10,859 research outputs found
The streaming -mismatch problem
We consider the streaming complexity of a fundamental task in approximate
pattern matching: the -mismatch problem. It asks to compute Hamming
distances between a pattern of length and all length- substrings of a
text for which the Hamming distance does not exceed a given threshold . In
our problem formulation, we report not only the Hamming distance but also, on
demand, the full \emph{mismatch information}, that is the list of mismatched
pairs of symbols and their indices. The twin challenges of streaming pattern
matching derive from the need both to achieve small working space and also to
guarantee that every arriving input symbol is processed quickly.
We present a streaming algorithm for the -mismatch problem which uses
bits of space and spends \ourcomplexity time on
each symbol of the input stream, which consists of the pattern followed by the
text. The running time almost matches the classic offline solution and the
space usage is within a logarithmic factor of optimal.
Our new algorithm therefore effectively resolves and also extends an open
problem first posed in FOCS'09. En route to this solution, we also give a
deterministic -bit encoding of all
the alignments with Hamming distance at most of a length- pattern within
a text of length . This secondary result provides an optimal solution to
a natural communication complexity problem which may be of independent
interest.Comment: 27 page
A Dialogue of Multipoles: Matched Asymptotic Expansion for Caged Black Holes
No analytic solution is known to date for a black hole in a compact
dimension. We develop an analytic perturbation theory where the small parameter
is the size of the black hole relative to the size of the compact dimension. We
set up a general procedure for an arbitrary order in the perturbation series
based on an asymptotic matched expansion between two coordinate patches: the
near horizon zone and the asymptotic zone. The procedure is ordinary
perturbation expansion in each zone, where additionally some boundary data
comes from the other zone, and so the procedure alternates between the zones.
It can be viewed as a dialogue of multipoles where the black hole changes its
shape (mass multipoles) in response to the field (multipoles) created by its
periodic "mirrors", and that in turn changes its field and so on. We present
the leading correction to the full metric including the first correction to the
area-temperature relation, the leading term for black hole eccentricity and the
"Archimedes effect". The next order corrections will appear in a sequel. On the
way we determine independently the static perturbations of the Schwarzschild
black hole in dimension d>=5, where the system of equations can be reduced to
"a master equation" - a single ordinary differential equation. The solutions
are hypergeometric functions which in some cases reduce to polynomials.Comment: 47 pages, 12 figures, minor corrections described at the end of the
introductio
The Factorized S-Matrix of CFT/AdS
We argue that the recently discovered integrability in the large-N CFT/AdS
system is equivalent to diffractionless scattering of the corresponding hidden
elementary excitations. This suggests that, perhaps, the key tool for finding
the spectrum of this system is neither the gauge theory's dilatation operator
nor the string sigma model's quantum Hamiltonian, but instead the respective
factorized S-matrix. To illustrate the idea, we focus on the closed fermionic
su(1|1) sector of the N=4 gauge theory. We introduce a new technique, the
perturbative asymptotic Bethe ansatz, and use it to extract this sector's
three-loop S-matrix from Beisert's involved algebraic work on the three-loop
su(2|3) sector. We then show that the current knowledge about semiclassical and
near-plane-wave quantum strings in the su(2), su(1|1) and sl(2) sectors of
AdS_5 x S^5 is fully consistent with the existence of a factorized S-matrix.
Analyzing the available information, we find an intriguing relation between the
three associated S-matrices. Assuming that the relation also holds in gauge
theory, we derive the three-loop S-matrix of the sl(2) sector even though this
sector's dilatation operator is not yet known beyond one loop. The resulting
Bethe ansatz reproduces the three-loop anomalous dimensions of twist-two
operators recently conjectured by Kotikov, Lipatov, Onishchenko and Velizhanin,
whose work is based on a highly complex QCD computation of Moch, Vermaseren and
Vogt.Comment: 38 pages, LaTeX, JHEP3.cl
The Parallelism Motifs of Genomic Data Analysis
Genomic data sets are growing dramatically as the cost of sequencing
continues to decline and small sequencing devices become available. Enormous
community databases store and share this data with the research community, but
some of these genomic data analysis problems require large scale computational
platforms to meet both the memory and computational requirements. These
applications differ from scientific simulations that dominate the workload on
high end parallel systems today and place different requirements on programming
support, software libraries, and parallel architectural design. For example,
they involve irregular communication patterns such as asynchronous updates to
shared data structures. We consider several problems in high performance
genomics analysis, including alignment, profiling, clustering, and assembly for
both single genomes and metagenomes. We identify some of the common
computational patterns or motifs that help inform parallelization strategies
and compare our motifs to some of the established lists, arguing that at least
two key patterns, sorting and hashing, are missing
Inferring Algebraic Effects
We present a complete polymorphic effect inference algorithm for an ML-style
language with handlers of not only exceptions, but of any other algebraic
effect such as input & output, mutable references and many others. Our main aim
is to offer the programmer a useful insight into the effectful behaviour of
programs. Handlers help here by cutting down possible effects and the resulting
lengthy output that often plagues precise effect systems. Additionally, we
present a set of methods that further simplify the displayed types, some even
by deliberately hiding inferred information from the programmer
One-loop quantization of rigid spinning strings in with mixed flux
We compute the one-loop correction to the classical dispersion relation of
rigid closed spinning strings with two equal angular momenta in the background supported with a mixture of R-R and NS-NS
three-form fluxes. This analysis is extended to the case of two arbitrary
angular momenta in the pure NS-NS limit. We perform this computation by means
of two different methods. The first method relies on the Euler-Lagrange
equations for the quadratic fluctuations around the classical solution, while
the second one exploits the underlying integrability of the problem through the
finite-gap equations. We find that the one-loop correction vanishes in the pure
NS-NS limit.Comment: 35 pages. v2: Minor changes and references updated. v3: Published
versio
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