Functional Generalized Additive Models

We introduce the functional generalized additive model (FGAM), a novel regression model for association studies between a scalar response and a functional predictor. We model the link-transformed mean response as the integral with respect to t of F{X(t), t} where F( ·, ·) is an unknown regression function and X(t) is a functional covariate. Rather than having an additive model in a finite number of principal components as by Müller and Yao (2008 Müller, H.G., and Yao, F. (2008), “Functional Additive Models,” Journal of the American Statistical Association, 103, 1534–1544.[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]), our model incorporates the functional predictor directly and thus our model can be viewed as the natural functional extension of generalized additive models. We estimate F( ·, ·) using tensor-product B-splines with roughness penalties. A pointwise quantile transformation of the functional predictor is also considered to ensure each tensor-product B-spline has observed data on its support. The methods are evaluated using simulated data and their predictive performance is compared with other competing scalar-on-function regression alternatives. We illustrate the usefulness of our approach through an application to brain tractography, where X(t) is a signal from diffusion tensor imaging at position, t, along a tract in the brain. In one example, the response is disease-status (case or control) and in a second example, it is the score on a cognitive test. The FGAM is implemented in R in the refund package. There are additional supplementary materials available online.     

Coherent States and Modified de Broglie-Bohm Complex Quantum Trajectories

This paper examines the nature of classical correspondence in the case of coherent states at the level of quantum trajectories. We first show that for a harmonic oscillator, the coherent state complex quantum trajectories and the complex classical trajectories are identical to each other. This congruence in the complex plane, not restricted to high quantum numbers alone, illustrates that the harmonic oscillator in a coherent state executes classical motion. The quantum trajectories we consider are those conceived in a modified de Broglie-Bohm scheme. Though quantum trajectory representations are widely discussed in recent years, identical classical and quantum trajectories for coherent states are obtained only in the present approach. We may note that this result for standard harmonic oscillator coherent states is not totally unexpected because of their holomorphic nature. The study is extended to coherent states of a particle in an infinite potential well and that in a symmetric Poschl-Teller potential by solving for the trajectories numerically. For the Gazeau-Klauder coherent state of the infinite potential well, almost identical classical and quantum trajectories are obtained whereas for the Poschl-Teller potential, though classical trajectories are not regained, a periodic motion results as t→∞. Similar features were found for the SUSY quantum mechanics-based coherent states of the Poschl-Teller potential too, but this time the pattern of complex trajectories is quite different from that of the previous case. Thus we find that the method is a potential tool in analyzing the properties of generalized coherent states.     

Enumerating Cube Tilings

Cube tilings formed by $n$ -dimensional $4\mathbb Z ^n$ -periodic hypercubes with side $2$ and integer coordinates are considered here. By representing the problem of finding such cube tilings within the framework of exact cover and using canonical augmentation, pairwise nonisomorphic 5-dimensional cube tilings are exhaustively enumerated in a constructive manner. There are 899,710,227 isomorphism classes of such tilings, and the total number of tilings is 638,560,878,292,512. It is further shown that starting from a 5-dimensional cube tiling and using a sequence of switching operations, it is possible to generate any other cube tiling.     

Identities for the Ramanujan zeta function

We prove formulas for special values of the Ramanujan tau zeta function. Our formulas show that L(Δ,k)$L(\mathrm{\Delta },k)$ is a period in the sense of Kontsevich and Zagier when k?12$k?12$. As an illustration, we reduce L(Δ,k)$L(\mathrm{\Delta },k)$ to explicit integrals of hypergeometric and algebraic functions when k∈{12,13,14,15}$k\in \{12,13,14,15\}$.     

The effectiveness of 1H decoupling in the 13C MAS NMR of paramagnetic solids: an experimental case study incorporating copper(II) amino acid complexes

The use of continuous-wave (CW) 1H decoupling has generally provided little improvement in the 13C MAS NMR spectroscopy of paramagnetic organic solids. Recent solid-state 13C NMR studies have demonstrated that at rapid magic-angle spinning rates CW decoupling can result in reductions in signal-to-noise and that 1H decoupling should be omitted when acquiring 13C MAS NMR spectra of paramagnetic solids. However, studies of the effectiveness of modern 1H decoupling sequences are lacking, and the performance of such sequences over a variety of experimental conditions must be investigated before 1H decoupling is discounted altogether. We have studied the performance of several commonly used advanced decoupling pulse sequences, namely the TPPM, SPINAL-64, XiX, and eDROOPY sequences, in 13C MAS NMR experiments performed under four combinations of the magnetic field strength (7.05 or 11.75T), rotor frequency (15 or 30kHz), and 1H rf-field strength (71, 100, or 140kHz). The effectiveness of these sequences has been evaluated by comparing the 13C signal intensity, linewidth at half-height, LWHH, and coherence lifetimes, T2('), of the methine carbon of copper(II) bis(dl-alanine) monohydrate, Cu(ala)(2).H2O, and methylene carbon of copper(II) bis(dl-2-aminobutyrate), Cu(ambut)(2), obtained with the advanced sequences to those obtained without 1H decoupling, with CW decoupling, and for fully deuterium labelled samples. The latter have been used as model compounds with perfect 1H decoupling and provide a measure of the efficiency of the 1H decoupling sequence. Overall, the effectiveness of 1H decoupling depends strongly on the decoupling sequence utilized, the experimental conditions and the sample studied. Of the decoupling sequences studied, the XiX sequence consistently yielded the best results, although any of the advanced decoupling sequences strongly outperformed the CW sequence and provided improvements over no 1H decoupling. Experiments performed at 7.05T demonstrate that the XiX decoupling sequence is the least sensitive to changes in the 1H transmitter frequency and may explain the superior performance of this decoupling sequence. Overall, the most important factor in the effectiveness of 1H decoupling was the carbon type studied, with the methylene carbon of Cu(ambut)(2) being substantially more sensitive to 1H decoupling than the methine carbon of Cu(ala)(2).H2O. An analysis of the various broadening mechanisms contributing to 13C linewidths has been performed in order to rationalize the different sensitivities of the two carbon sites under the four experimental conditions.     

Antibacterial Effectiveness of Rice Water (Starch)‐Capped Silver Nanoparticles Fabricated Rapidly in the Presence of Sunlight

Green synthesized silver nanoparticles (AgNPs) have enormous applications. Hence, there is an increasing demand to explore diverse bioresources for AgNP fabrication to make the process more cost‐effective and rapid as possible. Due to the abundantly present hydroxyl groups of rice starch, it provides ideal sites for metal ion complexation and thereby synthesis of nanoparticles with promising activity. So the study was designed to develop rapid, eco‐friendly and cost‐effective method for green AgNP synthesis using boiled rice water starch in the presence of sunlight irradiation. The starch‐capped nanoparticles (sAgNPs) formed in the study were found to have the surface plasmon absorbance at 439 nm. The study showed optimum yield of sAgNPs when 25% rice starch was treated with aqueous 1 mM AgNO₃ for 15 min in the presence of sunlight. Fourier transform infrared spectroscopy analysis provided mechanistic insight into the role of –OH groups of starch in the reduction of AgNO₃ to sAgNPs. On further characterization by X‐ray diffraction analysis, the sAgNPs were identified to have FCC crystal structure. At the same time, high‐resolution transmission electron microscopic analysis showed majority of sAgNPs to have spherical morphology, and dynamic light scattering study revealed the average particle size as 36.3 nm. Further confirmation on presence of AgNPs was carried out by energy‐dispersive X‐ray spectroscopy. Moreover, the sAgNPs exhibited promising antibacterial activity against foodborne pathogens, Salmonella Typhimurium and Staphylococcus aureus.     

Reduction vs. Addition: The Reaction of an Aluminyl Anion with 1,3,5,7‐Cyclooctatetraene

The potassium aluminyl complex K[Al(NON^Ar)] (NON=NON^Ar=[O(SiMe₂NAr)₂]^2?, Ar=2,6‐iPr₂C₆H₃) reacts with 1,3,5,7‐cyclooctatetraene (COT) to give K[Al(NON^Ar)(COT)]. The COT‐ligand is present in the asymmetric unit as a planar μ₂‐η²:η⁸‐bridge between Al and K, with additional K???π‐aryl interactions to neighboring molecules that generate a helical chain. DFT calculations indicate significant aromatic character, consistent with reduction to [COT]^2?. Addition of 18‐crown‐6 causes a rearrangement of the C₈‐carbocycle to form the isomeric 9‐aluminabicyclo[4.2.1]nona‐2,4,7‐triene anion.     

Generation and EPR Spectroscopy of the First Silenyl Radicals,R2C=Si.−R: Experiment and Theory

The first two persistent silenyl radicals (R₂C=Si^.?R), with a half‐life (t_1/2) of about 30 min, were generated and characterized by electron paramagnetic resonance (EPR) spectroscopy. The large hyperfine coupling constants (hfccs) (a(²⁹Si_α)=137.5–148.0 G) indicate that the unpaired electron has substantial s character. DFT calculations, which are in good agreement with the experimentally observed hfccs, predict a strongly bent structure (?C=Si?R=134.7–140.7°). In contrast, the analogous vinyl radical, R₂C=C^.?R (t_1/2≈3 h), exhibits a small hfcc (a(¹³C_α)=26.6 G) and has a nearly linear geometry (?C=C?R=168.7°).     

Nanostructuring of 1-butyl-4-methylpyridinium chloride in ionic liquid–iron oxide nanofluids

Journal of Thermal Analysis and Calorimetry - Understanding the behavior of ionic liquids (ILs) in ionic liquid-based nanofluids has great significance for its proper application. The phase changes...