A modification of the kuhn-tucker theorem technical report no. 1, 1 jun. - 31 dec. 1964

Modification of Kuhn-Tucker theorem for maximizing set of concave function

An optimal property of sequential decision procedures related to Bayes solutions

Optimal property of sequential decision procedure

A Note on the Stringy Embeddings of Certain N = 2 Dualities

Seiberg-Witten theory can be embedded in F-theory using D3 branes probing an orientifold geometry. The non-perturbative corrections in the orientifold picture map directly to the instanton corrections in the corresponding gauge theory that convert the classical moduli space to the quantum one. In this short review we argue that the recently proposed class of conformal Gaiotto models may also be embedded in F-theory. The F-theory constructions help us not only to understand the Gaiotto dualities but also to extend to the non-conformal cases with and without cascading behaviors. For the conformal cases, the near horizon geometries in F-theory capture both the UV and IR behaviors succinctly.Comment: 6 pages, LaTeX, Based on the talk given by K. D at the Theory Canada Conference June 2012; v2: Typos corrected and references adde

Unified Heat Kernel Regression for Diffusion, Kernel Smoothing and Wavelets on Manifolds and Its Application to Mandible Growth Modeling in CT Images

We present a novel kernel regression framework for smoothing scalar surface data using the Laplace-Beltrami eigenfunctions. Starting with the heat kernel constructed from the eigenfunctions, we formulate a new bivariate kernel regression framework as a weighted eigenfunction expansion with the heat kernel as the weights. The new kernel regression is mathematically equivalent to isotropic heat diffusion, kernel smoothing and recently popular diffusion wavelets. Unlike many previous partial differential equation based approaches involving diffusion, our approach represents the solution of diffusion analytically, reducing numerical inaccuracy and slow convergence. The numerical implementation is validated on a unit sphere using spherical harmonics. As an illustration, we have applied the method in characterizing the localized growth pattern of mandible surfaces obtained in CT images from subjects between ages 0 and 20 years by regressing the length of displacement vectors with respect to the template surface.Comment: Accepted in Medical Image Analysi

Quantum Melting of Charge Order due to Frustration in Two-Dimensional Quarter-Filled Systems

The effect of geometrical frustration in a two-dimensional 1/4-filled strongly correlated electron system is studied theoretically, motivated by layered organic molecular crystals. An extended Hubbard model on the square lattice is considered, with competing nearest neighbor Coulomb interaction, V, and that of next-nearest neighbor along one of the diagonals, V', which favor different charge ordered states. Based on exact diagonalization calculations, we find a metallic phase stabilized over a broad window at V' ~ V even for large Coulomb repulsion strengths as a result of frustrating the charge ordered states. Slightly modifying the lattice geometry relevant to the actual organic compounds does not alter the results, suggesting that this `quantum melting' of charge order is a robust feature of frustrated strongly correlated 1/4-filled systems.Comment: 5 pages, 4 figures, to be published in Phys. Rev.

Complementary Pair Density Wave and d-wave Checkerboard Order in High Temperature Superconductors

The competing orders in the particle-particle (P-P) channel and the particle-hole (P-H) channel have been proposed separately to explain the pseudogap physics in cuprates. By solving the Bogoliubov-deGennes equation self-consistently, we show that there is a general complementary connection between the d-wave checkerboard order (DWCB) in the particle-hole (P-H) channel and the pair density wave order (PDW) in the particle-particle (P-P) channel. A small pair density localization generates DWCB and PDW orders simultaneously. The result suggests that suppressing superconductivity locally or globally through phase fluctuation should induce both orders in underdoped cuprates. The presence of both DWCB and PDW orders with $4a \times 4a$ periodicity can explain the checkerboard modulation observed in FT-STS from STM and the puzzling dichotomy between the nodal and antinodal regions as well as the characteristic features such as non-dispersive Fermi arc in the pseudogap state

Journey of water in pine cones

Pine cones fold their scales when it rains to prevent seeds from short-distance dispersal. Given that the scales of pine cones consist of nothing but dead cells, this folding motion is evidently related to structural changes. In this study, the structural characteristics of pine cones are studied on micro-/macro-scale using various imaging instruments. Raindrops fall along the outer scales to the three layers (bract scales, fibers and innermost lignified structure) of inner pine cones. However, not all the layers but only the bract scales get wet and then, most raindrops move to the inner scales. These systems reduce the amount of water used and minimize the time spent on structural changes. The result shows that the pine cones have structural advantages that could influence the efficient motion of pine cones. This study provides new insights to understand the motion of pine cones and would be used to design a novel water transport system.119Ysciescopu

Formulating the Net Gain of MISO-SFN in the Presence of Self-Interferences

In this study, an analytical formula for multiple-input single-output single frequency network gain (MISO-SFNG) is investigated. To formulate the net MISO-SFNG, we derived the average signal to interference plus noise ratio (SINR) where the gain achieved by the distributed MISO diversity as a function of power imbalance is curve-fitted. Further, we analyzed the losses owing to self-interferences resulting from the delay spread and imperfect channel estimation. We verified the accuracy and effectiveness of the derived formula by comparing the measurement results with the analytical results. The derived formula helps to understand how various system factors affect the gain under a given condition. The formula can be used to evaluate the MISO-SFNG and to predict the MISO-SFN coverage in various system configurations