Synthesis and reactions of polymer-bound Ph3P=C=C=O: a quick route to tenuazonic acid and other optically pure 5-substituted tetramates

Polystyrene-bound cumulated ylide Ph3PCCO was prepared on a large scale in two steps. It reacts with Grignard compounds, amines and alcohols to give immobilized acyl, amide and ester ylides, respectively. Their Wittig reactions lead to alkenes free of phosphane oxide. Optically pure 5-substituted tetramates were obtained from reactions of resin-bound Ph3PCCO with alpha-ammonium esters in one step. The mycotoxin (-)-tenuazonic acid was accordingly prepared in just three steps.     

Cubic Forms Modulo One

By using a more efficient way of ‘almost diagonalizing’,known results on small fractional parts of general real cubicforms in a small number of variables, are improved. In particular,for ternary forms the method gives a bound superior to thatarising from simply reducing to a cubic form in one variable.2000 Mathematics Subject Classification 11D75, 11E76, 11J54.     

Stochastic control with exit time and constraints,application to small time attainability of sets

We study the existence of a solution of controlled stochastic differential equations remaining in a given set of constraints at any time smaller than the exit time of a given open set. We also investigate the small time attainability of a given closed set K, i.e., the property that, for all arbitrary small time horizon T and for all initial condition in a sufficiently small neighborhood of K, there exists a solution to the controlled stochastic differential equation which reaches K before T.     

Solid-state laser intensity stabilization at the 10(-8) level

A high-power, low-noise photodetector, in conjunction with a current shunt actuator, is used in an ac-coupled servo to stabilize the intensity of a 10-W cw Nd:YAG laser. A relative intensity noise of 1 x 10(-8) Hz(-1/2) at 10 Hz is achieved.     

F-18-FDG uptake is a reliable predictory of functional recovery of akinetic but viable infarct regions as defined by magnetic resonance imaging before and after revascularization

Identification of akinetic but viable myocardium is important for the selection of patients for coronary revascularization. In order to assess predictive values of end-diastolic wall thickness and dobutamine induced wall thickening obtained by magnetic resonance imaging (MRI) and [18F]Fluorodeoxyglucose uptake assessed by positron emission tomography (F-18-FDG-PET), these parameters were compared to recovery of left ventricular function after successful revascularization. Forty patients with chronic myocardial infarction and regional a- or dyskinesia by ventriculography underwent rest- and dobutamine-MRI studies (10 microg dobutamine/kg body weight/min) and F-18-FDG-PET. Viability of the infarct region was considered to be present if; 1) end-diastolic wall thickness was > or =5.5 mm; 2) dobutamine induced wall thickening > or =2 mm could be measured; and 3) normalized F-18-FDG-uptake was > or =50% in > or =50% of akinetic segments. Preserved end-diastolic wall thickness was found in 32/40 patients, functional improvement during dobutamine infusion in 26/40 patients and preserved F-18-FDG-uptake in 29/40 patients. After revascularization regional left ventricular function improved in 25/40 patients. Positive and negative predictive values and diagnostic accuracy were 78%, 100%, and 83% for preserved end-diastolic wall thickness, 92%, 93%, and 93% for dobutamine inducible contraction reserve and 86%, 100%, and 90% for preserved F-18-FDG-uptake. Quantitative assessment of dobutamine induced systolic wall thickening by MRI and F-18-FDG-uptake by PET are highly accurate techniques for the identification of viable myocardium and prediction of functional recovery after successful revascularization. Preserved end-diastolic wall thickness results in an overestimation of viable myocardium compared to functional improvement, but wall thickness <5.5 mm excludes recovery of regional function.     

Visualization of transport: NMR microscopy experiments with model objects for porous media with pore sizes down to 50 microm

Hydrodynamic flow and electric currents through model porous media were investigated. The transport rates through the individual pathways of the pore network are determined by the local width of the pore channels and by the driving mechanism. The model objects represent quasi two-dimensional random site percolation clusters. The calculated design was realized by milling the structure in polystyrene sheets. Velocity maps of stationary flow and current density maps of stationary currents through the cluster were acquired by magnetic resonance imaging methods. The findings were compared to the results of numerical simulations based on the same structure. Since the difference in the transport patterns of the different driving mechanisms are expected to be more pronounced in smaller pore spaces, ultra deep X-ray lithography has been used for the fabrication of downsized model objects with a spatial resolution of better than 50 microm and an aspect ratio as large as 20. First results obtained with these objects are reported.     

Investigating directed cortical interactions in time-resolved fMRI data using vector autoregressive modeling and Granger causality mapping

We present a framework aimed to reveal directed interactions of activated brain areas using time-resolved fMRI and vector autoregressive (VAR) modeling in the context of Granger causality. After describing the underlying mathematical concepts, we present simulations helping to characterize the conditions under which VAR modeling and Granger causality can reveal directed interactions from fluctuations in BOLD-like signal time courses. We apply the proposed approach to a dynamic sensorimotor mapping paradigm. In an event-related fMRI experiment, subjects performed a visuomotor mapping task for which the mapping of two stimuli (“faces” vs “houses”) to two responses (“left” or “right”) alternated periodically between the two possible mappings. Besides expected activity in sensory and motor areas, a fronto-parietal network was found to be active during presentation of a cue indicating a change in the stimulus-response (S-R) mapping. The observed network includes the superior parietal lobule and premotor areas. These areas might be involved in setting up and maintaining stimulus-response associations. The Granger causality analysis revealed a directed influence exerted by the left lateral prefrontal cortex and premotor areas on the left posterior parietal cortex.     

In vivo mapping of functional domains and axonal connectivity in cat visual cortex using magnetic resonance imaging

Noninvasive cognitive neuroimaging studies based on functional magnetic resonance imaging (fMRI) are of ever-increasing importance for basic and clinical neurosciences. The explanatory power of fMRI could be greatly expanded, however, if the pattern of the neuronal circuitry underlying functional activation could be made visible in an equally noninvasive manner. In this study, blood oxygenation level-dependent (BOLD)-based fMRI and diffusion tensor imaging (DTI) were performed in the same cat visual cortex, and the foci of fMRI activation utilized as seeding points for 3D DTI fiber reconstruction algorithms, thus providing the map of the axonal circuitry underlying visual information processing. The methods developed in this study will lay the foundation for in vivo neuroanatomy and the ability for noninvasive longitudinal studies of brain development.     

Small Solutions of Quadratic Diophantine Equations

We consider quadratic diophantine equations of the shape for a polynomial Q(X₁, ..., X_s) Z[X₁, ..., X_s] of degree 2.Let H be an upper bound for the absolute values of the coefficientsof Q, and assume that the homogeneous quadratic part of Q isnon-singular. We prove, for all s 3, the existence of a polynomialbound _s(H) with the following property: if equation (1) hasa solution x Z^s at all, then it has one satisfying For s = 3 and s = 4 no polynomial bounds _s(H) were previouslyknown, and for s 5 we have been able to improve existing boundsquite significantly. 2000 Mathematics Subject Classification11D09, 11E20, 11H06, 11P55.     

Unitals in Topological Affine Translation Planes Need Not Be Strictly Convex

We study the relationship of two incidence geometric convexity notions, namely, ovoids in real affine spaces and compact unitals of codimension 1 in topological affine translation planes. In [3] we showed that every ovoid in a translation plane is a unital, and we asked if the converse is true. Here we introduce the notion of a shell, which is distinctly weaker than that of an ovoid and still implies the unital property if the translation plane is properly chosen (and the shell is not too degenerate). We give an explicit example of a shell that is not an ovoid. The question remains whether or not conversely, every compact unital of codimension 1 in a translation plane is a shell.This paper was written while the third author was supported by a grant from DFG and TÜBITAK.Received March 12, 2002 Published online November 18, 2002