Improved Hardness of Approximation for Stackelberg Shortest-Path Pricing

We consider the Stackelberg shortest-path pricing problem, which is defined as follows. Given a graph G with fixed-cost and pricable edges and two distinct vertices s and t, we may assign prices to the pricable edges. Based on the predefined fixed costs and our prices, a customer purchases a cheapest s-t-path in G and we receive payment equal to the sum of prices of pricable edges belonging to the path. Our goal is to find prices maximizing the payment received from the customer. While Stackelberg shortest-path pricing was known to be APX-hard before, we provide the first explicit approximation threshold and prove hardness of approximation within 2−o(1). We also argue that the nicely structured type of instance resulting from our reduction captures most of the challenges we face in dealing with the problem in general and, in particular, we show that the gap between the revenue of an optimal pricing and the only known general upper bound can still be logarithmically large

Modeling Airline Frequency Competition for Airport Congestion Mitigation

Demand often exceeds capacity at congested airports. Airline frequency competition is partially responsible for the growing demand for airport resources. We propose a game-theoretic model for airline frequency competition under slot constraints. The model is solved to obtain a Nash equilibrium using a successive optimizations approach, wherein individual optimizations are performed using a dynamic programming-based technique. The model predictions are validated against actual frequency data, with the results indicating a close fit to reality. We use the model to evaluate different strategic slot allocation schemes from the perspectives of the airlines and the passengers. The most significant result of this research shows that a small reduction in the total number of allocated slots translates into a substantial reduction in flight and passenger delays and also a considerable improvement in airlines' profits

Solving ill-posed bilevel programs

This paper deals with ill-posed bilevel programs, i.e., problems admitting multiple lower-level solutions for some upper-level parameters. Many publications have been devoted to the standard optimistic case of this problem, where the difficulty is essentially moved from the objective function to the feasible set. This new problem is simpler but there is no guaranty to obtain local optimal solutions for the original optimistic problem by this process. Considering the intrinsic non-convexity of bilevel programs, computing local optimal solutions is the best one can hope to get in most cases. To achieve this goal, we start by establishing an equivalence between the original optimistic problem an a certain set-valued optimization problem. Next, we develop optimality conditions for the latter problem and show that they generalize all the results currently known in the literature on optimistic bilevel optimization. Our approach is then extended to multiobjective bilevel optimization, and completely new results are derived for problems with vector-valued upper- and lower-level objective functions. Numerical implementations of the results of this paper are provided on some examples, in order to demonstrate how the original optimistic problem can be solved in practice, by means of a special set-valued optimization problem

Long non-coding RNAs defining major subtypes of B cell precursor acute lymphoblastic leukemia

BACKGROUND: Long non-coding RNAs (lncRNAs) have emerged as a novel class of RNA due to its diverse mechanism in cancer development and progression. However, the role and expression pattern of lncRNAs in molecular subtypes of B cell acute lymphoblastic leukemia (BCP-ALL) have not yet been investigated. Here, we assess to what extent lncRNA expression and DNA methylation is driving the progression of relapsed BCP-ALL subtypes and we determine if the expression and DNA methylation profile of lncRNAs correlates with established BCP-ALL subtypes. METHODS: We performed RNA sequencing and DNA methylation (Illumina Infinium microarray) of 40 diagnosis and 42 relapse samples from 45 BCP-ALL patients in a German cohort and quantified lncRNA expression. Unsupervised clustering was applied to ascertain and confirm that the lncRNA-based classification of the BCP-ALL molecular subtypes is present in both our cohort and an independent validation cohort of 47 patients. A differential expression and differential methylation analysis was applied to determine the subtype-specific, relapse-specific, and differentially methylated lncRNAs. Potential functions of subtype-specific lncRNAs were determined by using co-expression-based analysis on nearby (cis) and distally (trans) located protein-coding genes. RESULTS: Using an integrative Bioinformatics analysis, we developed a comprehensive catalog of 1235 aberrantly dysregulated BCP-ALL subtype-specific and 942 relapse-specific lncRNAs and the methylation profile of three subtypes of BCP-ALL. The 1235 subtype-specific lncRNA signature represented a similar classification of the molecular subtypes of BCP-ALL in the independent validation cohort. We identified a strong correlation between the DUX4-specific lncRNAs and genes involved in the activation of TGF-β and Hippo signaling pathways. Similarly, Ph-like-specific lncRNAs were correlated with genes involved in the activation of PI3K-AKT, mTOR, and JAK-STAT signaling pathways. Interestingly, the relapse-specific lncRNAs correlated with the activation of metabolic and signaling pathways. Finally, we found 23 promoter methylated lncRNAs epigenetically facilitating their expression levels. CONCLUSION: Here, we describe a set of subtype-specific and relapse-specific lncRNAs from three major BCP-ALL subtypes and define their potential functions and epigenetic regulation. The subtype-specific lncRNAs are reproducible and can effectively stratify BCP-ALL subtypes. Our data uncover the diverse mechanism of action of lncRNAs in BCP-ALL subtypes defining which lncRNAs are involved in the pathogenesis of disease and are relevant for the stratification of BCP-ALL subtypes

Long non-coding RNAs defining major subtypes of B cell precursor acute lymphoblastic leukemia

Recent studies implicated that long non-coding RNAs (lncRNAs) may play a role in the progression and development of acute lymphoblastic leukemia, however, this role is not yet clear. In order to unravel the role of lncRNAs associated with B-cell precursor Acute Lymphoblastic Leukemia (BCP-ALL) subtypes, we performed transcriptome sequencing and DNA methylation array across 82 BCP-ALL samples from three molecular subtypes (DUX4, Ph-like, and Near Haploid or High Hyperdiploidy). Unsupervised clustering of BCP-ALL samples on the basis of their lncRNAs on transcriptome and DNA methylation profiles revealed robust clusters separating three molecular subtypes. Using extensive computational analysis, we developed a comprehensive catalog of 1235 aberrantly dysregulated BCP-ALL subtype-specific lncRNAs with altered expression and methylation patterns from three subtypes of BCP-ALL. By analyzing the co-expression of subtype-specific lncRNAs and protein-coding genes, we inferred key molecular processes in BCP-ALL subtypes. A strong correlation was identified between the DUX4 specific lncRNAs and activation of TGF-β and Hippo signaling pathways. Similarly, Ph-like specific lncRNAs were correlated with genes involved in activation of PI3K-AKT, mTOR, and JAK-STAT signaling pathways. Interestingly, the relapse-specific differentially expressed lncRNAs correlated with the activation of metabolic and signaling pathways. Finally, we showed a set of epigenetically altered lncRNAs facilitating the expression of tumor genes located at their cis location. Overall, our study provides a comprehensive set of novel subtype and relapse-specific lncRNAs in BCP-ALL. Our findings suggest a wide range of molecular pathways are associated with lncRNAs in BCP-ALL subtypes and provide a foundation for functional investigations that could lead to new therapeutic approaches