Some Further Evidence about Magnification and Shape in Neural Gas

Neural gas (NG) is a robust vector quantization algorithm with a well-known mathematical model. According to this, the neural gas samples the underlying data distribution following a power law with a magnification exponent that depends on data dimensionality only. The effects of shape in the input data distribution, however, are not entirely covered by the NG model above, due to the technical difficulties involved. The experimental work described here shows that shape is indeed relevant in determining the overall NG behavior; in particular, some experiments reveal richer and complex behaviors induced by shape that cannot be explained by the power law alone. Although a more comprehensive analytical model remains to be defined, the evidence collected in these experiments suggests that the NG algorithm has an interesting potential for detecting complex shapes in noisy datasets

Different flavors of diffusion in paramagnetic systems: unexpected NMR signal intensity and relaxation enhancements

Abstract The NMR community is well acquainted with different kinds of diffusion but, at the same time, there are several effects that are worth a better understanding for an improved design of molecular imaging and dynamic nuclear polarization experiments. Spin diffusion and chemical diffusion are known to play important roles in determining the NMR signal and relaxation enhancements caused by the presence of paramagnetic molecules in solution. Paramagnetic complexes are used as contrast agents in magnetic resonance imaging, due to their efficacy in selectively increase the relaxation rates of solvent water protons, as well as in dynamic nuclear polarization experiments to increase the NMR signal of desired molecules through polarization transfer from unpaired electrons. In this paper we review some recent, unexpected observations in these two areas, which seem related to spin and/or chemical diffusion, and demonstrate the need for a detailed understanding of the interplay of different phenomena. A deeper understanding of spin and chemical diffusion may thus result very important for an improved design of contrast agents for magnetic resonance imaging and for the optimization of hyperpolarization experiments

Solution of a Puzzle: High-Level Quantum-Chemical Treatment of Pseudocontact Chemical Shifts Confirms Classic Semiempirical Theory

A recently popularized approach for the calculation of pseudocontact shifts (PCSs) based on first-principles quantum chemistry (QC) leads to different results than the classic “semiempirical” equation involving the susceptibility tensor. Studies that attempted a comparison of theory and experiment led to conflicting conclusions with respect to the preferred theoretical approach. In this Letter, we show that after inclusion of previously neglected terms in the full Hamiltonian, one can deduce the semiempirical equations from a rigorous QC-based treatment. It also turns out that in the long-distance limit, one can approximate the complete A tensor in terms of the g tensor. By means of Kohn–Sham density functional theory calculations, we numerically confirm the long-distance expression for the A tensor and the theoretically predicted scaling behavior of the different terms. Our derivation suggests a computational strategy in which one calculates the susceptibility tensor and inserts it into the classic equation for the PCS

Theoretical analysis of the long-distance limit of NMR chemical shieldings

After some years of controversy, it was recently demonstrated how to obtain the correct long-distance limit [point-dipole approximation (PDA)] of pseudo-contact nuclear magnetic resonance chemical shifts from rigorous first-principles quantum mechanics [Lang et al., J. Phys. Chem. Lett. 11, 8735 (2020)]. This result confirmed the classical Kurland–McGarvey theory. In the present contribution, we elaborate on these results. In particular, we provide a detailed derivation of the PDA both from the Van den Heuvel–Soncini equation for the chemical shielding tensor and from a spin Hamiltonian approximation. Furthermore, we discuss in detail the PDA within the approximate density functional theory and Hartree–Fock theories. In our previous work, we assumed a relatively crude effective nuclear charge approximation for the spin–orbit coupling operator. Here, we overcome this assumption by demonstrating that the derivation is also possible within the fully relativistic Dirac equation and even without the assumption of a specific form for the Hamiltonian. Crucial ingredients for the general derivation are a Hamiltonian that respects gauge invariance, the multipolar gauge, and functional derivatives of the Hamiltonian, where it is possible to identify the first functional derivative with the electron number current density operator. The present work forms an important foundation for future extensions of the Kurland–McGarvey theory beyond the PDA, including induced magnetic quadrupole and higher moments to describe the magnetic hyperfine field

1H NMR Relaxometric Study of Chitosan-Based Nanogels Containing Mono- and Bis-Hydrated Gd(III) Chelates: Clues for MRI Probes of Improved Sensitivity

Hydrogel nanoparticles composed of chitosan and hyaluronate and incorporating Gd-based MRI contrast agents with different hydration number (e.g., [Gd(DOTA)(H2O)]− and [Gd(AAZTA)(H2O)2]−) were prepa..

Revisiting paramagnetic relaxation enhancements in slowly rotating systems: how long is the long range?

Cross-relaxation terms in paramagnetic systems that reorient rigidly with slow tumbling times can increase the effective longitudinal relaxation rates of protons of more than 1 order of magnitude. This is evaluated by simulating the time evolution of the nuclear magnetization using a complete relaxation rate-matrix approach. The calculations show that the Solomon dependence of the paramagnetic relaxation rates on the metal–proton distance (as r−6) can be incorrect for protons farther than 15 Å from the metal and thus can cause sizable errors in R1-derived distance restraints used, for instance, for protein structure determination. Furthermore, the chemical exchange of these protons with bulk water protons can enhance the relaxation rate of the solvent protons by far more than expected from the paramagnetic Solomon equation. Therefore, it may contribute significantly to the water proton relaxation rates measured at magnetic resonance imaging (MRI) magnetic fields in the presence of slow-rotating nanoparticles containing paramagnetic ions and a large number of exchangeable surface protons