59,435 research outputs found
Open minimal strings and open Gelfand-Dickey hierarchies
We study the connection between minimal Liouville string theory and
generalized open KdV hierarchies. We are interested in generalizing Douglas
string equation formalism to the open topology case. We show that combining the
results of the closed topology, based on the Frobenius manifold structure and
resonance transformations, with the appropriate open case modification, which
requires the insertion of macroscopic loop operators, we reproduce the
well-known result for the expectation value of a bulk operator for the FZZT
brane coupled to the general (q,p) minimal model. The matching of the results
of the two setups gives new evidence of the connection between minimal
Liouville gravity and the theory of Topological Gravity
Suffix Sorting via Matching Statistics
Funding Information: Academy of Finland grants 339070 and 351150 Publisher Copyright: © Zsuzsanna Lipták, Francesco Masillo, and Simon J. Puglisi.We introduce a new algorithm for constructing the generalized suffix array of a collection of highly similar strings. As a first step, we construct a compressed representation of the matching statistics of the collection with respect to a reference string. We then use this data structure to distribute suffixes into a partial order, and subsequently to speed up suffix comparisons to complete the generalized suffix array. Our experimental evidence with a prototype implementation (a tool we call sacamats) shows that on string collections with highly similar strings we can construct the suffix array in time competitive with or faster than the fastest available methods. Along the way, we describe a heuristic for fast computation of the matching statistics of two strings, which may be of independent interest.Peer reviewe
A sheaf-theoretic approach to pattern matching and related problems
AbstractWe present a general theory of pattern matching by adopting an extensional, geometric view of patterns. Representing the geometry of the pattern via a Grothendieck topology, the extension of the matching relation for a constant target and varying pattern forms a sheaf. We derive a generalized version of the Knuth-Morris-Pratt string-matching algorithm by gradually converting this extensional description into an intensional description, i.e., an algorithm. The generality of this approach is illustrated by briefly considering other applications: Earley's algorithm for parsing, Waltz filtering for scene analysis, matching modulo commutativity, and the n-queens problem
Remarks on Black Hole Instabilities and Closed String Tachyons
Physical arguments stemming from the theory of black-hole thermodynamics are
used to put constraints on the dynamics of closed-string tachyon condensation
in Scherk--Schwarz compactifications. A geometrical interpretation of the
tachyon condensation involves an effective capping of a noncontractible cycle,
thus removing the very topology that supports the tachyons. A semiclassical
regime is identified in which the matching between the tachyon condensation and
the black-hole instability flow is possible. We formulate a generalized
correspondence principle and illustrate it in several different circumstances:
an Euclidean interpretation of the transition from strings to black holes
across the Hagedorn temperature and instabilities in the brane-antibrane
system.Comment: harvmac, 20 pp, 4 eps figures. Contribution to Jacob Bekenstein's
Festschrif
The Generalized Asymptotic Equipartition Property: Necessary and Sufficient Conditions
Suppose a string generated by a memoryless source
with distribution is to be compressed with distortion no
greater than , using a memoryless random codebook with distribution
. The compression performance is determined by the ``generalized asymptotic
equipartition property'' (AEP), which states that the probability of finding a
-close match between and any given codeword , is
approximately , where the rate function can be
expressed as an infimum of relative entropies. The main purpose here is to
remove various restrictive assumptions on the validity of this result that have
appeared in the recent literature. Necessary and sufficient conditions for the
generalized AEP are provided in the general setting of abstract alphabets and
unbounded distortion measures. All possible distortion levels are
considered; the source can be stationary and ergodic; and the
codebook distribution can have memory. Moreover, the behavior of the matching
probability is precisely characterized, even when the generalized AEP is not
valid. Natural characterizations of the rate function are
established under equally general conditions.Comment: 19 page
Two-loop AdS_5 x S^5 superstring: testing asymptotic Bethe ansatz and finite size corrections
We continue the investigation of two-loop string corrections to the energy of
a folded string with a spin S in AdS_5 and an angular momentum J in S^5, in the
scaling limit of large J and S with ell=pi J/(lambda^(1/2) ln S)=fixed. We
compute the generalized scaling function at two-loop order f_2(ell) both for
small and large values of ell matching the predictions based on the asymptotic
Bethe ansatz. In particular, in the small ell expansion, we derive an exact
integral form for the ell-dependent coefficient of the Catalan's constant term
in f_2(ell). Also, by resumming a certain subclass of multi-loop Feynman
diagrams we obtain an exact expression for the leading (ln ell) part of
f(lambda^(1/2), ell) which is valid to any order in the alpha'~1/lambda^(1/2)
expansion. At large ell the string energy has a BMN-like expansion and the
first few leading coefficients are expected to be the same at weak and at
strong coupling. We provide a new example of this non-renormalization for the
term which is generated at two loops in string theory and at one-loop in gauge
theory (sub-sub-leading in 1/J). We also derive a simple algebraic formula for
the term of maximal transcendentality in f_2(ell) expanded at large ell. In the
second part of the paper we initiate the study of 2-loop finite size
corrections to the string energy by formally compactifying the spatial
world-sheet direction in the string action expanded near long fast-spinning
string. We observe that the leading finite-size corrections are of "Casimir"
type coming from terms containing at least one massless propagator. We consider
in detail the one-loop order (reproducing the leading Landau-Lifshitz model
prediction) and then focus on the two-loop contributions to the (1/ln S) term
(for J=0). We find that in a certain regularization scheme used to discard
power divergences the two-loop coefficient of the (1/ln S) term appears to
vanish.Comment: 50 pages, 4 figures v2: typos corrected, references adde
Asymptotic Bethe Ansatz S-matrix and Landau-Lifshitz type effective 2-d actions
Motivated by the desire to relate Bethe ansatz equations for anomalous
dimensions found on the gauge theory side of the AdS/CFT correspondence to
superstring theory on AdS_5 x S5 we explore a connection between the asymptotic
S-matrix that enters the Bethe ansatz and an effective two-dimensional quantum
field theory. The latter generalizes the standard ``non-relativistic''
Landau-Lifshitz (LL) model describing low-energy modes of ferromagnetic
Heisenberg spin chain and should be related to a limit of superstring effective
action. We find the exact form of the quartic interaction terms in the
generalized LL type action whose quantum
S-matrix matches the low-energy limit of the asymptotic S-matrix of the spin
chain of Beisert, Dippel and Staudacher (BDS). This generalises to all orders
in the `t Hooft coupling an earlier computation of Klose and Zarembo of the
S-matrix of the standard LL model. We also consider a generalization to the
case when the spin chain S-matrix contains an extra ``string'' phase and
determine the exact form of the LL 4-vertex corresponding to the low-energy
limit of the ansatz of Arutyunov, Frolov and Staudacher (AFS). We explain the
relation between the resulting ``non-relativistic'' non-local action and the
second-derivative string sigma model. We comment on modifications introduced by
strong-coupling corrections to the AFS phase. We mostly discuss the SU(2)
sector but also present generalizations to the SL(2) and SU(1|1) sectors,
confirming universality of the dressing phase contribution by matching the
low-energy limit of the AFS-type spin chain S-matrix with tree-level
string-theory S-matrix.Comment: 52 pages, 4 figures, Imperial-TP-AT-6-2; v2: new sections 7.3 and 7.4
computing string tree-level S-matrix in SL(2) and SU(1|1) sectors, references
adde
Construction of minimal DFAs from biological motifs
Deterministic finite automata (DFAs) are constructed for various purposes in
computational biology. Little attention, however, has been given to the
efficient construction of minimal DFAs. In this article, we define simple
non-deterministic finite automata (NFAs) and prove that the standard subset
construction transforms NFAs of this type into minimal DFAs. Furthermore, we
show how simple NFAs can be constructed from two types of patterns popular in
bioinformatics, namely (sets of) generalized strings and (generalized) strings
with a Hamming neighborhood
- …