Kernel dimension reduction in regression

We present a new methodology for sufficient dimension reduction (SDR). Our methodology derives directly from the formulation of SDR in terms of the conditional independence of the covariate $X$ from the response $Y$, given the projection of $X$ on the central subspace [cf. J. Amer. Statist. Assoc. 86 (1991) 316--342 and Regression Graphics (1998) Wiley]. We show that this conditional independence assertion can be characterized in terms of conditional covariance operators on reproducing kernel Hilbert spaces and we show how this characterization leads to an $M$-estimator for the central subspace. The resulting estimator is shown to be consistent under weak conditions; in particular, we do not have to impose linearity or ellipticity conditions of the kinds that are generally invoked for SDR methods. We also present empirical results showing that the new methodology is competitive in practice.Comment: Published in at http://dx.doi.org/10.1214/08-AOS637 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Seismic vulnerability assessment: Methodological elements and applications to the case of Romania

This paper is intended to present some studies undertaken in order to develop a seismic vulnerability estimation system to fit the needs of development of earthquake scenarios and of development of an integrated disaster risk management system for Romania. Methodological aspects are dealt with, in connection with the criteria of categorization of buildings, with the definition of parameters used for characterizing vulnerability, with the setting up of an inventory of buildings and with the calibration of parameters characterizing vulnerability. Action was initiated along the coordinates referred to in connection with the methodological aspects mentioned above. The approach was made, as far as possible, specific to the conditions of Romania. Some data on results obtained to date are presented.seismic vulnerability, vulnerability estimation, earthquake scenarios, categorization of buildings, inventory of buildings, expected earthquake impact

Mars simulated exposure and the characteristic Raman biosignatures of amino acids and halophilic microbes

Though Raman bands of α-amino acids (AA) are well documented, often only the strongest intensity bands are quoted as identifiers (e.g. Jenkins et al., 2005; De Gelder et al., 2007; Zhu et al., 2011). Unknown regolith mixtures on Mars-sampling missions could obscure these bands. Here the case is made for determining, via a statistical method, sets of characteristic bands to be used as identifiers, independent of band intensity or number of bands (Rolfe et al., 2016). AA have upwards of 25 potentially identifying bands and this method defines sets of 10–19 bands per AA. Examination of AA-doped Mars-like basalt resulted in a maximum of eight bands being identified, as some characteristic bands were obscured by mineral bands, including the strongest intensity band in some cases. This proved the need for characteristic bands to be defined, enabling successful identification of AA. The ESA ExoMars Rover mission will crush and then pass the sample to the Raman Laser Spectrometer. We crushed a Mars-like basalt to a similar grain size expected to be created by the rover. Our samples were doped with 1 % (by weight) AA samples, resulting in no detection of AA, because of loss of original spatial context and spaces between the grains. We recommend that Raman spectroscopy on future missions should be conducted before the sample is crushed. Halite-entombed halophilic microbes, known to survive being entombed, were exposed to Mars-like surface (including temperature, pressure, atmospheric composition and UV) and freeze-thaw cycle (plus pressure and atmospheric composition) conditions. This test on the survival of the microbes showed that survival rates quickly deteriorated in surface conditions, but freeze-thaw cycle samples had well preserved Raman biosignatures, indicating that similar signatures could be detectable on Mars if similar life persists in evaporitic material or brines today

The shape of high order correlation functions in CMB anisotropy maps

We present a phenomenological investigation of non-Gaussian effects that could be seen on CMB temperature maps. Explicit expressions for the temperature correlation functions are given for different types of primordial mode couplings. We argue that a simplified description of the radial transfer function for the temperature anisotropies allows to get insights into the general properties of the bi and tri-spectra. The accuracy of these results is explored together with the use of the small scale approximation to get explicit expressions of high order spectra. The bi-spectrum is found to have alternate signs for the successive acoustic peaks. Sign patterns for the trispectra are more complicated and depend specifically on the type of metric couplings. Local primordial couplings are found to give patterns that are different from those expected from weak lensing effects.Comment: 31 pages, 17 figures, submitted to Phys. Rev.

A theory for magnetic-field effects of nonmagnetic organic semiconducting materials

A universal mechanism for strong magnetic-field effects of nonmagnetic organic semiconductors is presented. A weak magnetic field (less than hundreds mT) can substantially change the charge carrier hopping coefficient between two neighboring organic molecules when the magnetic length is not too much longer than the molecule-molecule separation and localization length of electronic states involved. Under the illumination of lights or under a high electric field, the change of hopping coefficients leads also to the change of polaron density so that photocurrent, photoluminescence, electroluminescence, magnetoresistance and electrical-injection current become sensitive to a weak magnetic field. The present theory can not only explain all observed features, but also provide a solid theoretical basis for the widely used empirical fitting formulas.Comment: 4 pages, 2 figure

Brownian motion of a charged particle driven internally by correlated noise

We give an exact solution to the generalized Langevin equation of motion of a charged Brownian particle in a uniform magnetic field that is driven internally by an exponentially-correlated stochastic force. A strong dissipation regime is described in which the ensemble-averaged fluctuations of the velocity exhibit transient oscillations that arise from memory effects. Also, we calculate generalized diffusion coefficients describing the transport of these particles and briefly discuss how they are affected by the magnetic field strength and correlation time. Our asymptotic results are extended to the general case of internal driving by correlated Gaussian stochastic forces with finite autocorrelation times.Comment: 10 pages, 4 figures with subfigures, RevTeX, v2: revise

EPG-representations with small grid-size

In an EPG-representation of a graph $G$ each vertex is represented by a path in the rectangular grid, and $(v,w)$ is an edge in $G$ if and only if the paths representing $v$ an $w$ share a grid-edge. Requiring paths representing edges to be x-monotone or, even stronger, both x- and y-monotone gives rise to three natural variants of EPG-representations, one where edges have no monotonicity requirements and two with the aforementioned monotonicity requirements. The focus of this paper is understanding how small a grid can be achieved for such EPG-representations with respect to various graph parameters. We show that there are $m$-edge graphs that require a grid of area $\Omega(m)$ in any variant of EPG-representations. Similarly there are pathwidth-$k$ graphs that require height $\Omega(k)$ and area $\Omega(kn)$ in any variant of EPG-representations. We prove a matching upper bound of $O(kn)$ area for all pathwidth-$k$ graphs in the strongest model, the one where edges are required to be both x- and y-monotone. Thus in this strongest model, the result implies, for example, $O(n)$, $O(n \log n)$ and $O(n^{3/2})$ area bounds for bounded pathwidth graphs, bounded treewidth graphs and all classes of graphs that exclude a fixed minor, respectively. For the model with no restrictions on the monotonicity of the edges, stronger results can be achieved for some graph classes, for example an $O(n)$ area bound for bounded treewidth graphs and $O(n \log^2 n)$ bound for graphs of bounded genus.Comment: Appears in the Proceedings of the 25th International Symposium on Graph Drawing and Network Visualization (GD 2017