Limit Crossing for Decision Problems

Limit crossing is a methodology in which modified versions of a problem are solved and compared, yielding useful information about the original problem. Pruning rules that are used to exclude portions of search trees are excellent examples of the limit-crossing technique. In our previous work, we examined limit crossing for optimization problems. In this paper, we extend this methodology to decision problems. We demonstrate the use of limit crossing in our design of a tool for identifying K-SAT backbones. This tool is guaranteed to identify all of the backbone variables by solving at most n+1 formulae, where n is the total number of variables. While previous 3-SAT backbone research was limited to 28 variables, we have computed backbones for 200 variables. In addition to being useful for identifying backbones, this code can be used directly to solve a special class of QBF problem

Exploiting Bounds in Operations Research and Artificial Intelligence

Combinatorial optimization problems are ubiquitous in scientific research, engineering, and even our daily lives. A major research focus in developing combinatorial search algorithms has been on the attainment of efficient methods for deriving tight lower and upper bounds. These bounds restrict the search space of combinatorial optimization problems and facilitate the computa-tion of what might otherwise be intractable problems. In this paper, we survey the history of the use of bounds in both AI and OR. While research has been extensive in both domains, until very recently it has been too narrowly focused and has overlooked great opportunities to exploit bounds. In the past, the focus has been on the relaxations of constraints. We present methods for deriving bounds by tightening constraints, adding or deleting decision variables, and modifying the objective function. Then a formalization of the use of bounds as a two-step procedure is introduced. Finally, we discuss recent developments demonstrating how the use of this framework is conducive for eliciting methods that go beyond search-tree pruning

A Traveling Salesman\u27s Approach to Clustering Gene Expression Data

Given a matrix of values, rearrangement clustering involves rearranging the rows of the matrix and identifying cluster boundaries within the linear ordering of the rows. The TSP+k algorithm for rear-rangement clustering was presented in [3] and its implementation is described in this note. Using this code, we solve a 2,467-gene expression data clustering problem and identify “good” clusters that con-tain close to eight times the number of genes that were clustered by Eisen et al. (1998). Furthermore, we identify 106 functional groups that were overlooked in that paper. We make our implementation available to the general public for applications of gene expression data analysis

Cut-and-Solve: A Linear Search Strategy for Combinatorial Optimization Problems

Branch-and-bound and branch-and-cut use search trees to identify optimal solutions. In this paper, we introduce a linear search strategy which we refer to as cut-and-solve and prove optimality and completeness for this method. This search is different from traditional tree searching as there is no branching. At each node in the search path, a relaxed problem and a sparse problem are solved and a constraint is added to the relaxed problem. The sparse problems provide incumbent solutions. When the constraining of the relaxed problem becomes tight enough, its solution value becomes no better than the incumbent solution value. At this point, the incumbent solution is declared to be optimal. This strategy is easily adapted to be an anytime algorithm as an incumbent solution is found at the root node and continuously updated during the search. Cut-and-solve enjoys two favorable properties. Since there is no branching, there are no wrong subtrees in whihc the search may get lost. Furthermore, its memory requirements are nominal. For these reasons, it may be potentially useful as an alternative approach for problems that are difficult to solve using depth-first or best-first search tree methods. In this paper, we demonstrate the cut-and-solve strategy by implementing it for the Asymmetric Traveling Salesman Problem (ATSP). We compare this implementation with state-of-the-art ATSP solvers to validate the potential of this novel search strategy. Our code is available at our websites

Moving from capstones toward cornerstones: Successes and challenges in applying systems biology to identify mechanisms of autism spectrum disorders

The substantial progress in the last few years toward uncovering genetic causes and risk factors for autism spectrum disorders (ASDs) has opened new experimental avenues for identifying the underlying neurobiological mechanism of the condition. The bounty of genetic findings has led to a variety of data-driven exploratory analyses aimed at deriving new insights about the shared features of these genes. These approaches leverage data from a variety of different sources such as co-expression in transcriptomic studies, protein-protein interaction networks, gene ontologies (GOs) annotations, or multi-level combinations of all of these. Here, we review the recurrent themes emerging from these analyses and highlight some of the challenges going forward. Themes include findings that ASD associated genes discovered by a variety of methods have been shown to contain disproportionate amounts of neurite outgrowth/cytoskeletal, synaptic, and more recently Wnt-related and chromatin modifying genes. Expression studies have highlighted a disproportionate expression of ASD gene sets during mid fetal cortical development, particularly for rare variants, with multiple analyses highlighting the striatum and cortical projection and interneurons as well. While these explorations have highlighted potentially interesting relationships among these ASD-related genes, there are challenges in how to best transition these insights into empirically testable hypotheses. Nonetheless, defining shared molecular or cellular pathology downstream of the diverse genes associated with ASDs could provide the cornerstones needed to build toward broadly applicable therapeutic approaches

Allele-specific network reveals combinatorial interaction that transcends small effects in psoriasis GWAS

<div><p>Hundreds of genetic markers have shown associations with various complex diseases, yet the “missing heritability” remains alarmingly elusive. Combinatorial interactions may account for a substantial portion of this missing heritability, but their discoveries have been impeded by computational complexity and genetic heterogeneity. We present BlocBuster, a novel systems-level approach that efficiently constructs genome-wide, allele-specific networks that accurately segregate homogenous combinations of genetic factors, tests the associations of these combinations with the given phenotype, and rigorously validates the results using a series of unbiased validation methods. BlocBuster employs a correlation measure that is customized for single nucleotide polymorphisms and returns a multi-faceted collection of values that captures genetic heterogeneity. We applied BlocBuster to analyze psoriasis, discovering a combinatorial pattern with an odds ratio of 3.64 and Bonferroni-corrected p-value of 5.01×10⁻¹⁶. This pattern was replicated in independent data, reflecting robustness of the method. In addition to improving prediction of disease susceptibility and broadening our understanding of the pathogenesis underlying psoriasis, these results demonstrate BlocBuster's potential for discovering combinatorial genetic associations within heterogeneous genome-wide data, thereby transcending the limiting “small effects” produced by individual markers examined in isolation.</p></div

Human ​gephyrin is encompassed within giant functional noncoding yin–yang sequences

Gephyrin is a highly conserved gene that is vital for the organization of proteins at inhibitory receptors, molybdenum cofactor biosynthesis and other diverse functions. Its specific function is intricately regulated and its aberrant activities have been observed for a number of human diseases. Here we report a remarkable yin–yang haplotype pattern encompassing gephyrin. Yin–yang haplotypes arise when a stretch of DNA evolves to present two disparate forms that bear differing states for nucleotide variations along their lengths. The gephyrin yin–yang pair consists of 284 divergent nucleotide states and both variants vary drastically from their mutual ancestral haplotype, suggesting rapid evolution. Several independent lines of evidence indicate strong positive selection on the region and suggest these high-frequency haplotypes represent two distinct functional mechanisms. This discovery holds potential to deepen our understanding of variable human-specific regulation of gephyrin while providing clues for rapid evolutionary events and allelic migrations buried within human history

Efficient Reduced-Bias Genetic Algorithm (ERBGA) for Generic Community Detection Objectives

Community structure identification has been an important research area for biology, physics, information systems, and social sciences for studying properties of networks representing complex relationships. Lately, Genetic Algorithms (GAs) are being utilized for community detection. GAs are machine-learning methods that mimic natural selection. However, previous approaches suffer from some deficiencies: redundant representation and linearity assumption, that we will try to address. in. The algorithm presented here is a novel framework that addresses both of these above issues. This algorithm is also flexible as it is easily adapted to any given mathematical objective. Additionally, our approach doesn’t require prior information about the number of true communities in the network. Overall, our efficient approach holds potential for sifting out communities representing complex relationships in networks of interest across different domains

Linking crop traits to transcriptome differences in a progeny population of tetraploid potato

Background Potato is the third most consumed crop in the world. Breeding for traits such as yield, product quality and pathogen resistance are main priorities. Identifying molecular signatures of these and other important traits is important in future breeding efforts. In this study, a progeny population from a cross between a breeding line, SW93-1015, and a cultivar, Desiree, was studied by trait analysis and RNA-seq in order to develop understanding of segregating traits at the molecular level and identify transcripts with expressional correlation to these traits. Transcript markers with predictive value for field performance applicable under controlled environments would be of great value for plant breeding. Results A total of 34 progeny lines from SW93-1015 and Desiree were phenotyped for 17 different traits in a field in Nordic climate conditions and controlled climate settings. A master transcriptome was constructed with all 34 progeny lines and the parents through a de novo assembly of RNA-seq reads. Gene expression data obtained in a controlled environment from the 34 lines was correlated to traits by different similarity indices, including Pearson and Spearman, as well as DUO, which calculates the co-occurrence between high and low values for gene expression and trait. Our study linked transcripts to traits such as yield, growth rate, high laying tubers, late and tuber blight, tuber greening and early flowering. We found several transcripts associated to late blight resistance and transcripts encoding receptors were associated to Dickeya solani susceptibility. Transcript levels of a UBX-domain protein was negatively associated to yield and a GLABRA2 expression modulator was negatively associated to growth rate. Conclusion In our study, we identify 100's of transcripts, putatively linked based on expression with 17 traits of potato, representing both well-known and novel associations. This approach can be used to link the transcriptome to traits. We explore the possibility of associating the level of transcript expression from controlled, optimal environments to traits in a progeny population with different methods introducing the application of DUO for the first time on transcriptome data. We verify the expression pattern for five of the putative transcript markers in another progeny population