631 research outputs found
Graphs, Matrices, and the GraphBLAS: Seven Good Reasons
The analysis of graphs has become increasingly important to a wide range of
applications. Graph analysis presents a number of unique challenges in the
areas of (1) software complexity, (2) data complexity, (3) security, (4)
mathematical complexity, (5) theoretical analysis, (6) serial performance, and
(7) parallel performance. Implementing graph algorithms using matrix-based
approaches provides a number of promising solutions to these challenges. The
GraphBLAS standard (istc- bigdata.org/GraphBlas) is being developed to bring
the potential of matrix based graph algorithms to the broadest possible
audience. The GraphBLAS mathematically defines a core set of matrix-based graph
operations that can be used to implement a wide class of graph algorithms in a
wide range of programming environments. This paper provides an introduction to
the GraphBLAS and describes how the GraphBLAS can be used to address many of
the challenges associated with analysis of graphs.Comment: 10 pages; International Conference on Computational Science workshop
on the Applications of Matrix Computational Methods in the Analysis of Modern
Dat
Quantum to Classical Randomness Extractors
The goal of randomness extraction is to distill (almost) perfect randomness
from a weak source of randomness. When the source yields a classical string X,
many extractor constructions are known. Yet, when considering a physical
randomness source, X is itself ultimately the result of a measurement on an
underlying quantum system. When characterizing the power of a source to supply
randomness it is hence a natural question to ask, how much classical randomness
we can extract from a quantum system. To tackle this question we here take on
the study of quantum-to-classical randomness extractors (QC-extractors). We
provide constructions of QC-extractors based on measurements in a full set of
mutually unbiased bases (MUBs), and certain single qubit measurements. As the
first application, we show that any QC-extractor gives rise to entropic
uncertainty relations with respect to quantum side information. Such relations
were previously only known for two measurements. As the second application, we
resolve the central open question in the noisy-storage model [Wehner et al.,
PRL 100, 220502 (2008)] by linking security to the quantum capacity of the
adversary's storage device.Comment: 6+31 pages, 2 tables, 1 figure, v2: improved converse parameters,
typos corrected, new discussion, v3: new reference
Duality of privacy amplification against quantum adversaries and data compression with quantum side information
We show that the tasks of privacy amplification against quantum adversaries
and data compression with quantum side information are dual in the sense that
the ability to perform one implies the ability to perform the other. These are
two of the most important primitives in classical information theory, and are
shown to be connected by complementarity and the uncertainty principle in the
quantum setting. Applications include a new uncertainty principle formulated in
terms of smooth min- and max-entropies, as well as new conditions for
approximate quantum error correction.Comment: v2: Includes a derivation of an entropic uncertainty principle for
smooth min- and max-entropies. Discussion of the
Holevo-Schumacher-Westmoreland theorem remove
Object Protection in Distributed Systems
Withreferencetoadistributedsystemconsistingofnodesconnectedbyalocalareanetwork,we consider a salient aspect of the protection problem, the representation of access permissions and protection domains. We present a model of a protection system supporting typed objects. Possession of an access permission for a given object is certified by possession of an object pointer including the specification of a set of access rights. We associate an encryption key with each object and a password with each domain. Object pointers are stored in memory in a ciphertext form obtained by using the object key and including the value of the domain password. Each process is executed in a domain and can take advantage of a given object pointer only if this object pointer was encrypted by including the password of this domain. A set of protection primitives makes it possible to use object pointers for object reference and to control the movements of the objects across the network. The resulting protection environment is evaluated from a number of salient viewpoints, including ease of access right distribution and revocation, interprocess interaction and cooperation, protection against fraudulent actions of access right manipulation and stealing, storage overhead, and network traffic
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