Predicting Model and Algorithm in RNA Folding Structure Including Pseudoknots

Input Queued (IQ) switch architecture has been of interest due to its low memory bandwidth requirement. A scheduling algorithm is required to schedule the transfer of packets through cross-bar switch fabric at every time slot. The performance, that is throughput and delay, of a switch depends on the scheduling algorithm. The maximum weight matching (MWM) algorithm is known to deliver 100% throughput under any admissible traffic. Leonardi et. al. (2001) obtained a nontrivial bound on the delay for the MWM algorithm under admissible Bernoulli i.i.d. traffic. There has been a lot of interesting work done over time to analyze throughput of scheduling algorithms. But apart from the work of Leonardi et al. there has not been any work done to obtain bounds on delay of scheduling algorithms. The MWM algorithm is perceived to be a very good scheduling algorithm in general and simulations have suggested that it performs better than most of the known algorithms in terms of delay. But it is very complex to implement. Hence many simple to implement approximations to MWM have been proposed. In this paper, we study a class of algorithms to MWM, which always obtain a schedule whose weight W differs from the weight of MWM schedule W* by at most f(W*), where f(.) is a sub-linear function. We call this difference in weight as approximation distance of algorithm from MWM. We denote this class of algorithms by 1-APRX. We prove that any 1-APRX algorithm is stable, that is, it delivers upto 100% of throughput under any admissible Bernoulli i.i.d. input traffic. Under any admissible Bernoulli i.i.d. traffic, we obtain bounds on the average queue length(equivalently delay) of the 1-APRX algorithms using a Lyapunov function technique, which was motivated in Leonardi et al. The delay bounds obtained for the 1-APRX algorithm are linearly related with the approximation distance, which matches the intuition that the better the weight of the schedule, the better the algorithm will perform. Interestingly, simulations show a linear relationship between the average queue length (equivalently delay) and the approximation distance. Thus, the approximation distance of a scheduling algorithm can serve as a metric to differentiate between the performance of different stable algorithms, even though throughput may be same for these algorithms. We also obtain a novel heuristic tighter bound on the average queue length (equivalently delay) under uniform Bernoulli i.i.d. traffic for MWM using a very simple argument.

There are some NP-hard problems in the prediction of RNA structures. Prediction of RNA folding structure in RNA nucleotide sequence remains an unsolved challenge. We investigate the computing algorithm in RNA folding structural prediction based on extended structure and basin hopping graph, it is a computing mode of basin hopping graph in RNA folding structural prediction including pseudoknots. This study presents the predicting algorithm based on extended structure, it also proposes an improved computing algorithm based on barrier tree and basin hopping graph, which are the attractive approaches in RNA folding structural prediction. Many experiments have been implemented in Rfam14.1 database and PseudoBase database, the experimental results show that our two algorithms are efficient and accurate than the other existing algorithms.

A faster FPTAS for knapsack problem with cardinality constraint

Obtaining a matching in a graph satisfying a certain objective is an important class of graph problems. Matching algorithms have received attention for several decades. However, while there are efficient algorithms to obtain a maximum weight matching, not much is known about the maximum weight maximum cardinality, and maximum cardinality maximum weight matching problems for general graphs. Our contribution in this work is to show that for bounded weight input graphs one can obtain an algorithm for both maximum weight maximum cardinality (for real weights), and maximum cardinality maximum weight matching (for integer weights) by modifying the input and running the existing maximum weight matching algorithm. Also, given the current state of the art in maximum weight matching algorithms, we show that, for bounded weight input graphs, both maximum weight maximum cardinality, and maximum cardinality maximum weight matching have algorithms of similar complexities to that of maximum weight matching. Subsequently, we also obtain approximation algorithms for maximum weight maximum cardinality, and maximum cardinality maximum weight matching.

The delay and throughput characteristics of a packet switch depend mainly on the queueing scheme and the scheduling algorithm deployed at the switch. Early research on scheduling algorithms has mainly focused on maximum weight matching scheduling algorithms. It is known that maximum weight matching algorithms guarantee the stability of input-queued switches, but are impractical due to their high computational complexity. Later research showed that the less complex maximal matching algorithms can stabilize input-queued switches when they are deployed with a speed-up of two. For practical purposes, neither a high computational complexity nor a speed-up of two is desirable.In this paper, we investigate the application of matching algorithms that approximate maximum weight matching algorithms to scheduling problems. We show that while having a low computational complexity, they guarantee the stability of input queued switches when they are deployed with a moderate speed-up.In particular, we show that the improve_matching algorithm stabilizes input-queued switches when it is deployed with a speed-up of 3<over>2+ε.In a second step, we further improve on these results by proposing a class of maximal weight matching algorithms that stabilize an input-queued switch without any speed-up.Whereas initial research has only focused on scheduling algorithms that guarantee the stability of a single switch, recent work has shown how scheduling algorithms for single switches can be modified in order to design distributed scheduling algorithms that stabilize networks of input-queued switches. Using those results, we show that the switching algorithms proposed in this paper do not only stabilize a single switch, but also networks of input-queued switches.

#NFA refers to the problem of counting the words of length n accepted by a non-deterministic finite automaton. #NFA is #P-hard, and although fully-polynomial-time randomized approximation schemes (FPRAS) exist, they are all impractical. The first FPRAS for #NFA had a running time of Õ(n 17 m 17 ε -14 łog(δ -1 )), where m is the number of states in the automaton, δ ∈ (0,1] is the confidence parameter, and ε > 0 is the tolerance parameter (typically smaller than 1). The current best FPRAS achieved a significant improvement in the time complexity relative to the first FPRAS and obtained FPRAS with time complexity Õ((n 10 m 2 + n 6 m 3 )ε -4 łog 2 (δ -1 )). The complexity of the improved FPRAS is still too intimidating to attempt any practical implementation. In this paper, we pursue the quest for practical FPRAS for #NFA by presenting a new algorithm with a time complexity of O(n 2 m 3 łog(nm)ε -2 łog(δ -1 )). Observe that evaluating whether a word of length n is accepted by an NFA has a time complexity of O(nm 2 ). Therefore, our proposed FPRAS achieves sub-quadratic complexity with respect to membership checks.

In order to carry out biological functions, RNA molecules must fold into specific three-dimensional (3D) structures. Current experimental methods to determine RNA 3D structures are expensive and time consuming. With the recent advances in computational biology, RNA structure prediction is becoming increasingly reliable. This chapter describes a recently developed RNA structure prediction software, Vfold, a virtual bond-based RNA folding model. The main features of Vfold are the physics-based loop free energy calculations for various RNA structure motifs and a template-based assembly method for RNA 3D structure prediction. For illustration, we use the yybP-ykoY Orphan riboswitch as an example to show the implementation of the Vfold model in RNA structure prediction from the sequence.

The problem of predicting ribonucleic acid (RNA) structure with pseudoknots makes it NP–hard. To find optimal RNA pseudoknotted structure, we investigate the RNA pseudoknotted structure based on computational methods and models with minimum free energy (MFE). The contribution of this paper is to obtain an efficient algorithm for predicting RNA pseudoknotted structure with pseudoknots, and the algorithm takes O(n³) time and O(n²) space. The experimental test in PseudoBase and Rfam10.1 shows that the proposed algorithm is more effective and precise than other compared algorithms, and can predict arbitrary pseudoknots. Furthermore, we prove that there exists 1 + ε (ε > 0) polynomial time approximation scheme (PTAS) in searching maximum number of stackings. We also present a 2–approximation algorithm and analyse the approximation algorithm.

BackgroundAn increasing number of researchers have released novel RNA structure analysis and prediction algorithms for comparative approaches to structure prediction. Yet, independent benchmarking of these algorithms is rarely performed as is now common practice for protein-folding, gene-finding and multiple-sequence-alignment algorithms.ResultsHere we evaluate a number of RNA folding algorithms using reliable RNA data-sets and compare their relative performance.ConclusionsWe conclude that comparative data can enhance structure prediction but structure-prediction-algorithms vary widely in terms of both sensitivity and selectivity across different lengths and homologies. Furthermore, we outline some directions for future research.

Recently, we described a Maximum Weighted Matching (MWM) method for RNA structure prediction. The MWM method is capable of detecting pseudoknots and other tertiary base-pairing interactions in a computationally efficient manner (Cary and Stormo, Proceedings of the Third International Conference on Intelligent Systems for Molecular Biology, pp. 75-80, 1995). Here we report on the results of our efforts to improve the MWM method's predictive accuracy, and show how the method can be extended to detect base interactions formerly inaccessible to automated RNA modeling techniques. Improved performance in MWM structure prediction was achieved in two ways. First, new ways of calculating base pair likelihoods have been developed. These allow experimental data and combined statistical and thermodynamic information to be used by the program. Second, accuracy was improved by developing techniques for filtering out spurious base pairs predicted by the MWM program. We also demonstrate here a means by which the MWM folding method may be used to detect the presence of base triples in RNAs. http://www.cshl.org/mzhanglab/tabaska/j axpage. html tabaska@cshl.org

Sampling-Based Approximation Schemes for Capacitated Stochastic Inventory Control Models

Approximation algorithms for fractional knapsack problems

A Case-Based Reasoning System to Control Traffic at Signalized Intersections

In this paper, we introduce a model for Multiple-Input Multiple-Output (MIMO) Space Division Multiple Access (SDMA) into the analysis of a multi-hop millimeter wave network under the classic Network Utility Maximization (NUM) framework with Maximum Back Pressure scheduling (MBP). We show that the proof of convergence of MBP remains valid when we allow the scheduler to select multiple links to the same receiver in the same frame. Conventional MBP with a single link per receiver is traditionally implemented using the Maximum Weighted Matching (MWM) algorithm over the network graph. Under our modification, the problem becomes a Maximum Weighted Partition of the graph. Message Passing (MP) algorithms are efficient and have been successfully applied to graph partitioning problems in the past, so we use one to approximate the optimal MBP scheduling. Through simulation over a randomized mmWave picocell, we compare the MWM reference without SDMA, the efficient MP approximation, and the exact optimal MBP scheduler with SDMA (obtained by brute force). Simulations show that by leveraging SDMA in multi-hop mmWave network scheduling, a 50% capacity increase is obtained on average.

Determination of Ribonucleic Acid structure is challenging, in order to optimize the RNA pseudoknotted structure,the paper investigates the computational problem and complexity of predicting RNA structure. A new computational method and model with minimum free energy are adopted to predict RNA structure. The main contribution of the paper is to achieves an efficient approximation algorithm for finding RNA pseudoknotted structure and nested structures. We have compared with other algorithms in time complexity and space complexity, the approximation algorithm takes O(n3) time and O(n2) space,where n is the length of the RNA sequences. The experimental tests for a large database of RNA show that the algorithm is more exact and effective than the algorithms, the algorithm can predict arbitrary pseudoknots, and improve the a predicting accuracy.