From Dyck Paths to Standard Young Tableaux

Annals of Combinatorics - We present nine bijections between classes of Dyck paths and classes of standard Young tableaux (SYT). In particular, we consider SYT of flag and rectangular shapes, we...     

Minimal Model Fusion Rules From 2-Groups

The fusion rules for the (p,q)-minimal model representations of the Virasoro algebra are shown to come from the group in the following manner. There is a partition into disjoint subsets and a bijection between and the sectors of the (p,q)-minimal model such that the fusion rules correspond to where .     

Dispersion-free fiber transmission for femtosecond pulses by use of a dispersion-compensating fiber and a programmable pulse shaper

We demonstrate nearly distortionless 2.5-km fiber transmission of sub-500-fs pulses, using a combination of standard single-mode fiber, dispersion-compensating fiber, and a programmable pulse shaper for simultaneous quadratic and cubic dispersion compensation. The dispersion-compensating fiber corrects the bulk of the quadratic and the cubic phases for the single-mode fiber, and the fiber-pigtailed programmable pulse shaper exactly compensates the residual dispersion terms. Together these elements permit complete recompression of pulses, which first broaden by ~400 times in the single-mode fiber.     

A microfluidic processor for gene expression profiling of single human embryonic stem cells

The gene expression of human embryonic stem cells (hESC) is a critical aspect for understanding the normal and pathological development of human cells and tissues. Current bulk gene expression assays rely on RNA extracted from cell and tissue samples with various degree of cellular heterogeneity. These 'cell population averaging' data are difficult to interpret, especially for the purpose of understanding the regulatory relationship of genes in the earliest phases of development and differentiation of individual cells. Here, we report a microfluidic approach that can extract total mRNA from individual single-cells and synthesize cDNA on the same device with high mRNA-to-cDNA efficiency. This feature makes large-scale single-cell gene expression profiling possible. Using this microfluidic device, we measured the absolute numbers of mRNA molecules of three genes (B2M, Nodal and Fzd4) in a single hESC. Our results indicate that gene expression data measured from cDNA of a cell population is not a good representation of the expression levels in individual single cells. Within the G0/G1 phase pluripotent hESC population, some individual cells did not express all of the 3 interrogated genes in detectable levels. Consequently, the relative expression levels, which are broadly used in gene expression studies, are very different between measurements from population cDNA and single-cell cDNA. The results underscore the importance of discrete single-cell analysis, and the advantages of a microfluidic approach in stem cell gene expression studies.     

Complete dispersion compensation for 400-fs pulse transmission over10-km fiber link using dispersion compensating fiber and spectral phaseequalizer

We have demonstrated essentially complete dispersion compensation for 400-fs pulses over a 10-km fiber link using dispersion compensating fiber and a programmable femtosecond pulse shaper functioning as a spectral phase equalizer. The pulse shaper impresses adjustable quadratic and cubic phases onto the spectrum and removes all the residual dispersion and dispersion slope in the dispersion compensated fiber link. Our work shows that the pulse shaper technique provides a powerful and convenient tool for programmable fiber dispersion compensation over broad optical bandwidth. This allows distortion-free femtosecond pulse transmission over a fiber link in excess of 10 km without requiring the exact trimming of the dispersion-compensating fiber     

Direct measurement of fine structure changing collisional losses in cold trapped 85Rb

Using a technique that consists in ionizing atoms out of the 5P _1/2 fragments originated in the cold collision process, we have measured the contribution of the fine structure changing collision (FS) to the total trap loss rate of cold ⁸⁵Rb. Our results show that FS contribution is responsible for about 4% of the total trap loss. This result should stimulate new theoretical discussions involving exoergic cold collisions. Received 26 October 1998 and Received in final form 2 February 1999     

Numerical experiments with parallel two‐step W‐methods for DAEs

We study the numerical behavior of parallel two‐step W‐methods (PTSW methods) applied to index 2 and index 3 DAE test‐problems. In this experiments we do not observe an order reduction in the differential components of the solution and we obtain the same orders as in the ODE and index 1 case. Our methods perform comparably with RADAU for the test‐problems in sequential computations and superior in parallel mode. We conclude that PTSW methods are an interesting choice for solving DAEs, at least up to index 2.     

Structural Differences Between Biogenic Amorphous Calcium Carbonate Phases Using X‐ray Absorption Spectroscopy

We compare the organization of the first coordination shells around the calcium ion in biogenic ACC phases from three different sources. The results show that although the three biogenic samples have the same chemical composition, which is referred to collectively under the name “amorphous calcium carbonate”, they are structurally different from one another. These differences may be attributed to the diverse modes of formation of such biogenic materials and may account for their known variations in stability.