In the book Boolean Function Complexity by Stasys Jukna [7], two lower bound techniques for Tree-like Cutting Plane proofs (henceforth, “Tree-CP proofs”) using Karchmer-Widgerson type communication games (henceforth, “KW games”) are presented: The first, applicable to Tree-CP proofs with bounded coefficients, translates Ω(t) deterministic lower bounds on KW games to 2 logn) lower bounds on Tree...

We describe a novel method for the analysis of research activities of an organization by mapping that to a taxonomy tree of the field. The method constructs fuzzy membership profiles of the organization members or teams in terms of the taxonomy’s leaves (research topics), and then it generalizes them in two steps. These steps are: (i) fuzzy clustering research topics according to their thematic...

We present binary labelings for the angles of quadrangulations and plane Laman graphs, which are in analogy with Schnyder labelings for triangulations [W. Schnyder, Proc. 1st ACM-SIAM Symposium on Discrete Algorithms, 1990] and imply a special tree decomposition for quadrangulations. In particular, we show how to embed quadrangulations on a 2-book, so that each page contains a non-crossing alte...

We study weighted path lengths (depths) and distances for increasing tree families. For those subclasses of increasing tree families, which can be constructed via an insertion process, e.g., recursive trees, plane-oriented recursive trees and binary increasing trees, we can determine the limiting distribution which can be characterized as a generalized Dickman’s infinitely divisible distribution.

We associate with a plane meromorphic curve f a tree model T (f) based on its contact structure. Then we give a description of the y-derivative of f (resp. the Jacobian J(f, g)) in terms of T (f) (resp. T (fg)). We also characterize the regularity of f in terms of its tree.

A hyperbolic plane can be modeled by a structure called the enhanced binary tree. We study the ferromagnetic Ising model on top of the enhanced binary tree using the renormalization-group analysis in combination with transfer-matrix calculations. We find a reasonable agreement with Monte Carlo calculations on the transition point, and the resulting critical exponents suggest the mean-field surf...

Let P be a set of n points on the euclidean plane. Let Ls(P) and Lm(P) denote the lengths of the Steiner minimum tree and the minimum spanning tree on P, respectively. In 1968, Gilbert and Pollak conjectured that for any P, Ls(P) >/= (radical3/2)Lm(P). We provide an abridged proof for their conjecture in this paper.

The magnetic field of vortices in anisotropic superconducting films is considered the framework London approach. It found that at distances large relative to core size, normal film surface may change sign. We find attenuates as $1/r^3$ it does isotropic films, but anisotropy induces an angular dependence supercurrents which causes sign for parameters $\gamma=\lambda_2/\lambda_1>\sqrt{2}$ some p...

background: in general, measurements of solar ultraviolet (uv) radiation are related to horizontal surfaces. while the hu­mans walking and standing outdoors expose to the natural solar uv radiation, their eyes, cheeks, extremities, trunks, or many other anatomical sites are close to vertical plane and random orient to different directions. in this study, we character­ized the diurnal variations...