41,307 research outputs found
Constructions of new matroids and designs over GF(q)
A perfect matroid design (PMD) is a matroid whose flats of the same rank all
have the same size. In this paper we introduce the q-analogue of a PMD and its
properties. In order to do that, we first establish a new cryptomorphic
definition for q-matroids. We show that q-Steiner systems are examples of
q-PMD's and we use this q-matroid structure to construct subspace designs from
q-Steiner systems. We apply this construction to S(2, 3, 13; q) q-Steiner
systems and hence establish the existence of subspace designs with previously
unknown parameters
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Electricity Sector Reform in Developing Countries: A Survey of Empirical Evidence on Determinants and Performance
This paper reviews the empirical evidence on electricity reform in developing countries. We find that country institutions and sector governance play an important role in success and failure of reform; reforms appear to have increased operating efficiency and expanded access to urban customers; they have to a lesser degree passed on efficiency gains to customers, tackled distributional effects, or improved rural access. Moreover, some of the literature is not methodologically robust or on a par with general development economics literature and findings on some issues are limited and inconclusive while some important areas are yet to be addressed. Until we know more, implementation of reforms will be more based on ideology and economic theory rather than solid economic evidence.The World Bank Electricity Research Programme and the CMI Electricity Project (IR-45
The Perfect Binary One-Error-Correcting Codes of Length 15: Part II--Properties
A complete classification of the perfect binary one-error-correcting codes of
length 15 as well as their extensions of length 16 was recently carried out in
[P. R. J. \"Osterg{\aa}rd and O. Pottonen, "The perfect binary
one-error-correcting codes of length 15: Part I--Classification," IEEE Trans.
Inform. Theory vol. 55, pp. 4657--4660, 2009]. In the current accompanying
work, the classified codes are studied in great detail, and their main
properties are tabulated. The results include the fact that 33 of the 80
Steiner triple systems of order 15 occur in such codes. Further understanding
is gained on full-rank codes via switching, as it turns out that all but two
full-rank codes can be obtained through a series of such transformations from
the Hamming code. Other topics studied include (non)systematic codes, embedded
one-error-correcting codes, and defining sets of codes. A classification of
certain mixed perfect codes is also obtained.Comment: v2: fixed two errors (extension of nonsystematic codes, table of
coordinates fixed by symmetries of codes), added and extended many other
result
Linear recursive odometers and beta-expansions
The aim of this paper is to study the connection between different properties
related to -expansions. In particular, the relation between two
conditions, both ensuring pure discrete spectrum of the odometer, is analysed.
The first one is the so-called Hypothesis B for the -odometers and the
second one is denoted by (QM) and it has been introduced in the framework of
tilings associated to Pisot -numerations
The road to deterministic matrices with the restricted isometry property
The restricted isometry property (RIP) is a well-known matrix condition that
provides state-of-the-art reconstruction guarantees for compressed sensing.
While random matrices are known to satisfy this property with high probability,
deterministic constructions have found less success. In this paper, we consider
various techniques for demonstrating RIP deterministically, some popular and
some novel, and we evaluate their performance. In evaluating some techniques,
we apply random matrix theory and inadvertently find a simple alternative proof
that certain random matrices are RIP. Later, we propose a particular class of
matrices as candidates for being RIP, namely, equiangular tight frames (ETFs).
Using the known correspondence between real ETFs and strongly regular graphs,
we investigate certain combinatorial implications of a real ETF being RIP.
Specifically, we give probabilistic intuition for a new bound on the clique
number of Paley graphs of prime order, and we conjecture that the corresponding
ETFs are RIP in a manner similar to random matrices.Comment: 24 page
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