Topological phonon modes in filamentous structures

Topological phonon modes are robust vibrations localized at the edges of special structures. Their existence is determined by the bulk properties of the structures and, as such, the topological phonon modes are stable to changes occurring at the edges. The first class of topological phonons was recently found in 2-dimensional structures similar to that of Microtubules. The present work introduces another class of topological phonons, this time occurring in quasi one-dimensional filamentous structures with inversion symmetry. The phenomenon is exemplified using a structure inspired from that of actin Microfilaments, present in most live cells. The system discussed here is probably the simplest structure that supports topological phonon modes, a fact that allows detailed analysis in both time and frequency domains. We advance the hypothesis that the topological phonon modes are ubiquitous in the biological world and that living organisms make use of them during various processes.Comment: accepted for publication (Phys. Rev. E

Dimension-Free Empirical Entropy Estimation

We seek an entropy estimator for discrete distributions with fully empirical accuracy bounds. As stated, this goal is infeasible without some prior assumptions on the distribution. We discover that a certain information moment assumption renders the problem feasible. We argue that the moment assumption is natural and, in some sense, {\em minimalistic} -- weaker than finite support or tail decay conditions. Under the moment assumption, we provide the first finite-sample entropy estimates for infinite alphabets, nearly recovering the known minimax rates. Moreover, we demonstrate that our empirical bounds are significantly sharper than the state-of-the-art bounds, for various natural distributions and non-trivial sample regimes. Along the way, we give a dimension-free analogue of the Cover-Thomas result on entropy continuity (with respect to total variation distance) for finite alphabets, which may be of independent interest. Additionally, we resolve all of the open problems posed by J\"urgensen and Matthews, 2010

Inducing isotropic growth in multidimensional cesium lead halide perovskite nanocrystals

A new two‐step synthetic protocol to yield monodisperse spherical zero‐dimensional (0D) Cs4PbX6 nanocrystals (NCs) and three‐dimensional (3D) CsPbX3 NCs is described. The first step of the reaction involves the colloidal synthesis of spherical PbX2 seed NCs, which are subsequently converted to Cs4PbX6 and CsPbX3 NCs through hot injection of a Cs precursor at the desired reaction temperatures. By employing less reactive Pb and halide precursors, the reaction time was extended from several seconds to about five minutes, thereby allowing greater control during the crystallization and growth stages. The adjustment of halide ratios allows color tuning over a wide spectral range (411–669 nm) for CsPbX3 NCs, with high photoluminescence quantum yields (6–65 %) and narrow emission line widths (ca. 13–30 nm). We envisage our spherical NCs to become a starting point for shell growth (e.g., ZnS, CdS, PbS) by overcoming the difficulty of shell growth around thermodynamically unfavorable (i.e., high surface free energy) cuboid‐shaped NCs.NRF (Natl Research Foundation, S’pore)MOE (Min. of Education, S’pore