20 research outputs found
Non-Rectangular Convolutions and (Sub-)Cadences with Three Elements
The discrete acyclic convolution computes the 2n-1 sums sum_{i+j=k; (i,j) in
[0,1,2,...,n-1]^2} (a_i b_j) in O(n log n) time. By using suitable offsets and
setting some of the variables to zero, this method provides a tool to calculate
all non-zero sums sum_{i+j=k; (i,j) in (P cap Z^2)} (a_i b_j) in a rectangle P
with perimeter p in O(p log p) time.
This paper extends this geometric interpretation in order to allow arbitrary
convex polygons P with k vertices and perimeter p. Also, this extended
algorithm only needs O(k + p(log p)^2 log k) time.
Additionally, this paper presents fast algorithms for counting sub-cadences
and cadences with 3 elements using this extended method
Faster Queries for Longest Substring Palindrome After Block Edit
Palindromes are important objects in strings which have been extensively studied from combinatorial, algorithmic, and bioinformatics points of views. Manacher [J. ACM 1975] proposed a seminal algorithm that computes the longest substring palindromes (LSPals) of a given string in O(n) time, where n is the length of the string. In this paper, we consider the problem of finding the LSPal after the string is edited. We present an algorithm that uses O(n) time and space for preprocessing, and answers the length of the LSPals in O(l + log log n) time, after a substring in T is replaced by a string of arbitrary length l. This outperforms the query algorithm proposed in our previous work [CPM 2018] that uses O(l + log n) time for each query
Longest substring palindrome after edit
It is known that the length of the longest substring palindromes (LSPals) of a given string T of length n can be computed in O(n) time by Manacher\u27s algorithm [J. ACM \u2775]. In this paper, we consider the problem of finding the LSPal after the string is edited. We present an algorithm that uses O(n) time and space for preprocessing, and answers the length of the LSPals in O(log (min {sigma, log n })) time after single character substitution, insertion, or deletion, where sigma denotes the number of distinct characters appearing in T. We also propose an algorithm that uses O(n) time and space for preprocessing, and answers the length of the LSPals in O(l + log n) time, after an existing substring in T is replaced by a string of arbitrary length l
Optimal LZ-End Parsing Is Hard
LZ-End is a variant of the well-known Lempel-Ziv parsing family such that each phrase of the parsing has a previous occurrence, with the additional constraint that the previous occurrence must end at the end of a previous phrase. LZ-End was initially proposed as a greedy parsing, where each phrase is determined greedily from left to right, as the longest factor that satisfies the above constraint [Kreft & Navarro, 2010]. In this work, we consider an optimal LZ-End parsing that has the minimum number of phrases in such parsings. We show that a decision version of computing the optimal LZ-End parsing is NP-complete by showing a reduction from the vertex cover problem. Moreover, we give a MAX-SAT formulation for the optimal LZ-End parsing adapting an approach for computing various NP-hard repetitiveness measures recently presented by [Bannai et al., 2022]. We also consider the approximation ratio of the size of greedy LZ-End parsing to the size of the optimal LZ-End parsing, and give a lower bound of the ratio which asymptotically approaches 2
Detecting k-(Sub-)Cadences and Equidistant Subsequence Occurrences
The equidistant subsequence pattern matching problem is considered. Given a
pattern string and a text string , we say that is an
\emph{equidistant subsequence} of if is a subsequence of the text such
that consecutive symbols of in the occurrence are equally spaced. We can
consider the problem of equidistant subsequences as generalizations of
(sub-)cadences. We give bit-parallel algorithms that yield time
algorithms for finding -(sub-)cadences and equidistant subsequences.
Furthermore, and time algorithms, respectively for
equidistant and Abelian equidistant matching for the case , are shown.
The algorithms make use of a technique that was recently introduced which can
efficiently compute convolutions with linear constraints
Data structures for computing unique palindromes in static and non-static strings
A palindromic substring of a string is said to be a shortest
unique palindromic substring (SUPS) in for an interval if is a shortest palindromic substring such that occurs only once
in , and contains . The SUPS problem is, given a string
of length , to construct a data structure that can compute all the SUPSs for
any given query interval. It is known that any SUPS query can be answered in
time after -time preprocessing, where is the number
of SUPSs to output [Inoue et al., 2018]. In this paper, we first show that
is at most , and the upper bound is tight. We also show that the
total sum of lengths of minimal unique palindromic substrings of string ,
which is strongly related to SUPSs, is . Then, we present the first
-bits data structures that can answer any SUPS query in constant time.
Also, we present an algorithm to solve the SUPS problem for a sliding window
that can answer any query in time and update data structures in
amortized time, where is the size of the
window, and is the alphabet size. Furthermore, we consider the SUPS
problem in the after-edit model and present an efficient algorithm. Namely, we
present an algorithm that uses time for preprocessing and answers any
SUPS queries in time after single
character substitution. Finally, as a by-product, we propose a fully-dynamic
data structure for range minimum queries (RmQs) with a constraint where the
width of each query range is limited to poly-logarithmic. The constrained RmQ
data structure can answer such a query in constant time and support a
single-element edit operation in amortized constant time
Regulation of cell migration and cytokine production by HGF-like protein (HLP)/macrophage stimulating protein (MSP) in primary microglia
金沢大学がん研究所分子標的がん医療研究開発センターHGF-like protein (HLP)/macrophage stimulating protein (MSP) is the only structural relative of hepatocyte growth factor (HGF), and is involved in the regulation of peripheral macrophage activation. However the actions of HLP in microglia, a species of macrophage in the nervous system, which is closely involved in the neural degeneration and regeneration, is not yet understood. This study found that Ron, the receptor for HLP, is expressed in primary microglia using RT-PCR, immunocytochemical staining and Western blotting, and, thus, sought to elucidate the function of HLP on the primary microglia. HLP promoted microglial migration without affecting cell survival and proliferation. Furthermore, real-time quantitative RT-PCR analysis revealed that HLP greatly increased the mRNA of inflammatory, cytokines, including IL-6 and GM-CSF, and iNOS. These findings provide the first evidence that HLP has the potential to modulate inflammatory actions of microglia, which proposes novel aspects for the process of degeneration and/or regeneration of the brain