In statistical physics, Boltzmann-Shannon entropy provides good understanding for the equilibrium states of a number of phenomena. In statistics, the entropy corresponds to the maximum likelihood method, in which Kullback-Leibler divergence connects Boltzmann-Shannon entropy and the expected log-likelihood function. The maximum likelihood estimation has been supported for the optimal performanc...

We prove an area law for the entanglement entropy in gapped one dimensional quantum systems. The bound on the entropy grows surprisingly rapidly with the correlation length; we discuss this in terms of properties of quantum expanders and present a conjecture on completely positive maps which may provide an alternate way of arriving at an area law. We also show that, for gapped, local systems, t...

Global entropy solutions in BV for a scalar nonlocal conservation law with fading memory are constructed as limits of vanishing viscosity approximate solutions. The uniqueness and stability of entropy solutions in BV are established, which also yield the existence of entropy solutions in L∞ while the initial data is only in L∞. Moreover, if the memory kernel depends on a relaxation parameter ε ...

The recent development of the infrared cameras, the technologies of detection and tracking the target are under progress in the surveillance field, intelligent robot field, and the military field. Detection of infrared threat in IR defense systems are very important to use IR cameras. Many scholars have paid much attention to the study on spatial and temporal detections. Existing methods are fo...

the mechanical aspect of entropy-exergy relationship, together with the thermal aspect usually consid-ered, leads to an extended formulation of physical exergy based on both maximum useful work and maximum useful heat that are the outcome of available energy of a thermodynamic system. this approach suggests that a mechanical entropy can be studied, in addition to the already used thermal entrop...

Recent theoretical and empirical work has focused on the variability of network dynamics in maturation. Such variability seems to reflect the spontaneous formation and dissolution of different functional networks. We sought to extend these observations into healthy aging. Two different data sets, one EEG (total n = 48, ages 18-72) and one magnetoencephalography (n = 31, ages 20-75) were analyze...

Gathering the most information by picking the least amount of data is a common task in experimental design or when exploring an unknown environment in reinforcement learning and robotics. A widely used measure for quantifying the information contained in some distribution of interest is its entropy. Greedily minimizing the expected entropy is therefore a standard method for choosing samples in ...

The medical image registration algorithm uses the mutual information measure function that has many local extremes. Therefore, we propose our medical image registration algorithm that combines generalized mutual information with PSO-Powell hybrid algorithm and uses the objective measure function based on Renyi entropy. The Renyi entropy can remove the local extremes. We use the particle swarm o...

The thermodynamics of the diffuse, X-ray emitting gas in clusters of galaxies is linked to the entropy level of the external intergalactic medium at the epoch of accretion. In particular, models that successfully reproduce the properties of local X-ray clusters and groups require the presence of a minimum value for the entropy of the pre-collapse, intergalactic medium. Such an entropy floor can...

We find a linear instability of non-axisymmetric Rossby waves in a thin nonmagnetized Keplerian disk when there is a local maximum in the radial profile of a key function L(r) ≡ F(r)S2/Γ(r), where F−1 = ẑ · (∇× v)/Σ is the potential vorticity, S = P/ΣΓ is the entropy, Σ is the surface mass density, P is the vertically integrated pressure, and Γ is the adiabatic index. We consider in detail the ...