Explicit Solutions of Quadratic FBSDEs Arising From Quadratic Term Structure Models

We provide explicit solutions of certain forward-backward stochastic differential equations (FBSDEs) with quadratic growth. These particular FBSDEs are associated with quadratic term structure models of interest rates and characterize the zero-coupon bond price. The results of this paper are naturally related to similar results on affine term structure models of Hyndman (Math. Financ. Econ. 2(2):107–128, 2009) due to the relationship between quadratic functionals of Gaussian processes and linear functionals of affine processes. Similar to the affine case a sufficient condition for the explicit solutions to hold is the solvability in a fixed interval of Riccati-type ordinary differential equations. However, in contrast to the affine case, these Riccati equations are easily associated with those occurring in linear-quadratic control problems. We also consider quadratic models for a risky asset price and characterize the futures price and forward price of the asset in terms of similar FBSDEs. An example is considered, using an approach based on stochastic flows that is related to the FBSDE approach, to further emphasize the parallels between the affine and quadratic models. An appendix discusses solvability and explicit solutions of the Riccati equations.     

Multivariate statistical identification of human bladder carcinomas using ambient ionization imaging mass spectrometry

Diagnosis of human bladder cancer in untreated tissue sections is achieved by using imaging data from desorption electrospray ionization mass spectrometry (DESI-MS) combined with multivariate statistical analysis. We use the distinctive DESI-MS glycerophospholipid (GP) mass spectral profiles to visually characterize and formally classify twenty pairs (40 tissue samples) of human cancerous and adjacent normal bladder tissue samples. The individual ion images derived from the acquired profiles correlate with standard histological hematoxylin and eosin (H&E)-stained serial sections. The profiles allow us to classify the disease status of the tissue samples with high accuracy as judged by reference histological data. To achieve this, the data from the twenty pairs were divided into a training set and a validation set. Spectra from the tumor and normal regions of each of the tissue sections in the training set were used for orthogonal projection to latent structures (O-PLS) treated partial least-square discriminate analysis (PLS-DA). This predictive model was then validated by using the validation set and showed a 5% error rate for classification and a misclassification rate of 12%. It was also used to create synthetic images of the tissue sections showing pixel-by-pixel disease classification of the tissue and these data agreed well with the independent classification that uses histological data by a certified pathologist. This represents the first application of multivariate statistical methods for classification by ambient ionization although these methods have been applied previously to other MS imaging methods. The results are encouraging in terms of the development of a method that could be utilized in a clinical setting through visualization and diagnosis of intact tissue.     

Aqueous-phase deactivation and intramolecular [2 + 2 + 2] cycloaddition of oxanorbornadiene esters

Both inter- and intramolecular degradation pathways were identified for the aqueous phase deactivation of oxanorbornadiene (OND) electrophiles, and propargylic OND esters were found to undergo facile intramolecular [2 + 2 + 2] homo-Diels-Alder cycloaddition in polar media.     

Intercepting Wacker intermediates with arenes: C-H functionalization and dearomatization

An intramolecular cyclization cascade reaction has been developed utilizing a high valent palladium intermediate that generates a carbon-carbon and carbon-oxygen bond in a single transformation. This method provides rapid access to highly functionalized tricyclic scaffolds, including spirocyclic cyclohexadienones. Good yields and mild conditions are reported with high tolerance toward oxygen and water.     

Intra-operative optical diagnostics with vibrational spectroscopy

Established methods for characterization of tissue and diagnostics, for example histochemistry, magnetic resonance imaging (MRI), X-ray tomography, or positron emission tomography (PET), are mostly not suitable for intra-operative use. However, there is a clear need for an intra-operative diagnostics especially to identify the borderline between normal and tumor tissue. Currently, vibrational spectroscopy techniques (both Raman and infrared) complement the standard methods for tissue diagnostics. Vibrational spectroscopy has the potential for intra-operative use, because it can provide a biochemically based profile of tissue in real time and without requiring additional contrast agents, which may perturb the tissue under investigation. In addition, no electric potential needs to be applied, and the measurements are not affected by electromagnetic fields. Currently, promising approaches include Raman fiber techniques and nonlinear Raman spectroscopy. Infrared spectroscopy is also being used to examine freshly resected tissue ex vivo in the operating theater. The immense volume of information contained in Raman and infrared spectra requires multivariate analysis to extract relevant information to distinguish different types of tissue. The promise and limitations of vibrational spectroscopy methods as intra-operative tools are surveyed in this review.     

Quantum and classical study of surface characterization by three-dimensional helium atom scattering

Exact time-dependent wavepacket calculations of helium atom scattering from model symmetric, chiral, and hexagonal surfaces are presented and compared with their classical counterparts. Analysis of the momentum distribution of the scattered wavepacket provides a convenient method to obtain the resulting energy and angle resolved scattering distributions. The classical distributions are characterized by standard rainbow scattering from corrugated surfaces. It is shown that the classical results are closely related to their quantum counterparts and capture the qualitative features appearing therein. Both the quantum and classical distributions are capable of distinguishing between the structures of the three surfaces.     

Excited-state processes in first-generation phenyl-cored thiophene dendrimers

First generation dendrimers with three oligothiophene arms (meta-arranged, 3G1-nS) and four arms (ortho- and para-arranged, 4G1-nS) connected to a central phenyl core were investigated spectroscopically in solution. In all dendrimers, on an ultrafast time scale (<10 ps), two "cooling" processes convert the initially generated, "hot" exciton into the geometrically relaxed, "cold" exciton. A decrease in the triplet yield, particularly evident for the 4-arm dendrimers; intersystem crossing rate; and nonradiative triplet decay time with increasing number of bridging thiophene units n all meet with expectations from prior studies on linear oligothiophenes. A relatively fast internal conversion process (>0.6 ns(-1)) is observed in both dendrimer series, possibly due to increased twisting about the phenyl core that reduces the triplet yields considerably with respect to oligothiophenes. An anomalous shifting of the triplet-triplet absorption spectra characterizes the 4G1-nS dendrimers as unique from the 3G1-nS series in terms of the hindrance of torsional motion and confinement of excited states enforced by the arrangement of dendrons.     

Evaluation of methods to predict reactivity of gold nanoparticles

Several methods have appeared in the literature for predicting reactivity on metallic surfaces and on the surface of metallic nanoparticles. All of these methods have some relationship to the concept of frontier molecular orbital theory. The d-band theory of Hammer and N?rskov is perhaps the most widely used predictor of reactivity on metallic surfaces, and it has been successfully applied in many cases. Use of the Fukui function and the condensed Fukui function is well established in organic chemistry, but has not been so widely applied in predicting the reactivity of metallic nanoparticles. In this article, we will evaluate the usefulness of the condensed Fukui function in predicting the reactivity of a family of cubo-octahedral gold nanoparticles and make comparison with the d-band method.     

Poly[tetrakis(n‐propylammonium) [octa‐μ‐chlorido‐dichloridotrinickelate(II)]]: a hybrid organic–inorganic layer compound in the Cs4Mg3F10 structure type

The title compound, {(C₃H₁₀N)₄[Ni₃Cl₁₀]}_n, contains zigzag layers of tri‐μ‐chlorido‐bridged linear 2/m‐symmetric Ni₃Cl₁₂ segments, linked by mono‐μ‐chlorido quasi‐linear bridges to two other segments at each end. These inorganic layers are interleaved with interdigitated bilayers of mirror‐symmetric n‐propylammonium cations, the ammonium head groups of which are directed into the inorganic layers to form multiple N—H...Cl hydrogen bonds, while the propyl tail groups pack together in a tongue‐and‐groove manner in the center of the bilayer. The propyl groups are ordered at 100 K but disordered with opposite conformations on the mirror plane at 240 K.     

Diffusion tensor magnetic resonance imaging of the normal breast

Purpose

The objective of this study was to evaluate diffusion anisotropy of the breast parenchyma and assess the range and repeatability of diffusion tensor imaging (DTI) parameters in normal breast tissue.

Materials and Methods

The study was approved by our institutional review board and included 12 healthy females (median age, 36 years). Diffusion tensor imaging was performed at 1.5 T using a diffusion-weighted echo planar imaging sequence. Diffusion tensor imaging parameters including tensor eigenvalues (λ₁, λ₂, λ₃), fractional anisotropy (FA) and apparent diffusion coefficient (ADC) were measured for anterior, central and posterior breast regions.

Results

Mean normal breast DTI measures were λ₁=2.51×10⁻³ mm²/s, λ₂=1.89×10⁻³ mm²/s, λ₃=1.39×10⁻³ mm²/s, ADC=1.95±0.24×10⁻³ mm²/s and FA=0.29±0.05 for b=600 s/mm². Significant regional differences were observed for both FA and ADC (P<.05), with higher ADC in the central breast and higher FA in the posterior breast. Comparison of DTI values calculated using b=0, 600 s/mm² vs. b=0, 1000 s/mm², showed significant differences in ADC (P<.001), but not FA. Repeatability assessment produced within-subject coefficient of variations of 4.5% for ADC and 11.4% for FA measures.

Conclusion

This study demonstrates anisotropy of water diffusion in normal breast tissue and establishes a normative range of breast FA values. Attention to the influence of breast region and b value on breast DTI measurements may be important for clinical interpretation and standardization of techniques.