Measuring asymmetric temporal interdependencies in simulated and biological networks

We use a newly developed metric to characterize asymmetric temporal interdependencies in networks of coupled dynamical elements. We studied the formation of temporal ordering in a system of coupled Rossler oscillators for different connectivity ratios and network topologies and also applied the metric to investigate the functional structure of a biological network (cerebral ganglia of Helix snail). In the former example we show how the local ordering evolves to the global one as a function of structural parameters of the network, while in the latter we show spontaneous emergence of functional interdependence between two groups of electrodes.     

Singular perturbations in the interaction representation

A general method for treating highly singular perturbations V of self-adjoint operators H in Hilbert space is applied to the case of perturbations of $\text{(?}\text{id}\text{dx}\text{)}{}^{\mathrm{n}}$ in L₂ ($\text{R}$¹ by (multiplications by) distributions. A self-adjoint operator H_V that agrees with H + V in the usual sense when V is sufficiently regular, and is moreover a continuous function of V, within the class of distributions under consideration, in the strong operator topology for unbounded self-adjoint operators, is shown to exist. This operator H_V need not be semi-bounded, or determined by a sesquilinear form associated with H + V. The method proceeds by construction of the corresponding unitary propagator in the interaction representation, essentially e^?itHVe^itH, which is shown to be expressible as a uniformly convergent perturbative series for small times.     

Renormalization of the relativistic delta potential in one dimension

Several authors have noted an ambiguity with the Dirac equation in one dimension. In the case of a delta-function potential, the coupling constant is subject to an apparently arbitrary renormalization when the delta function is approximated in different ways. We explain these differences in terms of strong resolvent limits of self-adjoint operators onL ²(R), and obtain a precise formula for the renormalized coupling constant in the case of separable potentials. The examples in the literature follow as special cases.Research supported in part by a grant from the National Science Foundation.     

Singular perturbations in the interaction representation,II

Perturbations of $\text{(?Δ)}{}^{\mathrm{<mtext>m</mtext><mtext>2</mtext>}}\text{in}\text{L}{}^2\text{(R}{}^{\mathrm{k}}\text{),}\text{for}\text{k ? 1}$ and suitable m, by distributions V for which $\text{V}\text{?}\text{(k) = 0(¦k¦}{}^{\mathrm{\alpha }}\text{),}\text{where}\text{α =}\text{(m + 1 ? ε)}\text{2 ? k}\text{, 0 < ε ? m + 1 ? 2k}$, are shown to correspond to self-adjoint operators H_v, in such a way that H_v depends continuously on V, and agrees with H + V when V is sufficiently regular. These results extend joint work with Irving E. Segal [J. Functional Analysis38 (1980), 71–98], in which perturbations of $\text{(}\text{?id}\text{dx}\text{)}{}^{\mathrm{m}}$ by distributions V with bounded Fourier transforms in L²(R¹) were considered.     

Selective oxidation of poly(4-methylstyrene)

A range of new functional copolymers bearing aldehyde and carboxylic acid groups have been prepared by functionalization of poly(4-methylstyrene). These polymers have molecular weights from 2,000 to 16,500 and contain up to 20% aldehyde and up to 90% carboxylic acid groups. The reaction proceeds by selective catalytic oxidations with molecular oxygen or air in acetic acid/organic cosolvent mixtures in presence of cobalt acetate and sodium bromide or hydrogen bromide. The effects of reaction temperature, catalyst, co-solvents and oxygen partial pressure on the reaction are described. © 1995 John Wiley & Sons, Inc.     

Laser targeted photo-occlusion of rat choroidal neovascularization without collateral damage

Laser targeted photo-occlusion (LTO) is a novel method being developed to treat choroidal neovascular membranes (CNV) in age-related and other macular degenerations. A photosensitive agent, encapsulated in heat-sensitive liposomes, is administered intravenously. A low power laser warms the targeted tissue and releases a bolus of photosensitizer. The photosensitizer is activated after it clears from the normal choriocapillaris but not from the CNV. Forty-five experimental CNV were induced in seven rats. Five weeks after LTO, complete occlusion was observed by laser targeted angiography (LTA) in 76% of treated CNV, and partial occlusion was found in the remaining 24%. The tissues outside the CNV but within the area treated by LTO showed no flow alteration and no dye leakage. All untreated CNV were patent on LTA at 5 weeks. Light microscopy and electron microscopy confirmed the results in treated and control lesions. Moreover, treated areas next to lesions showed normal photoreceptors, retinal pigment epithelium (RPE), Bruch's membrane and choriocapillaris. These results indicate that LTO may improve current photodynamic therapy by alleviating the need for repeated treatments and by avoiding the long-term risks associated with damage to the RPE and occlusion of normal choriocapillaries.     

Associations between Longitudinal Gestational Weight Gain and Scalar Infant Birth Weight: A Bayesian Joint Modeling Approach

Despite the importance of maternal gestational weight gain, it is not yet conclusively understood how weight gain during different stages of pregnancy influences health outcomes for either mother or child. We partially attribute this to differences in and the validity of statistical methods for the analysis of longitudinal and scalar outcome data. In this paper, we propose a Bayesian joint regression model that estimates and uses trajectory parameters as predictors of a scalar response. Our model remedies notable issues with traditional linear regression approaches found in the clinical literature. In particular, our methodology accommodates nonprospective designs by correcting for bias in self-reported prestudy measures; truly accommodates sparse longitudinal observations and short-term variation without data aggregation or precomputation; and is more robust to the choice of model changepoints. We demonstrate these advantages through a real-world application to the Alberta Pregnancy Outcomes and Nutrition (APrON) dataset and a comparison to a linear regression approach from the clinical literature. Our methods extend naturally to other maternal and infant outcomes as well as to areas of research that employ similarly structured data.     

A Multitargeted Approach: Organorhodium Anticancer Agent Based on Vorinostat as a Potent Histone Deacetylase Inhibitor

The combination of more than one bioactive moiety in a multitargeted anticancer agent may result in synergistic activity of its components. Using this concept, bioorganometallic compounds were designed to feature a metal center, a 2‐pyridinecarbothioamide (PCA), and a hydroxamic acid, which is found in the anticancer drug vorinostat (SAHA). The organometallics showed inhibitory activity in the nanomolar range against histone deacetylases (HDACs) as the key target for SAHA. In particular, the Rh complex was a potent inhibitor of HDAC6 over HDAC1 and HDAC8. Whereas this complex was highly cytotoxic in human cancer cells, it showed low toxicity in hemolysis studies and zebrafish, demonstrating the role of the metal center. For this complex a slightly reduced expression of vascular endothelial growth factor receptor 2 (VEGFR2) was established, which was upregulated by SAHA. This finding indicates that the new organometallics display different modes of action than their bioactive components.     

Synthesis,characterization, and X-ray crystallographic structure of 1,3-dimethyl-2(3H)-imidazoleselone

The reaction of elemental Se with 1,3-dimethylimidazolium iodide in methanolic K₂CO₃ yields 1,3-dimethyl-2(3H)-imidazoleselone for which three addition products, two with bromine and one with iodomethane, have been synthesized and for which X-ray crystallographic analysis shows the structure to consist of a selenium-substituted planar heterocyclic ring with bond distances and angles significantly different from those noted for the previously reported sulfur analog [1,3-dimethyl-2(3H)-imidazolethione, dmit]. Crystal data: C₅H₈N₂Se, space group C mcm, M = 175.03, a = 8.625(3), b = 11.447(6), c = 6.900(4) Å, V = 681.24 ų, Z = 4, D_c = 1.707 g cm⁻³, D₀ = 1.68 g cm⁻³, λ = 0.71073 Å (Mo-K_α), μ = 5.35 mm⁻¹, R = 0.034, and R_w = 0.031.