The effect of the diffusion time and pulse gradient duration ratio on the diffraction pattern and the structural information estimated from q-space diffusion MR: experiments and simulations

q-Space diffusion MRI (QSI) provides a means of obtaining microstructural information about porous materials and neuronal tissues from diffusion data. However, the accuracy of this structural information depends on experimental parameters used to collect the MR data. q-Space diffusion MR performed on clinical scanners is generally collected with relatively long diffusion gradient pulses, in which the gradient pulse duration, δ, is comparable to the diffusion time, Δ. In this study, we used phantoms, consisting of ensembles of microtubes, and mathematical models to assess the effect of the ratio of the diffusion time and the duration of the diffusion pulse gradient, i.e., Δ/δ, on the MR signal attenuation vs. q, and on the measured structural information extracted therefrom. We found that for Δ/δ  1, the diffraction pattern obtained from q-space MR data are shallower than when the short gradient pulse (SGP) approximation is satisfied. For long δ the estimated compartment size is, as expected, smaller than the real size. Interestingly, for Δ/δ  1 the diffraction peaks are shifted to even higher q-values, even when δ is kept constant, giving the impression that the restricted compartments are even smaller than they are. When phantoms composed of microtubes of different diameters are used, it is more difficult to estimate the diameter distribution in this regime. Excellent agreement is found between the experimental results and simulations that explicitly account for the use of long duration gradient pulses. Using such experimental data and this mathematical framework, one can estimate the true compartment dimensions when long and finite gradient pulses are used even when Δ/δ  1.     

Gbit/s rate bipolar pulse modulation of semiconductor injection lasers

Using a bipolar drive current pulse shape and very low threshold (9 mA) lasers, zero-background pseudorandom optical pulses were generated and detected at a rate of up to 4 Gbit/s without a pattern effect. The drive current pulse consists of a forward pulse followed by a reverse pulse, each of 70 ps duration and about 400 mA amplitude. No DC bias was applied, which is a necessary condition for pattern-effect-free modulation.     

Time-reversal symmetry violation and the oscillating universe

The expressions for the fractional number ofK ⁰'s and¯K ⁰'s in a neutral kaon beam are discussed with reference to time-reversal asymmetry. The suggested relation between the sign of Re ( is the Lee-WuT-violation parameter) and the cosmological arrow of time ifCPT is broken is further clarified.Research sponsored by the Air Force Office of Scientific Research, Office of Aerospace Research, U.S. Air Force, under AFOSR grant number EOOAR-68-0010, through the European Office of Aerospace Research.     

Microscopic irreversibility in the neutral kaon system and the thermodynamical arrow of time I. CPT symmetric case

The master equation for the reduced density matrix of the neutral kaon system interacting with a (low temperature) boson gas is derived. The equation is transformed under time reversal (assuming CPT conservation) and the equations of motion in the direct and inverted time schemes are compared. The equations of motion are solved, in a perturbation method, and the explicit approach to thermodynamical equilibrium is described. The entropy production function for the kaonic decaying system is defined and calculated. It is shown that although the equilibrium state and the total entropy change during the approach to it are the same in both time schemes, the details of the entropy time dependence of a coherent initial state are different, thus suggesting a relation between microscopic and macroscopic arrows of time.     

Crossing fibers, diffractions and nonhomogeneous magnetic field: correction of artifacts by bipolar gradient pulses

In recent years, diffusion tensor imaging (DTI) and its variants have been used to describe fiber orientations and q-space diffusion MR was proposed as a means to obtain structural information on a micron scale. Therefore, there is an increasing need for complex phantoms with predictable microcharacteristics to challenge different indices extracted from the different diffusion MR techniques used. The present study examines the effect of diffusion pulse sequence on the signal decay and diffraction patterns observed in q-space diffusion MR performed on micron-scale phantoms of different geometries and homogeneities. We evaluated the effect of the pulse gradient stimulated-echo, the longitudinal eddy current delay (LED) and the bipolar LED (BPLED) pulse sequences. Interestingly, in the less homogeneous samples, the expected diffraction patterns were observed only when diffusion was measured with the BPLED sequence. We demonstrated the correction ability of bipolar diffusion gradients and showed that more accurate physical parameters are obtained when such a diffusion gradient scheme is used. These results suggest that bipolar gradient pulses may result in more accurate data if incorporated into conventional diffusion-weighted imaging and DTI.     

Derived Picard Groups of Finite-Dimensional Hereditary Algebras

Let A be a finite-dimensional algebra over a field k. The derived Picard group DPic _k (A) is the group of triangle auto-equivalences of D> ^b( mod A) induced by two-sided tilting complexes. We study the group DPic _k (A) when A is hereditary and k is algebraically closed. We obtain general results on the structure of DPic _k , as well as explicit calculations for many cases, including all finite and tame representation types. Our method is to construct a representation of DPic _k (A) on a certain infinite quiver ^irr. This representation is faithful when the quiver of A is a tree, and then DPic _k (A) is discrete. Otherwise a connected linear algebraic group can occur as a factor of DPic _k (A). When A is hereditary, DPic _k (A) coincides with the full group of k-linear triangle auto-equivalences of D^b( mod A). Hence, we can calculate the group of such auto-equivalences for any triangulated category D equivalent to D^b( mod A. These include the derived categories of piecewise hereditary algebras, and of certain noncommutative spaces introduced by Kontsevich and Rosenberg.     

Noncommutative localisation in algebraic K-theory II

In [Amnon Neeman, Andrew Ranicki, Noncommutative localisation in algebraic K-theory I, Geom. Topol. 8 (2004) 1385-1425] we proved a localisation theorem in the algebraic K-theory of noncommutative rings. The main purpose of the current article is to express the general theorem of the previous paper in a more user-friendly fashion, in a way more suitable for applications. In the process we compare our result to the existing theorems in the literature, showing how the previous paper improves all the existing results.It should be pointed out that there have been two very interesting recent preprints on related topics. The reader is referred to the beautiful papers of Krause [Henning Krause, Cohomological quotients and smashing localizations, http://wwwmath.upb.de/~hkrause/publications.html. [8]] and Dwyer [William G. Dwyer, Noncommutative localization in homotopy theory, preprint, http://www.nd.edu/~wgd/. [4]]. Krause studies the lifting of chain complexes and the relation with the telescope conjecture, and Dwyer generalises to the homotopy theoretic framework.