Perception of Motion and Architectural Form: Computational Relationships between Optical Flow and Perspective

Perceptual geometry refers to the interdisciplinary research whose objectives focuses on study of geometry from the perspective of visual perception, and in turn, applies such geometric findings to the ecological study of vision. Perceptual geometry attempts to answer fundamental questions in perception of form and representation of space through synthesis of cognitive and biological theories of visual perception with geometric theories of the physical world. Perception of form, space and motion are among fundamental problems in vision science. In cognitive and computational models of human perception, the theories for modeling motion are treated separately from models for perception of form.Comment: 10 pages, 13 figures, submitted and accepted in DoCEIS'2012 Conference: http://www.uninova.pt/doceis/doceis12/home/home.ph

Median inverse problem and approximating the number of kk-median inverses of a permutation

We introduce the "Median Inverse Problem" for metric spaces. In particular, having a permutation $\pi$ in the symmetric group $S_n$ (endowed with the breakpoint distance), we study the set of all $k$-subsets $\{x_1,...,x_k\}\subset S_n$ for which $\pi$ is a breakpoint median. The set of all $k$-tuples $(x_1,...,x_k)$ with this property is called the $k$-median inverse of $\pi$. Finding an upper bound for the cardinality of this set, we provide an asymptotic upper bound for the probability that $\pi$ is a breakpoint median of $k$ permutations $\xi_1^{(n)},...,\xi_k^{(n)}$ chosen uniformly and independently at random from $S_n$

Linkage of modules over Cohen-Macaulay rings

Inspired by the works in linkage theory of ideals, the concept of sliding depth of extension modules is defined to prove the Cohen-Macaulyness of linked module if the base ring is merely Cohen-Macaulay. Some relations between this new condition and other module-theory conditions such as G-dimension and sequentially Cohen-Macaulay are established. By the way several already known theorems in linkage theory are improved or recovered by new approaches.Comment: 12 Page

Twist-angle dependence of electron correlations in moir\'e graphene bilayers

Motivated by the recent observation of correlated insulator states and unconventional superconductivity in twisted bilayer graphene, we study the dependence of electron correlations on the twist angle and reveal the existence of strong correlations over a narrow range of twist-angles near the magic angle. Specifically, we determine the on-site and extended Hubbard parameters of the low-energy Wannier states using an atomistic quantum-mechanical approach. The ratio of the on-site Hubbard parameter and the width of the flat bands, which is an indicator of the strength of electron correlations, depends sensitively on the screening by the semiconducting substrate and the metallic gates. Including the effect of long-ranged Coulomb interactions significantly reduces electron correlations and explains the experimentally observed sensitivity of strong correlation phenomena on twist angle.Comment: 17 pages, 6 figure

Estimation of elastic and viscous properties of the left ventricle based on annulus plane harmonic behavior

Assessment of left ventricular (LV) function with an emphasis on contractility has been a challenge in cardiac mechanics during the recent decades. The LV function is usually described by the LV pressurevolume (P-V) diagram. The standard P-V diagrams are easy to interpret but difficult to obtain and require invasive instrumentation for measuring the corresponding volume and pressure data. In the present study, we introduce a technique that can estimate the viscoelastic properties of the LV based on harmonic behavior of the ventricular chamber and it can be applied non-invasively as well. The estimation technique is based on modeling the actual long axis displacement of the mitral annulus plane toward the cardiac base as a linear damped oscillator with time-varying coefficients. The time-varying parameters of the model were estimated by a standard Recursive Linear Least Squares (RLLS) technique. LV stiffness at end-systole and end diastole was in the range of 61.86-136.00 dyne/g.cm and 1.25-21.02 dyne/g.cm, respectively. The only input used in this model was the long axis displacement of the annulus plane, which can also be obtained non-invasively using tissue Doppler or MR imaging

Meson Structure Functions in Valon Model

Parton distributions in a {\it{valon}} in the next-to-leading order is used to determine the patron distributions in pion and kaon. The validity of the valon model is tested and shown that the partonic content of the valon is universal and independent of the valon type. We have evaluated the valon distribution in pion and kaon, and in particular it is shown that the results are in good agreement with the experimental data on pion structure in a wide range of $x=[10^{-4},1]$Comment: 13 pages with 7 figures included, The manuscript is revised, figures are added and some errors are corrected. Accepted for publication in Physical Review