Consistent Sets of Secondary Structures in Proteins

Ab initio predictions of secondary structures in proteins have to combine local predictions, based on short fragments of the protein sequence, with consistency restrictions, as not all locally plausible predictions may be simultaneously true. We use the fact that secondary structures are patterns of hydrogen bonds and that a single residue can participate in hydrogen bonds of at most one secondary structure. Consistency of fixed-sized pieces of secondary structures is the easiest to approximate and we formalize it as 1-2 matching problem. Consistency of entire secondary structures is a version of set packing. We also investigate how to form a simple problem if we add the requirement that the secondary structure and the loops that connect them fit together in a metric space. Every problem that we investigated is MAX-SNP hard and it has a constant factor approximation. Computational experience suggests that in biological instances, we can find nearly optimal solutions using heuristics.     

Self-optimizing generalized adaptive notch filters — comparison of three optimization strategies

The paper provides comparison of three different approaches to on-line tuning of generalized adaptive notch filters (GANFs) — the algorithms used for identification/tracking of quasi-periodically varying dynamic systems. Tuning is needed to adjust adaptation gains, which control tracking performance of GANF algorithms, to the unknown and/or time time-varying rate of system nonstationarity. Two out of three compared approaches are classical solutions — the first one incorporates sequential optimization of adaptation gains while the second one is based on the concept of parallel estimation. The main contribution of the paper is that it suggests the third way — it shows that the best results can be achieved when both approaches mentioned above are combined in a judicious way. Such joint sequential/parallel optimization preserves advantages of both treatments: adaptiveness (sequential approach) and robustness to abrupt changes (parallel approach). Additionally the paper shows how, using the concept of surrogate outputs, one can extend the proposed single-frequency algorithm to the multiple frequencies case, without falling into the complexity trap known as the “curse of dimensionality”.     

Accelerating scientific computations with mixed precision algorithms

On modern architectures, the performance of 32-bit operations is often at least twice as fast as the performance of 64-bit operations. By using a combination of 32-bit and 64-bit floating point arithmetic, the performance of many dense and sparse linear algebra algorithms can be significantly enhanced while maintaining the 64-bit accuracy of the resulting solution. The approach presented here can apply not only to conventional processors but also to other technologies such as Field Programmable Gate Arrays (FPGA), Graphical Processing Units (GPU), and the STI Cell BE processor. Results on modern processor architectures and the STI Cell BE are presented.

Program summary

Program title: ITER-REFCatalogue identifier: AECO_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AECO_v1_0.htmlProgram obtainable from: CPC Program Library, Queen's University, Belfast, N. IrelandLicensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 7211No. of bytes in distributed program, including test data, etc.: 41 862Distribution format: tar.gzProgramming language: FORTRAN 77Computer: desktop, serverOperating system: Unix/LinuxRAM: 512 MbytesClassification: 4.8External routines: BLAS (optional)Nature of problem: On modern architectures, the performance of 32-bit operations is often at least twice as fast as the performance of 64-bit operations. By using a combination of 32-bit and 64-bit floating point arithmetic, the performance of many dense and sparse linear algebra algorithms can be significantly enhanced while maintaining the 64-bit accuracy of the resulting solution.Solution method: Mixed precision algorithms stem from the observation that, in many cases, a single precision solution of a problem can be refined to the point where double precision accuracy is achieved. A common approach to the solution of linear systems, either dense or sparse, is to perform the LU factorization of the coefficient matrix using Gaussian elimination. First, the coefficient matrix A is factored into the product of a lower triangular matrix L and an upper triangular matrix U. Partial row pivoting is in general used to improve numerical stability resulting in a factorization PA=LU, where P is a permutation matrix. The solution for the system is achieved by first solving Ly=Pb (forward substitution) and then solving Ux=y (backward substitution). Due to round-off errors, the computed solution, x, carries a numerical error magnified by the condition number of the coefficient matrix A. In order to improve the computed solution, an iterative process can be applied, which produces a correction to the computed solution at each iteration, which then yields the method that is commonly known as the iterative refinement algorithm. Provided that the system is not too ill-conditioned, the algorithm produces a solution correct to the working precision.Running time: seconds/minutes     

A Monge-Ampère enhancement for semi-Lagrangian methods

Demanding the compatibility of semi-Lagrangian trajectory schemes with the fundamental Euler expansion formula leads to the Monge-Ampère (MA) nonlinear second-order partial differential equation. Given standard estimates of the departure points of flow trajectories, solving the associated MA problem provides a corrected solution satisfying a discrete Lagrangian form of the mass continuity equation to round-off error. The impact of the MA enhancement is discussed in two diverse limits of fluid dynamics applications: passive tracer advection in a steady cellular flow and in fully developed turbulence. Improvements of the overall accuracy of simulations depend on the problem and can be substantial.     

Information systems in modeling interactive computations on granules

In this paper, we discuss the importance of information systems in modeling interactive computations performed on (complex) granules and we propose a formal approach to interactive computations based on generalized information systems and rough sets which can be combined with other soft computing paradigms such as fuzzy sets or evolutionary computing, but also with machine learning and data mining techniques. Information systems are treated as dynamic granules used for representing the results of the interaction of attributes with the environment. Two kinds of attributes are distinguished, namely, the perception attributes, including sensory attributes, and the action attributes. Sensory attributes are the basic perception attributes, other perception attributes are constructed on the basis of the sensory ones. Actions are activated when their guards, being often complex and vague concepts, are satisfied to a satisfactory degree. The guards can be approximated on the basis of measurements performed by sensory attributes rather than defined exactly. Satisfiability degrees for guards are results of reasoning called the adaptive judgment. The approximations are induced using hierarchical modeling. We show that information systems can be used for modeling more advanced forms of interactions in hierarchical modeling. The role of hierarchical interactions is emphasized in the modeling of interactive computations. Some illustrative examples of interactions used in the ACT-R 6.0 system are reported. ACT-R 6.0 is based on a cognitive architecture and can be treated as an example of a highly interactive complex granule which can be involved in hierarchical interactions. For modeling of interactive computations, we propose much more general information systems than the studied dynamic information systems (see, e.g., Ciucci (2010) [8] and Pa?asiński and Pancerz (2010) [32]). For example, the dynamic information systems are making it possible to consider incremental changes in information systems. However, they do not contain the perception and action attributes necessary for modeling interactive computations, in particular for modeling intrastep interactions.     

Dynamic normal forms and dynamic characteristic polynomial

We present the first fully dynamic algorithm for computing the characteristic polynomial of a matrix. In the generic symmetric case, our algorithm supports rank-one updates in O(n²logn) randomized time and queries in constant time, whereas in the general case the algorithm works in O(n²klogn) randomized time, where k is the number of invariant factors of the matrix. The algorithm is based on the first dynamic algorithm for computing normal forms of a matrix such as the Frobenius normal form or the tridiagonal symmetric form. The algorithm can be extended to solve the matrix eigenproblem with relative error 2^−b in additional O(nlog²nlogb) time. Furthermore, it can be used to dynamically maintain the singular value decomposition (SVD) of a generic matrix. Together with the algorithm, the hardness of the problem is studied. For the symmetric case, we present an Ω(n²) lower bound for rank-one updates and an Ω(n) lower bound for element updates.     

Processor Efficient Parallel Matching

In this paper we consider the problem of finding perfect matchings in parallel. We present a RNC algorithm with almost optimal work with respect to sequential algorithms, i.e., it uses O(n ^ω ) processors, where ω is the matrix multiplication exponent. Our algorithm is based on an RNC algorithm for computing determinant of a degree one polynomial matrix which is of independent interest. Research supported by KBN grant 1P03A01830.     

On constructing an optimal consensus clustering from multiple clusterings

Computing a suitable measure of consensus among several clusterings on the same data is an important problem that arises in several areas such as computational biology and data mining. In this paper, we formalize a set-theoretic model for computing such a similarity measure. Roughly speaking, in this model we have k>1 partitions (clusters) of the same data set each containing the same number of sets and the goal is to align the sets in each partition to minimize a similarity measure. For k=2, a polynomial-time solution was proposed by Gusfield (Information Processing Letters 82 (2002) 159-164). In this paper, we show that the problem is MAX-SNP-hard for k=3 even if each partition in each cluster contains no more than 2 elements and provide a -approximation algorithm for the problem for any k.     

Model-based tracking by classification in a tiny discrete pose space

A method is presented for tracking 3D objects as they transform rigidly in space within a sparse range image sequence. The method operates in discrete space and exploits the coherence across image frames that results from the relationship between known bounds on the object's velocity and the sensor frame rate. These motion bounds allow the interframe transformation space to be reduced to a reasonable and indeed tiny size, comprising only tens or hundreds of possible states. The tracking problem is in this way cast into a classification framework, effectively trading off localization precision for runtime efficiency and robustness. The method has been implemented and tested extensively on a variety of freeform objects within a sparse range data stream comprising only a few hundred points per image. It has been shown to compare favorably against continuous domain iterative closest point (ICP) tracking methods, performing both more efficiently and more robustly. A hybrid method has also been implemented that executes a small number of ICP iterations following the initial discrete classification phase. This hybrid method is both more efficient than the ICP alone and more robust than either the discrete classification method or the ICP separately     

Security Policy Conflicts in Service-oriented Systems

This paper considers methods for knowledge exploitation in security policies for Service-Oriented Architecture (SOA) environments, discovering the modality conflicts in particular. Two algorithms for discovering SOA-specific modality conflicts are proposed. First, a trivial (ad-hoc) approach is presented and further extended by the improved algorithm which offers lower time complexity. The formal verification of the proposal is followed by experimental results confirming the expected supremacy of the improved algorithm.