Proper path‐factors and interval edge‐coloring of (3,4)‐biregular bigraphs

An interval coloring of a graph G is a proper coloring of E(G) by positive integers such that the colors on the edges incident to any vertex are consecutive. A (3,4)‐biregular bigraph is a bipartite graph in which each vertex of one part has degree 3 and each vertex of the other has degree 4; it is unknown whether these all have interval colorings. We prove that G has an interval coloring using 6 colors when G is a (3,4)‐biregular bigraph having a spanning subgraph whose components are paths with endpoints at 3‐valent vertices and lengths in {2, 4, 6, 8}. We provide several sufficient conditions for the existence of such a subgraph. © 2009 Wiley Periodicals, Inc. J Graph Theory     

Ultrasound velocity in human muscle in vivo: perspective for edema studies

The present study examines the association of the changes in ultrasound velocity measured at 1 MHz using 1.5 micros duration tone burst in the human soleus muscle in vivo with several pathologies including patients with chronic renal failure (CRF) and disorders of the cardiovascular system. Total 127 subjects were investigated, with approximately equal number of male and female subjects uniformly distributed by age, from 15 to 70 years old. Since molecular composition of the tissue is thought to have greater effect on the bulk ultrasound velocity, potential contribution of both water and fat, two main variable components of a muscle, were taken into account. Observed negative correlation of ultrasound velocity with the body mass index was considered a result of an elevated fat content. Based on the obtained data, presence of leg edemas results in a measurably lower ultrasound velocity in the soleus muscle. Unless patients had visibly detected leg edema, no difference between healthy individuals, patients with chronic heart failure, or CRF was found. Despite relatively high individual variations in velocity, ranging from 1530 to 1615 m/s, a statistically significant gender correlated difference between average values of the velocity was observed. No dependence of velocity on subject age was detected. An indirect confirmation of the muscle fluid homeostasis was revealed in patients with CRF undergoing hemodialysis procedure. After hemodialysis, a significantly smaller increase (0.3% in average) of ultrasound velocity in the soleus muscle was observed than otherwise could be expected if a uniform relative loss of total body fluids was assumed (1-1.3%). In general, the study findings set a premise for using ultrasound velocity as a potential quantitative parameter for edema assessment.     

Quasi-local action of curl-less vector potential on vortex dynamics in superconductors

Studies of the Abrikosov vortex motion in superconductors based on time-dependent Ginzburg–Landau equations reveal an opportunity to detect the values of the Aharonov–Bohm type curl-less vector potentials without closed-loop electron trajectories encompassing the magnetic flux.     

Application of the dual-frequency ultrasonometer for osteoporosis detection

The paper presents results of a clinical validation study of Bone UltraSonic Scanner (BUSS), a novel dual-frequency axial transmission ultrasonometer, developed by Artann Laboratories. Assessment of bone conditions is based on evaluating relative changes of the axial profiles of ultrasonic characteristics in long bones and utilizes bulk and guided acoustic waves. The objective of this study was to determine the ability of BUSS to discriminate osteoporosis development stages. A total of 93 menopausal and post-menopausal women divided into five groups from normal to advanced osteoporosis according to their DXA hip t-score were enrolled in the study. The 2D waveform profiles at low (0.1 MHz) and high (1 MHz) frequencies were obtained by scanning 15 cm along the proximal tibia.A multi-parametric linear classifier based on a set of the parameters derived from 2D acoustic waveform profiles has been developed. The efficiency of this classifier in differentiating osteoporosis from a normal sample was assessed using a receiver operating characteristic (ROC) curve analysis. Based on the ROC analysis, BUSS demonstrated 76% sensitivity and 70% specificity to DXA-identified osteoporosis. The area under the ROC curve, which is a measure of how well a parameter can distinguish between the two diagnostic groups (diseased/normal) was 79.3%. The study confirmed BUSS’s capability to discriminate between stages of bone atrophy and in particular to distinguish early changes induced by osteoporosis.     

Quantum theory of post-collision interaction in inner-shell photoionization

We have performed fully quantum-mechanical and relativistic calculations of the post-collision-interaction effect in x-ray-induced argonK?L ₂ L ₃(¹ D) Auger and xenonL ₂?L ₃ N ₄(J=3) Coster-Kronig-electron emission. The Dirac-Fock computations include a complete integration over intermediate one-hole continuum states in the lowest-order expression of the resonant double-photoionization cross section. The results are in excellent agreement with synchrotron-radiation measurements of the post-collision-interaction shifts. We have also made nonrelativistic Hartree-Fock test calculations of the argonK?L ₂ L ₃(¹ D) and xenonL ₃?M ₄ M ₅(¹ G ₄) Auger-electron line shapes. The quantum-mechanical results are compared with rigorous semiclassical calculations which have been made without using the stationary-phase approximation. The results of this computational analysis are interpreted in terms of an analytical line-shape formula based on asymptotic Coulomb wave functions. As a consequence the most salient features of the post-collision interaction in inner-shell photoionization are explained.     

Radiation force and shear motions in inhomogeneous media

An action of radiation force induced by ultrasonic beam in waterlike media such as biological tissues (where the shear modulus is small as compared to the bulk compressibility) is considered. A new, nondissipative mechanism of generation of shear displacement due to a smooth (nonreflecting) medium inhomogeneity is suggested, and the corresponding medium displacement is evaluated. It is shown that a linear primary acoustic field in nondissipative, isotropic elastic medium cannot excite a nonpotential radiation force and, hence, a shear motion, whereas even smooth inhomogeneity makes this effect possible. An example is considered showing that the generated displacement pulse can be significantly longer than the primary ultrasound pulse. It is noted that, unlike the dissipative effect, the nondissipative action on a localized inhomogeneity (such as a lesion in a tissue) changes its sign along the beam axis, thus stretching or compressing the focus area.     

Partial indices of a class of second order matrix-functions

The paper studies Winer-Hopf factorization problem for matrix-functions of the second order defined on the unit circle of the complex plane. The element G ₂₁ of these matrix-functions is assumed to be representable by combinations of the other three elements and two functions meromorphic in the interior and exterior of the circle. Some formulas for partial indices are obtained.     

Evaluation of Neurotropic Activity and Molecular Docking Study of New Derivatives of pyrano[4″,3″:4′,5′]pyrido[3′,2′:4,5]thieno[3,2-d]pyrimidines on the Basis of pyrano[3,4-c]pyridines

Background: Heterocyclic compounds and their fused analogs, which contain pharmacophore fragments such as pyridine, thiophene and pyrimidine rings, are of great interest due to their broad spectrum of biological activity. Chemical compounds containing two or more pharmacophore groups due to additional interactions with active receptor centers usually enhance biological activity and can even lead to a new type of activity. The search for new effective neurotropic drugs in the series of derivatives of heterocycles containing pharmacophore groups in organic, bioorganic and medical chemistry is a serious problem. Methods: Modern methodology of drugs involves synthesis, physicochemical study, molecular modeling and selection of active compounds through virtual screening and experimental evaluation of the biological activity of new chimeric compounds with pharmacophore fragments. For the synthesis of new compounds, classical organic methods were used and developed. For the evaluation of neurotropic activity of new synthesized compounds, some biological methods were used according to indicators characterizing anticonvulsant, sedative and antianxiety activity as well as side effects. For docking analysis, various soft ware packages and methods were used. Results: As a result of multistep reactions, 11 new, tri- and tetracyclic heterocyclic systems were obtained. The studied compounds exhibit protection against pentylenetetrazole (PTZ) seizures as well as some psychotropic effects. The biological assays evidenced that nine of the eleven studied compounds showed a high anticonvulsant activity by antagonism with pentylenetetrazole. The toxicity of the compounds is low, and they do not induce muscle relaxation in the studied doses. According to the study of psychotropic activity, it was found that the selected compounds have an activating behavior and anxiolytic effects on the “open field” and “elevated plus maze” (EPM) models. The data obtained indicate the anxiolytic (antianxiety) activity of the derivatives of tricyclic thieno[2,3-b]pyridines and tetracyclic pyridothieno[3,2-d]pyrimidin-8-ones, especially pronounced in compounds 3b–f and 4e. The studied compounds increase the latent time of first immobilization on the “forced swimming” (FS) model and exhibit antidepressant effects; compounds 3e and 3f especially exhibit these effects, similarly to diazepam. Docking studies revealed that compounds 3c and 4b bound tightly in the active site of γ-aminobutyric acid type A (GABA_A) receptors with a value of the scoring function that estimates free energy of binding (∆G) at −10.0 ± 5 kcal/mol. Compound 4e showed the best affinity ((∆G) at −11.0 ± 0.54 kcal/mol) and seems to be an inhibitor of serotonin (SERT) transporter. Compounds 3c–f and 4e practically bound with the groove of T4L of 5HT_1A and blocked it completely, while the best affinity observed was in compound 3f ((∆G) at −9.3 ± 0.46 kcal/mol). Conclusions: The selected compounds have an anticonvulsant, activating behavior and anxiolytic effects and at the same time exhibit antidepressant effects.     

Elastic properties of a protein-polymer-grafted surface

Surfaces grafted with poly(methyl methacrylate) (PMMA) and streptavidin were synthesized through click chemistry to investigate the role of surface stiffness on protein adsorption as the hydrophilic and hydrophobic surface coverage of the substituents vary. Surface topographies coupled with the nanoindentation results indicated that, with the appropriate selections of polymer coverage and chain length, the extent of non-specific protein adhesion could be controlled by the hydrophobic interactions between PMMA, biotin, and streptavidin. It was shown that, when the molecular weight and stiffness of PMMA was close to that of streptavidin, patchy PMMA morphologies were obtained, which help inhibit the non-specific adsorption of streptavidin.