Energy efficiency is closely related to the evolution of biological systems and is important to their information processing. In this paper, we calculated the excitation probability of a simple model of a bistable biological unit in response to pulsatile inputs, and its spontaneous excitation rate due to noise perturbation. Then we analytically calculated the mutual information, energy cost, and energy efficiency of an array of these bistable units. We found that the optimal number of units could maximize this arrays energy efficiency in encoding pulse inputs, which depends on the fixed energy cost. We conclude that demand for energy efficiency in biological systems may strongly influence the size of these systems under the pressure of natural selection.
We have carried out tilt magnetic field (B) studies of the u=12/5 fractional quantum Hall state in an ultra-high quality GaAs quantum well specimen. Its diagonal magneto-resistance Rxx shows a non-monotonic dependence on tilt angle (theta). It first increases sharply with increasing theta, reaches a maximal value of ~ 70 ohms at theta ~ 14^o, and then decreases at higher tilt angles. Correlated with this dependence of Rxx on theta, the 12/5 activation energy (Delta_{12/5}) also shows a non-monotonic tilt dependence. Delta_{12/5} first decreases with increasing theta. Around theta = 14^{o}, Delta_{12/5} disappears as Rxx becomes non-activated. With further increasing tilt angles, Delta_{12/5} reemerges and increases with theta. This tilt B dependence at u=12/5 is strikingly different from that of the well-documented 5/2 state and calls for more investigations on the nature of its ground state.
Using a 50-nm width, ultra-clean GaAs/AlGaAs quantum well, we have studied the Landau level filling factor $ u = 5/2$ fractional quantum Hall effect in a perpendicular magnetic field $B sim$ 1.7 T and determined its dependence on tilted magnetic fields. Contrary to all previous results, the 5/2 resistance minimum and the Hall plateau are found to strengthen continuously under an increasing tilt angle $0 < theta < 25^circ$ (corresponding to an in-plane magnetic field 0 $<$ $B_parallel$ $< 0.8$ T). In the same range of $theta$ the activation gaps of both the 7/3 and the 8/3 states are found to increase with tilt. The 5/2 state transforms into a compressible Fermi liquid upon tilt angle $theta > 60^circ$, and the composite fermion series [2+$p/(2ppm1)$], $p =$ 1, 2 can be identified. Based on our results, we discuss the relevance of a Skyrmion spin texture at $ u = 5/2$ associated with small Zeeman energy in wide quantum wells, as proposed by W$acute{text o}$js $et$ $al$., Phys. Rev. Lett. 104, 086801 (2010).
