E-Unification for Second-Order Abstract Syntax

Higher-order unification (HOU) concerns unification of (extensions of) ?-calculus and can be seen as an instance of equational unification (E-unification) modulo ??-equivalence of ?-terms. We study equational unification of terms in languages with arbitrary variable binding constructions modulo arbitrary second-order equational theories. Abstract syntax with general variable binding and parametrised metavariables allows us to work with arbitrary binders without committing to ?-calculus or use inconvenient and error-prone term encodings, leading to a more flexible framework. In this paper, we introduce E-unification for second-order abstract syntax and describe a unification procedure for such problems, merging ideas from both full HOU and general E-unification. We prove that the procedure is sound and complete

Magnetic structure and phase diagram in a spin-chain system: Ca3_3Co2_2O6_6

The low-temperature structure of the frustrated spin-chain compound Ca$_3$Co$_2$O$_6$ is determined by the ground state of the 2D Ising model on the triangular lattice. At high-temperatures it transforms to the honeycomb magnetic structure. It is shown that the crossover between the two magnetic structures at 12 K arises from the entropy accumulated in the disordered chains. This interpretation is in an agreement with the experimental data. General rules for for the phase diagram of frustrated Ising chain compounds are formulated.Comment: 4 pages, 2 figure

Content-based image filtering

This paper presents an adaptive content-based image denoising technique. This technique uses image area classification for two purposes: perform more precise filtering and decrease computation complexity compared to modern filters of the same quality performance. Overview of several top image filtering techniques was made. Spatial domain (LPA-ICI), transform domain (SW-DCT) and combined filters (SA-DCT and BM3D) were studied in order to understand basic principles of image denoising. Image area classification which gives reasonable division into classes with clearly distinguishable properties for image filtering was observed. We have chosen block-wise classification that maps each block to Texture , Smooth and Edge classes. Performance of discussed filters on image area classes was shown. Adaptive free parameters choise for filtering quality improvement was analysed. It was shown that for some classes best parameters set differs from the best parameter set for the entire image. Methods to improve denoising algorithms speed which we were using in our adaptive solution were proposed. The most suitable algorithms with appropriate parameters set for each image area class were chosen. Modi ed classi cation algorithm applied to noisy images was developed. Whereupon, a modi ed BM3D-based adaptive denoising algorithm was proposed. Finally, multiple tests were performed and verification of speed and quality performances improvement compared to a baseline BM3D algorithm was obtained

Nearest-Neighbor Correlations in Hubbard Model

The Hubbard Hamiltonian is investigated by means of a variational trial wave function of Gutzwiller's type. The wave function includes nearest - neighbor correlations in an explicit form. To calculate density matrices the method of Kikuchi's pseudoensemble is used. The case of half-filled fermionic band carefully investigated in the limit of a large number of lattice sites. The ground state energy and correlation functions are determined for lattices with z=2,4 and 6 nearest neighbors.Comment: minor revisions (additional figure, fig2 is redrawn, et al.) 8 pages, 3 Post Script figures, RevTex; accepted to Phys.Lett.