Strain-induced alignment in collagen gels

Collagen is the most abundant extracellular-network-forming protein in animal biology and is important in both natural and artificial tissues, where it serves as a material of great mechanical versatility. This versatility arises from its almost unique ability to remodel under applied loads into anisotropic and inhomogeneous structures. To explore the origins of this property, we develop a set of analysis tools and a novel experimental setup that probes the mechanical response of fibrous networks in a geometry that mimics a typical deformation profile imposed by cells in vivo. We observe strong fiber alignment and densification as a function of applied strain for both uncrosslinked and crosslinked collagenous networks. This alignment is found to be irreversibly imprinted in uncrosslinked collagen networks, suggesting a simple mechanism for tissue organization at the microscale. However, crosslinked networks display similar fiber alignment and the same geometrical properties as uncrosslinked gels, but with full reversibility. Plasticity is therefore not required to align fibers. On the contrary, our data show that this effect is part of the fundamental non-linear properties of fibrous biological networks.Comment: 12 pages, 7 figures. 1 supporting material PDF with 2 figure

A generalized few-state model for the first hyperpolarizability

The properties of molecules depend on their chemical structure, and thus, structure–property relations help design molecules with desired properties. Few-state models are often used to interpret experimental observations of non-linear optical properties. Not only the magnitude but also the relative orientation of the transition dipole moment vectors is needed for few-state models of the non-linear optical properties. The effect of the relative orientation of the transition dipole moment vectors is called dipole alignment, and this effect has previously been studied for multiphoton absorption properties. However, so far, no such studies are reported for the first hyperpolarizability. Here, we present a generalized few-state model for the static and dynamic first hyperpolarizability β, accounting for the effect of dipole alignment. The formulas derived in this work are general in the sense that they can be used for any few-state model, i.e., a two-state model, a three-state model, or, in general, an n-state model. Based on the formulas, we formulate minimization and maximization criteria for the alignment of transition dipole moment vectors. We demonstrate the importance of dipole alignment by applying the formulas to the static first hyperpolarizability of ortho-, meta-, and para-nitroaniline. The formulas and the analysis provide new ways to understand the structure–property relationship for β and can hence be used to fine-tune the magnitude of β in a molecule

Efficient Beam Alignment in Millimeter Wave Systems Using Contextual Bandits

In this paper, we investigate the problem of beam alignment in millimeter wave (mmWave) systems, and design an optimal algorithm to reduce the overhead. Specifically, due to directional communications, the transmitter and receiver beams need to be aligned, which incurs high delay overhead since without a priori knowledge of the transmitter/receiver location, the search space spans the entire angular domain. This is further exacerbated under dynamic conditions (e.g., moving vehicles) where the access to the base station (access point) is highly dynamic with intermittent on-off periods, requiring more frequent beam alignment and signal training. To mitigate this issue, we consider an online stochastic optimization formulation where the goal is to maximize the directivity gain (i.e., received energy) of the beam alignment policy within a time period. We exploit the inherent correlation and unimodality properties of the model, and demonstrate that contextual information improves the performance. To this end, we propose an equivalent structured Multi-Armed Bandit model to optimally exploit the exploration-exploitation tradeoff. In contrast to the classical MAB models, the contextual information makes the lower bound on regret (i.e., performance loss compared with an oracle policy) independent of the number of beams. This is a crucial property since the number of all combinations of beam patterns can be large in transceiver antenna arrays, especially in massive MIMO systems. We further provide an asymptotically optimal beam alignment algorithm, and investigate its performance via simulations.Comment: To Appear in IEEE INFOCOM 2018. arXiv admin note: text overlap with arXiv:1611.05724 by other author

Separable boundaries for non-hyperbolic groups

We exhibit examples of separable boundaries for non-hyperbolic groups. The main ingredient is the alignment property introduced by Furman in the study of rigidity properties of discrete subgroups of algebraic groups.Comment: 6 pages. The proof of Lemma 2.2 has been fixed; other minor change