Partial DNA Assembly: A Rate-Distortion Perspective

Earlier formulations of the DNA assembly problem were all in the context of perfect assembly; i.e., given a set of reads from a long genome sequence, is it possible to perfectly reconstruct the original sequence? In practice, however, it is very often the case that the read data is not sufficiently rich to permit unambiguous reconstruction of the original sequence. While a natural generalization of the perfect assembly formulation to these cases would be to consider a rate-distortion framework, partial assemblies are usually represented in terms of an assembly graph, making the definition of a distortion measure challenging. In this work, we introduce a distortion function for assembly graphs that can be understood as the logarithm of the number of Eulerian cycles in the assembly graph, each of which correspond to a candidate assembly that could have generated the observed reads. We also introduce an algorithm for the construction of an assembly graph and analyze its performance on real genomes.Comment: To be published at ISIT-2016. 11 pages, 10 figure

Self-Assembly of DNA Graphs and Postman Tours

DNA graph structures can self-assemble from branched junction molecules to yield solutions to computational problems. Self-assembly of graphs have previously been shown to give polynomial time solutions to hard computational problems such as 3-SAT and k-colorability problems. Jonoska et al. have proposed studying self-assembly of graphs topologically, considering the boundary components of their thickened graphs, which allows for reading the solutions to computational problems through reporter strands. We discuss weighting algorithms and consider applications of self-assembly of graphs and the boundary components of their thickened graphs to problems involving minimal weight Eulerian walks such as the Chinese Postman Problem and the Windy Postman Problem

Applications of network optimization

Includes bibliographical references (p. 41-48).Ravindra K. Ahuja ... [et al.]

Eulerian Paths with Regular Constraints

Labeled graphs, in which edges are labeled by letters from some alphabet Sigma, are extensively used to model many types of relations associated with actions, costs, owners, or other properties. Each path in a labeled graph induces a word in Sigma^* -- the one obtained by concatenating the letters along the edges in the path. Classical graph-theory problems give rise to new problems that take these words into account. We introduce and study the constrained Eulerian path problem. The input to the problem is a Sigma-labeled graph G and a specification L subseteq Sigma^*. The goal is to find an Eulerian path in G that satisfies L. We consider several classes of the problem, defined by the classes of G and L. We focus on the case L is regular and show that while the problem is in general NP-complete, even for very simple graphs and specifications, there are classes that can be solved efficiently. Our results extend work on Eulerian paths with edge-order constraints. We also study the constrained Chinese postman problem, where edges have costs and the goal is to find a cheapest path that contains each edge at least once and satisfies the specification. Finally, we define and study the Eulerian language of a graph, namely the set of words along its Eulerian paths

B-splines in EMD and Graph Theory in Pattern Recognition

With the development of science and technology, a large amount of data is waiting for further scientific exploration. We can always build up some good mathematical models based on the given data to analyze and solve the real life problems. In this work, we propose three types of mathematical models for different applications.;In chapter 1, we use Bspline based EMD to analysis nonlinear and no-stationary signal data. A new idea about the boundary extension is introduced and applied to the Empirical Mode Decomposition(EMD) algorithm. Instead of the traditional mirror extension on the boundary, we propose a ratio extension on the boundary.;In chapter 2 we propose a weighted directed multigraph for text pattern recognition. We set up a weighted directed multigraph model using the distances between the keywords as the weights of arcs. We then developed a keyword-frequency-distance-based algorithm which not only utilizes the frequency information of keywords but also their ordering information.;In chapter 3, we propose a centrality guided clustering method. Different from traditional methods which choose a center of a cluster randomly, we start clustering from a LEADER - a vertex with highest centrality score, and a new member is added into an existing community if the new vertex meet some criteria and the new community with the new vertex maintain a certain density.;In chapter 4, we define a new graph optimization problem which is called postman tour with minimum route-pair cost. And we model the DNA sequence assembly problem as the postman tour with minimum route-pair cost problem

An approach to solve job shop scheduling problem

“A biotechnology device manufacturer needs to devise effective scheduling algorithms for its testing devices. A device is a configuration of machines, each of which performs a specific task, such as washing, reading and cleaning. These devices are used to test human samples to diagnose diseases like cholera, malaria etc. Each test is a job, which is to be processed on these machines for a specific amount of time. Every job has its own pre defined sequence. These samples are to be processed simultaneously on machines owing to constraint that as soon as one machine completes processing a sample, it should be immediately processed by another machine. This constraint is significantly known as no- wait constraint. Given a set of jobs the web application assigns an optimal start time for each job owing to no-wait constraint. This results in reducing the overall time taken to process the jobs, which is formally known as makespan. The main objective of the project is to minimize the makespan. The application is specific to laboratory platform, which helps them to test the samples in optimal time. The heuristic, which I have implemented, is designed with future advancements in mind. The application can be extended to test different heuristic procedures by keeping the time tabling intact. The development environment to be used in this project will require Microsoft Visual Studio, C#, ASP.NET, and other real time chart tools like Microsoft Silverlight.

Washington University Record, November 21, 1996

https://digitalcommons.wustl.edu/record/1741/thumbnail.jp

Applications of network optimization

Includes bibliographical references (p. 41-48).Ravindra K. Ahuja ... [et al.]