The Measure of the Orthogonal Polynomials Related to Fibonacci Chains: The Periodic Case

The spectral measure for the two families of orthogonal polynomial systems related to periodic chains with N-particle elementary unit and nearest neighbour harmonic interaction is computed using two different methods. The interest is in the orthogonal polynomials related to Fibonacci chains in the periodic approximation. The relation of the measure to appropriately defined Green's functions is established.Comment: 19 pages, TeX, 3 scanned figures, uuencoded file, original figures on request, some misprints corrected, tbp: J. Phys.

VLA Detection of the Ionized Stellar Winds Arising from Massive Stars in the Galactic Center Arches Cluster

The Galactic center Arches stellar cluster, detected and studied until now only in the near-infrared, is comprised of at least one hundred massive (M>20 Msun) stars. Here we report the detection at centimeter wavelengths of radio continuum emission from eight radio sources associated with the cluster. Seven of these radio sources have rising spectral indices between 4.9 and 8.5 GHz and coincide spatially with the brightest stars in the cluster, as determine from JHK photometry and Brackett alpha and Brackett Gamma spectroscopy. Our results confirm the presence of powerful ionized winds in these stars. The eighth radio source has a nonthermal spectrum and its nature is yet unclear, but it could be associated with a lower mass young star in the cluster.Comment: 6 pages, 2 embedded figures, accepted to ApJLetter

Observation of discrete energy levels in a quantum confined system

Low temperature scanning tunneling microscope images and spectroscopic data have been obtained on subnanometer size Pb clusters fabricated using the technique of buffer layer assisted growth. Discrete energy levels were resolved in current-voltage characteristics as current peaks rather than current steps. Distributions of peak voltage spacings and peak current heights were consistent with Wigner-Dyson and Porter-Thomas distributions respectively, suggesting the relevance of random matrix theory to the description of the electronic eigenstates of the clusters. The observation of peaks rather than steps in the current-voltage characteristics is attributed to a resonant tunneling process involving the discrete energy levels of the cluster, the tip, and the states at the interface between the cluster and the substrate surface.Comment: 4 pages, 4 figure

A new physarum learner for network structure learning from biomedical data

A novel structure learning algorithm for Bayesian Networks based on a Physarum Learner is presented. The length of the connections within an initially fully connected Physarum-Maze is taken as the inverse Pearson correlation coefficient between the connected nodes. The Physarum Learner then estimates the shortest indirect paths between each pair of nodes. In each iteration, a score of the surviving edges is incremented. Finally, the highest scored connections are combined to form a Bayesian Network. The novel Physarum Learner method is evaluated with different configurations and compared to the LAGD Hill Climber showing comparable performance with respect to quality of training results and increased time efficiency for large data sets

Large Fourier transforms never exactly realized by braiding conformal blocks

Fourier transform is an essential ingredient in Shor's factoring algorithm. In the standard quantum circuit model with the gate set \{\U(2), \textrm{CNOT}\}, the discrete Fourier transforms $F_N=(\omega^{ij})_{N\times N},i,j=0,1,..., N-1, \omega=e^{\frac{2\pi i}{N}}$, can be realized exactly by quantum circuits of size $O(n^2), n=\textrm{log}N$, and so can the discrete sine/cosine transforms. In topological quantum computing, the simplest universal topological quantum computer is based on the Fibonacci (2+1)-topological quantum field theory (TQFT), where the standard quantum circuits are replaced by unitary transformations realized by braiding conformal blocks. We report here that the large Fourier transforms $F_N$ and the discrete sine/cosine transforms can never be realized exactly by braiding conformal blocks for a fixed TQFT. It follows that approximation is unavoidable to implement the Fourier transforms by braiding conformal blocks

Structural basis of the chiral selectivity of Pseudomonas cepacia lipase

To investigate the enantioselectivity of Pseudomonas cepacia lipase, inhibition studies were performed with SC- and RC-(RP,SP)-1,2-dialkylcarbamoylglycero-3-O-p-nitrophenyl alkylphosphonates of different alkyl chain lengths. P. cepacia lipase was most rapidly inactivated by RC-(RP,SP)-1,2-dioctylcarbamoylglycero-3-O-p-nitrophenyl octylphosphonate (RC-trioctyl) with an inactivation half-time of 75 min, while that for the SC-(RP,SP)-1,2-dioctylcarbamoylglycero-3-O-p-nitrophenyl octyl-phosphonate (SC-trioctyl) compound was 530 min. X-ray structures were obtained of P. cepacia lipase after reaction with RC-trioctyl to 0.29-nm resolution at pH 4 and covalently modified with RC-(RP,SP)-1,2-dibutylcarbamoylglycero-3-O-p-nitrophenyl butyl-phosphonate (RC-tributyl) to 0.175-nm resolution at pH 8.5. The three-dimensional structures reveal that both triacylglycerol analogues had reacted with the active-site Ser87, forming a covalent complex. The bound phosphorus atom shows the same chirality (SP) in both complexes despite the use of a racemic (RP,SP) mixture at the phosphorus atom of the triacylglycerol analogues. In the structure of RC-tributyl-complexed P. cepacia lipase, the diacylglycerol moiety has been lost due to an aging reaction, and only the butyl phosphonate remains visible in the electron density. In the RC-trioctyl complex the complete inhibitor is clearly defined; it adopts a bent tuning fork conformation. Unambiguously, four binding pockets for the triacylglycerol could be detected: an oxyanion hole and three pockets which accommodate the sn-1, sn-2, and sn-3 fatty acid chains. Van der Waals’ interactions are the main forces that keep the radyl groups of the triacylglycerol analogue in position and, in addition, a hydrogen bond to the carbonyl oxygen of the sn-2 chain contributes to fixing the position of the inhibitor.