A nonmonotone GRASP

A greedy randomized adaptive search procedure (GRASP) is an itera- tive multistart metaheuristic for difficult combinatorial optimization problems. Each GRASP iteration consists of two phases: a construction phase, in which a feasible solution is produced, and a local search phase, in which a local optimum in the neighborhood of the constructed solution is sought. Repeated applications of the con- struction procedure yields different starting solutions for the local search and the best overall solution is kept as the result. The GRASP local search applies iterative improvement until a locally optimal solution is found. During this phase, starting from the current solution an improving neighbor solution is accepted and considered as the new current solution. In this paper, we propose a variant of the GRASP framework that uses a new “nonmonotone” strategy to explore the neighborhood of the current solu- tion. We formally state the convergence of the nonmonotone local search to a locally optimal solution and illustrate the effectiveness of the resulting Nonmonotone GRASP on three classical hard combinatorial optimization problems: the maximum cut prob- lem (MAX-CUT), the weighted maximum satisfiability problem (MAX-SAT), and the quadratic assignment problem (QAP)

Antagonistic and cooperative AGO2-PUM interactions in regulating mRNAs.

Approximately 1500 RNA-binding proteins (RBPs) profoundly impact mammalian cellular function by controlling distinct sets of transcripts, often using sequence-specific binding to 3' untranslated regions (UTRs) to regulate mRNA stability and translation. Aside from their individual effects, higher-order combinatorial interactions between RBPs on specific mRNAs have been proposed to underpin the regulatory network. To assess the extent of such co-regulatory control, we took a global experimental approach followed by targeted validation to examine interactions between two well-characterized and highly conserved RBPs, Argonaute2 (AGO2) and Pumilio (PUM1 and PUM2). Transcriptome-wide changes in AGO2-mRNA binding upon PUM knockdown were quantified by CLIP-seq, and the presence of PUM binding on the same 3'UTR corresponded with cooperative and antagonistic effects on AGO2 occupancy. In addition, PUM binding sites that overlap with AGO2 showed differential, weakened binding profiles upon abrogation of AGO2 association, indicative of cooperative interactions. In luciferase reporter validation of candidate 3'UTR sites where AGO2 and PUM colocalized, three sites were identified to host antagonistic interactions, where PUM counteracts miRNA-guided repression. Interestingly, the binding sites for the two proteins are too far for potential antagonism due to steric hindrance, suggesting an alternate mechanism. Our data experimentally confirms the combinatorial regulatory model and indicates that the mostly repressive PUM proteins can change their behavior in a context-dependent manner. Overall, the approach underscores the importance of further elucidation of complex interactions between RBPs and their transcriptome-wide extent

GraphCombEx: A Software Tool for Exploration of Combinatorial Optimisation Properties of Large Graphs

We present a prototype of a software tool for exploration of multiple combinatorial optimisation problems in large real-world and synthetic complex networks. Our tool, called GraphCombEx (an acronym of Graph Combinatorial Explorer), provides a unified framework for scalable computation and presentation of high-quality suboptimal solutions and bounds for a number of widely studied combinatorial optimisation problems. Efficient representation and applicability to large-scale graphs and complex networks are particularly considered in its design. The problems currently supported include maximum clique, graph colouring, maximum independent set, minimum vertex clique covering, minimum dominating set, as well as the longest simple cycle problem. Suboptimal solutions and intervals for optimal objective values are estimated using scalable heuristics. The tool is designed with extensibility in mind, with the view of further problems and both new fast and high-performance heuristics to be added in the future. GraphCombEx has already been successfully used as a support tool in a number of recent research studies using combinatorial optimisation to analyse complex networks, indicating its promise as a research software tool

Optimal Deterministic Polynomial-Time Data Exchange for Omniscience

We study the problem of constructing a deterministic polynomial time algorithm that achieves omniscience, in a rate-optimal manner, among a set of users that are interested in a common file but each has only partial knowledge about it as side-information. Assuming that the collective information among all the users is sufficient to allow the reconstruction of the entire file, the goal is to minimize the (possibly weighted) amount of bits that these users need to exchange over a noiseless public channel in order for all of them to learn the entire file. Using established connections to the multi-terminal secrecy problem, our algorithm also implies a polynomial-time method for constructing a maximum size secret shared key in the presence of an eavesdropper. We consider the following types of side-information settings: (i) side information in the form of uncoded fragments/packets of the file, where the users' side-information consists of subsets of the file; (ii) side information in the form of linearly correlated packets, where the users have access to linear combinations of the file packets; and (iii) the general setting where the the users' side-information has an arbitrary (i.i.d.) correlation structure. Building on results from combinatorial optimization, we provide a polynomial-time algorithm (in the number of users) that, first finds the optimal rate allocations among these users, then determines an explicit transmission scheme (i.e., a description of which user should transmit what information) for cases (i) and (ii)

Quantitative profiling of BATF family proteins/JUNB/IRF hetero-trimers using Spec-seq

Additional file 6. Half site analysis for BATFx-JUNB-IRFx. (A) Single variants from half sites of these oligos in the library were used to generate energy logos. Bolded positions represent the half sites generated in B. (B) Energy logos from Spec-seq results of BATFx-JUNB-IRFx. The Y-axis is negative energy so the preferred sequence is on the top

Graph Networks as a Universal Machine Learning Framework for Molecules and Crystals

Graph networks are a new machine learning (ML) paradigm that supports both relational reasoning and combinatorial generalization. Here, we develop universal MatErials Graph Network (MEGNet) models for accurate property prediction in both molecules and crystals. We demonstrate that the MEGNet models outperform prior ML models such as the SchNet in 11 out of 13 properties of the QM9 molecule data set. Similarly, we show that MEGNet models trained on $\sim 60,000$ crystals in the Materials Project substantially outperform prior ML models in the prediction of the formation energies, band gaps and elastic moduli of crystals, achieving better than DFT accuracy over a much larger data set. We present two new strategies to address data limitations common in materials science and chemistry. First, we demonstrate a physically-intuitive approach to unify four separate molecular MEGNet models for the internal energy at 0 K and room temperature, enthalpy and Gibbs free energy into a single free energy MEGNet model by incorporating the temperature, pressure and entropy as global state inputs. Second, we show that the learned element embeddings in MEGNet models encode periodic chemical trends and can be transfer-learned from a property model trained on a larger data set (formation energies) to improve property models with smaller amounts of data (band gaps and elastic moduli)