On the finiteness of the classifying space for the family of virtually cyclic subgroups

Given a group G, we consider its classifying space for the family of virtually cyclic subgroups. We show for many groups, including for example, one-relator groups, acylindrically hyperbolic groups, 3-manifold groups and CAT(0) cube groups, that they do not admit a finite model for this classifying space unless they are virtually cyclic. This settles a conjecture due to Juan-Pineda and Leary for these classes of groups

Bioinspired Multifunctional Anti-icing Hydrogel

The recent anti-icing strategies in the state of the art mainly focused on three aspects: inhibiting ice nucleation, preventing ice propagation, and decreasing ice adhesion strength. However, it is has proved difficult to prevent ice nucleation and propagation while decreasing adhesion simultaneously, due to their highly distinct, even contradictory design principles. In nature, anti-freeze proteins (AFPs) offer a prime example of multifunctional integrated anti-icing materials that excel in all three key aspects of the anti-icing process simultaneously by tuning the structures and dynamics of interfacial water. Here, inspired by biological AFPs, we successfully created a multifunctional anti-icing material based on polydimethylsiloxane-grafted polyelectrolyte hydrogel that can tackle all three aspects of the anti-icing process simultaneously. The simplicity, mechanical durability, and versatility of these smooth hydrogel surfaces make it a promising option for a wide range of anti-icing applications

Asymptotic Behavior of Error Exponents in the Wideband Regime

In this paper, we complement Verd\'{u}'s work on spectral efficiency in the wideband regime by investigating the fundamental tradeoff between rate and bandwidth when a constraint is imposed on the error exponent. Specifically, we consider both AWGN and Rayleigh-fading channels. For the AWGN channel model, the optimal values of $R_z(0)$ and $\dot{R_z}(0)$ are calculated, where $R_z(1/B)$ is the maximum rate at which information can be transmitted over a channel with bandwidth $B/2$ when the error-exponent is constrained to be greater than or equal to $z.$ Based on this calculation, we say that a sequence of input distributions is near optimal if both $R_z(0)$ and $\dot{R_z}(0)$ are achieved. We show that QPSK, a widely-used signaling scheme, is near-optimal within a large class of input distributions for the AWGN channel. Similar results are also established for a fading channel where full CSI is available at the receiver.Comment: 59 pages, 6 figure