Propagation of Reactions in Inhomogeneous Media

Consider reaction‐diffusion equation u _t =Δ u + f (x,u ) with and general inhomogeneous ignition reaction f ≥ 0 vanishing at u = 0,1. Typical solutions 0 ≤ u ≤ 1 transition from 0 to 1 as time progresses, and we study them in the region where this transition occurs. Under fairly general qualitative hypotheses on f we show that in dimensions d ≤ 3, the Hausdorff distance of the superlevel sets {u ≥ ε } and {u ≥ 1‐ε} remains uniformly bounded in time for each ε ? (0,1). Thus, u remains uniformly in time close to the characteristic function of in the sense of Hausdorff distance of superlevel sets. We also show that each {u ≥ ε} expands with average speed (over any long enough time interval) between the two spreading speeds corresponding to any x ‐independent lower and upper bounds on f . On the other hand, these results turn out to be false in dimensions d ≥ 4, at least without further quantitative hypotheses on f . The proof for d ≤ 3 is based on showing that as the solution propagates, small values of u cannot escape far ahead of values close to 1. The proof for d ≥ 4 is via construction of a counterexample for which this fails. Such results were before known for d =1 but are new for general non‐periodic media in dimensions d ≥ 2 (some are also new for homogeneous and periodic media). They extend in a somewhat weaker sense to monostable, bistable, and mixed reaction types, as well as to transitions between general equilibria of the PDE and to solutions not necessarily satisfying . © 2016 Wiley Periodicals, Inc.     

Targeting Bayes factors with direct-path non-equilibrium thermodynamic integration

Thermodynamic integration (TI) for computing marginal likelihoods is based on an inverse annealing path from the prior to the posterior distribution. In many cases, the resulting estimator suffers from high variability, which particularly stems from the prior regime. When comparing complex models with differences in a comparatively small number of parameters, intrinsic errors from sampling fluctuations may outweigh the differences in the log marginal likelihood estimates. In the present article, we propose a TI scheme that directly targets the log Bayes factor. The method is based on a modified annealing path between the posterior distributions of the two models compared, which systematically avoids the high variance prior regime. We combine this scheme with the concept of non-equilibrium TI to minimise discretisation errors from numerical integration. Results obtained on Bayesian regression models applied to standard benchmark data, and a complex hierarchical model applied to biopathway inference, demonstrate a significant reduction in estimator variance over state-of-the-art TI methods.     

Zinc-phosphate nanoparticles with reversibly attached TNF-α analogs: an interesting concept for potential use in active immunotherapy

The authors’ intention was to prepare nanometer-sized zinc-phosphate nanoparticles that would be capable of binding histidine-rich TNF-α analogs onto their surface via a coordinative bond. Zinc-phosphate nanoparticles with a size of around 60 nm were prepared by a wet precipitation method and characterized using SEM, EDX, XRD, and DLS. First, BSA was bound as a testing protein, afterward two TNF-α analogs with decreased activity were bound to the described nanoparticles. The efficiency of binding and the existence of coordinative bond were confirmed with SDS-PAGE analysis. During binding, particle storage, and release experiments, the prepared TNF-α analogs retained their biological activity—hence the epitopes necessary for formation of antibodies stayed intact. The particle size did not change within a period of 2 weeks. No significant agglomeration was observed, the particles could be quickly dispersed in ultrasound. The present nanoparticles and the general approach of coordinative binding are widely applicable for natural and engineered histidine-rich proteins. The nanoparticles bearing appropriate TNF-α analogs could also be potentially used for active immunotherapy to tackle the chronic inflammatory diseases associated with pathogenically elevated levels of TNF-α.     

Some remarks on the two-body-problem in geometrodynamics

The interest in the two body problem in geometrodynamics and its present status are discussed. Special consideration is given to time-symmetric initial data. An equation relating the “bare mass energy,” the potential energy and the “vibrational energy” at the initial moment is proposed. The significance of coordinate conditions in dynamical equations is discussed next. Conditions implying maximal slicings of spacetime and harmonic coordinates in those slices are considered in detail, as they seem to be well suited for numerical calculations and for interpretation of the results of such calculations.     

Capillary gas chromatography-mass spectrometry of all 93 acyclic octenes and their identification in fluid catalytic cracked gasoline

The Kováts retention indices of all 93 acyclic octenes on polydimethylsiloxane and squalane as stationary phases as well as their mass spectra were measured. The means of gas chromatography-mass spectrometry (GC-MS) were used for confirmation of GC identification as well as for mass spectrometric deconvolution of the majority of gas chromatographic unseparated isomeric octene peaks. The distinction between corresponding E and Z acyclic octenes, that is either difficult or even impossible by means of GC-MS, was obtained on the basis of larger temperature coefficients of retention indices for Z isomeric octenes than for corresponding E isomers. The retention data expressed as homomorphy factors were correlated with the degree of branching, position of double bond, and position of alkyl group with respect to the double bond of acyclic octenes, and the structure-retention relationships were formulated. The 81 acyclic octenes were identified in FCC gasoline.     

Sum Rules and the Szegő Condition for Orthogonal Polynomials on the Real Line

We study the Case sum rules, especially C ₀ , for general Jacobi matrices. We establish situations where the sum rule is valid. Applications include an extension of Shohats theorem to cases with an infinite point spectrum and a proof that if lim n(a _n –1)= and lim nb _n = exist and 2<||, then the Szeg condition fails. Supported in part by NSF grant DMS-9707661.     

Computational Insights into β-Carboline Inhibition of Monoamine Oxidase A

Monoamine oxidases (MAOs) are an important group of enzymes involved in the degradation of neurotransmitters and their imbalanced mode of action may lead to the development of various neuropsychiatric or neurodegenerative disorders. In this work, we report the results of an in-depth computational study in which we performed a static and a dynamic analysis of a series of substituted β-carboline natural products, found mainly in roasted coffee and tobacco smoke, that bind to the active site of the MAO-A isoform. By applying molecular docking in conjunction with structure-based pharmacophores and molecular dynamics simulations coupled with dynamic pharmacophores, we extensively investigated the geometric aspects of MAO-A binding. To gain insight into the energetics of binding, we used the linear interaction energy (LIE) method and determined the key anchors that allow productive β-carboline binding to MAO-A. The results presented herein could be applied in the rational structure-based design and optimization of β-carbolines towards preclinical candidates that would target the MAO-A enzyme and would be applicable especially in the treatment of mental disorders such as depression.     

Synthesis,characterization and antimicrobial activity of pentagonal-bipyramidal isothiocyanato Co(II) and Ni(II) complexes with 2,6-diacetylpyridine bis(trimethylammoniumacetohydrazone)

Pentagonal-bipyramidal isothiocyanato Co(II) and Ni(II) complexes with condensation product of 2,6-diacetylpyridine and trimethylammoniumacetohydrazide (Girard’s T reagent) were synthesized and characterized by elemental analyses, IR and UV–vis spectra, molar conductivity, and magnetic susceptibility. Crystal structures of the Co(II) and Ni(II) complexes were also determined. Antimicrobial activities of the ligand and metal complexes were examined.     

Structural and magnetic properties of iron(II) complexes with 1,4,5,8,9,12-hexaazatriphenylene (HAT)

Reactions of Fe(II) salts with the ligand 1,4,5,8,9,12-hexaazatriphenylene (HAT) led to the isolation and characterization of four new compounds: [Fe3(HAT)(H2O)12](SO4)3.3.3H2O (1), [Fe2(HAT)(SO4)(H2O)5](SO4).2H2O.CH3OH (2), [Fe2(HAT)(SO4)(H2O)5](SO4).3H2O (3), and [Fe3Cl5(HAT)(CH3OH)4(H2O)]Cl (4). Compound 1 crystallizes as a trinuclear cluster in which HAT acts as a tris-chelating ligand. Compounds 2 and 3 are two polymorphs of an infinite one-dimensional structure in which the Fe atoms are coordinated to HAT and then connected into the chain through bridging sulfate anions. Compound 4 exhibits a similar chain structure, but with bridging chloride ligands. The magnetic behavior of the new compounds is indicative of weak antiferromagnetic coupling between the Fe(II) centers through the HAT ligand.