Boundedness of solutions of a system of integro-differential equations

Let b: [?1, 0] →$\text{R}$ be a nondecreasing, strictly convex C²-function with b(? 1) = 0, and let g: $\text{R}$ⁿ → $\text{R}$ⁿ be a locally Lipschitzian mapping, which is the gradient of a function G: $\text{R}$ⁿ → $\text{R}$. Consider the following vector-valued integro-differential equation of the Levin-Nohel type

$\text{x}\text{?}\text{(t)=?∝}{}_{\mathrm{?1}}{}^0\text{b(θ)g(x(t + θ))dθ}$

. (E) This equation is used in applications to model various viscoelastic phenomena. By LaSalle's invariance principle, every bounded solution x(t) goes to a connected set of zeros of g, as time t goes to infinity. It is the purpose of this paper to give several geometric criteria assuring the boundedness of solutions of (E) or some of its components.     

1H MRS detection of glycine residue of reduced glutathione in vivo

Glutathione (GSH) is a powerful antioxidant found inside different kinds of cells, including those of the central nervous system. Detection of GSH in the human brain using ¹H MR spectroscopy is hindered by low concentration and spectral overlap with other metabolites. Previous MRS methods focused mainly on the detection of the cysteine residue (GSH-Cys) via editing schemes. This study focuses on the detection of the glycine residue (GSH-Gly), which is overlapped by glutamate and glutamine (Glx) under physiological pH and temperature. The first goal of the study was to obtain the spectral parameters for characterization of the GSH-Gly signal under physiological conditions. The second goal was to investigate a new method of separating GSH-Gly from Glx in vivo. The characterization of the signal was carried out by utilization of numerical simulations as well as experiments over a wide range of magnetic fields (4.0–14 T). The proposed separation scheme utilizes J-difference editing to quantify the Glx contribution to separate it from the GSH-Gly signal. The presented method retains 100% of the GSH-Gly signal. The overall increase in signal to noise ratio of the targeted resonance is calculated to yield a significant SNR improvement compared to previously used methods that target GSH-Cys residue. This allows shorter acquisition times for in vivo human clinical studies.     

The Gauge–Bethe Correspondence and Geometric Representation Theory

The Gauge/Bethe correspondence of Nekrasov and Shatashvili relates the spectrum of integrable spin chains to the ground states of supersymmetric gauge theories. Up to now, this correspondence has been an observation; the underlying reason for its existence remaining elusive. We argue here that geometrical representation theory is a mathematical foundation of the Gauge/Bethe correspondence, and it provides a framework to study families of gauge theories in a unified way.     

Evaluation of aortic stenosis severity using 4D flow jet shear layer detection for the measurement of valve effective orifice area

Aims

The objective of this study was to evaluate the potential of 4D flow MRI to assess valve effective orifice area (EOA) in patients with aortic stenosis as determined by the jet shear layer detection (JSLD) method.

Methods and Results

An in-vitro stenosis phantom was used for validation and in-vivo imaging was performed in 10 healthy controls and 40 patients with aortic stenosis. EOA was calculated by the JSLD method using standard 2D phase contrast MRI (PC-MRI) and 4D flow MRI measurements (EOA_JSLD-2D and EOA_JSLD-4D, respectively). As a reference standard, the continuity equation was used to calculate EOA (EOA_CE) with the 2D PC-MRI velocity field and compared to the EOA_JSLD measurements. The in-vitro results exhibited excellent agreement between flow theory (EOA = 0.78 cm²) and experimental measurement (EOA_JSLD-4D = 0.78 ± 0.01 cm²) for peak velocities ranging from 0.9 to 3.7 m/s. In-vivo results showed good correlation and agreement between EOA_JSLD-2D and EOA_CE (r = 0.91, p < 0.001; bias: − 0.01 ± 0.38 cm²; agreement limits: 0.75 to − 0.77 cm²), and between EOA_JSLD-4D and EOA_CE (r = 0.95, p < 0.001; bias: − 0.09 ± 0.26 cm²; limits: 0.43 to − 0.62 cm²).

Conclusion

This study demonstrates the feasibility of measuring EOA_JSLD using 4D flow MRI. The technique allows for optimization of the EOA measurement position by visualizing the 3D vena contracta, and avoids potential sources of EOA_CE measurement variability.     

High-resolution imaging of single fluorescent molecules with the optical near-field of a metal tip

We show that a concentration of light at a metal tip allows near-field optical imaging of single fluorescent dye molecules at very high resolution, despite strong quenching effects. Details as small as 10 nm were observed in the fluorescence patterns of single Cy-3 dyes bound to the termini of DNA. Data evaluation by model fitting determines the positions of the dyes to an accuracy even better than 1 nm and also yields their 3D orientation. The metal tip simultaneously provides high-resolution topographic imaging complementing the optical signal for a detailed surface examination.     

Convergence of nonconforming multigrid methods without full elliptic regularity

We consider nonconforming multigrid methods for symmetric positive definite second and fourth order elliptic boundary value problems which do not have full elliptic regularity. We prove that there is a bound () for the contraction number of the -cycle algorithm which is independent of mesh level, provided that the number of smoothing steps is sufficiently large. We also show that the symmetric variable -cycle algorithm is an optimal preconditioner.

     

Empirical modeling of human face kinematics during speech using motion clustering

In this paper we present an algorithm for building an empirical model of facial biomechanics from a set of displacement records of markers located on the face of a subject producing speech. Markers are grouped into clusters, which have a unique primary marker and a number of secondary markers with an associated weight. Motion of the secondary markers is computed as the weighted sum of the primary markers of the clusters to which they belong. This model may be used to produce facial animations, by driving the primary markers with measured kinematic signals.     

Entanglement interferometry for precision measurement of atomic scattering properties

We report on a matter wave interferometer realized with entangled pairs of trapped 87Rb atoms. Each pair of atoms is confined at a single site of an optical lattice potential. The interferometer is realized by first creating a coherent spin superposition of the two atoms and then tuning the interstate scattering length via a Feshbach resonance. The selective change of the interstate scattering length leads to an entanglement dynamics of the two-particle state that can be detected in a Ramsey interference experiment. This entanglement dynamics is employed for a precision measurement of atomic interaction parameters. Furthermore, the interferometer allows us to separate lattice sites with one or two atoms in a nondestructive way.     

Controlled formation of ag nanoparticles by means of long-chain sodium polyacrylates in dilute solution

A new tool is presented to control formation of Ag nanoparticles. Small amounts of silver ions were added to dilute solutions of long-chain sodium polyacrylates (NaPA). Four NaPA samples covering a molar mass regime of 97 kD < or = Mw < or = 650 kD have been used. With amounts of added Ag(+) as low as 1-2% of the COO(-) groups of the polyanionic chains, significant changes could already be induced in the NaPA coils with 650 kD. If the NaPA concentration was kept below 0.1 g/L, the coils with 650 kD exhibited a significant coil shrinking in stable solutions. At larger NaPA concentrations, addition of Ag+ initiates an aggregation of the polyacrylate coils toward compact structures. Coil shrinking and aggregation was revealed by means of time-resolved static light scattering. If exposed to UV-radiation, small Ag particles formed within the shrunken anionic polyacrylate coils. The Ag nanoparticles were identified by means of an enhanced light scattering and a characteristic plasmon absorption band around 410 nm. No such Ag particle formation could be observed even at 5 times larger concentrations of Ag(+) and NaPA if the two smallest polyacrylate samples have been used under otherwise equal conditions. This molar mass sensitive response of NaPA to Ag(+)-addition suggests an interesting phenomenon: if the coil size of the NaPa chains, which act as Ag(+) collectors, is large enough, local Ag(+) concentration in these coil-shaped Ag(+) containers exceeds a critical value, and irradiation with UV generates Ag nanoparticles.