9,522 research outputs found
Multiplpe Choice Minority Game With Different Publicly Known Histories
In the standard Minority Game, players use historical minority choices as the
sole public information to pick one out of the two alternatives. However,
publishing historical minority choices is not the only way to present global
system information to players when more than two alternatives are available.
Thus, it is instructive to study the dynamics and cooperative behaviors of this
extended game as a function of the global information provided. We numerically
find that although the system dynamics depends on the kind of public
information given to the players, the degree of cooperation follows the same
trend as that of the standard Minority Game. We also explain most of our
findings by the crowd-anticrowd theory.Comment: Extensively revised, to appear in New J Phys, 7 pages with 4 figure
On the maximal number of cubic subwords in a string
We investigate the problem of the maximum number of cubic subwords (of the
form ) in a given word. We also consider square subwords (of the form
). The problem of the maximum number of squares in a word is not well
understood. Several new results related to this problem are produced in the
paper. We consider two simple problems related to the maximum number of
subwords which are squares or which are highly repetitive; then we provide a
nontrivial estimation for the number of cubes. We show that the maximum number
of squares such that is not a primitive word (nonprimitive squares) in
a word of length is exactly , and the
maximum number of subwords of the form , for , is exactly .
In particular, the maximum number of cubes in a word is not greater than
either. Using very technical properties of occurrences of cubes, we improve
this bound significantly. We show that the maximum number of cubes in a word of
length is between and . (In particular, we improve the
lower bound from the conference version of the paper.)Comment: 14 page
Computing Runs on a General Alphabet
We describe a RAM algorithm computing all runs (maximal repetitions) of a
given string of length over a general ordered alphabet in
time and linear space. Our algorithm outperforms all
known solutions working in time provided , where is the alphabet size. We conjecture that there
exists a linear time RAM algorithm finding all runs.Comment: 4 pages, 2 figure
On Extensions of Maximal Repeats in Compressed Strings
This paper provides an upper bound for several subsets of maximal repeats and
maximal pairs in compressed strings and also presents a formerly unknown
relationship between maximal pairs and the run-length Burrows-Wheeler
transform.
This relationship is used to obtain a different proof for the Burrows-Wheeler
conjecture which has recently been proven by Kempa and Kociumaka in "Resolution
of the Burrows-Wheeler Transform Conjecture".
More formally, this paper proves that a string with LZ77-factors and
without -th powers has at most runs in the
run-length Burrows-Wheeler transform and the number of arcs in the compacted
directed acyclic word graph of is bounded from above by
Linear Compressed Pattern Matching for Polynomial Rewriting (Extended Abstract)
This paper is an extended abstract of an analysis of term rewriting where the
terms in the rewrite rules as well as the term to be rewritten are compressed
by a singleton tree grammar (STG). This form of compression is more general
than node sharing or representing terms as dags since also partial trees
(contexts) can be shared in the compression. In the first part efficient but
complex algorithms for detecting applicability of a rewrite rule under
STG-compression are constructed and analyzed. The second part applies these
results to term rewriting sequences.
The main result for submatching is that finding a redex of a left-linear rule
can be performed in polynomial time under STG-compression.
The main implications for rewriting and (single-position or parallel)
rewriting steps are: (i) under STG-compression, n rewriting steps can be
performed in nondeterministic polynomial time. (ii) under STG-compression and
for left-linear rewrite rules a sequence of n rewriting steps can be performed
in polynomial time, and (iii) for compressed rewrite rules where the left hand
sides are either DAG-compressed or ground and STG-compressed, and an
STG-compressed target term, n rewriting steps can be performed in polynomial
time.Comment: In Proceedings TERMGRAPH 2013, arXiv:1302.599
Semi-Classical Quantization of Circular Strings in De Sitter and Anti De Sitter Spacetimes
We compute the {\it exact} equation of state of circular strings in the (2+1)
dimensional de Sitter (dS) and anti de Sitter (AdS) spacetimes, and analyze its
properties for the different (oscillating, contracting and expanding) strings.
The string equation of state has the perfect fluid form with
the pressure and energy expressed closely and completely in terms of elliptic
functions, the instantaneous coefficient depending on the elliptic
modulus. We semi-classically quantize the oscillating circular strings. The
string mass is being the Casimir operator,
of the -dS [-AdS] group, and is
the Hubble constant. We find \alpha'm^2_{\mbox{dS}}\approx 5.9n,\;(n\in N_0),
and a {\it finite} number of states N_{\mbox{dS}}\approx 0.17/(H^2\alpha') in
de Sitter spacetime; m^2_{\mbox{AdS}}\approx 4H^2n^2 (large ) and
N_{\mbox{AdS}}=\infty in anti de Sitter spacetime. The level spacing grows
with in AdS spacetime, while is approximately constant (although larger
than in Minkowski spacetime) in dS spacetime. The massive states in dS
spacetime decay through tunnel effect and the semi-classical decay probability
is computed. The semi-classical quantization of {\it exact} (circular) strings
and the canonical quantization of generic string perturbations around the
string center of mass strongly agree.Comment: Latex, 26 pages + 2 tables and 5 figures that can be obtained from
the authors on request. DEMIRM-Obs de Paris-9404
Algorithms to Compute the Lyndon Array
We first describe three algorithms for computing the Lyndon array that have
been suggested in the literature, but for which no structured exposition has
been given. Two of these algorithms execute in quadratic time in the worst
case, the third achieves linear time, but at the expense of prior computation
of both the suffix array and the inverse suffix array of x. We then go on to
describe two variants of a new algorithm that avoids prior computation of
global data structures and executes in worst-case n log n time. Experimental
evidence suggests that all but one of these five algorithms require only linear
execution time in practice, with the two new algorithms faster by a small
factor. We conjecture that there exists a fast and worst-case linear-time
algorithm to compute the Lyndon array that is also elementary (making no use of
global data structures such as the suffix array)
Phase diagram of an extended quantum dimer model on the hexagonal lattice
We introduce a quantum dimer model on the hexagonal lattice that, in addition
to the standard three-dimer kinetic and potential terms, includes a competing
potential part counting dimer-free hexagons. The zero-temperature phase diagram
is studied by means of quantum Monte Carlo simulations, supplemented by
variational arguments. It reveals some new crystalline phases and a cascade of
transitions with rapidly changing flux (tilt in the height language). We
analyze perturbatively the vicinity of the Rokhsar-Kivelson point, showing that
this model has the microscopic ingredients needed for the "devil's staircase"
scenario [E. Fradkin et al., Phys. Rev. B 69, 224415 (2004)], and is therefore
expected to produce fractal variations of the ground-state flux.Comment: Published version. 5 pages + 8 (Supplemental Material), 31
references, 10 color figure
- …