How Long to Read ON CONSTRUCTION & IDENTIFICATI

How Long Does it Take to Read ON CONSTRUCTION & IDENTIFICATI?

It takes the average reader 2 hours and 13 minutes to read ON CONSTRUCTION & IDENTIFICATI by Xiaoqing Cheng

Assuming a reading speed of 250 words per minute. Learn more

Description

This dissertation, "On Construction and Identification Problems in Probabilistic Boolean Networks" by Xiaoqing, Cheng, 程晓青, was obtained from The University of Hong Kong (Pokfulam, Hong Kong) and is being sold pursuant to Creative Commons: Attribution 3.0 Hong Kong License. The content of this dissertation has not been altered in any way. We have altered the formatting in order to facilitate the ease of printing and reading of the dissertation. All rights not granted by the above license are retained by the author. Abstract: In recent decades, rapidly evolving genomic technologies provide a platform for exploring the massive amount of genomic data. At the same time, it also triggers dramatic development in systems biology. A number of mathematical models have been proposed to understand the dynamical behavior of the biological systems. Among them, Boolean Network (BN) and its stochastic extension Probabilistic Boolean Network (PBN) have attracted much attention. Identification and construction problems are two kinds of vital problems in studying the behavior of a PBN. A novel problem of observability of singleton attractors was firstly proposed, which was defined as identifying the minimum number of consecutive nodes to discriminate different singleton attractors. It may help in finding biomarkers for different disease types, thus it plays a vital role in the study of signaling networks. The observability of singleton attractor problem can be solved in O(n) time, where n is the number of genes in a BN. Later, the problem was extended to discriminating periodical attractors. For the periodical case, one has to consider multiple time steps and a new algorithm was proposed. Moreover, one may also curious about identifying the minimum set of nodes that can determine uniquely the attractor cycles from the others in the network, this problem was also addressed. In order to study realistic PBNs, inference on the structure of PBNs from gene expression time series data was investigated. The number of samples required to uniquely determine the structure of a PBN was studied. Two models were proposed to study different classes of PBNs. Using theoretical analysis and computational experiments the structure of a PBN can be exactly identified with high probability from a relatively small number of samples for some classes of PBNs having bounded indegree. Furthermore, it is shown that there exist classes of PBNs for which it is impossible to uniquely determine their structure from samples under these two models. Constructing the structure of a PBN from a given probability transition matrix is another key problem. A projection-based gradient descent method was proposed for solving huge size constrained least square problems. It is a matrixfree iterative scheme for solving the minimizer of the captured problem. A convergence analysis of the scheme is given, and the algorithm is then applied to the construction of a PBN given its probability transition matrix. Efficiency and effectiveness of the proposed method are verified through numerical experiments. Semi-tensor product approach is another powerful tool in constructing of BNs. However, to our best knowledge, there is no result on the relationship of the structure matrix and transition matrix of a BN. It is shown that the probability structure matrix and probability transition matrix are similar matrices. Three main problems in PBN were discussed afterward: dynamics, steady-state distribution and the inverse problem. Numerical examples are provided to show the validity of our proposed theory. Subjects: Algebra, Boolean Genetic regulation - Mathematical models

How long is ON CONSTRUCTION & IDENTIFICATI?

ON CONSTRUCTION & IDENTIFICATI by Xiaoqing Cheng is 132 pages long, and a total of 33,264 words.

This makes it 45% the length of the average book. It also has 41% more words than the average book.

How Long Does it Take to Read ON CONSTRUCTION & IDENTIFICATI Aloud?

The average oral reading speed is 183 words per minute. This means it takes 3 hours and 1 minute to read ON CONSTRUCTION & IDENTIFICATI aloud.

What Reading Level is ON CONSTRUCTION & IDENTIFICATI?

ON CONSTRUCTION & IDENTIFICATI is suitable for students ages 10 and up.

Note that there may be other factors that effect this rating besides length that are not factored in on this page. This may include things like complex language or sensitive topics not suitable for students of certain ages.

When deciding what to show young students always use your best judgement and consult a professional.

Where Can I Buy ON CONSTRUCTION & IDENTIFICATI?

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