In recent years, there has been an increasing interest in planted (l, d) motif search (PMS) with applications to discovering significant segments in biological sequences. However, there has been little discussion about PMS over large alphabets. This paper focuses on motif stem search (MSS), which is recently introduced to search motifs on large-alphabet inputs. A motif stem is an l-length strin...

Time series motif discovery is important as the discovered motifs generally form the primitives for many data mining tasks. In this work, we examine the problem of discovering groups of motifs from different time series that exhibit some lag relationships. We define a new class of pattern called lagPatterns that captures the invariant ordering among motifs. lagPatterns characterize localized as...

arising from . We introduce the notion of p-exactness for a sequence and show that any interval of (*) not including Mn 2 or Mn+1 2 respectively, is p-exact for any prime p>0. This result can be extended to various submodules and quotient modules, and we give general constructions for permutation groups on 0 of order not divisible by p. If an interval of (*) , or an equivalent sequence arising ...

Exact values and bounds on the k-error linear complexity of p-periodic sequences which are constant on the cyclotomic classes are determined. This family of sequences includes sequences of discrete logarithms, Legendre sequences and Hall’s sextic residue sequence.

Abstract Fix an odd prime $p$. The results in this paper are modeled after work of Hesselholt and Hesselholt–Madsen on the $p$-typical absolute de Rham–Witt complex mixed characteristic. We have two primary results. 1st result is exact sequence that describes kernel restriction map over $A$, where $A$ ring integers algebraic extension $\textbf{Q}_p$ or a $p$-torsion-free perfectoid ring. 2nd de...

The p-dispersion-sum problem is the problem of locating p facilities at some of n prede-ned locations, such that the distance sum between the p facilities is maximized. The problem has applications in telecommunication (where it is desirable to disperse the transceivers in order to minimize interference problems), and in location of shops and service-stations (where the mutual competition shoul...

Extracting motifs from a set of DNA sequences is important in computational biology. Occurrence probability is a common used statistics to evaluate the statistical significance of a motif. A main problem is how to calculate the occurrence probability of the motif on the random model of DNA sequence efficiently and accurately. In this paper, we are interested in a particular motif model which is...

This paper deals with finding a generalized median stable matching (GMSM), introducedby Teo and Sethuraman (1998) as a fair stable marriage. Cheng (2008) showed that findingthe i-th GMSM is #P-hard in case of i = O(N), where N is the number of stable matchingsof an instance. She also gave an exact algorithm running in polynomial time in case ofi = O(log logN), and the comple...