We propose a two-step algorithm for almost unsupervised detection of linear structures, in particular, main axes in road networks, as seen in synthetic aperture radar (SAR) images. The first step is local and is used to extract linear features from the speckle radar image, which are treated as roadsegment candidates. We present two local line detectors as well as a method for fusing information from these detectors. In the second global step, we identify the real roads among the segment candidates by defining a Markov random field (MRF) on a set of segments, which introduces contextual knowledge about the shape of road objects. The influence of the parameters on the road detection is studied and results are presented for various real radar images. Index Terms-Markov random fields (MRF's), road detection, SAR images, statistical properties. NOMENCLATURE Number of looks of the radar image. Amplitude of pixel. Number of pixels in region. Empirical mean of region. Empirical variation coefficient of region. Exact mean-reflected intensity of region. , Exact and empirical contrasts between regions and. Ratio edge detector response between regions and. Ratio line detector (D1) response. Cross-correlation edge detector response between regions and. Cross-correlation line detector (D2) response. Decision threshold for variable. Probability-density function (pdf) of a random variable for value and parameter values. Cumulative distribution function of a random variable for value and parameter values .

We study large fluctuations of emitted radiation in the system of N non-interacting twolevel atoms. Two methods are used to calculate the probability of large fluctuations and the time dependence of excitation and emission. The first method is based on the large deviation principle for Markov processes. The second one uses an analogue of the quantum formalism for classical probability problems.Particularly we prove that in a large fluctuation limit approximately half of the atoms are excited. This fact is independent on the fraction of the excited atoms in equilibrium.

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We prove that for a ν-dimensional quantum crystal model of interacting anharmonic oscillators of mass m there exists m 0 such that in the light-mass domain 0 < m < m 0 the corresponding Gibbs state is analytic with respect to external field (conjugate to site displacements) for all temperatures T ≥ 0, i.e. including the ground state. This means that for the model with harmonic interaction and a symmetric double-well one-site potential, the light-mass quantum fluctuations suppress the symmetry breaking structural phase transition known in this model for ν ≥ 3 and m > M 0 ≥ m 0 , where M 0 is large enough. 922 Analyticity of the Gibbs State for a Quantum Anharmonic Crystal 923 phasize that similar to [15]-[18], our method does not solve the uniqueness problem in the DLR-sense in the light-mass domain at T = 0, since it does not prove the uniqueness of the Gibbs field of paths for this temperature, if the boundary trajectories do not have limited amplitudes.The main obstacle to making this conclusion is the noncompactness of the path ("spin") variables. However, since our Theorem 2 shows that in the light-mass domain m < m 0 there is no order parameter corresponding to the symmetry breaking structural phase transition that exists for m > M 0 , one could anticipate in this domain the uniqueness of the quantum Gibbs state for all temperatures including T = 0. For the proof in the case of the compact "spins" see [21]. Notice that this makes a striking difference between the quantum model and its classical analog corresponding formally to m → ∞ (or the Planck constant → 0): in the quantum case the suppression of any ordering is expected even at zero temperature, due to the tunneling microscopic quantum fluctuations for sufficiently light masses m < m 0 .

We estimate locations of the regions of the percolation and of the non-percolation in the plane (λ, β): the Poisson rate -the inverse temperature, for interacted particle systems in finite dimension Euclidean spaces. Our results about the percolation and about the nonpercolation are obtained under different assumptions. The intersection of two groups of the assumptions reduces the results to two dimension Euclidean space, R 2 , and to a potential function of the interactions having a hard core.The technics for the percolation proof is based on a contour method which is applied to a discretization of the Euclidean space. The technics for the non-percolation proof is based on the coupling of the Gibbs field with a branching process.