175 research outputs found
On the Doubly Sparse Compressed Sensing Problem
A new variant of the Compressed Sensing problem is investigated when the
number of measurements corrupted by errors is upper bounded by some value l but
there are no more restrictions on errors. We prove that in this case it is
enough to make 2(t+l) measurements, where t is the sparsity of original data.
Moreover for this case a rather simple recovery algorithm is proposed. An
analog of the Singleton bound from coding theory is derived what proves
optimality of the corresponding measurement matrices.Comment: 6 pages, IMACC2015 (accepted
Towards Collaborative Conceptual Exploration
In domains with high knowledge distribution a natural objective is to create
principle foundations for collaborative interactive learning environments. We
present a first mathematical characterization of a collaborative learning
group, a consortium, based on closure systems of attribute sets and the
well-known attribute exploration algorithm from formal concept analysis. To
this end, we introduce (weak) local experts for subdomains of a given knowledge
domain. These entities are able to refute and potentially accept a given
(implicational) query for some closure system that is a restriction of the
whole domain. On this we build up a consortial expert and show first insights
about the ability of such an expert to answer queries. Furthermore, we depict
techniques on how to cope with falsely accepted implications and on combining
counterexamples. Using notions from combinatorial design theory we further
expand those insights as far as providing first results on the decidability
problem if a given consortium is able to explore some target domain.
Applications in conceptual knowledge acquisition as well as in collaborative
interactive ontology learning are at hand.Comment: 15 pages, 2 figure
Running Genetic Algorithms in the Edge: A First Analysis
Nowadays, the volume of data produced by different kinds of devices is continuously growing, making even more difficult to solve the
many optimization problems that impact directly on our living quality. For instance, Cisco projected that by 2019 the volume of data will reach 507.5 zettabytes per year, and the cloud traffic will quadruple. This is not sustainable in the long term, so it is a need to move part of the intelligence from the cloud to a highly decentralized computing model. Considering this, we propose a ubiquitous intelligent system which is composed by different kinds of endpoint devices such as smartphones, tablets, routers, wearables, and any other CPU powered device. We want to use this to solve tasks useful for smart cities. In this paper, we analyze if these devices are suitable for this purpose and how we have to adapt the optimization algorithms to be efficient using heterogeneous hardware. To do this, we perform a set of experiments in which we measure the speed, memory usage, and battery consumption of these devices for a set of binary and combinatorial problems. Our conclusions reveal the strong and weak features of each device to run future algorihms in the border of the cyber-physical system.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech.
This research has been partially funded by the Spanish MINECO and FEDER projects TIN2014-57341-R (http://moveon.lcc.uma.es), TIN2016-81766-REDT (http://cirti.es), TIN2017-88213-R (http://6city.lcc.uma.es), the Ministry of Education of Spain (FPU16/02595
Weighing matrices and spherical codes
Mutually unbiased weighing matrices (MUWM) are closely related to an
antipodal spherical code with 4 angles. In the present paper, we clarify the
relationship between MUWM and the spherical sets, and give the complete
solution about the maximum size of a set of MUWM of weight 4 for any order.
Moreover we describe some natural generalization of a set of MUWM from the
viewpoint of spherical codes, and determine several maximum sizes of the
generalized sets. They include an affirmative answer of the problem of Best,
Kharaghani, and Ramp.Comment: Title is changed from "Association schemes related to weighing
matrices
A Family of Quantum Stabilizer Codes Based on the Weyl Commutation Relations over a Finite Field
Using the Weyl commutation relations over a finite field we introduce a
family of error-correcting quantum stabilizer codes based on a class of
symmetric matrices over the finite field satisfying certain natural conditions.
When the field is GF(2) the existence of a rich class of such symmetric
matrices is demonstrated by a simple probabilistic argument depending on the
Chernoff bound for i.i.d symmetric Bernoulli trials. If, in addition, these
symmetric matrices are assumed to be circulant it is possible to obtain
concrete examples by a computer program. The quantum codes thus obtained admit
elegant encoding circuits.Comment: 16 pages, 2 figure
Direct Construction of Recursive MDS Diffusion Layers using Shortened BCH Codes
MDS matrices allow to build optimal linear diffusion layers in block ciphers.
However, MDS matrices cannot be sparse and usually have a large description,
inducing costly software/hardware implementations. Recursive MDS matrices allow
to solve this problem by focusing on MDS matrices that can be computed as a
power of a simple companion matrix, thus having a compact description suitable
even for constrained environ- ments. However, up to now, finding recursive MDS
matrices required to perform an exhaustive search on families of companion
matrices, thus limiting the size of MDS matrices one could look for. In this
article we propose a new direct construction based on shortened BCH codes, al-
lowing to efficiently construct such matrices for whatever parameters.
Unfortunately, not all recursive MDS matrices can be obtained from BCH codes,
and our algorithm is not always guaranteed to find the best matrices for a
given set of parameters.Comment: Best paper award; Carlos Cid and Christian Rechberger. 21st
International Workshop on Fast Software Encryption, FSE 2014, Mar 2014,
London, United Kingdom. springe
On the Kernel of -Linear Hadamard Codes
The -additive codes are subgroups of ,
and can be seen as a generalization of linear codes over and
. A -linear Hadamard code is a binary Hadamard
code which is the Gray map image of a -additive code. It is
known that the dimension of the kernel can be used to give a complete
classification of the -linear Hadamard codes. In this paper, the
kernel of -linear Hadamard codes and its dimension are
established for . Moreover, we prove that this invariant only provides a
complete classification for some values of and . The exact amount of
nonequivalent such codes are given up to for any , by using
also the rank and, in some cases, further computations
Robust Non-Interactive Multiparty Computation Against Constant-Size Collusion
Non-Interactive Multiparty Computations (Beimel et al., Crypto 2014) is a very powerful notion equivalent (under some corruption model) to garbled circuits, Private Simultaneous Messages protocols, and obfuscation. We present robust solutions to the problem of Non-Interactive Multiparty Computation in the computational and information-theoretic models. Our results include the first efficient and robust protocols to compute any function in for constant-size collusions, in the information-theoretic setting and in the computational setting, to compute any function in for constant-size collusions, assuming the existence of one-way functions. Our constructions start from a Private Simultaneous Messages construction (Feige, Killian Naor, STOC 1994 and Ishai, Kushilevitz, ISTCS 1997) and transform it into a Non-Interactive Multiparty Computation for constant-size collusions.
We also present a new Non-Interactive Multiparty Computation protocol for symmetric functions with significantly better communication complexity compared to the only known one of Beimel et al
Partial spreads and vector space partitions
Constant-dimension codes with the maximum possible minimum distance have been
studied under the name of partial spreads in Finite Geometry for several
decades. Not surprisingly, for this subclass typically the sharpest bounds on
the maximal code size are known. The seminal works of Beutelspacher and Drake
\& Freeman on partial spreads date back to 1975, and 1979, respectively. From
then until recently, there was almost no progress besides some computer-based
constructions and classifications. It turns out that vector space partitions
provide the appropriate theoretical framework and can be used to improve the
long-standing bounds in quite a few cases. Here, we provide a historic account
on partial spreads and an interpretation of the classical results from a modern
perspective. To this end, we introduce all required methods from the theory of
vector space partitions and Finite Geometry in a tutorial style. We guide the
reader to the current frontiers of research in that field, including a detailed
description of the recent improvements.Comment: 30 pages, 1 tabl
- …