Versatile Near-Infrared Super-Resolution Imaging of Amyloid Fibrils with the Fluorogenic Probe CRANAD-2

CRANAD-2 is a fluorogenic curcumin derivative used for near-infrared detection and imaging in vivo of amyloid aggregates, which are involved in neurodegenerative diseases. We explore the performance of CRANAD-2 in two super-resolution imaging techniques, namely stimulated emission depletion (STED) and single-molecule localization microscopy (SMLM), with markedly different fluorophore requirements. By conveniently adapting the concentration of CRANAD-2, which transiently binds to amyloid fibrils, we show that it performs well in both techniques, achieving a resolution in the range of 45–55 nm. Correlation of SMLM with atomic force microscopy (AFM) validates the resolution of fine features in the reconstructed super-resolved image. The good performance and versatility of CRANAD-2 provides a powerful tool for near-infrared nanoscopic imaging of amyloids in vitro and in vivo.     

Wave turbulence and intermittency in directional wave fields

The evolution of surface gravity waves is driven by nonlinear interactions that trigger an energy cascade similarly to the one observed in hydrodynamic turbulence. This process, known as wave turbulence, has been found to display anomalous scaling with deviation from classical turbulent predictions due to the emergence of coherent and intermittent structures on the water surface. In the ocean, waves are spread over a wide range of directions, with a consequent attenuation of the nonlinear properties. A laboratory experiment in a large wave facility is presented to discuss the sensitivity of wave turbulence on the directional properties of model wave spectra. Results show that the occurrence of coherent and intermittent structures become less likely with the broadening of the wave directional spreading. There is no evidence, however, that intermittency completely vanishes.     

An investigation on the defect structures and spin Hamiltonian parameters for the two orthorhombic Ti3+ centers in ZnWO4

By employing the perturbation formulae of the spin Hamiltonian parameters (SHPs) (g factors g_xx, g_yy, g_zz, hyperfine structure constants A_xx, A_yy, A_zz and superhyperfine parameters A_xx׳, A_yy׳, A_zz׳) for a 3d¹ ion in orthorhombically elongated octahedra and tetrahedra, the defect structures and the experimental EPR spectra are theoretically and systematically investigated for the two orthorhombic Ti³⁺ centers C₁ and C₂ in ZnWO₄. Center C₁ is ascribed to the impurity Ti³⁺ at host W⁶⁺ site associated with two nearest neighbor oxygen vacancies due to charge compensation. The resultant tetrahedral [TiO₄]^5– cluster is determined to undergo the local orthorhombic elongation distortion, characterized by the axial distortion angle Δθ (=θ–θ₀≈–6.84°) of the local impurity-ligand bond angle θ related to θ₀ (≈54.74°) and the perpendicular distortion angle Δε (=ε–ε₀≈2.5°) related to ε₀ (≈45°) of an ideal tetrahedron because of the Jahn–Teller effect. Center C₂ is attributed to Ti³⁺ on Zn²⁺ site, and this octahedral [TiO₆]^9– cluster may experience the local axial elongation ΔZ (≈0.001 Ǻ) and the planar bond angle variation Δφ (≈9.1°) due to the Jahn–Teller effect, resulting in a more regular oxygen octahedron. All the calculated SHPs (i.e., g factors for both centers, the hyperfine structure constants for center C₂ and superhyperfine parameters of next nearest neighbor ligand W for center C₁) show good agreement with the observed values. However, the theoretical results based on the previous assignment of center C₁ as Ti³⁺ on W⁶⁺ site with only one nearest planar oxygen vacancy (i.e., five-fold coordinated octahedral [TiO₅]^7– cluster) show much worse agreement with the experimental data. The defect structures and the SHPs (especially the g anisotropies) are discussed for both centers. The present studies on the superhyperfine parameters of ligand W⁶⁺ for center C₁ would be helpful to further investigations on the superhyperfine interactions of cation ligands which were rather scarcely treated before.     

Generalized Jacobi spectral Galerkin method for fractional pantograph differential equation

This work is concerned with the extension of the Jacobi spectral Galerkin method to a class of nonlinear fractional pantograph differential equations. First, the fractional differential equation is converted to a nonlinear Volterra integral equation with weakly singular kernel. Second, we analyze the existence and uniqueness of solutions for the obtained integral equation. Then, the Galerkin method is used for solving the equivalent integral equation. The error estimates for the proposed method are also investigated. Finally, illustrative examples are presented to confirm our theoretical analysis.     

Estimation of multivariate binary density using orthogonal functions

In this paper, the authors studied certain properties of the estimate of Liang and Krishnaiah (1985, J. Multivariate Anal. 16, 162–172) for multivariate binary density. An alternative shrinkage estimate is also obtained. The above results are generalized to general orthonormal systems.     

CONCEPTUAL DESIGN STUDIES OF AN 84 GHz, 500 kW, CW GYROTRON

The feasibility of an 84 GHz, 500 kW, CW gyrotron for ECRH on an experimental tokamak will be presented in this paper. Mode competition and mode selection procedures are carefully investigated by considering various candidate modes and the TE_10,4 mode is chosen as the operating mode. A conventional cylindrical cavity resonator with weak input and output tapers and parabolic roundings is considered for interaction studies. Self-consistent, both single mode and time-dependent, calculations are carried out and power and efficiencies are computed for a typical set of beam parameters. The results show that an output power of well over 500 kW, CW and efficiency around 40% can be reached without a depressed collector.     

Approximation of bandlimited functions

Many signals encountered in science and engineering are approximated well by bandlimited functions. We provide suitable error bounds for the approximation of bandlimited functions by linear combinations of certain special functions—the prolate spheroidal wave functions of order 0. The coefficients in the approximating linear combinations are given explicitly via appropriate quadrature formulae.     

Well-Posedness by Perturbations of Variational Problems

In this paper, we consider the extension of the notion of well-posedness by perturbations, introduced by Zolezzi for optimization problems, to other related variational problems like inclusion problems and fixed-point problems. Then, we study the conditions under which there is equivalence of the well-posedness in the above sense between different problems. Relations with the so-called diagonal well-posedness are also given. Finally, an application to staircase iteration methods is presented.     

Bilateral generating functions and operational methods

Bilateral generating functions are those involving products of different types of polynomials. We show that operational methods offer a powerful tool to derive these families of generating functions. We study cases relevant to products of Hermite polynomials with Laguerre, Legendre and other polynomials. We also propose further extensions of the method which we develop here.