ARBic: An All-Round Biclustering Algorithm for Analyzing Gene Expression Data

Background: Identifying significant biclusters of genes with specific expression patterns is an effective approach to reveal functionally correlated genes in gene expression data. However, existing algorithms are limited to finding either broad or narrow biclusters but both due to failure of balancing between effectiveness and efficiency. Methods: We developed a new algorithm ARBic which can accurately identify any meaningful biclusters of shape no matter broad or narrow in a large scale gene expression data matrix, even when the values in the biclusters to be identified have the same distribution as that the background data has. ARBic is developed by integrating column-based and row-based strategies into biclustering procedure. The column-based strategy borrowed from ReBic, a recently published biclustering tool, prefers to narrow bicluters. The row-based strategy newly designed in this article by repeatedly finding a longest path in a specific directed graph prefers to broader ones. Result and Conclusion: When tested and compared to other seven salient biclustering algorithms on simulated datasets, ARBic achieved recovery, relevance and f1-scores 29% higher than the second best algorithm. Furthermore, ARBic substantially outperforms all of them on real datasets and robusts to noises, shapes of biclusters and types of datasets.Code: https://github.com/holyzews/ARBicData: https://doi.org/10.5281/zenodo.5121018

Valued Number And Set

In this essay, the new notion concerning longest path is introduced. Longest path has a close relation with the notion of diameter in graph. The classes of graph are studied in the terms of having the vertex with longest path. Valued number is the number of edges belong to the longest path in the matter of vertex. For every vertex, there’s a valued number and new notion of valued set is the generalization of valued number for the vertex when all vertices of the graphs are corresponded to a vertex which has the greater valued number. For any positive integer, there’s one graph in that, there’s vertex which its valued number is that. By deleting the vertices which don’t belong to valued set, new notion of new graph is up. It’s called valued graph. The comparison amid valued graph and initial graph is up, too.

Production Scheduling of Open Pit Mine Using Sequential Branch-and-Cut and Longest Path Algorithm: An Application from an African Copper Mine

Open pit mine production scheduling assigns mining blocks in different production periods for maximising profits after satisfying geotechnical and operational constraints. In this paper, two Open pit mine production scheduling models were applied in an African copper deposit. The first model is a traditional model with more tight resource constraints; the second model is a more robust model where resource constraints are relaxed by penalizing the objective function. Both the models were solved using two step algorithms: (a) year wise production scheduling using a sequential branch-and-cut algorithm; and (b) an iterative longest path algorithm to improve the solution generated from branch-and-cut. Results demonstrated that due to the tight constraints in Model 1, the optimizer was unable to generate a feasible solution after the first period, therefore the lower limit metal production constraint was eliminated to generate a feasible solution; however, Model 2 was able to generate a feasible solution for all periods. Results show that both the models generated nearly the same amount of ore, waste, metal content, and mine life. Model 2 generates relatively more net present value as compared to Model 1, whereas, the computational time required for solving the scheduling problem is relatively less for Model 1 than for Model 2.

A path recorder algorithm for Multiple Longest Common Subsequences (MLCS) problems

Motivation Searching the Longest Common Subsequences of many sequences is called a Multiple Longest Common Subsequence (MLCS) problem which is a very fundamental and challenging problem in many fields of data mining. The existing algorithms cannot be applicable to problems with long and large-scale sequences due to their huge time and space consumption. To efficiently handle large-scale MLCS problems, a Path Recorder Directed Acyclic Graph (PRDAG) model and a novel Path Recorder Algorithm (PRA) are proposed. Results In PRDAG, we transform the MLCS problem into searching the longest path from the Directed Acyclic Graph (DAG), where each longest path in DAG corresponds to an MLCS. To tackle the problem efficiently, we eliminate all redundant and repeated nodes during the construction of DAG, and for each node, we only maintain the longest paths from the source node to it but ignore all non-longest paths. As a result, the size of the DAG becomes very small, and the memory space and search time will be greatly saved. Empirical experiments have been performed on a standard benchmark set of both DNA sequences and protein sequences. The experimental results demonstrate that our model and algorithm outperform the related leading algorithms, especially for large-scale MLCS problems. Availability and implementation This program code is written by the first author and can be available at https://www.ncbi.nlm.nih.gov/nuccore and https://blog.csdn.net/wswguilin. Supplementary information Supplementary data are available at Bioinformatics online.

DEPTH FIRST SEARCH (DFS) UNTUK MENENTUKAN DIAMETER GRAF HIRARKI

Let G = (V, E) be a graph. The distance d (u, v) between two vertices u and v is the length of the shortest path between them. The diameter of the graph is the length of the longest path of the shortest paths between any two graph vertices (u ,v) of a graph, . In this paper we propose algorithms for finding diameter of a hierarchy graph using DFS. Diameter of the hierarchy graph using DFS algoritm is four.