with an origin and destination pair before we presented them with fictitious public transportation maps. Their task was to find the connecting route that required the minimum number of transfers. Based on participants' gaze behaviour, each trial was split into two phases: (1) the search for origin and destination phase, i.e., the initial phase of the trial until participants gazed at both origin and destination at least once and (2) the route planning and selection phase. Comparisons of other eye-tracking measures between these phases and the time to complete them, which depended on the complexity of the planning task, suggest that these two phases are indeed distinct and supported by different cognitive processes. For example, participants spent more time attending the centre of the map during the initial search phase, before directing their attention to connecting stations, where transitions between lines were possible. Our results provide novel insights into the psychological processes involved in route planning from maps. The findings are discussed in relation to the current theories of route planning