No Superluminal Signaling Implies Unconditionally Secure Bit Commitment

Bit commitment (BC) is an important cryptographic primitive for an agent to convince a mutually mistrustful party that she has already made a binding choice of 0 or 1 but only to reveal her choice at a later time. Ideally, a BC protocol should be simple, reliable, easy to implement using existing technologies, and most importantly unconditionally secure in the sense that its security is based on an information-theoretic proof rather than computational complexity assumption or the existence of a trustworthy arbitrator. Here we report such a provably secure scheme involving only one-way classical communications whose unconditional security is based on no superluminal signaling (NSS). Our scheme is inspired by the earlier works by Kent, who proposed two impractical relativistic protocols whose unconditional securities are yet to be established as well as several provably unconditionally secure protocols which rely on both quantum mechanics and NSS. Our scheme is conceptually simple and shows for the first time that quantum communication is not needed to achieve unconditional security for BC. Moreover, with purely classical communications, our scheme is practical and easy to implement with existing telecom technologies. This completes the cycle of study of unconditionally secure bit commitment based on known physical laws.Comment: This paper has been withdrawn by the authors due to a crucial oversight on an earlier work by A. Ken

Dynamics of Neural Networks with Continuous Attractors

We investigate the dynamics of continuous attractor neural networks (CANNs). Due to the translational invariance of their neuronal interactions, CANNs can hold a continuous family of stationary states. We systematically explore how their neutral stability facilitates the tracking performance of a CANN, which is believed to have wide applications in brain functions. We develop a perturbative approach that utilizes the dominant movement of the network stationary states in the state space. We quantify the distortions of the bump shape during tracking, and study their effects on the tracking performance. Results are obtained on the maximum speed for a moving stimulus to be trackable, and the reaction time to catch up an abrupt change in stimulus.Comment: 6 pages, 7 figures with 4 caption

Richardson's pair diffusion and the stagnation point structure of turbulence

DNS and laboratory experiments show that the spatial distribution of straining stagnation points in homogeneous isotropic 3D turbulence has a fractal structure with dimension D_s = 2. In Kinematic Simulations the time exponent gamma in Richardson's law and the fractal dimension D_s are related by gamma = 6/D_s. The Richardson constant is found to be an increasing function of the number of straining stagnation points in agreement with pair duffusion occuring in bursts when pairs meet such points in the flow.Comment: 4 pages; Submitted to Phys. Rev. Let

A Moving Bump in a Continuous Manifold: A Comprehensive Study of the Tracking Dynamics of Continuous Attractor Neural Networks

Understanding how the dynamics of a neural network is shaped by the network structure, and consequently how the network structure facilitates the functions implemented by the neural system, is at the core of using mathematical models to elucidate brain functions. This study investigates the tracking dynamics of continuous attractor neural networks (CANNs). Due to the translational invariance of neuronal recurrent interactions, CANNs can hold a continuous family of stationary states. They form a continuous manifold in which the neural system is neutrally stable. We systematically explore how this property facilitates the tracking performance of a CANN, which is believed to have clear correspondence with brain functions. By using the wave functions of the quantum harmonic oscillator as the basis, we demonstrate how the dynamics of a CANN is decomposed into different motion modes, corresponding to distortions in the amplitude, position, width or skewness of the network state. We then develop a perturbative approach that utilizes the dominating movement of the network's stationary states in the state space. This method allows us to approximate the network dynamics up to an arbitrary accuracy depending on the order of perturbation used. We quantify the distortions of a Gaussian bump during tracking, and study their effects on the tracking performance. Results are obtained on the maximum speed for a moving stimulus to be trackable and the reaction time for the network to catch up with an abrupt change in the stimulus.Comment: 43 pages, 10 figure