615,405 research outputs found
Sequential Pattern Mining with Multidimensional Interval Items
In real sequence pattern mining scenarios, the interval information between two item sets is very important. However, although existing algorithms can effectively mine frequent subsequence sets, the interval information is ignored. This paper aims to mine sequential patterns with multidimensional interval items in sequence databases. In order to address this problem, this paper defines and specifies the interval event problem in the sequential pattern mining task. Then, the interval event items framework is proposed to handle the multidimensional interval event items. Moreover, the MII-Prefixspan algorithm is introduced for the sequential pattern with multidimensional interval event items mining tasks. This algorithm adds the processing of interval event items in the mining process. We can get richer and more in line with actual needs information from mined sequence patterns through these methods. This scheme is applied to the actual website behaviour analysis task to obtain more valuable information for web optimization and provide more valuable sequence pattern information for practical problems. This work also opens a new pathway toward more efficient sequential pattern mining tasks
Topics in inference and decision-making with partial knowledge
Two essential elements needed in the process of inference and decision-making are prior probabilities and likelihood functions. When both of these components are known accurately and precisely, the Bayesian approach provides a consistent and coherent solution to the problems of inference and decision-making. In many situations, however, either one or both of the above components may not be known, or at least may not be known precisely. This problem of partial knowledge about prior probabilities and likelihood functions is addressed. There are at least two ways to cope with this lack of precise knowledge: robust methods, and interval-valued methods. First, ways of modeling imprecision and indeterminacies in prior probabilities and likelihood functions are examined; then how imprecision in the above components carries over to the posterior probabilities is examined. Finally, the problem of decision making with imprecise posterior probabilities and the consequences of such actions are addressed. Application areas where the above problems may occur are in statistical pattern recognition problems, for example, the problem of classification of high-dimensional multispectral remote sensing image data
On minima of sum of theta functions and Mueller-Ho Conjecture
Let and be the theta
function associated with the lattice .
In this paper we consider the following pair of minimization problems
where the parameter represents the competition of two
intertwining lattices. We find that as varies the optimal lattices admit
a novel pattern: they move from rectangular (the ratio of long and short side
changes from to 1), square, rhombus (the angle changes from to
) to hexagonal; furthermore, there exists a closed interval of
such that the optimal lattices is always square lattice. This is in sharp
contrast to optimal lattice shapes for single theta function (
case), for which the hexagonal lattice prevails. As a consequence, we give a
partial answer to optimal lattice arrangements of vortices in competing systems
of Bose-Einstein condensates as conjectured (and numerically and experimentally
verified) by Mueller-Ho \cite{Mue2002}.Comment: 42 pages; comments welcom
Some open problems on permutation patterns
This is a brief survey of some open problems on permutation patterns, with an
emphasis on subjects not covered in the recent book by Kitaev, \emph{Patterns
in Permutations and words}. I first survey recent developments on the
enumeration and asymptotics of the pattern 1324, the last pattern of length 4
whose asymptotic growth is unknown, and related issues such as upper bounds for
the number of avoiders of any pattern of length for any given . Other
subjects treated are the M\"obius function, topological properties and other
algebraic aspects of the poset of permutations, ordered by containment, and
also the study of growth rates of permutation classes, which are containment
closed subsets of this poset.Comment: 20 pages. Related to upcoming talk at the British Combinatorial
Conference 2013. To appear in London Mathematical Society Lecture Note Serie
On the Benefit of Merging Suffix Array Intervals for Parallel Pattern Matching
We present parallel algorithms for exact and approximate pattern matching
with suffix arrays, using a CREW-PRAM with processors. Given a static text
of length , we first show how to compute the suffix array interval of a
given pattern of length in
time for . For approximate pattern matching with differences or
mismatches, we show how to compute all occurrences of a given pattern in
time, where is the size of the alphabet
and . The workhorse of our algorithms is a data structure
for merging suffix array intervals quickly: Given the suffix array intervals
for two patterns and , we present a data structure for computing the
interval of in sequential time, or in
parallel time. All our data structures are of size bits (in addition to
the suffix array)
Problems in using social work records in assessing change
Thesis (M.S.)--Boston Universit
Interlocked permutations
The zero-error capacity of channels with a countably infinite input alphabet
formally generalises Shannon's classical problem about the capacity of discrete
memoryless channels. We solve the problem for three particular channels. Our
results are purely combinatorial and in line with previous work of the third
author about permutation capacity.Comment: 8 page
Governing Singularities of Schubert Varieties
We present a combinatorial and computational commutative algebra methodology
for studying singularities of Schubert varieties of flag manifolds.
We define the combinatorial notion of *interval pattern avoidance*. For
"reasonable" invariants P of singularities, we geometrically prove that this
governs (1) the P-locus of a Schubert variety, and (2) which Schubert varieties
are globally not P. The prototypical case is P="singular"; classical pattern
avoidance applies admirably for this choice [Lakshmibai-Sandhya'90], but is
insufficient in general.
Our approach is analyzed for some common invariants, including
Kazhdan-Lusztig polynomials, multiplicity, factoriality, and Gorensteinness,
extending [Woo-Yong'05]; the description of the singular locus (which was
independently proved by [Billey-Warrington '03], [Cortez '03],
[Kassel-Lascoux-Reutenauer'03], [Manivel'01]) is also thus reinterpreted.
Our methods are amenable to computer experimentation, based on computing with
*Kazhdan-Lusztig ideals* (a class of generalized determinantal ideals) using
Macaulay 2. This feature is supplemented by a collection of open problems and
conjectures.Comment: 23 pages. Software available at the authors' webpages. Version 2 is
the submitted version. It has a nomenclature change: "Bruhat-restricted
pattern avoidance" is renamed "interval pattern avoidance"; the introduction
has been reorganize
Longest Common Pattern between two Permutations
In this paper, we give a polynomial (O(n^8)) algorithm for finding a longest
common pattern between two permutations of size n given that one is separable.
We also give an algorithm for general permutations whose complexity depends on
the length of the longest simple permutation involved in one of our
permutations
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