Inapproximability of Edge-Disjoint Paths and low congestion routing on undirected graphs

In the undirected Edge-Disjoint Paths problem with Congestion (EDPwC), we are given an undirected graph with V nodes, a set of terminal pairs and an integer c. The objective is to route as many terminal pairs as possible, subject to the constraint that at most c demands can be routed through any edge in the graph. When c = 1, the problem is simply referred to as the Edge-Disjoint Paths (EDP) problem. In this paper, we study the hardness of EDPwC in undirected graphs.     

Comparison of Fourier transform infrared (FTIR) spectra of individual cells acquired using synchrotron and conventional sources

The ability of infrared (IR) spectroscopy to distinguish and map cancerous and non-cancerous tissue has opened the question of the origin of spectral differences between normal and cancerous cells. Given the size of human cells (about 12–50 μm in diameter), IR micro-spectroscopy (IR-MSP) is an ideal tool for studying individual cells, or fractions thereof. In this contribution, the methodology for collecting IR spectra of individual cells will be explored using spectrometers that employ either synchrotron or conventional (thermal) light sources. Although synchrotron-based measurements are superior to those of conventional instruments, particularly at apertures approaching the diffraction limit, the difference in spectral quality and data acquisition time has been reduced drastically for a new generation of conventional instruments.     

Properties and production of F-doped silica glass

Fluorine-doped silica glass is an optical material with high transmission in the vacuum ultraviolet region, specifically at 157 nm. This feature, along with low thermal expansion and ease of polishing make it the material of choice for the photomask substrate for the 157 nm lithography node. We report the synthesis of fluorine-doped silica glass using various dopants. Characterization of the glasses was achieved by measuring vacuum UV and IR spectra and by refractive index measurements. Transmission and refractive index are both found to depend on fluorine concentration.     

Dendritic mRNAs encode diversified functionalities in hippocampal pyramidal neurons

Background  

Targeted transport of messenger RNA and local protein synthesis near the synapse are important for synaptic plasticity. In order to gain an overview of the composition of the dendritic mRNA pool, we dissected out stratum radiatum (dendritic lamina) from rat hippocampal CA1 region and compared its mRNA content with that of stratum pyramidale (cell body layer) using a set of cDNA microarrays. RNAs that have over-representation in the dendritic fraction were annotated and sorted into function groups.     

A numerical and experimental study of batch sedimentation and viscous resuspension

A suspension of non‐neutrally buoyant, large, nearly monodisperse spheres is studied both in batch sedimentation and in shear between concentric rotating cylinders. We apply a continuum constitutive equation based on the diffusive flux model augmented with buoyancy terms derived by Acrivos and coworkers and discretize the resulting equation set with the finite element method. We simulate batch sedimentation using this method and obtain a reasonable match with experiment. Next used two‐dimensional NMR imaging to measure the evolution of solid fraction profiles in the same suspension undergoing flow between rotating concentric cylinders with two different initial conditions. Here, both gravity‐induced and shear‐induced particle migration are significant. Under these conditions, we have found that simulating the correct initial condition is critical to matching the experimental results. When this is done, the model results compare well with the experiments. Copyright © 2002 John Wiley & Sons, Ltd.     

Endor and eseem study of the radical obtained by γ irradiation of a single crystal of ammonium tartrate

The radical obtained by γ irradiation of a single crystal of ammonium tartrate has been identified by paramagnetic resonance spectroscopies. The proton hyperfine coupling tensors have been obtained, from the angular dependence of the ENDOR transition frequencies. ESEEM spectra of the radical have been also obtained. The intensities of the ESEEM lines are related to the depth of the modulation, which has a dramatic angular dependence.     

On equality in an upper bound for the restrained and total domination numbers of a graph

Let G=(V,E) be a graph. A set S⊆V is a restrained dominating set (RDS) if every vertex not in S is adjacent to a vertex in S and to a vertex in V?S. The restrained domination number of G, denoted by γ_r(G), is the minimum cardinality of an RDS of G. A set S⊆V is a total dominating set (TDS) if every vertex in V is adjacent to a vertex in S. The total domination number of a graph G without isolated vertices, denoted by γ_t(G), is the minimum cardinality of a TDS of G.Let δ and Δ denote the minimum and maximum degrees, respectively, in G. If G is a graph of order n with δ?2, then it is shown that γ_r(G)?n-Δ, and we characterize the connected graphs with δ?2 achieving this bound that have no 3-cycle as well as those connected graphs with δ?2 that have neither a 3-cycle nor a 5-cycle. Cockayne et al. [Total domination in graphs, Networks 10 (1980) 211-219] showed that if G is a connected graph of order n?3 and Δ?n-2, then γ_t(G)?n-Δ. We further characterize the connected graphs G of order n?3 with Δ?n-2 that have no 3-cycle and achieve γ_t(G)=n-Δ.     

Inter-DNA attraction mediated by divalent counterions

Can nonspecifically bound divalent counterions induce attraction between DNA strands? Here, we present experimental evidence demonstrating attraction between short DNA strands mediated by Mg2+ ions. Solution small angle x-ray scattering data collected as a function of DNA concentration enable model independent extraction of the second virial coefficient. As the [Mg2+] increases, this coefficient turns from positive to negative reflecting the transition from repulsive to attractive inter-DNA interaction. This surprising observation is corroborated by independent light scattering experiments. The dependence of the observed attraction on experimental parameters including DNA length provides valuable clues to its origin.