Indeterminacy of Holographic Quantum Geometry

An effective theory based on wave optics is used to describe indeterminacy of position in holographic spacetime with a UV cutoff at the Planck scale. Wavefunctions describing spacetime positions are modeled as complex disturbances of quasi-monochromatic radiation. It is shown that the product of standard deviations of two position wavefunctions in the plane of a holographic light sheet is equal to the product of their normal separation and the Planck length. For macroscopically separated positions the transverse uncertainty is much larger than the Planck length, and is predicted to be observable as a "holographic noise" in relative position with a distinctive shear spatial character, and an absolutely normalized frequency spectrum with no parameters once the fundamental wavelength is fixed from the theory of gravitational thermodynamics. The spectrum of holographic noise is estimated for the GEO600 interferometric gravitational-wave detector, and is shown to approximately account for currently unexplained noise between about 300 and 1400Hz. In a holographic world, this result directly and precisely measures the fundamental minimum interval of time.Comment: 4 pages, LaTeX. Considerably shortened from earlier version. Conclusions are unchanged. Submitted to PR

Eigenvalue variance bounds for Wigner and covariance random matrices

This work is concerned with finite range bounds on the variance of individual eigenvalues of Wigner random matrices, in the bulk and at the edge of the spectrum, as well as for some intermediate eigenvalues. Relying on the GUE example, which needs to be investigated first, the main bounds are extended to families of Hermitian Wigner matrices by means of the Tao and Vu Four Moment Theorem and recent localization results by Erd\"os, Yau and Yin. The case of real Wigner matrices is obtained from interlacing formulas. As an application, bounds on the expected 2-Wasserstein distance between the empirical spectral measure and the semicircle law are derived. Similar results are available for random covariance matrices

A measurement of noise created by fluctuating electrostatic charges on dielectric surfaces using a torsion balance

Future gravitational wave detectors could have their sensitivity significantly limited, at frequencies below 10 Hz, by the presence of fluctuating electrostatic charges on the dielectric surfaces of the detector optics. A confirmed observation of the effect of fluctuating charges, or charging noise, in a gravitational wave detector has still to be made and it has never been experimentally verified by any other means. This paper presents a direct measurement of the fluctuating force noise created by moving charges on a dielectric surface using a servo controlled torsion balance. The results confirm that the fluctuating force noise caused by excess charges can be best described by a Markov process with a single correlation time and has a frequency dependence of f<sup>-1</sup&gt

Field tests of a portable MEMS gravimeter

Gravimeters are used to measure density anomalies under the ground. They are applied in many different fields from volcanology to oil and gas exploration, but present commercial systems are costly and massive. A new type of gravity sensor has been developed that utilises the same fabrication methods as those used to make mobile phone accelerometers. In this study, we describe the first results of a field-portable microelectromechanical system (MEMS) gravimeter. The stability of the gravimeter is demonstrated through undertaking a multi-day measurement with a standard deviation of 5.58 × 10−6 ms−2 . It is then demonstrated that a change in gravitational acceleration of 4.5 × 10−5 ms−2 can be measured as the device is moved between the top and the bottom of a 20.7 m lift shaft with a signal-to-noise ratio (SNR) of 14.25. Finally, the device is demonstrated to be stable in a more harsh environment: a 4.5 × 10−4 ms−2 gravity variation is measured between the top and bottom of a 275-m hill with an SNR of 15.88. These initial field-tests are an important step towards a chip-sized gravity senso

Competitive titration in living sea urchin embryos of regulatory factors required for expression of the CyIIIa actin gene

Previous studies have located some twenty distinct sites within the 2.3 kb 5' regulatory domain of the sea urchin CyIIIa cytoskeletal actin gene, where there occur in vitro high-specificity interactions with nuclear DNA-binding proteins of the embryo. This gene is activated in late cleavage, exclusively in cells of the aboral ectoderm cell lineages. In this study, we investigate the functional importance in vivo of these sites of DNA-protein interaction. Sea urchin eggs were coinjected with a fusion gene construct in which the bacterial chloramphenicol acetyltransferase (CAT) reporter gene is under the control of the entire CyIIIa regulatory domain, together with molar excesses of one of ten nonoverlapping competitor subfragments of this domain, each of which contains one or a few specific site(s) of interaction. The exogenous excess binding sites competitively titrate the available regulatory factors away from the respective sites associated with the CyIIIa.CAT reporter gene. This provides a method for detecting in vivo sites within the regulatory domain that are required for normal levels of expression, without disturbing the structure of the regulatory domain. We thus identify five nonoverlapping regions of the regulatory DNA that apparently function as binding sites for positively acting transcriptional regulatory factors. Competition with a subfragment bearing an octamer site results in embryonic lethality. We find that three other sites display no quantitative competitive interference with CyIIIa.CAT expression, though as shown in the accompanying paper, two of these sites are required for control of spatial expression. We conclude that the complex CyIIIa regulatory domain must assess the state of many distinct and individually necessary interactions in order to properly regulate CyIIIa transcriptional activity in development

Spectropolarimetry of the 3.4 micron absorption feature in NGC 1068

In order to test the silicate-core/organic-mantle model of galactic interstellar dust, we have performed spectropolarimetry of the 3.4 micron C-H bond stretch that is characteristic of aliphatic hydrocarbons, using the nucleus of the Seyfert 2 galaxy, NGC 1068, as a bright, dusty background source. Polarization calculations show that, if the grains in NGC 1068 had the properties assigned by the core-mantle model to dust in the galactic diffuse ISM, they would cause a detectable rise in polarization over the 3.4 micron feature. No such increase is observed. We discuss modifications to the basic core-mantle model, such as changes in grain size or the existence of additional non-hydrocarbon aligned grain populations, which could better fit the observational evidence. However, we emphasize that the absence of polarization over the 3.4 micron band in NGC 1068 - and, indeed, in every line of sight examined to date - can be readily explained by a population of small, unaligned carbonaceous grains with no physical connection to the silicates.Comment: ApJ, accepte

Determinantal Correlations of Brownian Paths in the Plane with Nonintersection Condition on their Loop-Erased Parts

As an image of the many-to-one map of loop-erasing operation \LE of random walks, a self-avoiding walk (SAW) is obtained. The loop-erased random walk (LERW) model is the statistical ensemble of SAWs such that the weight of each SAW $\zeta$ is given by the total weight of all random walks $\pi$ which are inverse images of $\zeta$, \{\pi: \LE(\pi)=\zeta \}. We regard the Brownian paths as the continuum limits of random walks and consider the statistical ensemble of loop-erased Brownian paths (LEBPs) as the continuum limits of the LERW model. Following the theory of Fomin on nonintersecting LERWs, we introduce a nonintersecting system of $N$-tuples of LEBPs in a domain $D$ in the complex plane, where the total weight of nonintersecting LEBPs is given by Fomin's determinant of an $N \times N$ matrix whose entries are boundary Poisson kernels in $D$. We set a sequence of chambers in a planar domain and observe the first passage points at which $N$ Brownian paths $(\gamma_1,..., \gamma_N)$ first enter each chamber, under the condition that the loop-erased parts (\LE(\gamma_1),..., \LE(\gamma_N)) make a system of nonintersecting LEBPs in the domain in the sense of Fomin. We prove that the correlation functions of first passage points of the Brownian paths of the present system are generally given by determinants specified by a continuous function called the correlation kernel. The correlation kernel is of Eynard-Mehta type, which has appeared in two-matrix models and time-dependent matrix models studied in random matrix theory. Conformal covariance of correlation functions is demonstrated.Comment: v3: REVTeX4, 27 pages, 10 figures, corrections made for publication in Phys.Rev.

Mechanical loss of a hydroxide catalysis bond between sapphire substrates and its effect on the sensitivity of future gravitational wave detectors

Hydroxide catalysis bonds are low mechanical loss joints which are used in the fused silica mirror suspensions of current room temperature interferometric gravitational wave detectors, one of the techniques which was essential to allow the recent detection of gravitational radiation by LIGO. More sensitive detectors may require cryogenic techniques with sapphire as a candidate mirror and suspension material, and thus hydroxide catalysis bonds are under consideration for jointing sapphire. This paper presents the first measurements of the mechanical loss of such a bond created between sapphire substrates and measured down to cryogenic temperatures. The mechanical loss is found to be 0.03±0.01 at room temperature, decreasing to (3±1)×10−4 at 20 K. The resulting thermal noise of the bonds on several possible mirror suspensions is presented

Incremental Composition in Distributional Semantics

Despite the incremental nature of Dynamic Syntax (DS), the semantic grounding of it remains that of predicate logic, itself grounded in set theory, so is poorly suited to expressing the rampantly context-relative nature of word meaning, and related phenomena such as incremental judgements of similarity needed for the modelling of disambiguation. Here, we show how DS can be assigned a compositional distributional semantics which enables such judgements and makes it possible to incrementally disambiguate language constructs using vector space semantics. Building on a proposal in our previous work, we implement and evaluate our model on real data, showing that it outperforms a commonly used additive baseline. In conclusion, we argue that these results set the ground for an account of the non-determinism of lexical content, in which the nature of word meaning is its dependence on surrounding context for its construal

Incremental Composition in Distributional Semantics

Despite the incremental nature of Dynamic Syntax (DS), the semantic grounding of it remains that of predicate logic, itself grounded in set theory, so is poorly suited to expressing the rampantly context-relative nature of word meaning, and related phenomena such as incremental judgements of similarity needed for the modelling of disambiguation. Here, we show how DS can be assigned a compositional distributional semantics which enables such judgements and makes it possible to incrementally disambiguate language constructs using vector space semantics. Building on a proposal in our previous work, we implement and evaluate our model on real data, showing that it outperforms a commonly used additive baseline. In conclusion, we argue that these results set the ground for an account of the non-determinism of lexical content, in which the nature of word meaning is its dependence on surrounding context for its construal