Consistency of Regularization for Free Scalar Fields

In two dimensional constructive quantum field theory for scalar fields, it is necessary to regularize both the action and the total (Gaussian) volume. In this paper we consider the compatibility of these regularizations.      

Uncertainty Quantification for Modern High-Dimensional Regression via Scalable Bayesian Methods

Tremendous progress has been made in the last two decades in the area of high-dimensional regression, especially in the “large p, small n” setting. Such sample starved settings inevitably lead to models which are potentially very unstable and hence quite unreliable. To this end, Bayesian shrinkage methods have generated a lot of recent interest in the modern high-dimensional regression and model selection context. Such methods span the wide spectrum of modern regression approaches and include among others, spike-and-slab priors, the Bayesian lasso, ridge regression, and global-local shrinkage priors such as the Horseshoe prior and the Dirichlet–Laplace prior. These methods naturally facilitate tractable uncertainty quantification and have thus been used extensively across diverse applications. A common unifying feature of these models is that the corresponding priors on the regression coefficients can be expressed as a scale mixture of normals. This property has been leveraged extensively to develop various three-step Gibbs samplers to explore the corresponding intractable posteriors. The convergence of such samplers however is very slow in high dimensions settings, making them disconnected to the very setting that they are intended to work in. To address this challenge, we propose a comprehensive and unifying framework to draw from the same family of posteriors via a class of tractable and scalable two-step blocked Gibbs samplers. We demonstrate that our proposed class of two-step blocked samplers exhibits vastly superior convergence behavior compared to the original three-step sampler in high-dimensional regimes on simulated data as well as data from a variety of applications including gene expression data, infrared spectroscopy data, and socio-economic/law enforcement data. We also provide a detailed theoretical underpinning to the new method by deriving explicit upper bounds for the (geometric) rate of convergence, and by proving that the proposed two-step sampler has superior spectral properties. Supplementary material for this article is available online.     

Size and sequence and the volume change of protein folding

The application of hydrostatic pressure generally leads to protein unfolding, implying, in accordance with Le Chatelier's principle, that the unfolded state has a smaller molar volume than the folded state. However, the origin of the volume change upon unfolding, ΔV(u), has yet to be determined. We have examined systematically the effects of protein size and sequence on the value of ΔV(u) using as a model system a series of deletion variants of the ankyrin repeat domain of the Notch receptor. The results provide strong evidence in support of the notion that the major contributing factor to pressure effects on proteins is their imperfect internal packing in the folded state. These packing defects appear to be specifically localized in the 3D structure, in contrast to the uniformly distributed effects of temperature and denaturants that depend upon hydration of exposed surface area upon unfolding. Given its local nature, the extent to which pressure globally affects protein structure can inform on the degree of cooperativity and long-range coupling intrinsic to the folded state. We also show that the energetics of the protein's conformations can significantly modulate their volumetric properties, providing further insight into protein stability.     

Structure–property relationships in modified natural rubber latexes grafted with methyl methacrylate and vinyl neo‐decanoate

A series of modified natural rubber latexes (NRLs) grafted with poly(methyl methacrylate) (PMMA) were prepared by seeded emulsion polymerization with NRL as the seed polymer. Two different redox systems, cumene hydroperoxide (CHP)/tetraethylene pentamine (TEPA) and tert‐butyl hydroperoxide (t‐BHP)/TEPA, were used to initiate polymerization, and phase mixing was promoted by the addition of vinyl neo‐decanoate (VneoD). The CHP/TEPA system was more efficient than t‐BHP/TEPA for the grafting of secondary polymers in modified natural rubber (NR). The enhanced phase mixing in the presence of VneoD was attributed to the solubility parameter of the VneoD‐rich methyl methacrylate–VneoD copolymer formed late in the reaction, lying between that of PMMA and NR, and the extent to which this polymer was grafted to the NR backbone. The viscoelastic properties of the polymers were investigated as a function of composition, temperature, and frequency; changes in viscoelastic behavior consistent with the presence of a high‐T_g PMMA phase (where T_g is the glass‐transition temperature) were observed. This suggested a degree of phase mixing that increased with increasing VneoD content and increasing flux of oxygen‐centered radicals within the NR particles. More phase mixing resulted in poorer film formation, which was consistent with the localization of a high‐T_g secondary polymer phase near the particle surface. The apparent concentration of PMMA near the surface of the particles was also observed with transmission electron microscopy. The localization of PMMA near the particle surfaces was consistent with the presumed locus of radical generation in these systems: the redox couple used to initiate the polymerization consisted of an oil‐soluble hydroperoxide and a water‐soluble amine that reacted predominantly at the water/particle interface. The viscoelastic properties of the modified NRLs that were prepared suggest that these synthetic procedures provide a means of controlling phase mixing and branching, such as for improving the suitability of these modified rubbers in pressure‐sensitive‐adhesive formulations. © 2002 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 40: 809–822, 2002; DOI 10.1002/pola.10165     

The temperature‐dependent ballistic performance and the ductile‐to‐brittle transition in polymer networks

The temperature dependence of the ballistic impact performance of a series of transparent polymer networks is evaluated. A systematic series of homogeneous epoxy/propylene‐oxide‐based thermosets, a nanoscale phase‐separated epoxy/dual amine thermoset, and two homogeneous, completely aliphatic materials synthesized via ring‐opening metathesis polymerization are examined. The Vogel temperature (T_o) and the Kauzmann temperature (T_K) are critical parameters for scaling the temperature‐dependent ballistic impact performance of each class of materials. The ductile‐to‐brittle transition temperature in a series of propylene‐oxide amine‐cured epoxies occurs at the material T_K, corresponding to a sharp drop in fracture toughness and ballistic impact performance. Two aliphatic, ring‐opening metathesis polymerized materials are found to exhibit no clear transition from purely ductile to purely brittle behavior, but the temperature dependence is still scaled to a single curve when normalized by T_o. The cooperatively rearranging region (CRR) or the volume of this region is related to the breadth of temperatures over which these materials exhibit purely ductile deformation both quasi‐statically and at higher rates. The temperature‐dependent performance is discussed in the context of the configurational entropy. The breadth of the ductility window is related to the size of the CRR, calculated from calorimetric measurements at the resin T_g. Published 2019. This article is a U.S. Government work and is in the public domainin the USA. J. Polym. Sci., Part B: Polym. Phys. 2019 , 57, 511–523     

The psychophysics of tactile amplitude summation: a test of the nGamma nonlinear model

This research applied Gregson's n Gamma nonlinear model (Gregson 1988, 1992, 1995, 1998) to the process of tactile amplitude summation. Participants were presented with simultaneous pairs of vibrations and rated the total perceived intensity of the resultant percept as both the amplitude of the stimuli and their spatial separations were manipulated. The multidimensional response surface for each participant was then compared with that predicted by the 2 Gamma Case 2 model. While the fit between data and theory was strong in all cases (mean r triangle up 2 = .86), analysis of residuals revealed evidence of a second nonlinear process. In contrast, a multivariate version of the psychophysical function was found to account for a substantially smaller proportion of the variability in the data (mean r triangle up 2 = .67). The results confirmed that summative effects similar to those observed in other modalities occur in the tactile modality, and provide an initial demonstration that the mathematics of nonlinear dynamics may help to explain the processing of tactile patterns.     

Determination of mixed-mode stress intensity factors, fracture toughness, and crack turning angle for anisotropic foam material

A numerical and experimental investigation for determining mixed-mode stress intensity factors, fracture toughness, and crack turning angle for BX-265 foam insulation material, used by NASA to insulate the external tank (ET) for the space shuttle, is presented. BX-265 foam is a type of spray-on foam insulation (SOFI), similar to the material used to insulate attics in residential construction. This cellular material is a good insulator and is very lightweight. Breakup of segments of this foam insulation on the shuttle ET impacting the shuttle thermal protection tiles during liftoff is believed to have caused the space shuttle Columbia failure during re-entry. NASA engineers are interested in understanding the processes that govern the breakup/fracture of this material from the shuttle ET. The foam is anisotropic in nature and the required stress and fracture mechanics analysis must include the effects of the direction dependence on material properties. Material testing at NASA Marshall Space Flight Center (MSFC) has indicated that the foam can be modeled as a transversely isotropic material. As a first step toward understanding the fracture mechanics of this material, we present a general theoretical and numerical framework for computing stress intensity factors (SIFs), under mixed-mode loading conditions, taking into account the material anisotropy. We present SIFs for middle tension – M(T) – test specimens, using 3D finite element stress analysis (ANSYS) and FRANC3D fracture analysis software. SIF values are presented for a range of foam material orientations. Mode I fracture toughness of the material is determined based on the SIF value at failure load. We also present crack turning angles for anisotropic foam material under mixed-mode loading. The results represent a quantitative basis for evaluating the strength and fracture properties of anisotropic foam insulation material.     

Stereoselective synthesis of acetoacetate-derived enol triflates

A highly stereoselective method for preparing ( Z)- and ( E)-enol triflates derived from substituted acetoacetate derivatives is described. The salient feature of this methodology is the use of Schotten-Baumann-type conditions to control enolate geometry using either aqueous LiOH ( Z-selective) or aqueous (Me)(4)NOH ( E-selective) in combination with triflic anhydride to provide a practical and predictable approach to these valuable substrates.     

A bridge to coordination isomer selection in lanthanide(III) DOTA-tetraamide complexes

Interest in macrocyclic lanthanide complexes such as DOTA is driven largely through interest in their use as contrast agents for MRI. The lanthanide tetraamide derivatives of DOTA have shown considerable promise as PARACEST agents, taking advantage of the slow water exchange kinetics of this class of complex. We postulated that water exchange in these tetraamide complexes could be slowed even further by introducing a group to sterically encumber the space above the water coordination site, thereby hindering the departure and approach of water molecules to the complex. The ligand 8O2-bridged DOTAM was synthesized in a 34% yield from cyclen. It was found that the lanthanide complexes of this ligand did not possess a water molecule in the inner coordination sphere of the bound lanthanide. The crystal structure of the ytterbium complex revealed that distortions to the coordination sphere were induced by the steric constraints imposed on the complex by the bridging unit. The extent of the distortion was found to increase with increasing ionic radius of the lanthanide ion, eventually resulting in a complete loss of symmetry in the complex. Because this ligand system is bicyclic, the conformation of each ring in the system is constrained by that of the other; in consequence, inclusion of the bridging unit in the complexes means only a twisted square, antiprismatic coordination geometry is observed for lanthanide complexes of 8O2-bridged DOTAM.