Homotopy type of neighborhood complexes of Kneser graphs, $$\varvec{KG_{2,k}}$$

Schrijver (Nieuw Archief voor Wiskunde, 26(3) (1978) 454–461) identified a family of vertex critical subgraphs of the Kneser graphs called the stable Kneser graphs \(SG_{n,k}\). Björner and de Longueville (Combinatorica 23(1) (2003) 23–34) proved that the neighborhood complex of the stable Kneser graph \(SG_{n,k}\) is homotopy equivalent to a k-sphere. In this article, we prove that the homotopy type of the neighborhood complex of the Kneser graph \(KG_{2,k}\) is a wedge of \((k+4)(k+1)+1\) spheres of dimension k. We construct a maximal subgraph \(S_{2,k}\) of \(KG_{2,k}\), whose neighborhood complex is homotopy equivalent to the neighborhood complex of \(SG_{2,k}\). Further, we prove that the neighborhood complex of \(S_{2,k}\) deformation retracts onto the neighborhood complex of \(SG_{2,k}\).     

On Dual Configurational Forces

The dual conservation laws of elasticity are systematically re-examined by using both Noether's variational approach and Coleman–Noll–Gurtin's thermodynamics approach. These dual conservation laws can be interpreted as the dual configurational force, and therefore they provide the dual energy–momentum tensor. Some previously unknown and yet interesting results in elasticity theory have been discovered. As an example, we note the following duality condition between the configuration force (energy–momentum tensor) and the dual configuration force (dual energy–momentum tensor) ,

NeuroGenetic approach for combinatorial optimization: an exploratory analysis

Given the NP-Hard nature of many optimization problems, it is often impractical to obtain optimal solutions to large-scale problems in reasonable computing time. For this reason, heuristic and metaheuristic search approaches are used to obtain good solutions fast. However, these techniques often struggle to develop a good balance between local and global search. In this paper we propose a hybrid metaheuristic approach which we call the NeuroGenetic approach to search for good solutions for these large scale optimization problems by at least partially overcoming this challenge. The proposed NeuroGenetic approach combines the Augmented Neural Network (AugNN) and the Genetic Algorithm (GA) search approaches by interleaving the two. We chose these two approaches to hybridize, as they offer complementary advantages and disadvantages; GAs are very good at searching globally, while AugNNs are more proficient at searching locally. The proposed hybrid strategy capitalizes on the strong points of each approach while avoiding their shortcomings. In the paper we discuss the issues associated with the feasibility of hybridizing these two approaches and propose an interleaving algorithm. We also provide empirical evidence demonstrating the effectiveness of the proposed approach.     

A Simple and Complete Computational Analysis of MAP/R/1 Queue Using Roots

In this paper, we present (in terms of roots) a simple closed-form analysis for evaluating system-length distribution at three epochs of time (arbitrary, pre-arrival, and post-departure) and queueing-time distribution (virtual and actual) of the MAP/R/1 queue, where R represents the class of distributions whose Laplace–Stieltjes transforms are rational functions. Our analysis is based on roots of the associated characteristic equations of the (i) vector-generating function of system-length distribution and (ii) Laplace–Stieltjes transform of the virtual queueing-time distribution. The proposed method for evaluating boundary probabilities is an alternative to the matrix-analytic method as well as spectral method. Numerical aspects have been tested for a variety of arrival and service-time (including matrix-exponential (ME)) distributions and a sample of numerical outputs is presented. The method is analytically quite simple and easy to implement. It is hoped that the results obtained would prove to be beneficial to both theoreticians and practitioners.     

A novel approach for protein identification from complex cell proteome using modified peptide mass fingerprinting algorithm

A unique peptide based search algorithm for identification of protein mixture using PMF is proposed. The proposed search algorithm utilizes binary search and heapsort programs to generate frequency chart depicting the unique peptides corresponding to all proteins in a proteome. The use of binary search program significantly reduces the time for frequency chart preparation to ～2 s for a proteome comprising ～23 000 proteins. The algorithm was applied to a three‐protein mixture identification, host cell protein (HCP) analysis, and a simulation‐generated data set. It was found that the algorithm could identify at least one unique peptide of a protein even in the presence of fourfold higher concentration of another protein. In addition, two HCPs that are known to be difficult to remove were missed by MS/MS approach and were exclusively identified using the presented algorithm. Thus, the proposed algorithm when used along with standard proteomic approaches present avenues for enhanced protein identification efficiency, particularly for applications such as HCP analysis in biopharmaceutical research, where identification of low‐abundance proteins are generally not achieved due to dynamic range limitations between the target product and HCPs.     

On a conjecture of Lynch

Abstract

We comment on a conjecture of Lynch on annihilators of local cohomology.

Communicated by Lawrence Ein     

Facile synthesis and relaxation properties of novel bispolyazamacrocyclic Gd3+ complexes: an attempt towards calcium-sensitive MRI contrast agents

Three novel GdDO3A-type bismacrocyclic complexes, conjugated to Ca (2+) chelating moieties like ethylenediaminetetraacetic acid and diethylenetriamine pentaacetic acid bisamides, were synthesized as potential "smart" magnetic resonance imaging contrast agents. Their sensitivity toward Ca (2+) was studied by relaxometric titrations. A maximum relaxivity increase of 15, 6, and 32% was observed upon Ca (2+) binding for Gd 2L (1), Gd 2L (2), and Gd 2L (3), respectively (L (1) = N, N-bis{1-[{[({1-[1,4,7-tris(carboxymethyl)-1,4,7,10-tetraazacyclododecane-10-yl]eth-2-yl}amino)carbonyl]methyl}-(carboxymethyl)amino]eth-2-yl}aminoacetic acid; L (2) = N, N-bis[1-({[({alpha-[1,4,7-tris(carboxymethyl)-1,4,7,10-tetraazacyclododecane-10-yl]- p-tolylamino}carbonyl)methyl]-(carboxymethyl)}amino)eth-2-yl]aminoacetic acid; L (3) = 1,2-bis[{[({1-[1,4,7-tris(carboxymethyl)-1,4,7,10-tetraazacyclododecane-10-yl]eth-2-yl}amino)carbonyl]methyl}(carboxymethyl)amino]ethane). The apparent association constants are log K A = 3.6 +/- 0.1 for Gd 2L (1) and log K A = 3.4 +/- 0.1 for Gd 2L (3). For the interaction between Mg (2+) and Gd 2L (1), log K A = 2.7 +/- 0.1 has been determined, while no relaxivity change was detected with Gd 2L (3). Luminescence lifetime measurements on the Eu (3+) complexes in the absence of Ca (2+) gave hydration numbers of q = 0.9 (Eu 2L (1)), 0.7 (Eu 2L (2)), and 1.3 (Eu 2L (3)). The parameters influencing proton relaxivity of the Gd (3+) complexes were assessed by a combined nuclear magnetic relaxation dispersion (NMRD) and (17)O NMR study. Water exchange is relatively slow on Gd 2L (1) and Gd 2L (2) ( k ex (298) = 0.5 and 0.8 x 10 (6) s (-1)), while it is faster on Gd 2L (3) (k ex (298) = 80 x 10 (6) s (-1)); in any case, it is not sensitive to the presence of Ca (2+). The rotational correlation time, tau R (298), differs for the three complexes and reflects their rigidity. Due to the benzene linker, the Gd 2L (2) complex is remarkably rigid, with a correspondingly high relaxivity despite the low hydration number ( r 1 = 10.2 mM (-1)s (-1) at 60 MHz, 298 K). On the basis of all available experimental data from luminescence, (17)O NMR, and NMRD studies on the Eu (3+) and Gd (3+) complexes of L (1) and L (3) in the absence and in the presence of Ca (2+), we conclude that the relaxivity increase observed upon Ca (2+) addition can be mainly ascribed to the increase in the hydration number, and, to a smaller extent, to the Ca (2+)-induced rigidification of the complex.     

Applications of anisotropic slipline theory with non-uniform lattice rotation

Anisotropic slipline theory, with non-uniform lattice rotation field, is used to discuss new slipline solutions for the plane strain problems of punch indentation and mode 1 stationary crack in a ductile single crystal with piecewise linear yield locus. The proposed solution allows for both linear dislocation arrays and sectors with bulk dislocation density. Such features provide considerable latitude in the number of allowable stress discontinuities, and their orientation, when compared to the solutions which assume uniform lattice rotation.     

Generalizing a two-conformation model for describing salt and temperature effects on protein retention and stability in hydrophobic interaction chromatography

A two-conformation adsorption model that includes the effects of salt concentration and temperature on both stability and adsorption has been developed to describe the effects of secondary protein unfolding on hydrophobic interaction chromatography (HIC). The model has been applied to a biotech protein and to beta-lactoglobulin on Phenyl Sepharose 6FF low sub HIC media. Thermodynamic property models for adsorption and protein stability with parameters obtained from experimental chromatographic data successfully describe observed chromatographic behavior over ranges of temperature and salt concentration, provide predictions of distribution among different conformers, and give a basis for calculating trends in retention strength and stability with changing conditions, that might prove useful in HIC process development.