An estimate of the energy of neutrino-induced muons in MACRO is provided by a multiple Coulomb scattering measurement. The MACRO original upward-muon data sample has been subdivided according to the reconstructed muon energy. The results are interpreted in terms of neutrino oscillation

We consider directed planar graphs with an upward planar drawing on the rolling and standing cylinders. These classes extend the upward planar graphs in the plane. Here, we address the dual graphs. Our main result is a combinatorial characterization of these sets of upward planar graphs. It basically shows that the roles of the standing and the rolling cylinders are interchanged for their duals.

A measurement of the flux of neutrino-induced muons using the MACRO detector is presented. Different event topologies, corresponding to different neutrino parent energies can be detected. The upward throughgoing muon sample is the larger event sample. For this sample, produced by neutrinos having an average energy around 100 GeV, the ratio of the number of observed to expected events integrated...

An estimate of the energy of neutrino-induced muons in MACRO is provided by a multiple Coulomb scattering measurement. The MACRO original upward-muon data sample has been subdivided according to the reconstructed muon energy. Data in each subset are then compared with expected fluxes from atmospheric neutrinos. The results are interpreted in terms of neutrino oscillations.

The upward planarity testing problem is known to be NPhard. We describe an O(n)-time upward planarity testing and embedding algorithm for the class of digraphs that do not contain rigid triconnected components. We also present a new FPT algorithm that solves the upward planarity testing and embedding problem for general digraphs.

An upward drawing of a rooted tree is a drawing such that no parents are below their children. It is ordered if the edges to children appear in prescribed order around each vertex. It is well-known that any tree has an upward (unordered) drawing with width log(n+ 1). For ordered drawings, the best-known bounds for the width for binary trees is O(logn), while for arbitrary trees it is O(2 √ ). W...

The development of symbolic algebra transformed civilization. Since algebra is a recent cultural invention, however, algebraic reasoning must build on a foundation of more basic capacities. Past work suggests that spatial representations of number may be part of that foundation, but recent studies have failed to find relations between spatial-numerical associations and higher mathematical skill...

In this talk I review measurements and calculations of the flux of neutrinos produced by interactions of cosmic rays in the atmosphere. The main reason for interest in this subject is the apparent anomaly between the predicted and the observed ratio of νe to νμ. With the advent of Super-Kamiokande, we are on the threshold of an order of magnitude increase in the amount of data available to stud...