Genus distributions for two classes of graphs

The set of orientable imbeddings of a graph can be partitioned according to the genus of the imbedding surfaces. A genus-respecting breakdown of the number of orientable imbeddings is obtained for every graph in each of two infinite classes. It is proved that the genus distribution of any member of either class is strongly unimodal. These are the first two infinite classes of graphs for which such calculations have been achieved, except for a few classes, such as trees and cycles, whose members have all their cellular orientable imbeddings in the sphere

Fundamental Cycles and Graph Embeddings

In this paper we present a new Good Characterization of maximum genus of a graph which makes a common generalization of the works of Xuong, Liu, and Fu et al. Based on this, we find a new polynomially bounded algorithm to find the maximum genus of a graph

DNA-Modified Electrodes Fabricated Using Copper-Free Click Chemistry for Enhanced Protein Detection

A method of DNA monolayer formation has been developed using copper-free click chemistry that yields enhanced surface homogeneity and enables variation in the amount of DNA assembled; extremely low-density DNA monolayers, with as little as 5% of the monolayer being DNA, have been formed. These DNA-modified electrodes (DMEs) were characterized visually, with AFM, and electrochemically, and were found to facilitate DNA-mediated reduction of a distally bound redox probe. These low-density monolayers were found to be more homogeneous than traditional thiol-modified DNA monolayers, with greater helix accessibility through an increased surface area-to-volume ratio. Protein binding efficiency of the transcriptional activator TATA-binding protein (TBP) was also investigated on these surfaces and compared to that on DNA monolayers formed with standard thiol-modified DNA. Our low-density monolayers were found to be extremely sensitive to TBP binding, with a signal decrease in excess of 75% for 150 nM protein. This protein was detectable at 4 nM, on the order of its dissociation constant, with our low-density monolayers. The improved DNA helix accessibility and sensitivity of our low-density DNA monolayers to TBP binding reflects the general utility of this method of DNA monolayer formation for DNA-based electrochemical sensor development

Genus Distributions for Two Classes of Graphs

The set of orientable imbeddings of a graph can be partitioned according to the genus of the imbedding surfaces. A genus-respecting breakdown of the number of orientable imbeddings is obtained for every graph in each of two infinite classes. These are the first two infinite classes of graphs for which such calculations have been achieved, except for a few classes, such as trees and cycles, whose members have all their polygonal orientable imbeddings in the sphere

All-Optical Quantum Random Bit Generation from Intrinsically Binary Phase of Parametric Oscillators

True random number generators (RNGs) are desirable for applications ranging from cryptogra- phy to computer simulations. Quantum phenomena prove to be attractive for physical RNGs due to their fundamental randomness and immunity to attack [1]- [5]. Optical parametric down conversion is an essential element in most quantum optical experiments including optical squeezing [9], and generation of entangled photons [10]. In an optical parametric oscillator (OPO), photons generated through spontaneous down conversion of the pump initiate the oscillation in the absence of other inputs [11, 12]. This quantum process is the dominant effect during the oscillation build-up, leading to selection of one of the two possible phase states above threshold in a degenerate OPO [13]. Building on this, we demonstrate a novel all-optical quantum RNG in which the photodetection is not a part of the random process, and no post processing is required for the generated bit sequence. We implement a synchronously pumped twin degenerate OPO, which comprises two identical independent OPOs in a single cavity, and measure the relative phase states of the OPO outputs above threshold as a bit value. We show that the outcome is statistically random with 99% confidence. With the use of micro- and nanoscale OPO resonators, this technique offers a promise for simple, robust, and high-speed on-chip all-optical quantum random number generators

An upper limit on anomalous dust emission at 31 GHz in the diffuse cloud [LPH96]201.663+1.643

[LPH96]201.663+1.643, a diffuse H{\sc ii} region, has been reported to be a candidate for emission from rapidly spinning dust grains. Here we present Cosmic Background Imager (CBI) observations at 26-36 GHz that show no evidence for significant anomalous emission. The spectral index within the CBI band, and between CBI and Effelsberg data at 1.4/2.7 GHz, is consistent with optically thin free-free emission. The best-fitting temperature spectral index from 2.7 to 31 GHz, $\beta=-2.06 \pm 0.03$, is close to the theoretical value, $\beta=-2.12$ for $T_{e}=9100$ K. We place an upper limit of 24% ~ (2\sigma) for excess emission at 31 GHz as seen in a 6\arcmin FWHM beam. Current spinning dust models are not a good fit to the spectrum of LPH96. No polarized emission is detected in the CBI data with an upper limit of 2% on the polarization fraction.Comment: 5 pages, 3 figures, submitted to ApJ

A Multiplexed, Two-Electrode Platform for Biosensing Based on DNA-Mediated Charge Transport

We have developed a thin layer, multiplexed biosensing platform that features two working-electrode arrays for detecting small molecules, nucleic acid sequences, and DNA-binding proteins. DNA duplexes are patterned onto the primary electrode array, while a secondary electrode array is used both to initiate DNA monolayer formation and for electrochemical readout via DNA-mediated charge transport (DNA CT) chemistry. Electrochemical reduction of Cu(phendione)_2^(2+) (phendione is 1,10-phenanthroline-5,6-dione) at the secondary electrodes induces covalent attachment via click chemistry of ethynyl-labeled DNA probe duplexes onto the primary electrodes that have been treated with azide-terminated alkylthiols. Electrochemical impedance spectroscopy and cyclic voltammetry confirm that catalyst activation at the secondary electrode is essential to maintain the integrity of the DNA monolayer. Electrochemical readout of DNA CT processes that occur at the primary electrode is accomplished also at the secondary electrode. The two-electrode system enables the platform to function as a collector–generator using either ferrocyanide or ferricyanide as mediators with methylene blue and DNA charge transport. Electrochemical measurements at the secondary electrode eliminate the need for large background corrections. The resulting sensitivity of this platform enables the reliable and simultaneous detection of femtomoles of the transcription factors TATA-binding protein and CopG on a single multiplexed device

Label-free electrochemical detection of human methyltransferase from tumors

The role of abnormal DNA methyltransferase activity in the development and progression of cancer is an essential and rapidly growing area of research, both for improved diagnosis and treatment. However, current technologies for the assessment of methyltransferase activity, particularly from crude tumor samples, limit this work because they rely on radioactivity or fluorescence and require bulky instrumentation. Here, we report an electrochemical platform that overcomes these limitations for the label-free detection of human DNA(cytosine-5)-methyltransferase1 (DNMT1) methyltransferase activity, enabling measurements from crude cultured colorectal cancer cell lysates (HCT116) and biopsied tumor tissues. Our multiplexed detection system involving patterning and detection from a secondary electrode array combines low-density DNA monolayer patterning and electrocatalytically amplified DNA charge transport chemistry to measure selectively and sensitively DNMT1 activity within these complex and congested cellular samples. Based on differences in DNMT1 activity measured with this assay, we distinguish colorectal tumor tissue from healthy adjacent tissue, illustrating the effectiveness of this two-electrode platform for clinical applications