On the rapid computation of various polylogarithmic constants

We give algorithms for the computation of the -th digit of certain transcendental numbers in various bases. These algorithms can be easily implemented (multiple precision arithmetic is not needed), require virtually no memory, and feature run times that scale nearly linearly with the order of the digit desired. They make it feasible to compute, for example, the billionth binary digit of or on a modest work station in a few hours run time. We demonstrate this technique by computing the ten billionth hexadecimal digit of , the billionth hexadecimal digits of and , and the ten billionth decimal digit of . These calculations rest on the observation that very special types of identities exist for certain numbers like , , and . These are essentially polylogarithmic ladders in an integer base. A number of these identities that we derive in this work appear to be new, for example the critical identity for :

     

Microfluidic depletion of endothelial cells, smooth muscle cells, and fibroblasts from heterogeneous suspensions

Interactions between ligands and cell surface receptors can be exploited to design adhesion-based microfluidic cell separation systems. When ligands are immobilized on the microfluidic channel surfaces, the resulting cell capture devices offer the typical advantages of small sample volumes and low cost associated with microfluidic systems, with the added benefit of not requiring complex fabrication schemes or extensive operational infrastructure. Cell-ligand interactions can range from highly specific to highly non-specific. This paper describes the design of an adhesion-based microfluidic separation system that takes advantage of both types of interactions. A 3-stage system of microfluidic devices coated with the tetrapeptides arg-glu-asp-val (REDV), val-ala-pro-gly (VAPG), and arg-gly-asp-ser (RGDS) is utilized to deplete a heterogeneous suspension containing endothelial cells, smooth muscle cells, and fibroblasts. The ligand-coated channels together with a large surface area allow effective depletion of all three cell types in a stagewise manner.     

Peptide-mediated selective adhesion of smooth muscle and endothelial cells in microfluidic shear flow

Microfluidic devices have recently emerged as effective tools for cell separation compared to traditional techniques. These devices offer the advantages of small sample volumes, low cost, and high purity. Adhesion-based separation of cells from heterogeneous suspensions can be achieved by taking advantage of specific ligand-receptor interactions. The peptide sequences Arg-Glu-Asp-Val (REDV) and Val-Ala-Pro-Gly (VAPG) are known to bind preferentially to endothelial cells (ECs) and smooth muscle cells (SMCs), respectively. This article examines the roles of REDV and VAPG and fluid shear stress in achieving selective capture of ECs and SMCs in microfluidic devices. The adhesion of ECs in REDV-coated devices and SMCs in VAPG-coated devices increases significantly compared to that of the nontargeted cells with decreasing shear stress. Furthermore, the adhesion of these cells is shown to be independent of whether these cells flow through the devices as suspensions of only one cell type or as a heterogeneous suspension containing ECs, SMCs, and fibroblasts. Whereas the overall adhesion of cells in the devices is determined mainly by shear stress, the selectivity of adhesion depends on the type of peptide and on the device surface as well as on the shear stress.     

Thermomagnetic determination of Fe3O4 magnetic nanoparticle diameters for biomedical applications

The utility and promise of magnetic nanoparticles (MagNPs) for biomedicine rely heavily on accurate determination of the particle diameter attributes. While the average functional size and size distribution of the magnetic nanoparticles directly impact the implementation and optimization of nanobiotechnology applications in which they are employed, the determination of these attributes using electron microscopy techniques can be time-consuming and misrepresentative of the full nanoparticle population. In this work the average particle diameter and distribution of an ensemble of Fe₃O₄ ferrimagnetic nanoparticles are determined solely from temperature-dependent magnetization measurements; the results compare favorably to those obtained from extensive electron microscopy observations. The attributes of a population of biocompatible Fe₃O₄ nanoparticles synthesized by a thermal decomposition method are obtained from quantitative evaluation of a model that incorporates the distribution of superparamagnetic blocking temperatures represented through thermomagnetization data. The average size and size distributions are determined from magnetization data via temperature-dependent zero-field-cooled magnetization. The current work is unique from existing approaches based on magnetic measurement for the characterization of a nanoparticle ensemble as it provides both the average particle size as well as the particle size distribution.     

Temperature-sensitive resolution of cis- and trans-fatty acid isomers of partially hydrogenated vegetable oils on SP-2560 and CP-Sil 88 capillary columns

This study examines the effect of the column operating temperature of 100 m SP-2560 and CP-Sil 88 capillary gas chromatographic (GC) columns on the separation of cis- and trans-octadecenoic (18:1) isomers in partially hydrogenated vegetable oils. The overlapping GC peaks were measured at column isothermal temperatures of 170, 175, 180, 185, and 190 degrees C. With both columns, isothermal operation at 180 degrees C produced the fewest overlapping peaks of the cis and trans isomers. At this temperature, all trans-18:1 isomers, except 13t-18:1 (t = trans), 14t-18:1, and 15t-18:1 isomers were resolved from the cis-18:1 isomers. The peaks of the 13t-18:1 and 14t-18:1 isomer pair, which always elute together, overlapped peaks of the 6c-18:1 (c = cis), 7c-18:1, and 8c-18:1 isomers; the peak of the 15t-18:1 isomer overlapped the major cis-18:1 peak, which was mainly due to 9c-18:1. Isothermal operations above or below 180 degrees C produced some additional overlapping problems. At 185 and 190 degrees C, the peaks of the 16t-18:1 and 13c-18:1 isomers overlapped. At 175 and 170 degrees C, the 16t-18:1 peak overlapped the 14c-18:1 peak, and the peaks of the 13t + 14t-18:1 isomer pair partially overlapped the major cis-18:1 peak. The separation of 11c-20:1 and alpha-linolenic acid and its geometric isomers was also affected by the column operating temperature. Isothermal operation of the SP-2560 column at 180 degrees C produced a baseline separation of 11c-20:1 and alpha-linolenic acid and its geometric isomers, whereas with the CP-Sil 88 column the best resolution was obtained at 170 degrees C. The results of this study show that the SP-2560 capillary column has a slight advantage over the CP-Sil 88 column for the simultaneous resolution of all the fatty acids generally found in partially hydrogenated vegetable oils.