66,583 research outputs found
Matrix Models on Large Graphs
We consider the spherical limit of multi-matrix models on regular target
graphs, for instance single or multiple Potts models, or lattices of arbitrary
dimension. We show, to all orders in the low temperature expansion, that when
the degree of the target graph , the free energy becomes
independent of the target graph, up to simple transformations of the matter
coupling constant. Furthermore, this universal free energy contains
contributions only from those surfaces which are made up of ``baby universes''
glued together into trees, all non-universal and non-tree contributions being
suppressed by inverse powers of . Each order of the free energy is put
into a simple, algebraic form.Comment: 19pp. (uses harvmac and epsf), PUPT-139
Renormalization group approach to chaotic strings
Coupled map lattices of weakly coupled Chebychev maps, so-called chaotic
strings, may have a profound physical meaning in terms of dynamical models of
vacuum fluctuations in stochastically quantized field theories. Here we present
analytic results for the invariant density of chaotic strings, as well as for
the coupling parameter dependence of given observables of the chaotic string
such as the vacuum expectation value. A highly nontrivial and selfsimilar
parameter dependence is found, produced by perturbative and nonperturbative
effects, for which we develop a mathematical description in terms of suitable
scaling functions. Our analytic results are in good agreement with numerical
simulations of the chaotic dynamics.Comment: 36 pages, 18 figures - v2 contains slightly more than the published
versio
Pattern matching in Lempel-Ziv compressed strings: fast, simple, and deterministic
Countless variants of the Lempel-Ziv compression are widely used in many
real-life applications. This paper is concerned with a natural modification of
the classical pattern matching problem inspired by the popularity of such
compression methods: given an uncompressed pattern s[1..m] and a Lempel-Ziv
representation of a string t[1..N], does s occur in t? Farach and Thorup gave a
randomized O(nlog^2(N/n)+m) time solution for this problem, where n is the size
of the compressed representation of t. We improve their result by developing a
faster and fully deterministic O(nlog(N/n)+m) time algorithm with the same
space complexity. Note that for highly compressible texts, log(N/n) might be of
order n, so for such inputs the improvement is very significant. A (tiny)
fragment of our method can be used to give an asymptotically optimal solution
for the substring hashing problem considered by Farach and Muthukrishnan.Comment: submitte
A Minimal Periods Algorithm with Applications
Kosaraju in ``Computation of squares in a string'' briefly described a
linear-time algorithm for computing the minimal squares starting at each
position in a word. Using the same construction of suffix trees, we generalize
his result and describe in detail how to compute in O(k|w|)-time the minimal
k-th power, with period of length larger than s, starting at each position in a
word w for arbitrary exponent and integer . We provide the
complete proof of correctness of the algorithm, which is somehow not completely
clear in Kosaraju's original paper. The algorithm can be used as a sub-routine
to detect certain types of pseudo-patterns in words, which is our original
intention to study the generalization.Comment: 14 page
Calculation of Graviton Scattering Amplitudes using String-Based Methods
Techniques based upon the string organisation of amplitudes may be used to
simplify field theory calculations. We apply these techniques to perturbative
gravity and calculate all one-loop amplitudes for four-graviton scattering with
arbitrary internal particle content. Decomposing the amplitudes into
contributions arising from supersymmetric multiplets greatly simplifies these
calculations. We also discuss how unitarity may be used to constrain the
amplitudes.Comment: 25 pages +5 figs. , SWAT-94-37 UCLA/TEP/94/30, Plain TeX. (Typos in
eqns. fixed
Universal Compressed Text Indexing
The rise of repetitive datasets has lately generated a lot of interest in
compressed self-indexes based on dictionary compression, a rich and
heterogeneous family that exploits text repetitions in different ways. For each
such compression scheme, several different indexing solutions have been
proposed in the last two decades. To date, the fastest indexes for repetitive
texts are based on the run-length compressed Burrows-Wheeler transform and on
the Compact Directed Acyclic Word Graph. The most space-efficient indexes, on
the other hand, are based on the Lempel-Ziv parsing and on grammar compression.
Indexes for more universal schemes such as collage systems and macro schemes
have not yet been proposed. Very recently, Kempa and Prezza [STOC 2018] showed
that all dictionary compressors can be interpreted as approximation algorithms
for the smallest string attractor, that is, a set of text positions capturing
all distinct substrings. Starting from this observation, in this paper we
develop the first universal compressed self-index, that is, the first indexing
data structure based on string attractors, which can therefore be built on top
of any dictionary-compressed text representation. Let be the size of a
string attractor for a text of length . Our index takes
words of space and supports locating the
occurrences of any pattern of length in
time, for any constant . This is, in particular, the first index
for general macro schemes and collage systems. Our result shows that the
relation between indexing and compression is much deeper than what was
previously thought: the simple property standing at the core of all dictionary
compressors is sufficient to support fast indexed queries.Comment: Fixed with reviewer's comment
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