8,109 research outputs found
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unconditionally secure bit commitment based on known physical laws.Comment: This paper has been withdrawn by the authors due to a crucial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
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