Recently a new recursion relation for tree-level gluon amplitudes in gauge theory has been discovered. We solve this recursion to obtain explicit formulas for the closed set of amplitudes with arbitrarily many positive and negative helicity gluons in a split helicity configuration. The solution admits a simple diagrammatic expansion in terms of ‘zigzag’ diagrams. We comment on generalizations o...

The atomic, electronic, and magnetic properties of vacancy structures with triangular shape related to their growth in single hexagonal boron nitride (h-BN) sheet are investigated using density functional theory calculations. We find that the optimized structures of triangular vacancies depend on the vacancy sizes with N-terminated zigzag edge. Then, vacancy structures obtained during the vacan...

In reasoning tasks involving the maintenance of consistent databases (so called "constraint net­ works") it is customary to enforce local consistency conditions in order to simplify the construc­ tion of a globally coherent model of the data. In this paper we present a relationship between the sizes of the variables' domains and the level of local consistency sufficient to ensure global con­ si...

3. Prerequisites for the workshop. They are mentioned or reviewed in sect. 1 of [17]: class field theory, especially local class field theory; elliptic curves over finite, local and global fields, some basic things about the set of Diophantine geometry conjectures the theory of Mochizuki deals with, basics of (classical) anabelian geometry. For the latter Ch.4 of [21] is a very easy to read sou...

UNLABELLED The reverse hierarchy theory (Hochstein and Ahissar, 2002) makes strong, but so far untested, predictions on conscious vision. In this theory, local details encoded in lower-order visual areas are unconsciously processed before being automatically and rapidly combined into global information in higher-order visual areas, where conscious percepts emerge. Contingent on current goals, l...

augmented downhill simplex method (adsm) is introduced here, that is a heuristic combination of downhill simplex method (dsm) with random search algorithm. in fact, dsm is an interpretable nonlinear local optimization method. however, it is a local exploitation algorithm; so, it can be trapped in a local minimum. in contrast, random search is a global exploration, but less efficient. here, rand...

Introduction. 1 1. Derivations and differentials 6 2. Log Calabi-Yau spaces: local structure and deformation theory 16 2.1. Local structure 16 2.2. Deformation theory 25 3. Cohomology of log Calabi-Yau spaces 38 3.1. Local calculations 38 3.2. Global calculations 46 3.3. The Hodge decomposition 59 4. Basechange and the cohomology of smoothings 67 5. Monodromy and the logarithmic Gauss-Manin con...

The theory of sparse graph limits concerns itself with versions of local convergence and global convergence, see e.g. [41]. Informally, in local convergence we look at a large neighborhood around a random uniformly chosen vertex in a graph and in global convergence we observe the whole graph from afar. In this note rather than surveying the general theory we will consider some concrete examples...

The article investigates aspects of globality with respect to music theory and especially mathematical and computer-aided music theory. The local/global dichotomy is applied (a) to the discipline such from a cultural semiotic point of view, (b) to the strategies of scientific knowledge management dogmatics, modeling and hermeneutics, and (c) to the musictheoretical discourse subjects. A detaile...

Augmented Downhill Simplex Method (ADSM) is introduced here, that is a heuristic combination of Downhill Simplex Method (DSM) with Random Search algorithm. In fact, DSM is an interpretable nonlinear local optimization method. However, it is a local exploitation algorithm; so, it can be trapped in a local minimum. In contrast, random search is a global exploration, but less efficient. Here, rand...