OPTICAL SURFACE ROUGHNESS MEASUREMENT OF MACHINED SURFACES

An optical method is described that makes measurement of surface roughness of machined parts in a wide roughness range possible. The apparatus based on a diode laser can be mounted on CNC machining centers as diagnostic tool for checking tool wear. Principles of operation and calibration results are described

Neural Variability and Sampling-Based Probabilistic Representations in the Visual Cortex

Neural responses in the visual cortex are variable, and there is now an abundance of data characterizing how the magnitude and structure of this variability depends on the stimulus. Current theories of cortical computation fail to account for these data; they either ignore variability altogether or only model its unstructured Poisson-like aspects. We develop a theory in which the cortex performs probabilistic inference such that population activity patterns represent statistical samples from the inferred probability distribution. Our main prediction is that perceptual uncertainty is directly encoded by the variability, rather than the average, of cortical responses. Through direct comparisons to previously published data as well as original data analyses, we show that a sampling-based probabilistic representation accounts for the structure of noise, signal, and spontaneous response variability and correlations in the primary visual cortex. These results suggest a novel role for neural variability in cortical dynamics and computations.European Union-FP7 (Marie Curie Intra-European Fellowship, Marie Curie CIG), Hungarian Academy of Sciences (Lendulet Award), Swartz Foundation, Swiss National Science Foundation, National Science Foundation, Wellcome Trus

Dealing with adversity: religiosity or science? Evidence from the great influenza pandemic

How do societies respond to adversity? After a negative shock, separate strands of research document either an increase in religiosity or a boost in innovation efforts. In this paper, we show that both reactions can occur at the same time, driven by different individuals within society. The setting of our study is the 1918-1919 influenza pandemic in the United States. To measure religiosity, we construct a novel indicator based on naming patterns of newborns. We measure innovation through the universe of granted patents. Exploiting plausibly exogenous county-level variation in exposure to the pandemic, we provide evidence that more-affected counties become both more religious and more innovative. Looking within counties, we uncover heterogeneous responses: individuals from more religious backgrounds further embrace religion, while those from less religious backgrounds become more likely to choose a scientific occupation. Facing adversity widens the distance in religiosity between science-oriented individuals and the rest of the population, and it increases the polarization of religious beliefs

Managing water through change and uncertainty: comparing lessons from the adaptive co-management literature to recent policy developments in England

Water management is set to become increasingly variable and unpredictable, in particular because of climate change. This paper investigates the extent to which water policy in England provides an enabling environment for ‘adaptive co-management’, which its proponents claim can achieve the dual objective of ecosystem protection and livelihood sustainability under conditions of change and uncertainty. Five policy categories are derived from a literature review, and are used to conduct a directed content analysis of seven key water policy documents. The findings reveal that although, in part, English water policy serves as an enabling environment for adaptive co-management, there is a level of discrepancy between substantive aspects of the five policy categories and water policy in England. Addressing these discrepancies will be important if English water policy is to allow for the emergence of processes, like adaptive co-management, that are capable of coping with the challenges that lie ahead

An Empirical Process Central Limit Theorem for Multidimensional Dependent Data

Let $(U_n(t))_{t\in\R^d}$ be the empirical process associated to an $\R^d$-valued stationary process $(X_i)_{i\ge 0}$. We give general conditions, which only involve processes $(f(X_i))_{i\ge 0}$ for a restricted class of functions $f$, under which weak convergence of $(U_n(t))_{t\in\R^d}$ can be proved. This is particularly useful when dealing with data arising from dynamical systems or functional of Markov chains. This result improves those of [DDV09] and [DD11], where the technique was first introduced, and provides new applications.Comment: to appear in Journal of Theoretical Probabilit

Statistical Consequences of Devroye Inequality for Processes. Applications to a Class of Non-Uniformly Hyperbolic Dynamical Systems

In this paper, we apply Devroye inequality to study various statistical estimators and fluctuations of observables for processes. Most of these observables are suggested by dynamical systems. These applications concern the co-variance function, the integrated periodogram, the correlation dimension, the kernel density estimator, the speed of convergence of empirical measure, the shadowing property and the almost-sure central limit theorem. We proved in \cite{CCS} that Devroye inequality holds for a class of non-uniformly hyperbolic dynamical systems introduced in \cite{young}. In the second appendix we prove that, if the decay of correlations holds with a common rate for all pairs of functions, then it holds uniformly in the function spaces. In the last appendix we prove that for the subclass of one-dimensional systems studied in \cite{young} the density of the absolutely continuous invariant measure belongs to a Besov space.Comment: 33 pages; companion of the paper math.DS/0412166; corrected version; to appear in Nonlinearit

Tail probabilities of St. Petersburg sums, trimmed sums, and their limit

We provide exact asymptotics for the tail probabilities $\mathbb{P} \{S_{n,r} > x\}$ as $x \to \infty$, for fix $n$, where $S_{n,r}$ is the $r$-trimmed partial sum of i.i.d. St. Petersburg random variables. In particular, we prove that although the St. Petersburg distribution is only O-subexponential, the subexponential property almost holds. We also determine the exact tail behavior of the $r$-trimmed limits.Comment: 24 pages, 2 figure