Going Off the Grid: Iterative Model Selection for Biclustered Matrix Completion

We consider the problem of performing matrix completion with side information on row-by-row and column-by-column similarities. We build upon recent proposals for matrix estimation with smoothness constraints with respect to row and column graphs. We present a novel iterative procedure for directly minimizing an information criterion to select an appropriate amount of row and column smoothing, namely, to perform model selection. We also discuss how to exploit the special structure of the problem to scale up the estimation and model selection procedure via the Hutchinson estimator, combined with a stochastic Quasi-Newton approach. Supplementary material for this article is available online.     

Exploration of Nano-Saturns: A Spectacular Sphere–Ring Supramolecular System

Saturn-like systems consisting of nanoscale rings and spheres are fascinating motifs in supramolecular chemistry. Several ring molecules are known to include spherical molecules at the center of the cavity via noncovalent attractive interactions. In this Minireview, we generalize the molecular design, the structural features, and the supramolecular chemistry of such “nano-Saturns”, which consist of monocyclic rings and fullerene spheres (mainly C₆₀), on the basis of previous experimental and theoretical studies. Ring molecules are classified into three types (loop, belt, and disk) according to their shapes and possible interactions. Whereas typical belt-shaped rings tend to form tight complexes due to the wide contact area via π–π interactions, flat disk-shaped rings generally form weak complexes due to the narrow contact area mainly via CH–π interactions. In spite of the small association energies, disk-shaped rings are attractive because such rings can mimic the planet Saturn precisely as exemplified by an anthracene cyclic hexamer–C₆₀ complex.     

Order-Stability in Complex Biological,Social, and AI-Systems from Quantum Information Theory

This paper is our attempt, on the basis of physical theory, to bring more clarification on the question “What is life?” formulated in the well-known book of Schrödinger in 1944. According to Schrödinger, the main distinguishing feature of a biosystem’s functioning is the ability to preserve its order structure or, in mathematical terms, to prevent increasing of entropy. However, Schrödinger’s analysis shows that the classical theory is not able to adequately describe the order-stability in a biosystem. Schrödinger also appealed to the ambiguous notion of negative entropy. We apply quantum theory. As is well-known, behaviour of the quantum von Neumann entropy crucially differs from behaviour of classical entropy. We consider a complex biosystem S composed of many subsystems, say proteins, cells, or neural networks in the brain, that is, S=(Si). We study the following problem: whether the compound system S can maintain “global order” in the situation of an increase of local disorder and if S can preserve the low entropy while other Si increase their entropies (may be essentially). We show that the entropy of a system as a whole can be constant, while the entropies of its parts rising. For classical systems, this is impossible, because the entropy of S cannot be less than the entropy of its subsystem Si. And if a subsystems’s entropy increases, then a system’s entropy should also increase, by at least the same amount. However, within the quantum information theory, the answer is positive. The significant role is played by the entanglement of a subsystems’ states. In the absence of entanglement, the increasing of local disorder implies an increasing disorder in the compound system S (as in the classical regime). In this note, we proceed within a quantum-like approach to mathematical modeling of information processing by biosystems—respecting the quantum laws need not be based on genuine quantum physical processes in biosystems. Recently, such modeling found numerous applications in molecular biology, genetics, evolution theory, cognition, psychology and decision making. The quantum-like model of order stability can be applied not only in biology, but also in social science and artificial intelligence.     

Mechanosensitive membrane probes: push-pull papillons

ABSTRACT

Design, synthesis and evaluation of push-pull N,N′-diphenyl-dihydrodibenzo[a,c]phenazines are reported. Consistent with theoretical predictions, donors and acceptors attached to the bent mechanophore are shown to shift absorption maxima to either red or blue, depending on their positioning in the chromophore. Redshifted excitation of push-pull fluorophores is reflected in redshifted emission of both bent and planar excited states. The intensity ratios of the dual emission in more and less polar solvents imply that excited-state (ES) planarization decelerates with increasing fluorophore macrodipole, presumably due to attraction between the wings of closed papillons. ES planarization of highly polarisable papillons is not observed in lipid bilayer membranes. All push-pull papillon amphiphiles excel with aggregation-induced emission (AIE) from bent ES as micelles in water and mechanosensitivity in viscous solvents. They are not solvatochromic and only weakly fluorescent (QY < 4%).     

How Does Solvation Affect the Binding of Hydrophilic Amino Saccharides to Cucurbit[7]uril with Exceptional Anomeric Selectivity?

Cucurbit[7]uril (CB[7]) is known to bind strongly to hydrophilic amino saccharide guests with exceptional α‐anomer selectivities under aqueous conditions. Single‐crystal X‐ray crystallography and computational methods were used to elucidate the reason behind this interesting phenomenon. The crystal structures of protonated galactosamine (GalN) and glucosamine (GluN) complexes confirm the inclusion of α anomers inside CB[7] and disclose the details of the host–guest binding. Whereas computed gas‐phase structures agree with these crystal structures, gas‐phase binding free energies show preferences for the β‐anomer complexes over their α counterparts, in striking contrast to the experimental results under aqueous conditions. However, when the solvation effect is considered, the binding structures drastically change and the preference for the α anomers is recovered. The α anomers also tend to bind more tightly and leave less space in the CB[7] cavity toward inclusion of only one water molecule, whereas loosely bound β anomers leave more space toward accommodating two water molecules, with markedly different hydrogen‐bonding natures. Surprisingly, entropy seems to contribute significantly to both anomeric discrimination and binding. This suggests that of all the driving factors for the strong complexation of the hydrophilic amino saccharide guests, water mediation plays a crucial role in the anomer discrimination.