5,039 research outputs found
Packing subgroups in solvable groups
We show that any subgroup of a (virtually) nilpotent-by-polycyclic group
satisfies the bounded packing property of Hruska-Wise. In particular, the same
is true about metabelian groups and linear solvable groups. However, we find an
example of a finitely generated solvable group of derived length 3 which admits
a finitely generated subgroup without the bounded packing property. In this
example the subgroup is a metabelian retract also. Thus we obtain a negative
answer to Problem 2.27 of Hruska-Wise. On the other hand, we show that
polycyclic subgroups of solvable groups satisfy the bounded packing property.Comment: 8 pages, no figur
Low Energy Lorentz Violation in Polymer Quantization Revisited
In previous work, it had been shown that polymer quantized scalar field
theory predicts that even an inertial observer can experience spontaneous
excitations. This prediction was shown to hold at low energies. However, in
these papers it was assumed that the polymer scale is constant. But it is
possible to relax this condition and obtain a larger class of theories where
the polymer scale is a function of momentum. Does the prediction of low energy
Lorentz violation hold for all of these theories? In this paper we prove that
it does. We also obtain the modified rates of radiation for some of these
theories.Comment: Acknowledgements update
The Secure Link Prediction Problem
Link Prediction is an important and well-studied problem for social networks.
Given a snapshot of a graph, the link prediction problem predicts which new
interactions between members are most likely to occur in the near future. As
networks grow in size, data owners are forced to store the data in remote cloud
servers which reveals sensitive information about the network. The graphs are
therefore stored in encrypted form.
We study the link prediction problem on encrypted graphs. To the best of our
knowledge, this secure link prediction problem has not been studied before. We
use the number of common neighbors for prediction. We present three algorithms
for the secure link prediction problem. We design prototypes of the schemes and
formally prove their security. We execute our algorithms in real-life datasets.Comment: This has been accepted for publication in Advances in Mathematics of
Communications (AMC) journa
Moving forward with complexity and diversity
The chief meaningful characteristic of Futures Studies is ontological and epistemological insecurity, not confidence from chaos. Our experienced world is continuously being reconstructed through flows of information and actions. There are more worlds than we could ever know. The best we can hope for is awareness from flows
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