Identification of small inhomogeneities of extreme conductivity by boundary measurements: a theorem on continuous dependence

We consider an electrostatic problem for a conductor consisting of finitely many small inhomogeneities of extreme conductivity, embedded in a spatially varying reference medium. Firstly we establish an asymptotic formula for the voltage potential in terms of the reference voltage potential, the location of the inhomogeneities and their geometry. Secondly we use this representation formula to prove a Lipschitz-continuous dependence estimate for the corresponding inverse problem. This estimate bounds the difference in the location and in certain geometric properties of two sets of inhomogeneities by the difference in the boundary voltage potentials corresponding to a fixed current distribution.     

MR imaging of excessively obese patients: the use of an open permanent magnet

Excessive obesity can pose a limitation to both clinical and radiographic evaluation. Although CT and MR have revolutionized head and body imaging, patients with weights above 300 lb present a restriction of these imaging modalities. Magnetic resonance imaging (MRI) is well suited for imaging excessively obese patients, because the RF used does not have difficulty in penetrating large amounts of adipose tissue as ionizing radiation or sound waves does. The limitations of conventional MR imaging in these obese patients are the gantry size and the table weight limit. The recent development of a new low field MR imager with a larger gantry size and greater weight capacity, has the potential for imaging obese patients that cannot be evaluated by standard CT or MR. In this paper, we report our experience in imaging nine excessively obese patients with weights between 350 and 490 lb using a permanent magnet operating at 0.064 T.     

Configurations Maximizing the Number of Pairs of Hamming-Adjacent Lattice Points

The following question is considered: Which sets of k lattice points among the n^d points in a d-dimensional cube of length n maximize the number of pairs of points differing in only one coordinate? It is shown that maximal configurations for any (d, n, k) are obtained by choosing the first k points in a lexicographic ordering of the points by coordinates. Some possible generalizations of the problem are discussed.     

The shape of axisymmetric rotating fluid

The equations for axisymmetric self-gravitating rotating fluid have been studied extensively since Poincaré. The model derives its primary interest from celestial mechanics, where it can be used to study the geometry of stars and planets. Existence of a solution for both the compressible and the incompressible cases is known. The smoothness of the boundary of the fluid is studied, and, in particular, it is proved that the rotating fluid has at most a finite number of rings.     

Analog Retinal Redshifts Visible Absorption of QuasAr Transmembrane Voltage Sensors into Near-infrared

Opsin-based transmembrane voltage sensors (OTVSs) are increasingly important tools for neuroscience enabling neural function in complex brain circuits to be explored in live, behaving animals. However, the visible wavelengths required for fluorescence excitation of the current generation of OTVSs limit optogenetic imaging in the brain to depths of only a few mm due to the strong absorption and scattering of visible light by biological tissues. We report that substitution of the native A1 retinal chromophore of the widely used QuasAr1/2 OTVSs with the retinal analog MMAR containing a methylamino-modified dimethylphenyl ring results in over a 100-nm redshift of the maxima of the absorption and fluorescence emission bands to near 700 and 840 nm, respectively. FT-Raman spectroscopy reveals that at pH 7 QuasAr1 with both the A1 and MMAR chromophores possess predominantly an all-trans protonated Schiff base configuration with the MMAR chromophore exhibiting increased torsion of the polyene single-/double-bond system similar to the O-intermediate of the BR photocycle. In contrast, the A1 and the MMAR chromophores of QuasAr2 exist partially in a 13-cis PSB configuration. These results demonstrate that QuasArs containing the MMAR chromophore are attractive candidates for use as NIR-OTVSs, especially for applications such as deep brain imaging.     

PRIMARY PHOTOCHEMISTRY OF BACTERIORHODOPSIN: COMPARISON OF FOURIER TRANSFORM INFRARED DIFFERENCE SPECTRA WITH RESONANCE RAMAN SPECTRA

Abstract —Fourier transform infrared (FTIR) difference spectra of the BR→rK transition in bacteriorhodopsin at 77→K are compared with analogous resonance Raman difference spectra obtained using a spinning sample cell at 77→K. The vibrational frequencies observed in the FTIR spectra of native purple membrane and of purple membrane regenerated with 15-deuterioretinal are in good agreement with the frequencies observed in the Raman spectra, indicating that the lines in the FTIR difference spectra arise predominantly from retinal chromophore vibrations. This agreement confirms that the spinning cell method for obtaining resonance Raman spectra of K minimizes potential contributions from unwanted photoproducts. The unexpected similarity between the resonance Raman scattering intensities and the FTIR absorption intensities for BR and K is discussed in terms of the delocalized electronic structure of the chromophore. Finally, comparison of the Schiff base regions of the K Raman and FTIR spectra provide additional information on the assignment of its Schiff base vibration.     

Computations of cuspidal cohomology of congruence subgroups of SL(3, Z)

Algorithms are presented which find a basis of the vector space of cuspidal cohomology of certain congruence subgroups of SL(3, $\text{Z}$) and which determine the action of the Hecke operators on this space. These algorithms were implemented on a computer. Four pairs of cuspidal classes were found with prime level less than 100. Tables are given of the eigenvalues of the first few Hecke operators on these classes.     

A canonical restricted version of van der waerden’s theorem

It is shown that there is a subsetS of integers containing no (k+1)-term arithmetic progression such that if the elements ofS are arbitrarily colored (any number of colors),S will contain ak-term arithmetic progression for which all of its terms have the same color, or all have distinct colors.