Spatially variant regularization of lateral displacement measurement using variance

The purpose of this work is to confirm the effectiveness of our proposed spatially variant displacement component-dependent regularization for our previously developed ultrasonic two-dimensional (2D) displacement vector measurement methods, i.e., 2D cross-spectrum phase gradient method (CSPGM), 2D autocorrelation method (AM), and 2D Doppler method (DM). Generally, the measurement accuracy of lateral displacement spatially varies and the accuracy is lower than that of axial displacement that is accurate enough. This inaccurate measurement causes an instability in a 2D shear modulus reconstruction. Thus, the spatially variant lateral displacement regularization using the lateral displacement variance will be effective in obtaining an accurate lateral strain measurement and a stable shear modulus reconstruction than a conventional spatially uniform regularization. The effectiveness is verified through agar phantom experiments. The agar phantom [60 mm (height) × 100 mm (lateral width) × 40 mm (elevational width)] that has, at a depth of 10 mm, a circular cylindrical inclusion (dia. = 10 mm) of a higher shear modulus (2.95 and 1.43 × 10⁶ N/m², i.e., relative shear modulus, 2.06) is compressed in the axial direction from the upper surface of the phantom using a commercial linear array type transducer that has a nominal frequency of 7.5-MHz. Because a contrast-to-noise ratio (CNR) expresses the detectability of the inhomogeneous region in the lateral strain image and further has almost the same sense as that of signal-to-noise ratio (SNR) for strain measurement, the obtained results show that the proposed spatially variant lateral displacement regularization yields a more accurate lateral strain measurement as well as a higher detectability in the lateral strain image (e.g., CNRs and SNRs for 2D CSPGM, 2.36 vs 2.27 and 1.74 vs 1.71, respectively). Furthermore, the spatially variant lateral displacement regularization yields a more stable and more accurate 2D shear modulus reconstruction than the uniform regularization (however, for the regularized relative shear modulus reconstructions, slightly accurate, e.g., for 2D CSPGM, 1.51 vs 1.50). These results indicate that the spatially variant displacement component-dependent regularization will enable the 2D shear modulus reconstruction to be used as practical diagnostic and monitoring tools for the effectiveness of various noninvasive therapy techniques of soft tissue diseases (e.g., breast, liver cancers). Application of the regularization to the elevational displacement will also increase the stability of a three-dimensional (3D) reconstruction.     

The equilibrium states for semigroups of rational maps

We consider the dynamics of skew product maps associated with finitely generated semigroups of rational maps on the Riemann sphere. We show that under some conditions on the dynamics and the potential function ψ, there exists a unique equilibrium state for ψ and a unique exp(P(ψ) − ψ)-conformal measure, where P(ψ) denotes the topological pressure of ψ. The research of M. Urbański was supported in part by the NSF Grant DMS 0400481. H. Sumi thanks University of North Texas for kind hospitality, during his stay there.     

Perturbation method for determining the group of invariance of hierarchical models

We propose a perturbation method for determining the (largest) group of invariance of a toric ideal defined in [S. Aoki, A. Takemura, The largest group of invariance for Markov bases and toric ideals, J. Symbolic Comput. 43 (5) (2008) 342–358]. In the perturbation method, we investigate how a generic element in the row space of the configuration defining a toric ideal is mapped by a permutation of the indeterminates. Compared to the proof by Aoki and Takemura which was based on stabilizers of a subset of indeterminates, the perturbation method gives a much simpler proof of the group of invariance. In particular, we determine the group of invariance for a general hierarchical model of contingency tables in statistics, under the assumption that the numbers of the levels of the factors are generic. We prove that it is a wreath product indexed by a poset related to the intersection poset of the maximal interaction effects of the model.     

A new type of fixed point theorem in metric spaces

We prove a generalization of Edelstein’s fixed point theorem. Though there are thousands of fixed point theorems in metric spaces, our theorem is a new type of theorem.     

Best proximity points for cyclic Meir–Keeler contractions

We introduce a notion of cyclic Meir–Keeler contractions and prove a theorem which assures the existence and uniqueness of a best proximity point for cyclic Meir–Keeler contractions. This theorem is a generalization of a recent result due to Eldred and Veeramani.     

Evaluation of an ODS column modified with zwitterionic/nonionic mixed surfactants and its application to direct injection determination of inorganic anions.

An octadecylsilica (ODS) column modified with zwitterionic/nonionic mixed surfactants was evaluated for the direct injection determination of inorganic anions in biological fluids by ion chromatography. A zwitterionic surfactant (sulfobetaine-type) and a nonionic surfactant (polyoxyethylene-type) were used for a stationary-phase modification. When aqueous electrolyte solutions with concentrations of sub-mM to several mM were used as a mobile phase, the zwitterionic surfactant coated on the ODS surface exhibited unique separation selectivity for ionic species, while the nonionic surfactant coated on the ODS might have formed a hydrophilic network over the ODS surface and restricted matrix proteins from adsorbing on the stationary phase. Consequently, the mixed surfactant-modified column system allowed an efficient ion chromatographic separation of inorganic anions as well as a size-exclusive removal of column-fouling proteins. This separation system was applied to the direct injection determination of UV-absorbing anions in human saliva. The detection limits for nitrite, nitrate, iodide and thiocyanate were 3.1, 2.7, 4.5 and 25 microM, respectively, with UV detection at 210 nm (injection volume; 20 microl), and their relative standard deviations for 5 replicate measurements of saliva samples spiked with 100 microM each of those anions were 1.4, 0.9, 2.2 and 5.5%, respectively.     

Synthesis of a highly luminescent three-dimensional pyrene dye based on the spirobifluorene skeleton

We have synthesized a highly luminescent (log e > 5.0, F > 0.9) pyrene dye based on a spirobifluorene skeleton [2,2',7,7'-tetrakis(7-tert-butyl-1-pyrenyl)-9,9'-spirobi[9H-fluorene; 4-PySBF]. The use of spirobifluorene prevents fluorescence quenching by intramolecular energy transfer and/or electron transfer among the chromophores in the excited state. The emission spectra of 4-PySBF exhibited a red shift of 20 nm in comparison to a model compound [9,9'-dioctyl-2,7-bis(7-tert-butyl-1-pyrenyl)-9H-fluorene; 2-PyF], but its UV-Vis spectrum remained unchanged.     

Photochemical tuning of the helical structure of cholesteric liquid crystals by photoisomerization of chiral azobenzenes, and their structural effects

Several chiral azobenzene compounds having different chiral substituents were synthesized. A cholesteric phase was induced by mixing each chiral azobenzene compound with a host non-chiral nematic liquid crystal (E44). The helical twisting power (HTP) as well as the change in HTP by trans-cis photoisomerization of the chiral azobenzene compound was dependent on the structure of the chiral substituents. A compensated nematic phase was induced by combination of E44, a chiral azobenzene compound and a non-photochromic chiral compound. Reversible switching between the compensated nematic phase and cholesteric phase was brought about by trans-cis photoisomerization of the chiral azobenzene compound in the liquid crystalline systems. An azobenzene compound substituted with a menthyl group showed the highest efficiency as the trigger for the switching; this efficiency was related to the compactness of the chiral group substituted within the azobenzene core moiety.     

Kaon interferometry in heavy-ion collisions at the CERN SPS

K⁺K⁺ and K^–K^– correlations from S+Pb collisions at 200 GeV/c per nucleon and K⁺K⁺ correlations from p+Pb collisions at 450 GeV/c per nucleon, are presented as measured by the focusing spectrometer of the NA44 experiment at CERN. Multidimensional fits are performed in order to characterize the kaon-emission volume, which is found to be smaller than the pion-emission volume.