2,986 research outputs found
String Synchronizing Sets: Sublinear-Time BWT Construction and Optimal LCE Data Structure
Burrows-Wheeler transform (BWT) is an invertible text transformation that,
given a text of length , permutes its symbols according to the
lexicographic order of suffixes of . BWT is one of the most heavily studied
algorithms in data compression with numerous applications in indexing, sequence
analysis, and bioinformatics. Its construction is a bottleneck in many
scenarios, and settling the complexity of this task is one of the most
important unsolved problems in sequence analysis that has remained open for 25
years. Given a binary string of length , occupying machine
words, the BWT construction algorithm due to Hon et al. (SIAM J. Comput., 2009)
runs in time and space. Recent advancements (Belazzougui,
STOC 2014, and Munro et al., SODA 2017) focus on removing the alphabet-size
dependency in the time complexity, but they still require time.
In this paper, we propose the first algorithm that breaks the -time
barrier for BWT construction. Given a binary string of length , our
procedure builds the Burrows-Wheeler transform in time and
space. We complement this result with a conditional lower bound
proving that any further progress in the time complexity of BWT construction
would yield faster algorithms for the very well studied problem of counting
inversions: it would improve the state-of-the-art -time
solution by Chan and P\v{a}tra\c{s}cu (SODA 2010). Our algorithm is based on a
novel concept of string synchronizing sets, which is of independent interest.
As one of the applications, we show that this technique lets us design a data
structure of the optimal size that answers Longest Common
Extension queries (LCE queries) in time and, furthermore, can be
deterministically constructed in the optimal time.Comment: Full version of a paper accepted to STOC 201
Nonminimal supersymmetric standard model with lepton number violation
We carry out a detailed analysis of the nonminimal supersymmetric standard
model with lepton number violation. The model contains a unique trilinear
lepton number violating term in the superpotential which can give rise to
neutrino masses at the tree level. We search for the gauged discrete symmetries
realized by cyclic groups which preserve the structure of the associated
trilinear superpotential of this model, and which satisfy the constraints of
the anomaly cancellation. The implications of this trilinear lepton number
violating term in the superpotential and the associated soft supersymmetry
breaking term on the phenomenology of the light neutrino masses and mixing is
studied in detail. We evaluate the tree and loop level contributions to the
neutrino mass matrix in this model. We search for possible suppression
mechanism which could explain large hierarchies and maximal mixing angles.Comment: Latex file, 43 pages, 2 figure
A Characterization of Infinite LSP Words
G. Fici proved that a finite word has a minimal suffix automaton if and only
if all its left special factors occur as prefixes. He called LSP all finite and
infinite words having this latter property. We characterize here infinite LSP
words in terms of -adicity. More precisely we provide a finite set of
morphisms and an automaton such that an infinite word is LSP if
and only if it is -adic and all its directive words are recognizable by
SU(5) Grand Unification in Extra Dimensions and Proton Decay
We analyse proton decay in the context of simple supersymmetric SU(5) grand
unified models with an extra compact spatial dimension described by the
orbifold S^1/(Z_2 x Z_2'). Gauge and Higgs degrees of freedom live in the bulk,
while matter fields can only live at the fixed point branes. We present an
extended discussion of matter interactions on the brane. We show that proton
decay is naturally suppressed or even forbidden by suitable implementations of
the parity symmetries on the brane. The corresponding mechanism does not affect
the SU(5) description of fermion masses also including the neutrino sector,
where Majorana mass terms remain allowed.Comment: 11 page
Characterization of infinite LSP words and endomorphisms preserving the LSP property
Answering a question of G. Fici, we give an -adic characterization of
thefamily of infinite LSP words, that is, the family of infinite words having
all their left special factors as prefixes.More precisely we provide a finite
set of morphisms and an automaton such that an infinite word is
LSP if and only if it is -adic and one of its directive words is
recognizable by .Then we characterize the endomorphisms that preserve
the property of being LSP for infinite words.This allows us to prove that there
exists no set of endomorphisms for which the set of infinite LSP words
corresponds to the set of -adic words. This implies that an automaton is
required no matter which set of morphisms is used.Comment: arXiv admin note: text overlap with arXiv:1705.0578
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