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

Dizziness and Convergence Insufficiency in Children: Screening and Management

International audienceObjective: In children screened for dizziness with vergence disorders, we tested short and long term efficacy of orthoptic vergence training (OVT) and instructions to reduce screen usage.Methods: Prospective study: Of the 179 children referred for vertigo or dizziness (over 3 years) with ophthalmological disorder as the only problem after complete oto-neuro-vestibular testing, 69 presented vergence insufficiency, and 49 accepted to participate in this study. 109 healthy children served as controls. All subjects had classic orthoptic evaluation and video binocular movement recordings during various oculomotor tasks. Patients were evaluated before OVT (M0), 3 months after the end of OVT (M3) and 9 months after the end of OVT (M9). Statistics compared orthoptic and oculomotor parameters between patients and controls over time with one-way ANCOVA, and mixed models, controlling for age and gender.Results: Patients reported vertigo that was usually rotatory, lasting <15 min, associated with or alternating with headache (50%). Their exposure to small video screens and TV was intensive (∼3.6 h per day). At M0, all orthoptic and oculomotor parameters were statistically different in patients relative to controls (p < 0.0001) except for divergence. At M3, vertigo symptoms had disappeared in all of the patients, and all eye movement parameters improved significantly (p < 0.0001). At M9, this improvement remained stable or continued.Conclusion: Vergence disorders (assessed by abnormal orthoptic and oculomotor parameters) can generate symptoms of dizziness in children. Orthoptic treatment and instruction to reduce screen usage has a significant and long term effect on vertigo symptoms as well as oculomotor performances. Dizzy children should be screened for vergence disorders

Challenges for identifying the neural mechanisms that support spatial navigation: the impact of spatial scale.

Spatial navigation is a fascinating behavior that is essential for our everyday lives. It involves nearly all sensory systems, it requires numerous parallel computations, and it engages multiple memory systems. One of the key problems in this field pertains to the question of reference frames: spatial information such as direction or distance can be coded egocentrically-relative to an observer-or allocentrically-in a reference frame independent of the observer. While many studies have associated striatal and parietal circuits with egocentric coding and entorhinal/hippocampal circuits with allocentric coding, this strict dissociation is not in line with a growing body of experimental data. In this review, we discuss some of the problems that can arise when studying the neural mechanisms that are presumed to support different spatial reference frames. We argue that the scale of space in which a navigation task takes place plays a crucial role in determining the processes that are being recruited. This has important implications, particularly for the inferences that can be made from animal studies in small scale space about the neural mechanisms supporting human spatial navigation in large (environmental) spaces. Furthermore, we argue that many of the commonly used tasks to study spatial navigation and the underlying neuronal mechanisms involve different types of reference frames, which can complicate the interpretation of neurophysiological data

Context-Aware Semantic Association Ranking

Discovering complex and meaningful relationships, which we call Semantic Associations, is an important challenge. Just as ranking of documents is a critical component of today\u27s search engines, ranking of relationships will be essential in tomorrow\u27s semantic search engines that would support discovery and mining of the Semantic Web. Building upon our recent work on specifying types of Semantic Associations in RDF graphs, which are possible to create through semantic metadata extraction and annotation, we discuss a framework where ranking techniques can be used to identify more interesting and more relevant Semantic Associations. Our techniques utilize alternative ways of specifying the context using ontology. This enables capturing users\u27 interests more precisely and better quality results in relevance ranking

Comparison of Stochastic Methods for the Variability Assessment of Technology Parameters

This paper provides and compares two alternative solutions for the simulation of cables and interconnects with the inclusion of the effects of parameter uncertainties, namely the Polynomial Chaos (PC) method and the Response Surface Modeling (RSM). The problem formulation applies to the telegraphers equations with stochastic coefficients. According to PC, the solution requires an expansion of the unknown parameters in terms of orthogonal polynomials of random variables. On the contrary, RSM is based on a least-square polynomial fitting of the system response. The proposed methods offer accuracy and improved efficiency in computing the parameter variability effects on system responses with respect to the conventional Monte Carlo approach. These approaches are validated by means of the application to the stochastic analysis of a commercial multiconductor flat cable. This analysis allows us to highlight the respective advantages and disadvantages of the presented method