Geometric Influences II: Correlation Inequalities and Noise Sensitivity

In a recent paper, we presented a new definition of influences in product spaces of continuous distributions, and showed that analogues of the most fundamental results on discrete influences, such as the KKL theorem, hold for the new definition in Gaussian space. In this paper we prove Gaussian analogues of two of the central applications of influences: Talagrand's lower bound on the correlation of increasing subsets of the discrete cube, and the Benjamini-Kalai-Schramm (BKS) noise sensitivity theorem. We then use the Gaussian results to obtain analogues of Talagrand's bound for all discrete probability spaces and to reestablish analogues of the BKS theorem for biased two-point product spaces.Comment: 20 page

Strong noise sensitivity and random graphs

The noise sensitivity of a Boolean function describes its likelihood to flip under small perturbations of its input. Introduced in the seminal work of Benjamini, Kalai and Schramm [Inst. Hautes \'{E}tudes Sci. Publ. Math. 90 (1999) 5-43], it was there shown to be governed by the first level of Fourier coefficients in the central case of monotone functions at a constant critical probability $p_c$. Here we study noise sensitivity and a natural stronger version of it, addressing the effect of noise given a specific witness in the original input. Our main context is the Erd\H{o}s-R\'{e}nyi random graph, where already the property of containing a given graph is sufficiently rich to separate these notions. In particular, our analysis implies (strong) noise sensitivity in settings where the BKS criterion involving the first Fourier level does not apply, for example, when $p_c\to0$ polynomially fast in the number of variables.Comment: Published at http://dx.doi.org/10.1214/14-AOP959 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org

Combustion instabilities: mating dance of chemical, combustion, and combustor dynamics

Combustion instabilities exist as consequences of interactions among three classes of phenomena: chemistry and chemical dynamics; combustion dynamics; and combustor dynamics. These dynamical processes take place simultaneously in widely different spatial scales characterized by lengths roughly in the ratios (10^(-3) - 10^(-6)):1:(10^3-10^6). However, due to the wide differences in the associated characteristic velocities, the corresponding time scales are all close. The instabilities in question are observed as oscillations having a time scale in the range of natural acoustic oscillations. The apparent dominance of that single macroscopic time scale must not be permitted to obscure the fact that the relevant physical processes occur on three disparate length scales. Hence, understanding combustion instabilities at the practical level of design and successful operation is ultimately based on understanding three distinct sorts of dynamics

Using a qualitative approach to explore the human response to vibration in residential environments in the United Kingdom

As a growing number of areas in the UK become ever more densely populated, increasing construction work is being undertaken and transportation networks built in order to cope with the growing population. The development of this infrastructure, coupled with the mechanisation of modern life, often results in exposure to various types of vibration from a range of sources such as rail, road traffic and construction activity causing considerable disturbance. The study of vibration effects within residential settings is a developing area of research. Previous research on ambient stressors in residential environments has focused primarily on noise; one of the most prevalent environmental stressors in living environments. Some noise surveys have highlighted vibration as a contributor to noise annoyance while others have explored the combined effects of noise and vibration on human response. Research on vibration is largely a quantitative effort using laboratory experiments or social surveys with associated vibration measurements in order to establish dose-response relationships. However, as the human response to vibration is particularly diverse and complex this paper aims to explore how qualitative methodologies can compliment the quantitative approach to vibration research. People’s experiences, expectations and attitudes vary with regards to vibration, the noise it produces, and the source it derives from. For the pragmatic researcher qualitative methodologies can help unravel some of these issues, providing a further understanding of the complexities of the human response to vibration in residential environments

Different sensitivities of two optical magnetometers realized in the same experimental arrangement

In this article, operation of optical magnetometers detecting static (DC) and oscillating (AC) magnetic fields is studied and comparison of the devices is performed. To facilitate the comparison, the analysis is carried out in the same experimental setup, exploiting nonlinear magneto-optical rotation. In such a system, a control over static-field magnitude or oscillating-field frequency provides detection of strength of the DC or AC fields. Polarization rotation is investigated for various light intensities and AC-field amplitudes, which allows to determine optimum sensitivity to both fields. With the results, we demonstrate that under optimal conditions the AC magnetometer is about ten times more sensitive than its DC counterpart, which originates from different response of the atoms to the fields. Bandwidth of the magnetometers is also analyzed, revealing its different dependence on the light power. Particularly, we demonstrate that bandwidth of the AC magnetometer can be significantly increased without strong deterioration of the magnetometer sensitivity. This behavior, combined with the ability to tune the resonance frequency of the AC magnetometer, provide means for ultra-sensitive measurements of the AC field in a broad but spectrally-limited range, where detrimental role of static-field instability is significantly reduced.Comment: 9 pages, 6 figure

Characterization of gasoline/ethanol blends by infrared and excess infrared spectroscopy

This work was supported by the Northern Research Partnership (NRP) in Scotland and the Scottish Sensor Systems Centre (SSSC) funded by the Scottish Funding Council (SFC).Peer reviewedPostprin