Distributional properties of exponential functionals of Levy processes

We study the distribution of the exponential functional I(\xi,\eta)=\int_0^{\infty} \exp(\xi_{t-}) \d \eta_t, where $\xi$ and $\eta$ are independent L\'evy processes. In the general setting using the theories of Markov processes and Schwartz distributions we prove that the law of this exponential functional satisfies an integral equation, which generalizes Proposition 2.1 in Carmona et al "On the distribution and asymptotic results for exponential functionals of Levy processes". In the special case when $\eta$ is a Brownian motion with drift we show that this integral equation leads to an important functional equation for the Mellin transform of $I(\xi,\eta)$, which proves to be a very useful tool for studying the distributional properties of this random variable. For general L\'evy process $\xi$ ($\eta$ being Brownian motion with drift) we prove that the exponential functional has a smooth density on $\r \setminus \{0\}$, but surprisingly the second derivative at zero may fail to exist. Under the additional assumption that $\xi$ has some positive exponential moments we establish an asymptotic behaviour of \p(I(\xi,\eta)>x) as $x\to +\infty$, and under similar assumptions on the negative exponential moments of $\xi$ we obtain a precise asympotic expansion of the density of $I(\xi,\eta)$ as $x\to 0$. Under further assumptions on the L\'evy process $\xi$ one is able to prove much stronger results about the density of the exponential functional and we illustrate some of the ideas and techniques for the case when $\xi$ has hyper-exponential jumps.Comment: In this version we added a remark after Theorem 1 about extra conditions required for validity of equation (2.3

Estimate of Tilt Instability of Mesa-Beam and Gaussian-Beam Modes for Advanced LIGO

Sidles and Sigg have shown that advanced LIGO interferometers will encounter a serious tilt instability, in which symmetric tilts of the mirrors of an arm cavity cause the cavity's light beam to slide sideways, so its radiation pressure exerts a torque that increases the tilt. Sidles and Sigg showed that the strength T of this torque is 26.2 times greater for advanced LIGO's baseline cavities -- nearly flat spherical mirrors which support Gaussian beams (``FG'' cavities), than for nearly concentric spherical mirrors which support Gaussian beams with the same diffraction losses as the baseline case -- ``CG'' cavities: T^{FG}/T^{CG} = 26.2. This has motivated a proposal to change the baseline design to nearly concentric, spherical mirrors. In order to reduce thermoelastic noise in advanced LIGO, O'Shaughnessy and Thorne have proposed replacing the spherical mirrors and their Gaussian beams by ``Mexican-Hat'' (MH) shaped mirrors which support flat-topped, ``mesa'' shaped beams. In this paper we compute the tilt-instability torque for advanced-LIGO cavities with nearly flat MH mirrors and mesa beams (``FM'' cavities) and nearly concentric MH mirrors and mesa beams (``CM'' cavities), with the same diffraction losses as in the baseline FG case. We find that the relative sizes of the restoring torques are T^{CM}/T^{CG} = 0.91, T^{FM}/T^{CG} = 96, T^{FM}/T^{FG} = 3.67. Thus, the nearly concentric MH mirrors have a weaker tilt instability than any other configuration. Their thermoelastic noise is the same as for nearly flat MH mirrors, and is much lower than for spherical mirrors.Comment: 10 pages, 3 figures, 4 table

Joint source-channel coding for a quantum multiple access channel

Suppose that two senders each obtain one share of the output of a classical, bivariate, correlated information source. They would like to transmit the correlated source to a receiver using a quantum multiple access channel. In prior work, Cover, El Gamal, and Salehi provided a combined source-channel coding strategy for a classical multiple access channel which outperforms the simpler "separation" strategy where separate codebooks are used for the source coding and the channel coding tasks. In the present paper, we prove that a coding strategy similar to the Cover-El Gamal-Salehi strategy and a corresponding quantum simultaneous decoder allow for the reliable transmission of a source over a quantum multiple access channel, as long as a set of information inequalities involving the Holevo quantity hold.Comment: 21 pages, v2: minor changes, accepted into Journal of Physics

ANALYSIS OF ATHLETES’ STATIC-DYNAMIC STABILITY

INTRODUCTION: The ability to maintain balance and static-kinetic stability is particularly important for athletes. The balance function realizes a stable connection between the individual and the environment, resulting in “spatial” stabilization. This means that the environment is perceived as “stable,” that man lives, moves or stays in a stable surrounding. That is why this fact is of particular importance in the training process of figure skaters, gymnasts and other athletes. Different tests are made for their selection and for assessment of the training process. This paper presents a method for computer processing of results from craniocorporographic examinations (CCG) of athletes at standard and sensitized Romberg’s standing test and Unterberger-Fukuda stepping test. The aim is to compare the sensitivity and reliability of those tests

Discovery of a 270 Hz X-Ray Burst Oscillation in the X-Ray Dipper 4U 1916-053

We report the discovery of a highly coherent oscillation in a type-I X-ray burst observed from 4U 1916-053 by the Rossi X-ray Timing Explorer (RXTE). The oscillation was most strongly detected approx. 1 s after the burst onset at a frequency of 269.3 Hz, and it increased in frequency over the following 4 seconds of the burst decay to a maximum of around 272 Hz. The total measured drift of 3.58 +/- 0.41 Hz (1 sigma) represents the largest fractional change in frequency (1.32 +/- 0.15 %) yet observed in any burst oscillation. If the asymptotic frequency of the oscillation is interpreted in terms of a decoupled surface burning layer, the implied neutron star spin period is around 3.7 ms. However, the expansion of the burning layer required to explain frequency drift during the burst is around 80 m, substantially larger than expected theoretically (assuming rigid rotation). The oscillation was not present in the persistent emission before the burst, nor in the initial rise. When detected its amplitude was 6-12% (RMS) with a roughly sinusoidal profile. The burst containing the oscillation showed no evidence for photospheric radius expansion, while at least 5 of the other 9 bursts observed from the source by RXTE during 1996 and 1998 did. No comparable oscillations were detected in the other bursts. A pair of kilohertz quasi-periodic oscillations (QPOs) has been previously reported from this source with a mean separation of 348 +/- 12 Hz. 4U 1916-053 is the first example of a source where the burst oscillation frequency is significantly smaller than the frequency separation of the kHz QPOs.Comment: 8 pages, 2 figures, 2 tables; accepted for ApJ Letter

Implications of eocene-age philippine sea and forearc basalts for initiation and early history of the izu-bonin-mariana arc

Whole-rock isotope ratio (Hf, Nd, Pb, Sr) and trace element data for basement rocks at ocean drilling Sites U1438, 1201 and 447 immediately west of the KPR (Kyushu-Palau Ridge) are compared to those of FAB (forearc basalts) previously interpreted to be the initial products of IBM subduction volcanism. West-of-KPR basement basalts (drill sites U1438, 1201, 447) and FAB occupy the same Hf-Nd and Pb-Pb isotopic space and share distinctive source characteristics with εHf mostly >16.5 and up to εHf =19.8, which is more radiogenic than most Indian mid-ocean ridge basalts (MORB). Lead isotopic ratios are depleted, with ²⁰⁶Pb/²⁰⁴Pb = 17.8-18.8 accompanying relatively high ²⁰⁸Pb/²⁰⁴Pb, indicating an Indian-MORB source unlike that of West Philippine Basin plume basalts. Some Sr isotopes show affects of seawater alteration, but samples with ⁸⁷Sr/⁸⁶Sr8.0 appear to preserve magmatic compositions and also indicate a common source for west-of-KPR basement and FAB. Trace element ratios resistant to seawater alteration (La/Yb, Lu/Hf, Zr/Nb, Sm/Nd) in west-of-KPR basement are generally more depleted than normal MORB and so also appear similar to FAB. At Site U1438, only andesite sills intruding sedimentary rocks overlying the basement have subduction-influenced geochemical characteristics (εNd ∼6.6, εHf ∼13.8, La/Yb > 2.5, Nd/Hf ∼9). The key characteristic that unites drill site basement rocks west of KPR and FAB is the nature of their source, which is more depleted in lithophile trace elements than average MORB but with Hf, Nd, and Pb isotope ratios that are common in MORB. The lithophile element-depleted nature of FAB has been linked to initiation of IBM subduction in the Eocene, but Sm-Nd model ages and errorchron relationships in Site U1438 basement indicate that the depleted character of the rocks is a regional characteristic that was produced well prior to the time of subduction initiation and persists today in the source of modern IBM arc volcanic rocks with Sm/Nd>0.34 and εNd ∼9.0

Fundamental limitations to information transfer in accelerated frames

We study communication between an inertial observer and one of two causally-disconnected counter accelerating observers. We will restrict the quantum channel considering inertial-to-accelerated bipartite classical and quantum communication over different sets of Unruh modes (single-rail or dual-rail encoding). We find that the coherent information (and therefore, the amount of entanglement that can be generated via state merging protocol) in this strongly restricted channel presents some interesting monogamy properties between the inertial and only one of the accelerated observers if we take a fixed choice of the Unruh mode used in the channel. The optimization of the controllable parameters is also studied and we find that they deviate from the values usually employed in the literature.Comment: 7 pages, 6 figure

Temporal evolution of proto-Izu–Bonin–Mariana arc volcanism over 10 Myr: Constraints from statistical analysis of melt inclusion compositions

International Ocean Discovery Program (IODP) Expedition 351 ‘Izu–Bonin–Mariana (IBM) Arc Origins’ drilled Site U1438, situated in the northwestern region of the Philippine Sea. Here volcaniclastic sediments and the igneous basement of the proto-IBM volcanic arc were recovered. To gain a better understanding of the magmatic processes and evolution of the proto-IBM arc, we studied melt inclusions hosted in fresh igneous minerals and sampled from 30–40 Myr old deposits, reflecting the maturation of arc volcanism following subduction initiation at 52 Ma. We performed a novel statistical analysis on the major element composition of 237 representative melt inclusions selected from a previously published dataset, covering the full age range between 30 and 40 Ma. In addition, we analysed volatiles (H2O, S, F and Cl) and P2O5 by secondary ion mass spectrometry for a subset of 47 melt inclusions selected from the dataset. Based on statistical analysis of the major element composition of melt inclusions and by considering their trace and volatile element compositions, we distinguished five main clusters of melt inclusions, which can be further separated into a total of eight subclusters. Among the eight subclusters, we identified three major magma types: (1) enriched medium-K magmas, which form a tholeiitic trend (30–38 Ma); (2) enriched medium-K magmas, which form a calc-alkaline trend (30–39 Ma); (3) depleted low-K magmas, which form a calc-alkaline trend (35–40 Ma). We demonstrate the following: (1) the eruption of depleted low-K calc-alkaline magmas occurred prior to 40 Ma and ceased sharply at 35 Ma; (2) the eruption of depleted low-K calc-alkaline magmas, enriched medium-K calc-alkaline magmas and enriched medium-K tholeiitic magmas overlapped between 35 and 38–39 Ma; (3) the eruption of enriched medium-K tholeiitic and enriched medium-K calc-alkaline magmas became predominant thereafter at the proto-IBM arc. Identification of three major magma types is distinct from the previous work, in which enriched medium-K calc-alkaline magmas and depleted low-K calc-alkaline magmas were not identified. This indicates the usefulness of our statistical analysis as a powerful tool to partition a mixture of multivariable geochemical datasets, such as the composition of melt inclusions in this case. Our data suggest that a depleted mantle source had been replaced by an enriched mantle source owing to convection beneath the proto-IBM arc from >40 to 35 Ma. Finally, thermodynamic modelling indicates that the overall geochemical variation of melt inclusions assigned to each cluster can be broadly reproduced either by crystallization differentiation assuming P = 50 MPa (∼2 km deep) and ∼2 wt% H2O (almost saturated H2O content at 50 MPa) or P = 300 MPa (∼15 km deep) and ∼6 wt% H2O (almost saturated H2O content at 300 MPa). Assuming oxygen fugacity (fO2) of log fO2 equal to +1 relative to the nickel–nickel oxide (NNO) buffer best reproduces the overall geochemical variation of melt inclusions, but assuming more oxidizing conditions (log fO2 = +1 to +2 NNO) probably reproduces the geochemical variation of enriched medium-K and calc-alkaline melt inclusions (30–39 Ma)

Basalt derived from highly refractory mantle sources during early Izu-Bonin-Mariana arc development

The magmatic character of early subduction zone and arc development is unlike mature systems. Low-Ti-K tholeiitic basalts and boninites dominate the early Izu-Bonin-Mariana (IBM) system. Basalts recovered from the Amami Sankaku Basin (ASB), underlying and located west of the IBM’s oldest remnant arc, erupted at ~49 Ma. This was 3 million years after subduction inception (51-52 Ma) represented by forearc basalt (FAB), at the tipping point between FAB-boninite and typical arc magmatism. We show ASB basalts are low-Ti-K, aluminous spinel-bearing tholeiites, distinct compared to mid-ocean ridge (MOR), backarc basin, island arc or ocean island basalts. Their upper mantle source was hot, reduced, refractory peridotite, indicating prior melt extraction. ASB basalts transferred rapidly from pressures (~0.7-2 GPa) at the plagioclase-spinel peridotite facies boundary to the surface. Vestiges of a polybaric-polythermal mineralogy are preserved in this basalt, and were not obliterated during persistent recharge-mix-tap-fractionate regimes typical of MOR or mature arcs

Evaluating tephrochronology in the permafrost peatlands of Northern Sweden

Tephrochronology is an increasingly important tool for the dating of sediment and peat profiles for palaeoecological, palaeoclimatic and archaeological research. However, although much work has been done on tephra in temperate peatlands, there have been very few in-depth investigations of permafrost peatlands. Here we present the analysis of nine peatland cores from Abisko, northern Sweden, and show that the presence of tephra layers may be highly variable even over a scale of <10 km. Using electron probe microanalysis (EPMA) combined with age-depth profiles compiled from radiocarbon (14C) and 210Pb dating of peat records, we identify the Hekla 1104, Hekla 1158, Hekla-Selsund and the Hekla 4 tephra layers. We also infer the presence of the Askja 1875 tephra, in addition to an unassigned tephra dating from between 1971–1987 AD in two separate cores. Five of the nine analysed cores do not contain distinct tephra layers. Volcanic ash deposits in northern Scandinavia are subject to both regional-scale variations in climate and atmospheric circulation, and local-scale variations on the order of tens of kilometres in topography, vegetation, snow cover, and ground permeability. The extreme inconsistency of tephra preservation within a small study area (∼3000 km2) brings into question the reliability of tephrochronology within permafrost peatlands, and highlights the necessity of alternative methods for dating peat profiles in this region