Belief-Propagation for Weighted b-Matchings on Arbitrary Graphs and its Relation to Linear Programs with Integer Solutions

We consider the general problem of finding the minimum weight \bm-matching on arbitrary graphs. We prove that, whenever the linear programming (LP) relaxation of the problem has no fractional solutions, then the belief propagation (BP) algorithm converges to the correct solution. We also show that when the LP relaxation has a fractional solution then the BP algorithm can be used to solve the LP relaxation. Our proof is based on the notion of graph covers and extends the analysis of (Bayati-Shah-Sharma 2005 and Huang-Jebara 2007}. These results are notable in the following regards: (1) It is one of a very small number of proofs showing correctness of BP without any constraint on the graph structure. (2) Variants of the proof work for both synchronous and asynchronous BP; it is the first proof of convergence and correctness of an asynchronous BP algorithm for a combinatorial optimization problem.Comment: 28 pages, 2 figures. Submitted to SIAM journal on Discrete Mathematics on March 19, 2009; accepted for publication (in revised form) August 30, 2010; published electronically July 1, 201

Parallelisation and application of AD3 as a method for solving large scale combinatorial auctions

Auctions, and combinatorial auctions (CAs), have been successfully employed to solve coordination problems in a wide range of application domains. However, the scale of CAs that can be optimally solved is small because of the complexity of the winner determination problem (WDP), namely of finding the bids that maximise the auctioneer’s revenue. A way of approximating the solution of a WDP is to solve its linear programming relaxation. The recently proposed Alternate Direction Dual Decomposition algorithm (AD3) has been shown to ef- ficiently solve large-scale LP relaxations. Hence, in this paper we show how to encode the WDP so that it can be approximated by means of AD3. Moreover, we present PAR-AD3, the first parallel implementation of AD3. PAR-AD3 shows to be up to 12.4 times faster than CPLEX in a single-thread execution, and up to 23 times faster than parallel CPLEX in an 8-core architecture. Therefore PAR- AD3 becomes the algorithm of choice to solve large-scale WDP LP relaxations for hard instances. Furthermore, PAR-AD3 has potential when considering large- scale coordination problems that must be solved as optimisation problems.Research supported by MICINN projects TIN2011-28689-C02-01, TIN2013-45732-C4-4-P and TIN2012-38876-C02-01Peer reviewe

An Exact Algorithm for Side-Chain Placement in Protein Design

Computational protein design aims at constructing novel or improved functions on the structure of a given protein backbone and has important applications in the pharmaceutical and biotechnical industry. The underlying combinatorial side-chain placement problem consists of choosing a side-chain placement for each residue position such that the resulting overall energy is minimum. The choice of the side-chain then also determines the amino acid for this position. Many algorithms for this NP-hard problem have been proposed in the context of homology modeling, which, however, reach their limits when faced with large protein design instances. In this paper, we propose a new exact method for the side-chain placement problem that works well even for large instance sizes as they appear in protein design. Our main contribution is a dedicated branch-and-bound algorithm that combines tight upper and lower bounds resulting from a novel Lagrangian relaxation approach for side-chain placement. Our experimental results show that our method outperforms alternative state-of-the art exact approaches and makes it possible to optimally solve large protein design instances routinely

Inferring PDZ Domain Multi-Mutant Binding Preferences from Single-Mutant Data

Many important cellular protein interactions are mediated by peptide recognition domains. The ability to predict a domain's binding specificity directly from its primary sequence is essential to understanding the complexity of protein-protein interaction networks. One such recognition domain is the PDZ domain, functioning in scaffold proteins that facilitate formation of signaling networks. Predicting the PDZ domain's binding specificity was a part of the DREAM4 Peptide Recognition Domain challenge, the goal of which was to describe, as position weight matrices, the specificity profiles of five multi-mutant ERBB2IP-1 domains. We developed a method that derives multi-mutant binding preferences by generalizing the effects of single point mutations on the wild type domain's binding specificities. Our approach, trained on publicly available ERBB2IP-1 single-mutant phage display data, combined linear regression-based prediction for ligand positions whose specificity is determined by few PDZ positions, and single-mutant position weight matrix averaging for all other ligand columns. The success of our method as the winning entry of the DREAM4 competition, as well as its superior performance over a general PDZ-ligand binding model, demonstrates the advantages of training a model on a well-selected domain-specific data set

Survey propagation at finite temperature: application to a Sourlas code as a toy model

In this paper we investigate a finite temperature generalization of survey propagation, by applying it to the problem of finite temperature decoding of a biased finite connectivity Sourlas code for temperatures lower than the Nishimori temperature. We observe that the result is a shift of the location of the dynamical critical channel noise to larger values than the corresponding dynamical transition for belief propagation, as suggested recently by Migliorini and Saad for LDPC codes. We show how the finite temperature 1-RSB SP gives accurate results in the regime where competing approaches fail to converge or fail to recover the retrieval state

Ranitidine Use and Incident Cancer in a Multinational Cohort

Importance: Ranitidine, the most widely used histamine-2 receptor antagonist (H2RA), was withdrawn because of N-nitrosodimethylamine impurity in 2020. Given the worldwide exposure to this drug, the potential risk of cancer development associated with the intake of known carcinogens is an important epidemiological concern. Objective: To examine the comparative risk of cancer associated with the use of ranitidine vs other H2RAs. Design, Setting, and Participants: This new-user active comparator international network cohort study was conducted using 3 health claims and 9 electronic health record databases from the US, the United Kingdom, Germany, Spain, France, South Korea, and Taiwan. Large-scale propensity score (PS) matching was used to minimize confounding of the observed covariates with negative control outcomes. Empirical calibration was performed to account for unobserved confounding. All databases were mapped to a common data model. Database-specific estimates were combined using random-effects meta-analysis. Participants included individuals aged at least 20 years with no history of cancer who used H2RAs for more than 30 days from January 1986 to December 2020, with a 1-year washout period. Data were analyzed from April to September 2021. Exposure: The main exposure was use of ranitidine vs other H2RAs (famotidine, lafutidine, nizatidine, and roxatidine). Main Outcomes and Measures: The primary outcome was incidence of any cancer, except nonmelanoma skin cancer. Secondary outcomes included all cancer except thyroid cancer, 16 cancer subtypes, and all-cause mortality. Results: Among 1 183 999 individuals in 11 databases, 909 168 individuals (mean age, 56.1 years; 507 316 [55.8%] women) were identified as new users of ranitidine, and 274 831 individuals (mean age, 58.0 years; 145 935 [53.1%] women) were identified as new users of other H2RAs. Crude incidence rates of cancer were 14.30 events per 1000 person-years (PYs) in ranitidine users and 15.03 events per 1000 PYs among other H2RA users. After PS matching, cancer risk was similar in ranitidine compared with other H2RA users (incidence, 15.92 events per 1000 PYs vs 15.65 events per 1000 PYs; calibrated meta-analytic hazard ratio, 1.04; 95% CI, 0.97-1.12). No significant associations were found between ranitidine use and any secondary outcomes after calibration. Conclusions and Relevance: In this cohort study, ranitidine use was not associated with an increased risk of cancer compared with the use of other H2RAs. Further research is needed on the long-term association of ranitidine with cancer development.</p

A Comparative Study of Modern Inference Techniques for Structured Discrete Energy Minimization Problems

International audienceSzeliski et al. published an influential study in 2006 on energy minimization methods for Markov Random Fields (MRF). This study provided valuable insights in choosing the best optimization technique for certain classes of problems. While these insights remain generally useful today, the phenomenal success of random field models means that the kinds of inference problems that have to be solved changed significantly. Specifically , the models today often include higher order interactions, flexible connectivity structures, large label-spaces of different car-dinalities, or learned energy tables. To reflect these changes, we provide a modernized and enlarged study. We present an empirical comparison of more than 27 state-of-the-art optimization techniques on a corpus of 2,453 energy minimization instances from diverse applications in computer vision. To ensure reproducibility, we evaluate all methods in the OpenGM 2 framework and report extensive results regarding runtime and solution quality. Key insights from our study agree with the results of Szeliski et al. for the types of models they studied. However, on new and challenging types of models our findings disagree and suggest that polyhedral methods and integer programming solvers are competitive in terms of runtime and solution quality over a large range of model types

Algorithm for backrub motions in protein design

Motivation: The Backrub is a small but kinematically efficient side-chain-coupled local backbone motion frequently observed in atomic-resolution crystal structures of proteins. A backrub shifts the Cα–Cβ orientation of a given side-chain by rigid-body dipeptide rotation plus smaller individual rotations of the two peptides, with virtually no change in the rest of the protein. Backrubs can therefore provide a biophysically realistic model of local backbone flexibility for structure-based protein design. Previously, however, backrub motions were applied via manual interactive model-building, so their incorporation into a protein design algorithm (a simultaneous search over mutation and backbone/side-chain conformation space) was infeasible