Immunoglobulin Go: Synergy of Combinatorics for Catalysis

Combinatorics of Go

We present several results concerning the number of positions and games of Go. We derive recurrences for L(m,n), the number of legal positions on an m× n board, and develop a dynamic programming algorithm which computes L(m,n) in time O(mnλ) and space O(mλ), for some constant λ < 5.4. An implementation of this algorithm lets us list L(n, n) for n ≤ 17. For bigger boards, we prove existence of a...

Bimetallic redox synergy in oxidative palladium catalysis.

Polynuclear transition metal complexes, which are embedded in the active sites of many metalloenzymes, are responsible for effecting a diverse array of oxidation reactions in nature. The range of chemical transformations remains unparalleled in the laboratory. With few noteworthy exceptions, chemists have primarily focused on mononuclear transition metal complexes in developing homogeneous cata...

Synergy between experimental and computational approaches to homogeneous photoredox catalysis.

In this Frontiers article, we highlight how state-of-the-art density functional theory calculations can contribute to the field of homogeneous photoredox catalysis. We discuss challenges in the fields and potential solutions to be found at the interface between theory and experiment. The exciting opportunities and insights that can arise through such an interdisciplinary approach are highlighted.

The Order Steps of an Analytic Combinatorics

‎Analytic combinatorics aims to enable precise quantitative predictions of the properties of large combinatorial structures‎. ‎This theory has emerged over recent decades as essential both for the analysis of algorithms and for the study of scientific models in many disciplines‎, ‎including probability theory‎, ‎statistical physics‎, ‎computational biology and information theory‎. ‎With a caref...

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