25,830 research outputs found
Ring Learning With Errors: A crossroads between postquantum cryptography, machine learning and number theory
The present survey reports on the state of the art of the different
cryptographic functionalities built upon the ring learning with errors problem
and its interplay with several classical problems in algebraic number theory.
The survey is based to a certain extent on an invited course given by the
author at the Basque Center for Applied Mathematics in September 2018.Comment: arXiv admin note: text overlap with arXiv:1508.01375 by other
authors/ comment of the author: quotation has been added to Theorem 5.
Chiral Magnetic Skyrmions with Arbitrary Topological Charge ("skyrmionic sacks")
We show that continuous and spin-lattice models of chiral ferro- and
antiferromagnets provide the existence of an infinite number of stable soliton
solutions of any integer topological charge. A detailed description of the
morphology of new skyrmions and the corresponding energy dependencies are
provided. The considered model is general, and is expected to predict a
plethora of particle-like states which may occur in various chiral magnets
including atomic layers, e.g., PdFe/Ir(111), rhombohedral GaVS
semiconductor, B20-type alloys as MnFeGe, MnFeSi,
FeCoSi, CuOSeO, acentric tetragonal Heusler compounds
Reliable Physical Layer Network Coding
When two or more users in a wireless network transmit simultaneously, their
electromagnetic signals are linearly superimposed on the channel. As a result,
a receiver that is interested in one of these signals sees the others as
unwanted interference. This property of the wireless medium is typically viewed
as a hindrance to reliable communication over a network. However, using a
recently developed coding strategy, interference can in fact be harnessed for
network coding. In a wired network, (linear) network coding refers to each
intermediate node taking its received packets, computing a linear combination
over a finite field, and forwarding the outcome towards the destinations. Then,
given an appropriate set of linear combinations, a destination can solve for
its desired packets. For certain topologies, this strategy can attain
significantly higher throughputs over routing-based strategies. Reliable
physical layer network coding takes this idea one step further: using
judiciously chosen linear error-correcting codes, intermediate nodes in a
wireless network can directly recover linear combinations of the packets from
the observed noisy superpositions of transmitted signals. Starting with some
simple examples, this survey explores the core ideas behind this new technique
and the possibilities it offers for communication over interference-limited
wireless networks.Comment: 19 pages, 14 figures, survey paper to appear in Proceedings of the
IEE
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