On stability and controllability of conjunctive Boolean networks

A Boolean network (BN) is a finite state discrete time dynamical system. At each step, each variable takes a value from a binary set. The value update rule for each variable is a local function which depends only on a selected subset of variables. BNs have been used in modeling gene regulatory networks. We focus in this thesis on a special class of BNs, termed as conjunctive Boolean networks (CBNs). A BN is conjunctive if the associated value update rule is comprised of only AND operations. It is known that any trajectory of a finite dynamical system will enter a periodic orbit. Periodic orbits of a CBN are now completely understood. We first characterize in this thesis all periodic orbits of a CBN. In particular, we establish a bijection between the set of periodic orbits and the set of binary necklaces of a certain length. We further investigate the stability of a periodic orbit. Specifically, we perturb a state in the periodic orbit by changing the value of a single entry of the state. The trajectory, with the perturbed state being the initial condition, will enter another (possibly the same) periodic orbit in finite time steps. We then provide a complete characterization of all such transitions from one periodic orbit to another. In particular, we construct a digraph, with the vertices being the periodic orbits, and the (directed) edges representing the transitions among the orbits. We call such a digraph the stability structure of the CBN. We then investigate the orbit-controllability and state-controllability of a CBN. We ask the question of how one can steer a CBN to enter any periodic orbit or to reach any final state, from any initial state. Suppose that there is a selected subset of variables whose values can be controlled for some finite time steps, while other variables still follow the value update rule during all time. We establish in the thesis a necessary and sufficient condition for this subset such that the trajectory, with any initial condition, will enter any desired periodic orbit or reach any final state. We also provide algorithms specifying the methods of manipulating the values of these variables to realize these control goals

The Periodic Behavior of a Threshold Model on Directed Graphs

This thesis investigates a discrete-time deterministic binary threshold model over a directed graph. At each time step, each agent updates the value it holds to the value held by the majority of its incoming neighbors at the last time step. It has been proved in the literature that if the underlying graph is undirected, then for any initial condition, the solution of the threshold model will enter into a periodic solution with the period being no larger than two. Examples can be generated to show that in the cases when the underlying graph is directed, even though the solution will still be periodic, the period of the solution exhibits richer possibilities. This thesis computes the periods of all possible periodic solutions of the model over a certain class of directed graphs, including a single directed cycle and a composition of two directed cycles. It is shown that in the case when the graph is a single directed cycle, all possible periods are divisors of the size of the cycle (i.e., the number of edges). It is also shown that in the case when the graph is a composition of two directed cycles, all possible periods are common divisors of the sizes of the two cycles. The analysis used in this thesis is generalizable to more complex graphs.Ope

InterMitoBase: An annotated database and analysis platform of protein-protein interactions for human mitochondria

<p>Abstract</p> <p>Background</p> <p>The mitochondrion is an essential organelle which plays important roles in diverse biological processes, such as metabolism, apoptosis, signal transduction and cell cycle. Characterizing protein-protein interactions (PPIs) that execute mitochondrial functions is fundamental in understanding the mechanisms underlying biological functions and diseases associated with mitochondria. Investigations examining mitochondria are expanding to the system level because of the accumulation of mitochondrial proteomes and human interactome. Consequently, the development of a database that provides the entire protein interaction map of the human mitochondrion is urgently required.</p> <p>Results</p> <p>InterMitoBase provides a comprehensive interactome of human mitochondria. It contains the PPIs in biological pathways mediated by mitochondrial proteins, the PPIs between mitochondrial proteins and non-mitochondrial proteins as well as the PPIs between mitochondrial proteins. The current version of InterMitoBase covers 5,883 non-redundant PPIs of 2,813 proteins integrated from a wide range of resources including PubMed, KEGG, BioGRID, HPRD, DIP and IntAct. Comprehensive curations have been made on the interactions derived from PubMed. All the interactions in InterMitoBase are annotated according to the information collected from their original sources, GenBank and GO. Additionally, InterMitoBase features a user-friendly graphic visualization platform to present functional and topological analysis of PPI networks identified. This should aid researchers in the study of underlying biological properties.</p> <p>Conclusions</p> <p>InterMitoBase is designed as an integrated PPI database which provides the most up-to-date PPI information for human mitochondria. It also works as a platform by integrating several on-line tools for the PPI analysis. As an analysis platform and as a PPI database, InterMitoBase will be an important database for the study of mitochondria biochemistry, and should be particularly helpful in comprehensive analyses of complex biological mechanisms underlying mitochondrial functions.</p

Essays on Applied Optimization Models

This dissertation studies several different optimization problems, and consists of five chapters. In Chapter 1, we consider a multiperiod binary Knapsack problem, along with several extensions. We propose fully polynomial time approximation schemes to these problems where applicable. We also prove the performance guarantee of some greedy algorithms, and propose parameterized approximation algorithms for some extensions. In Chapter 2, we propose several models to aggregate the distributed energy resources, where the aggregator can be profit-seeking or regulated. We design the two-part pricing mechanism for the aggregator to achieve full market efficiency. In Chapter 3, we analyze the sample complexity of decentralized Q-learning algorithms for stochastic games, in both the tabular case and the case with linear function approximation. In Chapter 4, we design a power purchase agreement (PPA), where a firm signs a long term contract with a renewable energy generator. The contract specifies a one-time transfer payment by the firm to the renewable energy generator, as an investment to build new renewable energy facilities. The firm then owns all the generation from these facilities for an extended period of time. We formulate the firm's decision on when to sign the PPA as an optimal stopping problem, and analyze the firm's optimal policies. Chapter 5 is motivated by an application in freight forwarding, where we formulate the freight forwarder's decisions on the assignment of shipments to containers as an integer program, which turns out to be a combination of the bin packing problem and the generalized assignment problem. We propose several heuristics for this problem and run numerical experiments on their performances

Ecological Function Value of Tropical Forests in the Central Mountainous Areas of Hainan Island

The integrated value of the ecological function of tropical forests in the central mountainous areas of Hainan Island was 33.0648 billion yuan•a-1 in 2010 (soil improvement, soil consolidation, soil nutrient maintenance, water storage and moisture regulation, water purification, carbon sequestration, oxygen releasing, air purification, biodiversity conservation, eco-tourism), equivalent to 16.1% of GDP in Hainan Province this year (205.212 billion yuan). The tropical forests in the central mountainous areas of Hainan Island make great contribution to Hainan Island's ecology, and play an important role in maintaining the stability of the ecological environment in Hainan Island. Through the understanding of major ecological function value of tropical forests, it is necessary to make people cherish the tropical forests in the central ecological function conservation areas of Hainan Province, and spontaneously throw themselves into the ecological environment protection and construction, to promote the rapid and sustainable development of construction in Hainan Province as an international tourism island