Is the Riemann zeta function in a short interval a 1-RSB spin glass ?

Fyodorov, Hiary & Keating established an intriguing connection between the maxima of log-correlated processes and the ones of the Riemann zeta function on a short interval of the critical line. In particular, they suggest that the analogue of the free energy of the Riemann zeta function is identical to the one of the Random Energy Model in spin glasses. In this paper, the connection between spin glasses and the Riemann zeta function is explored further. We study a random model of the Riemann zeta function and show that its two-overlap distribution corresponds to the one of a one-step replica symmetry breaking (1-RSB) spin glass. This provides evidence that the local maxima of the zeta function are strongly clustered.Comment: 20 pages, 1 figure, Minor corrections, References update

Geometrical Insights for Implicit Generative Modeling

Learning algorithms for implicit generative models can optimize a variety of criteria that measure how the data distribution differs from the implicit model distribution, including the Wasserstein distance, the Energy distance, and the Maximum Mean Discrepancy criterion. A careful look at the geometries induced by these distances on the space of probability measures reveals interesting differences. In particular, we can establish surprising approximate global convergence guarantees for the $1$-Wasserstein distance,even when the parametric generator has a nonconvex parametrization.Comment: this version fixes a typo in a definitio

Molecular dynamics simulations suggest that RNA three-way junctions can act as flexible RNA structural elements in the ribosome

We present extensive explicit solvent molecular dynamics analysis of three RNA three-way junctions (3WJs) from the large ribosomal subunit: the 3WJ formed by Helices 90–92 (H90–H92) of 23S rRNA; the 3WJ formed by H42–H44 organizing the GTPase associated center (GAC) of 23S rRNA; and the 3WJ of 5S rRNA. H92 near the peptidyl transferase center binds the 3′-CCA end of amino-acylated tRNA. The GAC binds protein factors and stimulates GTP hydrolysis driving protein synthesis. The 5S rRNA binds the central protuberance and A-site finger (ASF) involved in bridges with the 30S subunit. The simulations reveal that all three 3WJs possess significant anisotropic hinge-like flexibility between their stacked stems and dynamics within the compact regions of their adjacent stems. The A-site 3WJ dynamics may facilitate accommodation of tRNA, while the 5S 3WJ flexibility appears to be essential for coordinated movements of ASF and 5S rRNA. The GAC 3WJ may support large-scale dynamics of the L7/L12-stalk region. The simulations reveal that H42–H44 rRNA segments are not fully relaxed and in the X-ray structures they are bent towards the large subunit. The bending may be related to L10 binding and is distributed between the 3WJ and the H42–H97 contact

Geodesics and the competition interface for the corner growth model

We study the directed last-passage percolation model on the planar square lattice with nearest-neighbor steps and general i.i.d. weights on the vertices, out- side of the class of exactly solvable models. Stationary cocycles are constructed for this percolation model from queueing fixed points. These cocycles serve as bound- ary conditions for stationary last-passage percolation, solve variational formulas that characterize limit shapes, and yield existence of Busemann functions in directions where the shape has some regularity. In a sequel to this paper the cocycles are used to prove results about semi-infinite geodesics and the competition interface

Infrared Multiple Photon Dissociation Action Spectroscopy and Theoretical Studies of Diethyl Phosphate Complexes: Effects of Protonation and Sodium Cationization on Structure

The gas-phase structures of deprotonated, protonated, and sodium-cationized complexes of diethyl phosphate (DEP) including [DEP − H]−, [DEP + H]+, [DEP + Na]+, and [DEP − H + 2Na]+ are examined via infrared multiple photon dissociation (IRMPD) action spectroscopy using tunable IR radiation generated by a free electron laser, a Fourier transform ion cyclotron resonance mass spectrometer (FT-ICR MS) with an electrospray ionization (ESI) source, and theoretical electronic structure calculations. Measured IRMPD spectra are compared to linear IR spectra calculated at the B3LYP/6-31G(d,p) level of theory to identify the structures accessed in the experimental studies. For comparison, theoretical studies of neutral complexes are also performed. These experiments and calculations suggest that specific geometric changes occur upon the binding of protons and/or sodium cations, including changes correlating to nucleic acid backbone geometry, specifically P–O bond lengths and ∠OPO bond angles. Information from these observations may be used to gain insight into the structures of more complex systems, such as nucleotides and solvated nucleic acids

RNA Structural Dynamics As Captured by Molecular Simulations: A Comprehensive Overview

With both catalytic and genetic functions, ribonucleic acid (RNA) is perhaps the most pluripotent chemical species in molecular biology, and its functions are intimately linked to its structure and dynamics. Computer simulations, and in particular atomistic molecular dynamics (MD), allow structural dynamics of biomolecular systems to be investigated with unprecedented temporal and spatial resolution. We here provide a comprehensive overview of the fast-developing field of MD simulations of RNA molecules. We begin with an in-depth, evaluatory coverage of the most fundamental methodological challenges that set the basis for the future development of the field, in particular, the current developments and inherent physical limitations of the atomistic force fields and the recent advances in a broad spectrum of enhanced sampling methods. We also survey the closely related field of coarse-grained modeling of RNA systems. After dealing with the methodological aspects, we provide an exhaustive overview of the available RNA simulation literature, ranging from studies of the smallest RNA oligonucleotides to investigations of the entire ribosome. Our review encompasses tetranucleotides, tetraloops, a number of small RNA motifs, A-helix RNA, kissing-loop complexes, the TAR RNA element, the decoding center and other important regions of the ribosome, as well as assorted others systems. Extended sections are devoted to RNA-ion interactions, ribozymes, riboswitches, and protein/RNA complexes. Our overview is written for as broad of an audience as possible, aiming to provide a much-needed interdisciplinary bridge between computation and experiment, together with a perspective on the future of the field

Thienoisoindigo-Based Semiconductor Nanowires Assembled with 2-Bromobenzaldehyde via Both Halogen and Chalcogen Bonding

We fabricated nanowires of a conjugated oligomer and applied them to organic field-effect transistors (OFETs). The supramolecular assemblies of a thienoisoindigo-based small molecular organic semiconductor (TIIG-Bz) were prepared by co-precipitation with 2-bromobenzaldehyde (2-BBA) via a combination of halogen bonding (XB) between the bromide in 2-BBA and electron-donor groups in TIIG-Bz, and chalcogen bonding (CB) between the aldehyde in 2-BBA and sulfur in TIIG-Bz. It was found that 2-BBA could be incorporated into the conjugated planes of TIIG-Bz via XB and CB pairs, thereby increasing the pi - pi stacking area between the conjugated planes. As a result, the driving force for one-dimensional growth of the supramolecular assemblies via pi - pi stacking was significantly enhanced. TIIG-Bz/2-BBA nanowires were used to fabricate OFETs, showing significantly enhanced charge transfer mobility compared to OFETs based on pure TIIG-Bz thin films and nanowires, which demonstrates the benefit of nanowire fabrication using 2-BB

Stationary cocycles and Busemann functions for the corner growth model

We study the directed last-passage percolation model on the planar square lattice with nearest-neighbor steps and general i.i.d. weights on the vertices, out- side of the class of exactly solvable models. Stationary cocycles are constructed for this percolation model from queueing fixed points. These cocycles serve as bound- ary conditions for stationary last-passage percolation, solve variational formulas that characterize limit shapes, and yield existence of Busemann functions in directions where the shape has some regularity. In a sequel to this paper the cocycles are used to prove results about semi-infinite geodesics and the competition interface

Adsorption at cell surface and cellular uptake of silica nanoparticles with different surface chemical functionalizations: impact on cytotoxicity

International audienceSilica nanoparticles are particularly interesting for medical applications because of the high inertness and chemical stability of silica material. However, at the nanoscale their innocuousness must be carefully verified before clinical use. The aim of this study was to investigate the in vitro biological toxicity of silica nanoparticles depending on their surface chemical functionalization. To that purpose, three kinds of 50 nm fluorescent silica-based nanoparticles were synthesized: 1) sterically stabilized silica nanoparticles coated with neutral polyethylene glycol (PEG) molecules, 2) positively charged silica nanoparticles coated with amine groups and 3) negatively charged silica nanoparticles coated with carboxylic acid groups. RAW 264.7 murine macrophages were incubated for 20 hours with each kind of nanoparticles. Their cellular uptake and adsorption at the cell membrane were assessed by a fluorimetric assay and cellular responses were evaluated in terms of cytotoxicity, pro-inflammatory factor production and oxidative stress. Results showed that the highly positive charged nanoparticle, were the most adsorbed at cell surface and triggered more cytotoxicity than other nanoparticles types. To conclude, this study clearly demonstrated that silica nanoparticles surface functionalization represents a key parameter in their cellular uptake and biological toxicity