One of the most famous ranking methods for digraphs is by Copeland score. The score a node in digraph difference between its outdegree (i.e. number outgoing arcs) and indegree ingoing arcs). In score, ranked higher, higher this paper, we deal with an alternative method to rank nodes according their out- indegree, namely degree ratio, i.e. divided indegree. To avoid dividing zero, add 1 both as ...

Abstract Modelling soil erosion and sediment transport are vital to assess the impact of flash floods. However, limited research works have studied transport, especially in Egypt. This paper employs HEC-HMS lumped hydrological model predict load due flood event 9th March 2014 Wadi Billi, The Modified USLE has been used calculate total upland erosion, while Laursen-Copeland simulate streams’ pot...

The original possible winner problem is: Given an unweighted election with partial preferences and a distinguished candidate c, can the preferences be extended to total ones such that c wins? We introduce a novel variant of this problem in which not some of the voters’ preferences are uncertain but some of their weights. Not much has been known previously about the weighted possible winner prob...

Primordial magnetic fields may be created in collisions of expanding bubbles in a first-order cosmological phase transition and later serve as seed fields for galactic magnetic fields. Here I present results from numerical and analytical studies of U(1) bubble collisions done in collaboration with Ed Copeland and Paul Saffin. I also reveal preliminary results from analytical studies of SU(2)×U(...

Classical results in social choice theory on the susceptibility of voting rules to strategic manipulation make the assumption that the manipulator has complete information regarding the preferences of the other voters. In reality, however, voters only have incomplete information, which limits their ability to manipulate. We explore how these limitations affect both the manipulability of voting ...

We introduce a notion of “statistical robustness” for voting rules. We say that a voting rule is statistically robust if the winner for a profile of ballots is most likely to be the winner of any random sample of the profile, for any positive sample size. We show that some voting rules, such as plurality, veto, and random ballot, are statistically robust, while others, such as approval, score v...

The original possible winner problem is: Given an unweighted election with partial preferences and a distinguished candidate c, can the preferences be extended to total ones such that c wins? We introduce a novel variant of this problem in which not some of the voters’ preferences are uncertain but some of their weights. Not much has been known previously about the weighted possible winner prob...

Rank aggregation is the problem of generating an overall ranking from a set of individual votes which is as close as possible to the (unknown) correct ranking. The challenge is that votes are often both noisy and incomplete. Existing work focuses on the most likely ranking for a particular noise model. Instead, we focus on minimising the error, i.e., the expected distance between the aggregated...

Condorcet extensions have long held a prominent place in social choice theory. A extension will return the winner as unique whenever such an alternative exists. However, definition of does not take into account possible manipulation by voters. profile where all agents vote truthfully may winner, but this end up set winners if are acting strategically. Focusing on class tournament solutions, we ...