We enumerate and classify all stationary logarithmic configurations of d + 2 d+2 </inline-formu...

We show that the known bounded-depth proofs of the Weak Pigeonhole Principle PHP 2n n in size n O(log(n)) are not optimal in terms of size. More precisely, we give a size-depth trade-oo upper bound: there are proofs of size n O(d(log(n)) 2=d) and depth O(d). This solves an open problem of Maciel, Pitassi and Woods (2000). Our technique requires formalizing the ideas underlying Nepomnja s cij's ...

We study a long standing open problem on the mixing time of Kac’s random walk on SO(n,R) by random rotations. We obtain an upper bound mix = O(n log n) for the weak convergence which is close to the trivial lower bound Ω(n). This improves the upper bound O(n log n) by Diaconis and Saloff-Coste [9]. The proof is a variation on the coupling technique we develop to bound the mixing time for compac...

A partition (C1, C2, ..., Cq) of G = (V,E) into clusters of strong (respectively, weak) diameter d, such that the supergraph obtained by contracting each Ci is -colorable is called a strong (resp., weak) (d, )-network-decomposition. Network-decompositions were introduced in a seminal paper by Awerbuch, Goldberg, Luby and Plotkin in 1989. Awerbuch et al. showed that strong (exp{O(√log n log log ...

This paper considers the problem of computing the weak visibility polygon (WVP) of any query line segment pq (or WVP(pq)) inside a given simple polygon P. We present an algorithm that preprocesses P and creates a data structure from which WVP(pq) is efficiently reported in an output sensitive manner. Our algorithm needs O(n log n) time and O(n) space in the preprocessing phase to report WVP(pq)...

Aims. We determine carbon, oxygen, and their isotopic abundances based on CO and OH spectra in 23 red giant stars, and identify possible origin of difficulty in abundance analysis of cool luminous stars. Methods. We apply the line-by-line analysis based on the classical micro-turbulent model and 1 D model photospheres. Results. We found purely empirically that there is a critical value of log W...

This editor’s note gives an overview of the content this issue which is sponsored by Oregon Sea Grant.