A Sharp Threshold for k‐Colorability

Let k be a fixed integer and f_k(n, p) denote the probability that the random graph G(n, p) is k‐colorable. We show that for k≥3, there exists d_k(n) such that for any ϵ>0, (1) As a result we conclude that for sufficiently large n the chromatic number of G(n, d/n) is concentrated in one value for all but a small fraction of d>1. ©1999 John Wiley & Sons, Inc. Random Struct. Alg., 14, 63–70, 1999     

Depolarized light scattering from critical polymer blends

Depolarized light scattering of binary polymer blends in disordered state near the demixing critical point is considered both theoretically and experimentally. It is shown that the depolarized scattering in such systems is predominantly due to double scattering processes induced by composition fluctuations. For long enough polymer chains, this scattering is stronger than the contribution from intrinsic anisotropy fluctuations. The general equation for the static and dynamic double scattering function is obtained in terms of the system structure factor. The scattering functions are calculated both analytically and numerically (dynamic part) for polymer blends. We found that the depolarized intensity depends on the polymerization degree N and the relative distance from the critical point τ = 1 – χ*/χ (where χ is the Flory‐Huggins interaction parameter and χ* its critical value) as I_vh ∼︁ N²/τ², which is in good agreement with the experimental data. It is also shown that the dynamic scattering function is decaying non‐exponentially. We calculate the relaxation rate and the non‐exponentiality parameter as functions of the scattering angle and τ. These theoretical predictions are compared with experimental data for three chemically different blends.     

Pattern recognition system for the discrimination of multiple sclerosis from cerebral microangiopathy lesions based on texture analysis of magnetic resonance images

In this study, a pattern recognition system has been developed for the discrimination of multiple sclerosis (MS) from cerebral microangiopathy (CM) lesions based on computer-assisted texture analysis of magnetic resonance images. Twenty-three textural features were calculated from MS and CM regions of interest, delineated by experienced radiologists on fluid attenuated inversion recovery images and obtained from 11 patients diagnosed with clinically definite MS and from 18 patients diagnosed with clinically definite CM. The probabilistic neural network classifier was used to construct the proposed pattern recognition system and the generalization of the system to unseen data was evaluated using an external cross validation process. According to the findings of the present study, statistically significant differences exist in the values of the textural features between CM and MS: MS regions were darker, of higher contrast, less homogeneous and rougher as compared to CM.     

Enhancing the discrimination accuracy between metastases, gliomas and meningiomas on brain MRI by volumetric textural features and ensemble pattern recognition methods

Three-dimensional (3D) texture analysis of volumetric brain magnetic resonance (MR) images has been identified as an important indicator for discriminating among different brain pathologies. The purpose of this study was to evaluate the efficiency of 3D textural features using a pattern recognition system in the task of discriminating benign, malignant and metastatic brain tissues on T1 postcontrast MR imaging (MRI) series. The dataset consisted of 67 brain MRI series obtained from patients with verified and untreated intracranial tumors. The pattern recognition system was designed as an ensemble classification scheme employing a support vector machine classifier, specially modified in order to integrate the least squares features transformation logic in its kernel function. The latter, in conjunction with using 3D textural features, enabled boosting up the performance of the system in discriminating metastatic, malignant and benign brain tumors with 77.14%, 89.19% and 93.33% accuracy, respectively. The method was evaluated using an external cross-validation process; thus, results might be considered indicative of the generalization performance of the system to "unseen" cases. The proposed system might be used as an assisting tool for brain tumor characterization on volumetric MRI series.     

The Other Face of Bunsen's Cacodyl Disulfide,Me2As(S)‐S‐AsMe2: The Lewis‐Base Behaviour Towards Heavy Metal Cations

The reaction of Bunsen's cacodyl disulfide, Me₂As(S)‐S‐AsMe₂, with heavy metal cations in methanol produces insoluble salts (complexes) of dimethyldithioarsinic acid, Me₂AsS₂H, and dimethyl arsenium ion, Me₂As:⁺. This arsenium ion prefers to react with Me₂As(S)‐S‐AsMe₂, when in excess, compared to AcO^? or MeOH/H₂O and it is also reactive towards sulfur (S_x, x = 1‐8) producing the stabilized dimethylarsino sulfenium cation, . The complexes (Me₂AsS₂)_xM (x = 1 or 2) are unstable in the presence of their own heavy metal cations decomposing to colored solids. In an attempt to prepare salts of Me₂AsSH, the reactions of (Me₂AsS₂)_xM with triphenylphosphine and trimethyl phosphite gave the metal sulfide and Me₂As‐S‐AsMe₂ instead.     

Formation of alkane‐phosphonic acid self‐assembled monolayers on alumina: an in situ SPR study

The formation process of n‐alkane phosphonic acid CH₃ (CH₂)_n?1 PO(OH)₂ (n = 10,12,14,18) self‐assembled monolayers (SAMs), deposited from ethanol solutions on aluminum oxide, has been monitored in situ using surface plasmon resonance (SPR) spectroscopy. In addition, the two‐solvent approach is used to obtain both film thickness and refractive index of the fully formed adsorbed layers. A densely packed adsorbed layer is formed only for the longest molecules with n = 18. The chain length and solution concentration dependence of formation kinetics are studied, and the existence of two distinct kinetic steps is revealed. Fittings of the experimental results with various kinetic models are performed. Our analysis suggests that during the first kinetic step, a transition from a lying‐down to a standing‐up phase takes place, and the growth of this standing‐up phase is governed by second‐order kinetics. The second slow kinetic step is described by a modified first‐order Langmuir law. Copyright © 2009 John Wiley & Sons, Ltd.     

Higher-order accurate polyspectral estimation with flat-top lag-windows

Improved performance in higher-order spectral density estimation is achieved using a general class of infinite-order kernels. These estimates are asymptotically less biased but with the same order of variance as compared to the classical estimators with second-order kernels. A simple, data-dependent algorithm for selecting the bandwidth is introduced and is shown to be consistent with estimating the optimal bandwidth. The combination of the specialized family of kernels with the new bandwidth selection algorithm yields a considerably improved polyspectral estimator surpassing the performances of existing estimators using second-order kernels. Bispectral simulations with several standard models are used to demonstrate the enhanced performance with the proposed methodology.     

Development of recombinant protein-based influenza vaccine. Expression and affinity purification of H1N1 influenza virus neuraminidase

The influenza virus surface glycoprotein antigen neuraminidase (NA) is a crucial viral enzyme with many potential medical applications; therefore, the development of efficient upstream and downstream processing strategy for the expression and purification of NA is of high importance. In the present work the NA gene from the H1N1 influenza virus strain A/Beijing/262/95 was cloned from viral RNA and expressed in expresSF+ insect cells using the baculovirus expression vector system (BVES). A limited affinity-ligand library was synthesized and evaluated for its ability to bind and purify the recombinant H1N1 neuraminidase. Affinity-ligand design was based on mimicking the interactions of the lock-and-key (LAK) motif (Phe-Gly-Gln), a common structural moiety found in the subunit interface of glutathione S-transferase I (GST I), and plays an important structural role in subunit-subunit recognition. Solid-phase combinatorial chemistry was used to synthesize 13 variants of the lock-and-key lead ligand (Phe-Trz-X, where X was selected alpha-amino acid) using the 1,3,5-triazine moiety (Trz) as the scaffold for assembly. One immobilized ligand, bearing phenylalanine and isoleucine linked on the chlorotriazine ring (Phe-Trz-Ile), displayed high affinity for NA. Absorption equilibrium and molecular modeling studies were carried out to provide a detailed picture of Phe-Trz-Ile interaction with NA. This LAK-mimetic affinity adsorbent was exploited in the development of a facile purification protocol for NA, which led to 335-fold purification in a single-step. The present purification procedure is the most efficient reported so far for recombinant NA.     

Diffusion damping during adiabatic z-rotation pulses for NMR spectroscopy in inhomogeneous magnetic fields

High-resolution nuclear magnetic resonance spectra from samples located in inhomogeneous static and radio frequency magnetic fields can be obtained by applying a train of z-rotation radio frequency pulses to repeatedly refocus the inhomogeneous broadening during signal detection. z-rotation pulses based on an adiabatic double passage are effective over wide bandwidths using a limited amount of radio frequency power at the expense of being time consuming and, consequently, sensitive to motion of the spin bearing molecules. The signal damping resulting from molecular self-diffusion during the pulse was studied experimentally and using Brownian dynamics simulations. The results show that the analytical expression for diffusion damping during a double spin echo is a reasonable approximation for the signal decay during an adiabatic z-rotation pulse. Methods to alleviate the effects of diffusion are discussed.     

Enhancing the acquisition efficiency of fast magnetic resonance imaging via broadband encoding of signal content

Current efficient magnetic resonance imaging (MRI) methods such as parallel-imaging and k-t methods encode MR signals using a set of effective encoding functions other than the Fourier basis. This work revisits the proposition of directly manipulating the set of effective encoding functions at the radiofrequency excitation step in order to increase MRI efficiency. This approach, often termed "broadband encoding," enables the application of algebraic matrix factorization technologies to extract efficiency by representing and encoding MR signal content in a compacted form. Broadband imaging equivalents of fast multiecho, parallel and k-t MRI are developed and analyzed. The potential of these techniques to increase the time efficiency of data acquisition is experimentally verified on a commercial MRI scanner using simple spin-echo imaging. A three-dimensional gradient-echo dynamic imaging application that demonstrates the potential benefits of this approach compared to the present state of the art for certain applications is also presented.