Perhaps more than any other “-omics” endeavor, the accuracy and level of detail obtained from mapping the major connection pathways in the living human brain with diffusion MRI depend on the ...capabilities of the imaging technology used. The current tools are remarkable; allowing the formation of an “image” of the water diffusion probability distribution in regions of complex crossing fibers at each of half a million voxels in the brain. Nonetheless our ability to map the connection pathways is limited by the image sensitivity and resolution, and also the contrast and resolution in encoding of the diffusion probability distribution.
The goal of our Human Connectome Project (HCP) is to address these limiting factors by re-engineering the scanner from the ground up to optimize the high b-value, high angular resolution diffusion imaging needed for sensitive and accurate mapping of the brain's structural connections. Our efforts were directed based on the relative contributions of each scanner component. The gradient subsection was a major focus since gradient amplitude is central to determining the diffusion contrast, the amount of T2 signal loss, and the blurring of the water PDF over the course of the diffusion time. By implementing a novel 4-port drive geometry and optimizing size and linearity for the brain, we demonstrate a whole-body sized scanner with Gmax=300mT/m on each axis capable of the sustained duty cycle needed for diffusion imaging. The system is capable of slewing the gradient at a rate of 200T/m/s as needed for the EPI image encoding. In order to enhance the efficiency of the diffusion sequence we implemented a FOV shifting approach to Simultaneous MultiSlice (SMS) EPI capable of unaliasing 3 slices excited simultaneously with a modest g-factor penalty allowing us to diffusion encode whole brain volumes with low TR and TE. Finally we combine the multi-slice approach with a compressive sampling reconstruction to sufficiently undersample q-space to achieve a DSI scan in less than 5min. To augment this accelerated imaging approach we developed a 64-channel, tight-fitting brain array coil and show its performance benefit compared to a commercial 32-channel coil at all locations in the brain for these accelerated acquisitions.
The technical challenges of developing the over-all system are discussed as well as results from SNR comparisons, ODF metrics and fiber tracking comparisons. The ultra-high gradients yielded substantial and immediate gains in the sensitivity through reduction of TE and improved signal detection and increased efficiency of the DSI or HARDI acquisition, accuracy and resolution of diffusion tractography, as defined by identification of known structure and fiber crossing.
•Approach for advancing the sensitivity of the diffusion connectivity measurement.•Optimization of Gmax=300mT/m gradient, RF coil and sequence.•Improved sensitivity and diffusion contrast in high quality DSI/Q Ball.
In this contribution we present the results of a study on land mobile satellite channel models for satellite systems with multiple satellites. The slow fading of our channel model for several ...satellites is based on a Markov channel state model for joint processes while the probability density function (PDF) of the signal amplitude within each state is fitted to the Loo distribution. The correlation between two satellite channels and the channel spatial autocorrelation have also been studied. We show that a channel state model that uses a Markov state model of order one or of a fixed higher order is not appropriate if the state duration is of very high importance, which can be the case in the process of system planning. Therefore, we propose a dynamic higher order Markov state model for joint processes that depends on the current state duration. This approach models precisely any PDF of the channel state duration for both single and multiple satellite broadcasting systems while having a significantly lower computational complexity than a fixed higher order Markov model. It models the channel states of the whole system correctly, as well as the channel states of each satellite observed independently. It is able to capture the state correlation between multiple satellites. We also study possible approximations of the proposed models in order to reduce their computational complexity while having a good PDF match. Our channel state models are validated by measurements.
MIMO systems are already state-of-the-art in terrestrial systems. With the availability of satellites with higher EIRP the high spectrum efficiency offered by MIMO systems becomes applicable to ...satellite-based systems, too. The MIMOSA project covers the evaluation of the satellite MIMO channel characteristics by field measurements. In particular, the estimated capacity increase for mobile reception is evaluated. The measurements have been completed, but the analysis is still ongoing. This paper describes the measurement setup and includes selected results from the statistical analysis.
The Lévy Swap Market Model Eberlein, E.; Liinev, J.
Applied mathematical finance.,
05/2007, Letnik:
14, Številka:
2
Journal Article
Recenzirano
Models driven by Lévy processes are attractive since they allow for better statistical fitting than classical diffusion models. The dynamics of the forward swap rate process is derived in a ...semimartingale setting and a Lévy swap market model is introduced. In order to guarantee positive rates, the swap rates are modelled as ordinary exponentials. The model starts with the most distant rate, which is driven by a non-homogeneous Lévy process. Via backward induction the remaining swap rates are constructed such that they become martingales under the corresponding forward swap measures. Finally it is shown how swaptions can be priced using bilateral Laplace transforms.
Time consistency of Lévy models Eberlein, E.; zkan, F.
Quantitative finance,
02/2003, Letnik:
3, Številka:
1
Journal Article
Recenzirano
Time consistency of the models used is an important ingredient to improve risk management. The empirical investigation in this article gives evidence for some models driven by Lévy processes to be ...highly consistent. This means that they provide a good statistical fit of empirical distributions of returns not only on the timescale used for calibration but on various other timescales as well. As a result these models produce more reliable risk numbers and derivative prices.
Probability distortions for constructing nonlinear G-expectations for the bid and ask or lower and upper prices in continuous time are here extended to the direct use of measure distortions. Fairly ...generally measure distortions can be constructed as probability distortions applied to an exponential distribution function on the half line. The valuation methodologies are extended beyond contract valuation to the valuation of economic activities with infinite lives. Explicit computations illustrate the procedures for stock indices and insurance loss processes.
The Lévy term structure model due to Eberlein and Raible is extended to non-homogeneous driving processes. The classes of equivalent martingale and local martingale measures for various filtrations ...are characterized. It turns out that in a number of standard situations the martingale measure is unique. Reprinted by permission of Springer
As a generalization of the Gaussian Heath–Jarrow–Morton term structure model, we present a new class of bond price models that can be driven by a wide range of Lévy processes. We deduce the forward ...and short rate processes implied by this model and prove that, under certain assumptions, the short rate is Markovian if and only if the volatility structure has either the Vasicek or the Ho–Lee form. Finally, we compare numerically forward rates and European call option prices in a model driven by a hyperbolic Lévy motion with those in the Gaussian model.
Two price economies in continuous time Eberlein, Ernst; Madan, Dilip; Pistorius, Martijn ...
Annals of finance,
02/2014, Letnik:
10, Številka:
1
Journal Article
Static and discrete time pricing operators for two price economies are reviewed and then generalized to the continuous time setting of an underlying Hunt process. The continuous time operators define ...nonlinear partial integro–differential equations that are solved numerically for the three valuations of bid, ask and expectation. The operators employ concave distortions by inducing a probability into the infinitesimal generator of a Hunt process. This probability is then distorted. Two nonlinear operators based on different approaches to truncating small jumps are developed and termed
for quadratic variation and
for normalized Lévy. Examples illustrate the resulting valuations. A sample book of derivatives on a single underlier is employed to display the gap between the bid and ask values for the book and the sum of comparable values for the components of the book.
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