A Discussion of Probability Functions and Constraints from a Variational Perspective

Set-Valued and Variational Analysis - Probability constraints are a popular modelling mechanism in applications. They help to model feasible decisions when the latter are taken prior to observing...     

Hydrodynamic Limit of the Symmetric Exclusion Process on a Compact Riemannian Manifold

Journal of Statistical Physics - We consider the symmetric exclusion process on suitable random grids that approximate a compact Riemannian manifold. We prove that a class of random walks on these...     

Spectral estimates for saddle point matrices arising in weak constraint four‐dimensional variational data assimilation

We consider the large sparse symmetric linear systems of equations that arise in the solution of weak constraint four‐dimensional variational data assimilation, a method of high interest for numerical weather prediction. These systems can be written as saddle point systems with a 3 × 3 block structure but block eliminations can be performed to reduce them to saddle point systems with a 2 × 2 block structure, or further to symmetric positive definite systems. In this article, we analyse how sensitive the spectra of these matrices are to the number of observations of the underlying dynamical system. We also obtain bounds on the eigenvalues of the matrices. Numerical experiments are used to confirm the theoretical analysis and bounds.     

Supramolecular Recognition Influences Magnetism in [X@HVIV8VV14O54]6− Self‐Assemblies with Symmetry‐Breaking Guest Anions

Mixed‐valence polyoxovanadates(IV/V) have emerged as one of the most intricate class of supramolecular all‐inorganic host species, able to encapsulate a wide variety of smaller guest templates during their self‐assembly formation process. As showcased herein, the incorporation of guests, though governed solely by ultra‐weak electrostatic and van der Waals interactions, can cause drastic effects on the electronic and magnetic characteristics of the shell complex of the polyoxovanadate. We address the question of methodology for the magnetochemical analysis of virtually isostructural {V^IV/V₂₂O₅₄}‐type polyoxoanions of D_2d symmetry enclosing diamagnetic VO₂F₂^? (C_2v), SCN^? (C_∞v), or ClO₄^? (T_d) template anions. These induce different polarization effects related to differences in their geometric structures, symmetry, ion radii, and valence shells, eventually resulting in a supramolecular modulation of magnetic exchange between the V(3d) electrons that are partly delocalized over the {V₂₂O₅₄} shells. We also include the synthesis and characterization of the novel [V^VO₂F₂@HV^IV₈V^V₁₄O₅₄]^6? system that comprises the rarely encountered discrete difluorovanadate anion as a quasi‐isolated guest species.     

Properties and applications of precision oligomer materials; where organic and polymer chemistry join forces

Precise oligomeric materials constitute a growing area of research with implications for various applications as well as fundamental studies. Notably, this field of science which can be termed macro-organic chemistry, draws inspiration from both traditional polymer chemistry and organic synthesis, combining the molecular precision of organic chemistry with the materials properties of macromolecules. Discrete oligomers enable access to unprecedented materials properties, for example, in self-assembled structures, crystallization, or optical properties. The degree of control over oligomer structures resembles many biological systems and enables the design of materials with tailored properties and the development of fundamental structure–property relationships. This Review highlights recent developments in macro-organic chemistry from synthetic concepts to materials properties, with a focus on self-assembly and molecular recognition. Finally, an outlook for future research directions is provided.     

The Plasticity of the Carbohydrate Recognition Domain Dictates the Exquisite Mechanism of Binding of Human Macrophage Galactose-Type Lectin

The human macrophage galactose-type lectin (MGL), expressed on macrophages and dendritic cells (DCs), modulates distinct immune cell responses by recognizing N-acetylgalactosamine (GalNAc) containing structures present on pathogens, self-glycoproteins, and tumor cells. Herein, NMR spectroscopy and molecular dynamics (MD) simulations were used to investigate the structural preferences of MGL against different GalNAc-containing structures derived from the blood group A antigen, the Forssman antigen, and the GM2 glycolipid. NMR spectroscopic analysis of the MGL carbohydrate recognition domain (MGL-CRD, C181-H316) in the absence and presence of methyl α-GalNAc (α-MeGalNAc), a simple monosaccharide, shows that the MGL-CRD is highly dynamic and its structure is strongly altered upon ligand binding. This plasticity of the MGL-CRD structure explains the ability of MGL to accommodate different GalNAc-containing molecules. However, key differences are observed in the recognition process depending on whether the GalNAc is part of the blood group A antigen, the Forssman antigen, or GM2-derived structures. These results are in accordance with molecular dynamics simulations that suggest the existence of a distinct MGL binding mechanism depending on the context of GalNAc moiety presentation. These results afford new perspectives for the rational design of GalNAc modifications that fine tune MGL immune responses in distinct biological contexts, especially in malignancy.