216 research outputs found
On an effective solution of the optimal stopping problem for random walks
We find a solution of the optimal stopping problem for the case when a reward function is an integer power function of a random walk on an infinite time interval. It is shown that an optimal stopping time is a first crossing time through a level defined as the largest root of Appell's polynomial associated with the maximum of the random walk. It is also shown that a value function of the optimal stopping problem on the finite interval {0, 1, . . . , T} converges with an exponential rate as T → ∞ to the limit under the assumption that jumps of the random walk are exponentially bounded
Anderson localization of classical waves in weakly scattering one-dimensional Levy lattices
© 2018 American Physical Society. Anderson localization of classical waves in weakly scattering one-dimensional Levy lattices is studied analytically and numerically. The disordered medium is composed of layers with alternating refractive indices and with thickness disorder distributed according to the Pareto distribution ∼1/x(α+1). In Levy lattices the variance (or both variance and mean) of a random parameter does not exist, which leads to a different functional form for the localization length. In this study an equation for the localization length is obtained, and it is found to be in excellent agreement with the numerical calculations throughout the spectrum. The explicit asymptotic equations for the localization lengths for both short and long wavelengths have been deduced. It is shown that the localization length tends to a constant at short wavelengths and it is determined by the layer interface Fresnel coefficient. At the long wavelengths the localization length is proportional to the power of the wavelength ∼λα for 12, where the variance of the random distribution exists, the localization length attains its classical long-wavelength asymptotic form ∼λ2
Improving the Segmentation of Anatomical Structures in Chest Radiographs using U-Net with an ImageNet Pre-trained Encoder
Accurate segmentation of anatomical structures in chest radiographs is
essential for many computer-aided diagnosis tasks. In this paper we investigate
the latest fully-convolutional architectures for the task of multi-class
segmentation of the lungs field, heart and clavicles in a chest radiograph. In
addition, we explore the influence of using different loss functions in the
training process of a neural network for semantic segmentation. We evaluate all
models on a common benchmark of 247 X-ray images from the JSRT database and
ground-truth segmentation masks from the SCR dataset. Our best performing
architecture, is a modified U-Net that benefits from pre-trained encoder
weights. This model outperformed the current state-of-the-art methods tested on
the same benchmark, with Jaccard overlap scores of 96.1% for lung fields, 90.6%
for heart and 85.5% for clavicles.Comment: Presented at the First International Workshop on Thoracic Image
Analysis (TIA), MICCAI 201
Decision Support System for Urbanization of the Northern Part of the Volga-Akhtuba Floodplain (Russia) on the Basis of Interdisciplinary Computer Modeling
There is a computer decision support system (CDSS) for urbanization of the
northern part of the Volga-Akhtuba floodplain. This system includes subsystems
of cognitive and game-theoretic analysis, geoinformation and hydrodynamic
simulations. The paper presents the cognitive graph, two-level and three-level
models of hierarchical games for the cases of uncontrolled and controlled
development of the problem situation. We described the quantitative analysis of
the effects of different strategies for the spatial distribution of the
urbanized territories. For this reason we conducted the territory zoning
according to the level of negative consequences of urbanization for various
agents. In addition, we found an analytical solution for games with the linear
dependence of the average flooded area on the urbanized area. We numerically
computed a game equilibrium for dependences derived from the imitational
geoinformation and hydrodynamic modeling of flooding. As the result, we showed
that the transition to the three-level management system and the implementation
of an optimal urbanization strategy minimize its negative consequences.Comment: 14 pages, 5 figures; Conference: Creativity in Intelligent
Technologies and Data Science. CIT&DS 201
Supersymmetric QCD: Exact Results and Strong Coupling
We revisit two longstanding puzzles in supersymmetric gauge theories. The
first concerns the question of the holomorphy of the coupling, and related to
this the possible definition of an exact (NSVZ) beta function. The second
concerns instantons in pure gluodynamics, which appear to give sensible, exact
results for certain correlation functions, which nonetheless differ from those
obtained using systematic weak coupling expansions. For the first question, we
extend an earlier proposal of Arkani-Hamed and Murayama, showing that if their
regulated action is written suitably, the holomorphy of the couplings is
manifest, and it is easy to determine the renormalization scheme for which the
NSVZ formula holds. This scheme, however, is seen to be one of an infinite
class of schemes, each leading to an exact beta function; the NSVZ scheme,
while simple, is not selected by any compelling physical consideration. For the
second question, we explain why the instanton computation in the pure
supersymmetric gauge theory is not reliable, even at short distances. The
semiclassical expansion about the instanton is purely formal; if infrared
divergences appear, they spoil arguments based on holomorphy. We demonstrate
that infrared divergences do not occur in the perturbation expansion about the
instanton, but explain that there is no reason to think this captures all
contributions from the sector with unit topological charge. That one expects
additional contributions is illustrated by dilute gas corrections. These are
infrared divergent, and so difficult to define, but if non-zero give order one,
holomorphic, corrections to the leading result. Exploiting an earlier analysis
of Davies et al, we demonstrate that in the theory compactified on a circle of
radius beta, due to infrared effects, finite contributions indeed arise which
are not visible in the formal limit that beta goes to infinity.Comment: 28 pages, two references added, one typo correcte
Structures and waves in a nonlinear heat-conducting medium
The paper is an overview of the main contributions of a Bulgarian team of
researchers to the problem of finding the possible structures and waves in the
open nonlinear heat conducting medium, described by a reaction-diffusion
equation. Being posed and actively worked out by the Russian school of A. A.
Samarskii and S.P. Kurdyumov since the seventies of the last century, this
problem still contains open and challenging questions.Comment: 23 pages, 13 figures, the final publication will appear in Springer
Proceedings in Mathematics and Statistics, Numerical Methods for PDEs:
Theory, Algorithms and their Application
Group Analysis of the Novikov Equation
We find the Lie point symmetries of the Novikov equation and demonstrate that
it is strictly self-adjoint. Using the self-adjointness and the recent
technique for constructing conserved vectors associated with symmetries of
differential equations, we find the conservation law corresponding to the
dilations symmetry and show that other symmetries do not provide nontrivial
conservation laws. Then we investigat the invariant solutions
The Cosmic Microwave Background and Particle Physics
In forthcoming years, connections between cosmology and particle physics will
be made increasingly important with the advent of a new generation of cosmic
microwave background (CMB) experiments. Here, we review a number of these
links. Our primary focus is on new CMB tests of inflation. We explain how the
inflationary predictions for the geometry of the Universe and primordial
density perturbations will be tested by CMB temperature fluctuations, and how
the gravitational waves predicted by inflation can be pursued with the CMB
polarization. The CMB signatures of topological defects and primordial magnetic
fields from cosmological phase transitions are also discussed. Furthermore, we
review current and future CMB constraints on various types of dark matter (e.g.
massive neutrinos, weakly interacting massive particles, axions, vacuum
energy), decaying particles, the baryon asymmetry of the Universe,
ultra-high-energy cosmic rays, exotic cosmological topologies, and other new
physics.Comment: 43 pages. To appear in Annual Reviews of Nuclear and Particle Scienc
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