Computation of the Transient in Max-Plus Linear Systems via SMT-Solving

This paper proposes a new approach, grounded in Satisfiability Modulo Theories (SMT), to study the transient of a Max-Plus Linear (MPL) system, that is the number of steps leading to its periodic regime. Differently from state-of-the-art techniques, our approach allows the analysis of periodic behaviors for subsets of initial states, as well as the characterization of sets of initial states exhibiting the same specific periodic behavior and transient. Our experiments show that the proposed technique dramatically outperforms state-of-the-art methods based on max-plus algebra computations for systems of large dimensions.Comment: The paper consists of 22 pages (including references and Appendix). It is accepted in FORMATS 2020 First revisio

CUDASW++2.0: enhanced Smith-Waterman protein database search on CUDA-enabled GPUs based on SIMT and virtualized SIMD abstractions

<p>Abstract</p> <p>Background</p> <p>Due to its high sensitivity, the Smith-Waterman algorithm is widely used for biological database searches. Unfortunately, the quadratic time complexity of this algorithm makes it highly time-consuming. The exponential growth of biological databases further deteriorates the situation. To accelerate this algorithm, many efforts have been made to develop techniques in high performance architectures, especially the recently emerging many-core architectures and their associated programming models.</p> <p>Findings</p> <p>This paper describes the latest release of the CUDASW++ software, CUDASW++ 2.0, which makes new contributions to Smith-Waterman protein database searches using compute unified device architecture (CUDA). A parallel Smith-Waterman algorithm is proposed to further optimize the performance of CUDASW++ 1.0 based on the single instruction, multiple thread (SIMT) abstraction. For the first time, we have investigated a partitioned vectorized Smith-Waterman algorithm using CUDA based on the virtualized single instruction, multiple data (SIMD) abstraction. The optimized SIMT and the partitioned vectorized algorithms were benchmarked, and remarkably, have similar performance characteristics. CUDASW++ 2.0 achieves performance improvement over CUDASW++ 1.0 as much as 1.74 (1.72) times using the optimized SIMT algorithm and up to 1.77 (1.66) times using the partitioned vectorized algorithm, with a performance of up to 17 (30) billion cells update per second (GCUPS) on a single-GPU GeForce GTX 280 (dual-GPU GeForce GTX 295) graphics card.</p> <p>Conclusions</p> <p>CUDASW++ 2.0 is publicly available open-source software, written in CUDA and C++ programming languages. It obtains significant performance improvement over CUDASW++ 1.0 using either the optimized SIMT algorithm or the partitioned vectorized algorithm for Smith-Waterman protein database searches by fully exploiting the compute capability of commonly used CUDA-enabled low-cost GPUs.</p

Testing statistical significance scores of sequence comparison methods with structure similarity

BACKGROUND: In the past years the Smith-Waterman sequence comparison algorithm has gained popularity due to improved implementations and rapidly increasing computing power. However, the quality and sensitivity of a database search is not only determined by the algorithm but also by the statistical significance testing for an alignment. The e-value is the most commonly used statistical validation method for sequence database searching. The CluSTr database and the Protein World database have been created using an alternative statistical significance test: a Z-score based on Monte-Carlo statistics. Several papers have described the superiority of the Z-score as compared to the e-value, using simulated data. We were interested if this could be validated when applied to existing, evolutionary related protein sequences. RESULTS: All experiments are performed on the ASTRAL SCOP database. The Smith-Waterman sequence comparison algorithm with both e-value and Z-score statistics is evaluated, using ROC, CVE and AP measures. The BLAST and FASTA algorithms are used as reference. We find that two out of three Smith-Waterman implementations with e-value are better at predicting structural similarities between proteins than the Smith-Waterman implementation with Z-score. SSEARCH especially has very high scores. CONCLUSION: The compute intensive Z-score does not have a clear advantage over the e-value. The Smith-Waterman implementations give generally better results than their heuristic counterparts. We recommend using the SSEARCH algorithm combined with e-values for pairwise sequence comparisons

Measuring Global Credibility with Application to Local Sequence Alignment

Computational biology is replete with high-dimensional (high-D) discrete prediction and inference problems, including sequence alignment, RNA structure prediction, phylogenetic inference, motif finding, prediction of pathways, and model selection problems in statistical genetics. Even though prediction and inference in these settings are uncertain, little attention has been focused on the development of global measures of uncertainty. Regardless of the procedure employed to produce a prediction, when a procedure delivers a single answer, that answer is a point estimate selected from the solution ensemble, the set of all possible solutions. For high-D discrete space, these ensembles are immense, and thus there is considerable uncertainty. We recommend the use of Bayesian credibility limits to describe this uncertainty, where a (1−α)%, 0≤α≤1, credibility limit is the minimum Hamming distance radius of a hyper-sphere containing (1−α)% of the posterior distribution. Because sequence alignment is arguably the most extensively used procedure in computational biology, we employ it here to make these general concepts more concrete. The maximum similarity estimator (i.e., the alignment that maximizes the likelihood) and the centroid estimator (i.e., the alignment that minimizes the mean Hamming distance from the posterior weighted ensemble of alignments) are used to demonstrate the application of Bayesian credibility limits to alignment estimators. Application of Bayesian credibility limits to the alignment of 20 human/rodent orthologous sequence pairs and 125 orthologous sequence pairs from six Shewanella species shows that credibility limits of the alignments of promoter sequences of these species vary widely, and that centroid alignments dependably have tighter credibility limits than traditional maximum similarity alignments

Boolean dynamics revisited through feedback interconnections

Boolean models of physical or biological systems describe the global dynamics of the system and their attractors typically represent asymptotic behaviors. In the case of large networks composed of several modules, it may be difficult to identify all the attractors. To explore Boolean dynamics from a novel viewpoint, we will analyse the dynamics emerging from the composition of two known Boolean modules. The state transition graphs and attractors for each of the modules can be combined to construct a new asymptotic graph which will (1) provide a reliable method for attractor computation with partial information; (2) illustrate the differences in dynamical behavior induced by the updating strategy (asynchronous, synchronous, or mixed); and (3) show the inherited organization/structure of the original network’s state transition graph.publishe

Qualitative Analysis of Mammalian Circadian Oscillations: Cycle Dynamics and Robustness

International audienceIn asynchronous Boolean models, periodic solutions are represented by terminal strongly connected graphs, which are typically composed of hundreds of states and transitions. For biological systems, it becomes a challenging task to compare such mathematical objects with biological knowledge, or interpret the transitions inside an attractor in terms of the sequence of events in a biological cycle. A recent methodology generates summary graphs to help visualizing complex asynchronous attractors and order the dynamic progression based on known biological data. In this article we apply this method to a Boolean model of the mammalian circadian clock, for which the summary graph recovers the main phases of the cycle, in the expected order. It also provides a detailed view of the attractor, suggesting improvements in the design of the model's logical rules and highlighting groups of transitions that are essential for the attractor's robustness