Identifying functional modules in protein–protein interaction networks: an integrated exact approach

Motivation: With the exponential growth of expression and protein–protein interaction (PPI) data, the frontier of research in systems biology shifts more and more to the integrated analysis of these large datasets. Of particular interest is the identification of functional modules in PPI networks, sharing common cellular function beyond the scope of classical pathways, by means of detecting differentially expressed regions in PPI networks. This requires on the one hand an adequate scoring of the nodes in the network to be identified and on the other hand the availability of an effective algorithm to find the maximally scoring network regions. Various heuristic approaches have been proposed in the literature

Reduction techniques for the prize collecting Steiner tree problem and the maximum‐weight connected subgraph problem

The concept of reduction has frequently distinguished itself as a pivotal ingredient of exact solving approaches for the Steiner tree problem in graphs. In this article we broaden the focus and consider reduction techniques for three Steiner problem variants that have been extensively discussed in the literature and entail various practical applications: The prize‐collecting Steiner tree problem, the rooted prize‐collecting Steiner tree problem and the maximum‐weight connected subgraph problem. By introducing and subsequently deploying numerous new reduction methods, we are able to drastically decrease the size of a large number of benchmark instances, already solving more than 90% of them to optimality. Furthermore, we demonstrate the impact of these techniques on exact solving, using the example of the state‐of‐the‐art Steiner problem solver SCIP‐Jack

SCIP-Jack—a solver for STP and variants with parallelization extensions

This is the author accepted manuscript. The final version is available from Springer Verlag via the DOI in this record The Steiner tree problem in graphs is a classical problem that commonly arises in practical applications as one of many variants. While often a strong relationship between different Steiner tree problem variants can be observed, solution approaches employed so far have been prevalently problemspecific. In contrast, this paper introduces a general-purpose solver that can be used to solve both the classical Steiner tree problem and many of its variants without modification. This versatility is achieved by transforming various problem variants into a general form and solving them by using a state-ofthe-art MIP-framework. The result is a high-performance solver that can be employed in massively parallel environments and is capable of solving previously unsolved instances.German Federal Ministry of Education and Researc

Mathematical Programming Algorithms for Spatial Cloaking

We consider a combinatorial optimization problem for spatial information cloaking. The problem requires computing one or several disjoint arborescences on a graph from a predetermined root or subset of candidate roots, so that the number of vertices in the arborescences is minimized but a given threshold on the overall weight associated with the vertices in each arborescence is reached. For a single arborescence case, we solve the problem to optimality by designing a branch-and-cut exact algorithm. Then we adapt this algorithm for the purpose of pricing out columns in an exact branch-and-price algorithm for the multiarborescence version. We also propose a branch-and-price-based heuristic algorithm, where branching and pricing, respectively, act as diversification and intensification mechanisms. The heuristic consistently finds optimal or near optimal solutions within a computing time, which can be three to four orders of magnitude smaller than that required for exact optimization. From an application point of view, our computational results are useful to calibrate the values of relevant parameters, determining the obfuscation level that is achieved

On Solving Close Enough Orienteering Problem with Overlapped Neighborhoods

The Close Enough Traveling Salesman Problem (CETSP) is a well-known variant of the classic Traveling Salesman Problem whereby the agent may complete its mission at any point within a target neighborhood. Heuristics based on overlapped neighborhoods, known as Steiner Zones (SZ), have gained attention in addressing CETSPs. While SZs offer effective approximations to the original graph, their inherent overlap imposes constraints on the search space, potentially conflicting with global optimization objectives. Here we present the Close Enough Orienteering Problem with Non-uniform Neighborhoods (CEOP-N), which extends CETSP by introducing variable prize attributes and non-uniform cost considerations for prize collection. To tackle CEOP-N, we develop a new approach featuring a Randomized Steiner Zone Discretization (RSZD) scheme coupled with a hybrid algorithm based on Particle Swarm Optimization (PSO) and Ant Colony System (ACS) - CRaSZe-AntS. The RSZD scheme identifies sub-regions for PSO exploration, and ACS determines the discrete visiting sequence. We evaluate the RSZD's discretization performance on CEOP instances derived from established CETSP instances, and compare CRaSZe-AntS against the most relevant state-of-the-art heuristic focused on single-neighborhood optimization for CEOP. We also compare the performance of the interior search within SZs and the boundary search on individual neighborhoods in the context of CEOP-N. Our results show CRaSZe-AntS can yield comparable solution quality with significantly reduced computation time compared to the single-neighborhood strategy, where we observe an averaged 140.44% increase in prize collection and 55.18% reduction of execution time. CRaSZe-AntS is thus highly effective in solving emerging CEOP-N, examples of which include truck-and-drone delivery scenarios.Comment: 26 pages, 10 figure

Methods for Utilizing Co-expression Networks for Biological Insight

The explosion of high-throughput Omics assays in past 15 years has led to a revolution in the quantity of data and the number of data types which are available to biological researchers. This has necessitated a second revolution in the development of analytical tools to handle this wealth and variety of data. No longer is it practical for a researcher to simply examine a list of differentially expressed compounds and draw meaningful insight about the biological processes at hand; these differentially expressed compounds must be put into context with each other, and integrated with existing biological knowledge. Co-expression techniques, where the simultaneous expression of two or more compounds is analyzed, have become a powerful tool for biological insight in high-throughput Omics settings. The primary goal of this dissertation is to develop techniques for identifying and characterizing patterns of co-expression. In our first project, we develop a Differentially Weighted Factor Model for estimating covariance matrices related through structured experimental design. Our factor model allows us to estimate common structural elements using all available data, and to estimate unique structural elements in a condition specific manner. We develop a method for visualizing the resulting estimates, and implement the method in an R package, DWFM. The second project presents a method using the Prize Collecting Steiner Tree algorithm to integrate and identify modules in lipid and untargeted metabolomic assays in a data-driven manner. These assays are integrated over a co-expression network specific to the applied setting in question, allowing us to capture modules unique to this setting. Our final project presents a second technique for identifying modules of co-expressed biomolecules. This technique addresses a major limitation of PCST based approaches, namely that one is required to choose a cutoff to obtain a list of differentially expressed compounds used as input into the algorithm. Additionally, this second method utilizes a meta-analytic inspired approach to identify patterns of co-expression across multiple data sets, thus reducing the impact of a single noisy assay.PHDStatisticsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/143996/1/tealg_1.pd