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Abstract: In non-binary constraint satisfaction problems, the study of local consistencies that only prune values from domains has so far been largely limited to generalized arc consistency or weaker local consistency properties. This is in contrast with binary constraints where numerous such domain filtering consistencies have been proposed. In this paper we present a detailed theoretical, algorithmic and empirical study of domain filtering consistencies for non-binary problems. We study three domain filtering consistencies that are inspired by corresponding variable based domain filtering consistencies for binary problems. These consistencies are stronger than generalized arc consistency, but weaker than pairwise consistency, which is a strong consistency that removes tuples from constraint relations. Among other theoretical results, and contrary to expectations, we prove that these new consistencies do not reduce to the variable based definitions of their counterparts on binary constraints. We propose a number of algorithms to achieve the three consistencies. One of these algorithms has a time complexity comparable to that for generalized arc consistency despite performing more pruning. Experiments demonstrate that our new consistencies are promising as they can be more efficient than generalized arc consistency on certain non-binary problems. [Copyright &y& Elsevier]

Abstract: A recent and effective approach to probabilistic inference calls for reducing the problem to one of weighted model counting (WMC) on a propositional knowledge base. Specifically, the approach calls for encoding the probabilistic model, typically a Bayesian network, as a propositional knowledge base in conjunctive normal form (CNF) with weights associated to each model according to the network parameters. Given this CNF, computing the probability of some evidence becomes a matter of summing the weights of all CNF models consistent with the evidence. A number of variations on this approach have appeared in the literature recently, that vary across three orthogonal dimensions. The first dimension concerns the specific encoding used to convert a Bayesian network into a CNF. The second dimensions relates to whether weighted model counting is performed using a search algorithm on the CNF, or by compiling the CNF into a structure that renders WMC a polytime operation in the size of the compiled structure. The third dimension deals with the specific properties of network parameters (local structure) which are captured in the CNF encoding. In this paper, we discuss recent work in this area across the above three dimensions, and demonstrate empirically its practical importance in significantly expanding the reach of exact probabilistic inference. We restrict our discussion to exact inference and model counting, even though other proposals have been extended for approximate inference and approximate model counting. [Copyright &y& Elsevier]

Abstract: Due to its excellent rate–distortion performance, set partitioning in hierarchical trees (SPIHT) has become the state-of-the-art algorithm for image compression. However, the algorithm does not fully provide the desired features of progressive transmission, spatial scalability and optimal visual quality, at very low bit rate coding. Furthermore, the use of three linked lists for recording the coordinates of wavelet coefficients and tree sets during the coding process becomes the bottleneck of a fast implementation of the SPIHT. In this paper, we propose a listless modified SPIHT (LMSPIHT) approach, which is a fast and low memory image coding algorithm based on the lifting wavelet transform. The LMSPIHT jointly considers the advantages of progressive transmission, spatial scalability, and incorporates human visual system (HVS) characteristics in the coding scheme; thus it outperforms the traditional SPIHT algorithm at low bit rate coding. Compared with the SPIHT algorithm, LMSPIHT provides a better compression performance and a superior perceptual performance with low coding complexity. The compression efficiency of LMSPIHT comes from three aspects. The lifting scheme lowers the number of arithmetic operations of the wavelet transform. Moreover, a significance reordering of the modified SPIHT ensures that it codes more significant information belonging to the lower frequency bands earlier in the bit stream than that of the SPIHT to better exploit the energy compaction of the wavelet coefficients. HVS characteristics are employed to improve the perceptual quality of the compressed image by placing more coding artifacts in the less visually significant regions of the image. Finally, a listless implementation structure further reduces the amount of memory and improves the speed of compression by more than 51% for a 512×512 image, as compared with that of the SPIHT algorithm. [Copyright &y& Elsevier]

Abstract: Let be a hereditary abelian -category with tilting object and denote the bounded derived category of . This paper is devoted to a study of suspended subcategories of by means of their Ext-projectives. [Copyright &y& Elsevier]

Abstract: Proposed in this paper is a unified, robust algorithm for the input–output analysis of planar, spherical and spatial four-bar linkages. Robustness is needed to account for architecture and algebraic singularities that are likely to occur, for example, when conducting an iterative optimization of the linkage at hand. The unified feature of the algorithm is based on the algebra of dual numbers and the Principle of Transference, which allows the extension of the algorithm developed for spherical linkages to their spatial counterparts by a simple dualization of the real geometric relations derived for the former. Numerical examples are included to demonstrate the application of the algorithm. [Copyright &y& Elsevier]

Abstract: In this paper, an improved approach to blind deconvolution of LTI systems incorporating phase unwrapping is presented. The method can recover a noise-free estimate of the logarithm of the system transfer function which enables reconstruction of the system. The algorithm is fast due to simple computation and accurate as it includes phase unwrapping. The proposed method is compared via simulation with other methods, selected as representative of both bispectrum- and bicepstrum-based techniques. In general, it performs as well as or much better than the other methods considered. The proposed method is also shown to perform well under low signal-to-noise ratios. [Copyright &y& Elsevier]

Abstract: In this paper, a bicriteria solid transportation problem with stochastic parameters is investigated. Three mathematical models are constructed for the problem, including expected value goal programming model, chance-constrained goal programming model and dependent-chance goal programming model. A hybrid algorithm is also designed based on the random simulation algorithm and tabu search algorithm to solve the models. At last, some numerical experiments are presented to show the performance of models and algorithm. [Copyright &y& Elsevier]

Abstract: Imposing constraints is a way to incorporate information into the sequence alignment procedure. In this paper, a general model for constrained alignment is proposed so that analyses admitted are more flexible and that different pattern definitions can be treated in a simple unified way. We give a polynomial time algorithm for pairwise constrained alignment for the generalized formulation, and prove the inapproximability of the problem when the number of sequences can be arbitrary. In addition, previous works deal only with the case that the patterns in the constraint have to occur in the output alignment in the same order as that specified by the input. It is of both theoretical and practical interest to investigate the case when the order is no longer limited. We show that the problem is not approximable even when the number of sequences is two. We also give the NPO-completeness results for the problems with bounds imposed on the objective function value. [Copyright &y& Elsevier]

Abstract: This paper proposes a model that generalizes the linear consecutive k-out-of-r-from-n: G system to multi-state case. In this model the system consists of n linearly ordered multi-state components. Both the system and its components can have different states: from complete failure up to perfect functioning. The system is in state j or above if and only if at least k j components out of r consecutive are in state j or above. An algorithm is provided for evaluating reliability of a special case of multi-state consecutive k-out-of-r-from-n: G system. The algorithm is based on the application of the total probability theorem and on the application of a special case taken from the [Jinsheng Huang, Ming J. Zuo, Member IEEE and Yanhong Wu, Generalized multi-state k-out-of-n: G system, IEEE Trans. Reliab. 49(1) (2000) 105–111.]. Also numerical results of the formerly published test examples and new examples are given. [Copyright &y& Elsevier]

Abstract: Constructing symmetric drawings of graphs is NP-hard. In this paper, we present a new method for drawing graphs symmetrically based on group theory. More formally, we define an -geometric automorphism group as a subgroup of the automorphism group of a graph that can be displayed as symmetries of a drawing of the graph in dimensions. Then we present an algorithm to find all 2- and 3-geometric automorphism groups of a given graph. We implement the algorithm using Magma [http://magma.maths.usyd.edu.au] and the experimental results show that our approach is very efficient in practice. We also present a drawing algorithm to display 2- and 3-geometric automorphism groups. [Copyright &y& Elsevier]

Abstract: The 2-factor index of a graph G, denoted by is the smallest integer m such that the m-iterated line graph of G contains a 2-factor. In this paper, we provide a formula for , and point out that there is a polynomial time algorithm to determine . [Copyright &y& Elsevier]

This paper concerns construction of additive stretched spanners with few edges for -vertex graphs having a tree-decomposition into bags of diameter at most , i.e., the tree-length graphs. For such graphs we construct additive -spanners with edges, and additive -spanners with edges. This provides new upper bounds for chordal graphs for which . We also show a lower bound, and prove that there are graphs of tree-length for which every multiplicative -spanner (and thus every additive -spanner) requires edges. [Copyright &y& Elsevier]

Abstract: Geometric algorithms are based on geometric objects such as points, lines and circles. The term kernel refers to a collection of representations for constant-size geometric objects and operations on these representations. This paper describes how such a geometry kernel can be designed and implemented in C++, having special emphasis on adaptability, extensibility and efficiency. We achieve these goals following the generic programming paradigm and using templates as our tools. These ideas are realized and tested in Cgal, the Computational Geometry Algorithms Library, see http://www.cgal.org/. [Copyright &y& Elsevier]

Abstract: This paper introduces a new mathematical approach that combines the concepts of dimensional reduction and Krylov subspace techniques for use in the model reduction problem for large-scale systems. Krylov subspace methods for model reduction uses the Arnoldi algorithm in order to construct the bases for controllability, observability, and oblique subspaces of state space realization. The newly developed algorithm uses principal component analysis along with Krylov oblique projection model reduction technique to provide computationally efficient and inexpensive model reduction method. To demonstrate the effectiveness of the proposed hybrid scheme the residual error, forward error and stability response analyses have been performed for various randomly generated large-scale systems. [Copyright &y& Elsevier]

Abstract: Given a sequence of real numbers and an integer parameter , the problem studied in this paper is to compute subsequences of consecutive elements with the sums of their elements being the largest, the second largest, …, and the th largest among all possible range sums of the input sequence. For any value of , , we design a fast algorithm that takes time in the worst case to compute and rank all such subsequences. We also prove that our algorithm is optimal for by providing a matching lower bound. Moreover, our algorithm is an improvement over the previous results on the maximum sum subsequences problem (where only the subsequences are requested and no ordering with respect to their relative sums will be determined). Furthermore, given the fact that we have computed the th largest sums, our algorithm retrieves the th largest sum in time, after time of preprocessing. [Copyright &y& Elsevier]

Abstract: A well-known formula of Tutte and Berge expresses the size of a maximum matching in a graph G in terms of what is usually called the deficiency. A subset X of for which this deficiency is attained is called a Tutte set of G. While much is known about maximum matchings, less is known about the structure of Tutte sets. We explored the structural aspects of Tutte sets in another paper. Here, we consider the algorithmic complexity of finding Tutte sets in a graph. We first give two polynomial algorithms for finding a maximal Tutte set. We then consider the complexity of finding a maximum Tutte set, and show it is NP-hard for general graphs, as well as for several interesting restricted classes such as planar graphs. By contrast, we show we can find maximum Tutte sets in polynomial time for graphs of level 0 or 1, elementary graphs, and 1-tough graphs. [Copyright &y& Elsevier]

Abstract: The entire mathematical software engineering process should be driven by the need to build products that conform to their requirements, and to demonstrate, as early in the development cycle as possible, the quality of each component. Quality cannot be tested into a product; it must be built in from the start. Furthermore, mathematical software engineers should follow some rules in order to achieve the accuracy, modularity, deferred commitment, reusability and naturalness. It’ astonishing simple to implement complex mathematical algorithms in unstructured programming but it’s harmful to “reinvent the wheel” every time you create a program. In this paper, I am going to examine the importance of Object-orientated programming in Mathematics. [Copyright &y& Elsevier]

This paper addresses a spatial estimation model which uses fuzzy clustering algorithm and assesses the aquifer porosity based on point cumulative semimadogram (PCSM) measure. In order to obtain the estimated porosity values, the model employs standard regional dependence function (SRDF) which provides weights for different regional locations depending on the distances from the reference site. The proposed methodology has three stages: (1) structure identification; (2) spatial dependence measure; and (3) interpolation. The model has been tested using a real data set which was taken from an aquifer in Turkey. The performance evaluations indicate that the new methodology can be applied in geological based domains. [Copyright &y& Elsevier]

In this paper, we propose a new recursive framework for camera resectioning and apply it to off-line video-based augmented reality. Our method is based on an unscented particle filter and an independent Metropolis–Hastings chain, which deal with nonlinear dynamic systems without local linearization, and lead to more accurate results than other nonlinear filters. The proposed method has some desirable properties for camera resectioning: Since it does not rely on erroneous linear solutions, initialization problems do not occur, in contrast to the previous resectioning methods. Jittering error can be reduced by considering consistency and coherency between adjacent frames in our recursive framework. Our method is fairly accurate comparable to nonlinear optimization methods, which in general have higher levels of computation and complexity. As a result, the proposed algorithm outperforms the standard camera resectioning algorithm. We verify the effectiveness of our method through several experiments using synthetic and real image sequences comparing the estimation performance with other linear and nonlinear methods. [Copyright &y& Elsevier]

Univariate decision tree algorithms are widely used in data mining because (i) they are easy to learn (ii) when trained they can be expressed in rule based manner. In several applications mainly including data mining, the dataset to be learned is very large. In those cases it is highly desirable to construct univariate decision trees in reasonable time. This may be accomplished by parallelizing univariate decision tree algorithms. In this paper, we first present two different univariate decision tree algorithms C4.5 and univariate linear discriminant tree. We show how to parallelize these algorithms in three ways: (i) feature based; (ii) node based; (iii) data based manners. Experimental results show that performance of the parallelizations highly depend on the dataset and the node based parallelization demonstrate good speedups. [Copyright &y& Elsevier]

Lie operators are known to be effective in detecting very small degrees of object motions such as scaling, rotations and deformations. In this paper, we apply multiple Lie operators in combination to increase the accuracy of the conventional translation-only motion estimation. We propose the following three motion estimation methods using Lie operators with varying computational complexities, including the serial search, iterative search and the dynamic programming like search methods. We seek to study the tradeoffs allowed by the different combinations of Lie operators between the improved accuracy and the extra computational complexity associated with estimating the motion parameters. Both analytical and experimental results show that the proposed Lie-operator approaches can offer significant increases in the accuracy of the motion estimation with only low to moderate increase in the computational complexity. We also demonstrate that the iterative search method based on Lie operators has much lower complexity than motion search using an affine motion model for small motion parameters, while providing accuracy improvements very close to those attainable by the affine model approach. [Copyright &y& Elsevier]

In this paper a linear algorithm is derived for constructing B-spline control nets for spline developable surfaces of arbitrary degree and number of pieces. Control vertices are written in terms of five free parameters related to the type of developable surface. Aumann''s algorithm for constructing Bézier developable surfaces is recovered as a particular case. [Copyright &y& Elsevier]

Abstract: In this paper, by using the theories and methods of mathematical analysis and computer algebra, a reliable algorithm of finite difference method for solving singular perturbation problems was established, a new matlab procedure ehssp was implemented, too. Several linear and non-linear problems are presented to illustrate the implementation of the program. [Copyright &y& Elsevier]

Abstract: In this paper, we discuss some more generalized iterative schemes for solving the large sparse saddle point problems proposed by Ling and Hu [X.F. Ling, X.Z. Hu, On the iterative algorithm for large sparse saddle point problems, Appl. Math. Comput. 178 (2006) 372–379.], and apply the preconditioned GMRES to accelerate the convergence. Numerical experiments are reported that show the effectiveness of the proposed methods. [Copyright &y& Elsevier]

Abstract: There are various techniques for reconstructing phylogenetic trees from data, and in this context the problem of determining how distant two such trees are from each other arises naturally. Various metrics for measuring the distance between two phylogenies have been defined. Another way of comparing two trees and is to compute the so called maximum agreement forest of these trees. Informally, the number of components of an agreement forest tells how many edges from each of and need to be cut so that the resulting forests agree, after performing all forced edge contractions. This problem is -hard even when the input trees have maximum degree 2. Hein et al. [J. Hein, T. Jiang, L. Wang, K. Zhang, On the complexity of comparing evolutionary trees, Discrete Applied Mathematics 71 (1996) 153–169] presented an approximation algorithm for it, claimed to have performance ratio 3. We show that the performance ratio of the algorithm proposed by Hein et al. is 4, and we also present two new 3-approximation algorithms for this problem. We show how to modify one of the algorithms into a -approximation algorithm for trees with bounded degree , . Finally, we report on some computational experiments comparing the performance of the algorithms presented in this paper. [Copyright &y& Elsevier]

Abstract: The use of an event-to-event solution scheme for pseudodynamic testing is investigated in this paper. A standard pseudodynamic solution procedure is extended to include an event-to-event scheme. An adaptive event prediction method is developed using the local equilibrium energy error. The accuracy and efficiency of the standard and modified schemes are examined for a variety of problems. The analysis results show that numerical errors are controlled while decreasing the number of experimental load steps. The event-to-event scheme is shown to be suitable for pseudodynamic testing. [Copyright &y& Elsevier]

As the cost of genome sequencing continues to drop, comparison of large sequences becomes tantamount to our understanding of evolution and gene function. Rapid genome alignment stands to play a fundamental role in furthering biological understanding. In 2002, a fast algorithm based on statistical estimation called super pairwise alignment (SPA) was developed by Shen et al. The method was proved to be much faster than traditional dynamic programming algorithms, while it suffered small drop in accuracy. In this paper, we propose a new method based on SPA that target analysis of large-scale genomes. The new method, named super genome alignment (SGA), applies Yang–Keiffer coding theory to alignment and results in a grammar-based algorithm. SGA has the same computational complexity as its predecessor SPA, and it can process large-scale genomes. SGA is tested by using numerous pairs of microbial and eukaryotic genomes, which serve as the benchmark to compare it with the competing BLASTZ method. When compared with BLASTZ, the result shows that SGA is significantly faster by at least an order of magnitude (for some genome pairs the differences is as large at two orders of magnitude), and suffers on average only about 1% loss of the similarity of alignment. [Copyright &y& Elsevier]

Abstract: We consider the classical limit analysis problem of frame structures made up of rigid perfectly plastic members and involving some supports in unilateral frictional contact with the ground. A direct formulation as a mixed complementarity problem (MCP) is used. For the Coulomb case, which forms the focus of this paper, the corresponding MCP may admit multiple upper bound collapse load solutions. In order to identify the least upper bound solution, we propose two algorithms. The first one attempts to enumerate the possible multiple solutions, or at least map the solution space if the solutions are connected. The second scheme tries to find the least upper bound by directly formulating and solving a single nonconvex optimization problem, known in the literature as a mathematical program with equilibrium constraints (MPEC). Two simple examples are provided to illustrate application of these approaches. They also serve to highlight some key features of such structures. [Copyright &y& Elsevier]

Magnetic resonance angiography (MRA) provides three-dimensional data of vascular structures by visualising the flowing blood signal. Algorithms dedicated to vessel segmentation generally detect the cerebral vascular tree by only seeking this high intensity blood signal in MRA data. The method presented in this paper proposes a different strategy which consists in using both MRA and classical MRI in order to integrate a priori anatomical knowledge for guidance of the vessel segmentation process. It then uses mathematical morphology tools to carry out a simultaneous segmentation of both blood signal in MRA and blood and wall signal in MRI, enabling to take advantage of a larger amount of information than previously proposed methods. This method is dedicated to the superior sagittal sinus segmentation; however, similar strategies could be considered for segmentation of other vascular structures. It has been performed on a database composed of 9 couples of MRA and MRI, providing results which have been validated and compared to other ones obtained with a region-growing algorithm. Their validation tends to prove that the proposed method is reliable even when the vascular signal is inhomogeneous or contains artifacts. [Copyright &y& Elsevier]

This paper further investigates a new approach for self-dual morphological processing, where eroded images have all shapes shrunk in a contrast-invariant way. In the binary case, we operate on a given image with morphological operators in the so-called “adjacency lattice,” which is intimately related to the image’s adjacency tree. These operators are generalized to grayscale images by means of the so-called “shape-tree semilattice,” which is based on the tree of shapes of the given image. Apart of reviewing their original definition, different algorithms for computing the shape-tree morphological operators are addressed. [Copyright &y& Elsevier]

Abstract: Exclusion algorithms have been used recently to find all solutions of a system of nonlinear equations or to find the global minimum of a function over a compact domain. These algorithms are based on a minimization condition that can be applied to each cell in the domain. In this paper, we consider Lipschitz functions of order and give a new minimization condition for the exclusion algorithm. Furthermore, convergence and complexity results are presented for such algorithm. [Copyright &y& Elsevier]

We consider basic conceptual graphs, namely simple conceptual graphs (SGs), which are equivalent to the existential conjunctive positive fragment of first-order logic. The fundamental problem, deduction, is performed by a graph homomorphism called projection. The existence of a projection from a SG Q to a SG G means that the knowledge represented by Q is deducible from the knowledge represented by G. In this framework, a knowledge base is composed of SGs representing facts and a query is itself a SG. We focus on the issue of querying SGs, which highlights another fundamental problem, namely query answering. Each projection from a query to a fact defines an answer to the query, with an answer being itself a SG. The query answering problem asks for all answers to a query. This paper introduces atomic negation into this framework. Several understandings of negation are explored, which are all of interest in real world applications. In particular, we focus on situations where, in the context of incomplete knowledge, classical negation is not satisfactory because deduction can be proven but there is no answer to the query. We show that intuitionistic deduction captures the notion of an answer and can be solved by projection checking. Algorithms are provided for all studied problems. They are all based on projection. They can thus be combined to deal with several kinds of negation simultaneously. Relationships with problems on conjunctive queries in databases are recalled and extended. Finally, we point out that this discussion can be put in the context of semantic web databases. [Copyright &y& Elsevier]

In this paper, we propose a new operator, histogram-by, which provides a grouping for continuous domains, which partitions records into several groups by given ranges of the target attributes. The histogram-by operator can be represented as histogram-by clause in the SQL statement, and can be easily amenable to query optimization. As the application of the histogram-by operator, we introduce a multi-dimensional histogram query, which returns aggregate values of all ranges specified by the histogram-by clause. To process the query efficiently, we propose effective algorithms using aggregate R-trees. Our experimental results show that our algorithms are reliable in terms of performance over the synthetic and real-world datasets. [Copyright &y& Elsevier]

The use of rules in a distributed environment creates new challenges for the development of active rule execution models. In particular, since a single event can trigger multiple rules that execute over distributed sources of data, it is important to make use of concurrent rule execution whenever possible. This paper presents the details of the integration rule scheduling (IRS) algorithm. Integration rules are active database rules that are used for component integration in a distributed environment. The IRS algorithm identifies rule conflicts for multiple rules triggered by the same event through static, compile-time analysis of the read and write sets of each rule. A unique aspect of the algorithm is that the conflict analysis includes the effects of nested rule execution that occurs as a result of using an execution model with an immediate coupling mode. The algorithm therefore identifies conflicts that may occur as a result of the concurrent execution of different rule triggering sequences. The rules are then formed into a priority graph before execution, defining the order in which rules triggered by the same event should be processed. Rules with the same priority can be executed concurrently. The IRS algorithm guarantees confluence in the final state of the rule execution. The IRS algorithm is applicable for rule scheduling in both distributed and centralized rule execution environments. [Copyright &y& Elsevier]

Choices in business processes are often based on the process history saved as a log-file listing events and their time stamps. In this paper we introduce LogLogics, a finite-path variant of the Timed Propositional Temporal Logic with Past, which can be in particular used for specifying guards in business process models. The novelty is due to the presence of boundary points corresponding to the starting and current observation points, which gives rise to a three-valued logic allowing us to distinguish between temporal formulas that hold for any log extended with some possible past and future (true), those that do not hold for any extended log (false) and those that hold for some but not all extended logs (unknown). We reduce the check of the truth value of a LogLogics formula to a check on a finite abstraction and present an evaluation algorithm. We also define LogLogics patterns for commonly occurring properties. [Copyright &y& Elsevier]

Neural gas (NG) constitutes a very robust clustering algorithm which can be derived as stochastic gradient descent from a cost function closely connected to the quantization error. In the limit, an NG network samples the underlying data distribution. Thereby, the connection is not linear, rather, it follows a power law with magnification exponent different from the information theoretically optimum one in adaptive map formation. There exists a couple of schemes to explicitly control the exponent such as local learning which leads to a small change of the learning algorithm of NG. Batch NG constitutes a fast alternative optimization scheme for NG vector quantizers which has been derived from the same cost function and which constitutes a fast Newton optimization scheme. It possesses the same magnification factor (different from 1) as standard online NG. In this paper, we propose a method to integrate magnification control by local learning into batch NG. Thereby, the key observation is a link of local learning to an underlying cost function which opens the way towards alternative, e.g.batch optimization schemes. We validate the learning rule derived from this altered cost function in an artificial experimental setting and we demonstrate the benefit of magnification control to sample rare events for a real data set. [Copyright &y& Elsevier]

Abstract: Modeling of multibody systems is an important though demanding field of application for interval arithmetic. Interval modeling of dynamics is particularly challenging, not least because of the differential equations which have to be solved in the process. Most modeling tools transform these equations into a (non-autonomous) initial value problem, interval algorithms for solving of which are known. The challenge then consists in finding interfaces between these algorithms and the modeling tools. This includes choosing between “symbolic” and “numerical” modeling environments, transforming the usually non-autonomous resulting system into an autonomous one, ensuring conformity of the new interval version to the old numerical, etc. In this paper, we focus on modeling multibody systems’ dynamics with the interval extension of the “numerical” environment MOBILE, discuss the techniques which make the uniform treatment of interval and non-interval modeling easier, comment on the wrapping effect, and give reasons for our choice of MOBILE by comparing the results achieved with its help with those obtained by analogous symbolic tools. [Copyright &y& Elsevier]

Abstract: This paper presents a simple, computationally efficient technique for the optimum balancing of four-bar linkages. The methodology is based on the maximum recursiveness of the dynamic equations for the evaluation of bearing forces. Besides, the balancing problem is posed as an optimum problem for which the optimality criteria and the constraints are formulated. Mass distribution of linkage is embedded in the constraints to obtain physically feasible linkage. The formulation is very generic and can be easily extended to multi-loop as well. [Copyright &y& Elsevier]

Abstract: For the earliest arrival flow problem one is given a network with capacities and transit times on its arcs , together with a source and a sink vertex . The objective is to send flow from s to t that moves through the network over time, such that for each time the maximum possible amount of flow up to this time reaches t. If, for each , this flow is a maximum flow for time horizon , then it is called earliest arrival flow. In practical applications a higher congestion of an arc in the network often implies a considerable increase in transit time. Therefore, in this paper we study the earliest arrival problem for the case that the transit time of each arc in the network at each time depends on the flow on this particular arc at that time . For constant transit times it has been shown by Gale that earliest arrival flows exist for any network. We give examples, showing that this is no longer true for flow-dependent transit times. For that reason we define a relaxed version of this problem where the objective is to find flows that are almost earliest arrival flows. In particular, we are interested in flows that, for each , need only -times longer to send the maximum flow to the sink. We give both constant lower and upper bounds on ; furthermore, we present a constant factor approximation algorithm for this problem. [Copyright &y& Elsevier]

Abstract: In this paper a new and very efficient algorithm to compute the inverse kinematics of a general 6R serial kinematic chain is presented. The main idea is to make use of classical multidimensional geometry to structure the problem and to use the geometric information before starting the elimination process. For the geometric pre-processing we utilize the Study model of Euclidean displacements, sometimes called kinematic image, which identifies a displacement with a point on a six dimensional quadric in seven dimensional projective space P 7. The 6R-chain is broken up in the middle to form two open 3R-chains. The kinematic image of a 3R-chain turns out to be a Segre-manifold consisting of a one parameter set of 3-spaces. The intersection of two Segre-manifolds and yields 16 points which are the kinematic images representing the 16 solutions of the inverse kinematics. Algebraically this procedure means that we have to solve a system of seven linear equations and one resultant to arrive at the univariate 16 degree polynomial. From this step in the algorithm we get two out of the six joint angles and the remaining four angles are obtained straight forward by solving the inverse kinematics of two 2R-chains. [Copyright &y& Elsevier]

Abstract: We developed an algorithm in Kıymaz and Mirasyedioğlu [O. Kıymaz and Ş. Mirasyedioğlu, An algorithmic approach to exact power series solutions of second order linear homogeneous differential equations with polynomial coefficients, Appl. Math. Comp. 139 (1) (2003) 165–178] for computing exact power series solutions of second order linear homogeneous differential equations with polynomial coefficients, near a point x = x 0. In this paper we present a symbolic algorithm to compute the exact power series solutions of nth order linear homogeneous differential equations with polynomial coefficients, near an ordinary point. [Copyright &y& Elsevier]

Abstract: In this paper, a bilevel time minimizing assignment problem is studied in which the aim is to find an optimal partition of the set of n facilities into two mutually disjoint subsets L 1 and L 2 where, L 1 contains m facilities called Level-I facilities and L 2 contains the remaining (n − m) facilities termed as Level-II facilities. The partition is to be optimal in the sense that for this partition the sum of the completion times of the jobs assigned to Level-I and Level-II facilities is the least. It is assumed that all the jobs are to be done, each facility works only on one job, and on each job only one facility works. Further Level-II facilities start working simultaneously on their respective assigned jobs only after Level-I facilities, working in parallel, have finished their jobs. For a feasible assignment denotes the completion time of the jobs assigned to Level-I facilities and that of the jobs assigned to Level-II facilities. Depending on m is greater or smaller than (n − m), the pairs of the type and of the completion times of the jobs assigned to Level-I and Level-II facilities are generated and an optimal partition of the set of n facilities is determined corresponding to the pair for which is the least. To obtain the global minimizer of the proposed problem, a polynomial time algorithm is presented which has been coded in C++ and an empirical analysis has been carried out with the help of randomly generated test problems. [Copyright &y& Elsevier]

Abstract: This paper mainly discusses the following two problems: The necessary and sufficient conditions for the existence of and the expressions for the general solutions of Problem I are given. Moreover, the optimal approximation solution, an algorithm and a numerical example of Problem II are provided. [Copyright &y& Elsevier]

The Lai-Chen algorithm, an extended feedback control scheme of the original Chen- Lai algorithm, was proposed to gradually make an arbitrarily given discrete-time dynamical system chaotic in terms of possessing positive Lyapunov exponents with uniformly bounded orbits. In this paper, based on the Monte Carlo method, we further study the distribution of the controlled Lyapunov exponents generated by the Lai-Chen algorithm. [Copyright &y& Elsevier]

Abstract: An algorithmic characterization of H-matrices was provided by Huang et al. [Comput. Math. Appl. 48 (2004) 1587–1601]. In this paper, we propose a new non-parameter method, which is always convergent in finite iterative steps for H-matrices and needs fewer number of iterations than that of Huang et al.; we also provide an improved algorithm for a general matrix, which decreases the wasteful computations when the given matrix is not an H-matrix. Several numerical examples for the effectiveness of the proposed algorithms are presented. [Copyright &y& Elsevier]

Abstract: This paper presents a simple and fast deblurring algorithm. Assuming a Gaussian blur, the exact solution requires the solution of the backward heat equation which is an ill-posed problem. Our solution consists of a truncation of a Neumann’s expansion of the backward heat operator followed by a forward heat operator to stabilize the procedure. The running time of the algorithm is proportional to the number of pixels in the image. For large digital pictures, our algorithm is more than ten times faster than a standard Matlab deblurring algorithm with similar or better outputs. [Copyright &y& Elsevier]

Abstract: This paper investigates a variant of the general problem of assigning channels to the stations of a wireless network when the graph representing the possible interferences is a matrogenic graph. In our problem, channels assigned to adjacent vertices must be at least 2 apart, while channels assigned to vertices at distance 2 must be different. An exact linear time algorithm is provided for the class of threshold graphs. For matrogenic and matroidal graphs approximate algorithms are given. Consequently, previously known results concerning subclasses of cographs, split graphs and graphs with diameter 2 are improved. [Copyright &y& Elsevier]

Abstract: In this paper, properties of planar (2D) grids are addressed in a mathematical point of view, and a novel algorithm for recognizing distorted grids with perspective transformations is presented. The proposed approach contains three parts: (a) recognizing parameters of affinely distorted grids by fitting Gaussian mixture models (GMMs) to grid spectrums, (b) rebuilding the grid structures via a generating iteration based on the acquired parameters, and (c) eliminating nonlinear effects caused by perspective transformations with the median of infinite lines from local structures (MILLS) method. All parts are precise and robust to local distortions, the absence of elements, and outliers. The accuracy and robustness are demonstrated by quantitative statistics in experiments on synthesis grids and real grid images. [Copyright &y& Elsevier]

Abstract: A pyramid structure is a collection of connected mesh structures. It is well known that a pyramid structure of size n has a diameter of log n, which immediately leads to a natural routing algorithm, using only links between adjacent meshes. However, such paths are often unavailable because of the existence of faulty nodes and/or links. In this paper, we present the concept and technical details of an alternative routing algorithm, based on a collection of bypassing paths, for the potentially faulty pyramid structures that makes use of the links both within and between meshes contained in such structures. We also study some of the mathematical properties of this set of bypassing paths, including their average lengths, to suggest a characterization of the proposed alternative routing algorithm. [Copyright &y& Elsevier]

Abstract: In this paper we develop a new mathematical approach to the pattern formation problem in biology. This problem was first posed mathematically by A.M. Turing, however some principal questions were left open (for example, whether there exists a “universal” mathematical model that allows one to obtain any spatio-temporal patterns). Here we consider the pattern formation ability of some class of genetic circuits. First, we show that the genetic circuits are capable of generating arbitrary spatio-temporal patterns. Second, we give upper and lower bounds on the number of genes in a circuit generating a given pattern. A connection between the complexity of gene interaction and the pattern complexity is found. We investigate the stochastic stability of patterning algorithms. Results are consistent with experimental data. [Copyright &y& Elsevier]