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A Hungarian scaling is a diagonal scaling of a matrix that is typically applied along with a permutation to a sparse linear system before calling a direct or iterative solver. A matrix that has been Hungarian scaled and reordered has all entries of modulus less than or equal to 1 and entries of modulus 1 on the diagonal. An important fact that has been largely overlooked by the previous research into Hungarian scaling of linear systems is that a given matrix typically has a range of possible Hungarian scalings, and direct or iterative solvers may behave quite differently under each of these scalings. Since standard algorithms for computing Hungarian scalings return only one scaling, it is natural to ask whether a superior performing scaling can be obtained by searching within the set of all possible Hungarian scalings. To this end we propose a method for computing a Hungarian scaling that is optimal from the point of view of a measure of diagonal dominance. Our method uses max-balancing, which minimizes the largest off-diagonal entries in the scaled and permuted matrix. Numerical experiments illustrate the increased diagonal dominance produced by max-balanced Hungarian scaling as well as the reduced need for row interchanges in Gaussian elimination with partial pivoting and the improved stability of LU factorizations without pivoting. We additionally find that applying the max-balancing scaling before computing incomplete LU preconditioners improves the convergence rate of certain iterative methods. Our numerical experiments also show that the Hungarian scaling returned by the HSL code MC64 has performance very close to that of the optimal max-balanced Hungarian scaling, which further supports the use of this code in practice. [ABSTRACT FROM AUTHOR]

This paper studies sparse super-resolution in arbitrary dimensions. More precisely, it develops a theoretical analysis of support recovery for the so-called beurling least angle regression (BLASSO) method, which is an off-the-grid generalization of 1 regularization (also known as the least angle regression). While super-resolution is of paramount importance in overcoming the limitations of many imaging devices, its theoretical analysis is still lacking beyond the one-dimensional case. The reason is that in the two-dimensional (2-D) case and beyond, the relative position of the spikes enters the picture, and different geometrical configurations lead to different stability properties. Our first main contribution is a connection, in the limit where the spikes cluster at a given point, between solutions of the dual of the BLASSO problem and the least interpolant space for Hermite polynomial interpolation. This interpolation space, introduced by De Boor, can be computed by Gaussian elimination and lead to an algorithmic description of limiting solutions to the dual problem. With this construction at hand, our second main contribution is a detailed analysis of the support stability and super-resolution effect in the case of a pair of spikes. This includes in particular a sharp analysis of how the signal-to-noise ratio should scale with respect to the separation distance between the spikes. Lastly, numerical simulations on different classes of kernels show the applicability of this theory and highlight the richness of super-resolution in 2-D. [ABSTRACT FROM AUTHOR]

Abstract In this paper we calibrate the strength of the soundness of a set theory KP ω + (Π 1 -Collection) with the assumption that 'there exists an uncountable regular ordinal' in terms of the existence of ordinals. [ABSTRACT FROM AUTHOR]

The Bunch--Parlett algorithm, the Bunch-Kaufman algorithm, the bounded Bunch-- Kaufman algorithm, and Aasen's algorithm are four well-kno wn methods for solving symmetric indefinite linear systems, yet the last three methods are known to suffer from potential numerical instability. In this work, we develop a randomized complete pivoting (RCP) algorithm for solving symmetric indefinite linear systems of equations. RCP is comparable to the Bunch-Kaufman algorithm and Aasen's algorithm in computational efficiency, but still enjoys theoretical element growth and bounded entries in the factorization comparable to that of the Bunch-Parlett algorithm, up to a theoretical failure probability that exponentially decays with an oversampling parameter. In terms of the boundedness of entries in L, the Bunch-Parlett algorithm, the bounded Bunch-Kaufman algorithm, and Aasen's algorithm have maxi

The ϵ-substitution method is a technique for giving consistency proofs for theories of arithmetic. We use this technique to give a proof of the consistency of the impredicative theory ID1 using a variant of the cut-elimination formalism introduced by Mints. [ABSTRACT FROM AUTHOR]

Quasiconvex functions present some difficulties in global optimization, because their graph contains “flat parts”; thus, a local minimum is not necessarily the global minimum. In this paper, we show that any lower semicontinuous quasiconvex function may be written as a composition of two functions, one of which is nondecreasing, and the other is quasiconvex with the property that every local minimum is global minimum. Thus, finding the global minimum of any lower semicontinuous quasiconvex function is equivalent to finding the minimum of a quasiconvex function, which has no local minima other than its global minimum. The construction of the decomposition is based on the notion of “adjusted sublevel set.” In particular, we study the structure of the class of sublevel sets, and the continuity properties of the sublevel set operator and its corresponding normal operator. [ABSTRACT FROM AUTHOR]

A single-elimination (SE) tournament is a popular way to select a winner both in sports competitions and in elections. A natural and well-studied question is the tournament fixingproblem (TFP): given the set of all pairwise match outcomes, can a tournament organizer rig an SE tournament by adjusting the initial seeding so that the organizer's favorite player wins? We prove new sufficient conditions on the pairwise match outcome information and the favorite player, under which there is guaranteed to be a seeding where the player wins the tournament. Our results greatly generalize previous results. We also investigate the relationship between the set of players that can win an SE tournament under some seeding (so-called SE winners) and other traditional tournament solutions. In addition, we generalize and strengthen prior work on probabilistic models for generating tournaments. For instance, we show that every player in an n player tournament generated by the Condorcet random model will be an SE winner even when the noise is as small as possible, p = ϴ(ln n / n); prior work only had such results for p ≥ Ω(√ln n / n). We also establish new results for significantly more general generative models. [ABSTRACT FROM AUTHOR]

We describe a new quantifier elimination algorithm for real closed fields based on Thom encoding and sign determination. The complexity of this algorithm is elementary recursive and its proof of correctness is completely algebraic. In particular, the notion of connected components of semialgebraic sets is not used. [ABSTRACT FROM AUTHOR]

For a system of three first-order partial differential equations with three independent variables, we obtain sufficient conditions for one component of the solution to satisfy a third-order Bianchi equation. We also obtain conditions for the solvability of this system by quadratures. [ABSTRACT FROM AUTHOR]

We present a binary analysis framework based on symbolic execution with the distinguishing capability to execute stepwise forward and also backward through the execution tree. It was developed internally at Bitdefender and code-named RIVER. The framework provides components such as a taint engine, a dynamic symbolic execution engine, and integration with Z3 for constraint solving. In this paper we will provide details on the framework and give an example of analysis on binary code. [ABSTRACT FROM AUTHOR]

We study a class of homotopies between maps from 4-manifolds to surfaces which we call cusp merges. These homotopies naturally appear in the uniqueness problems for certain pictorial descriptions of 4-manifolds derived from maps to the 2-sphere (for example, broken Lefschetz fibrations, wrinkled fibrations, or Morse 2-functions). Our main results provide a classification of cusp merge homotopies in terms of suitably framed curves in the source manifold, as well as a fairly explicit description of a parallel transport diffeomorphism associated to a cusp merge homotopy. The latter is the key ingredient in understanding how the aforementioned pictorial descriptions change under homotopies involving cusp merges. We apply our methods to the uniqueness problem of surface diagrams of 4-manifolds and describe algorithms to obtain surface diagrams for total spaces of (achiral) Lefschetz fibrations and 4-manifolds of the form M × S1, where M is a 3-manifold. Along the way we provide extensive background material about maps to surfaces and homotopies thereof and develop a theory of parallel transport that generalizes the use of gradient flows in Morse theory [ABSTRACT FROM AUTHOR]

In 2007 Cortés and Peña introduced a pivoting strategy for the Neville elimination of nonsingular sign regular matrices and called it two-determinant pivoting. Neville elimination has been very useful for obtaining theoretical and practical properties for totally positive (negative) matrices and other related types of matrices. A real matrix is said to be almost strictly sign regular if all its nontrivial minors of the same order have the same strict sign. In this paper, some nice properties related with the application of Neville elimination with two-determinant pivoting strategy to almost strictly sign regular matrices are presented. [ABSTRACT FROM AUTHOR]

We prove that if T is a complete theory with weak elimination of imaginaries, then there is an explicit bijection between strict independence relations for T and strict independence relations for Teq. We use this observation to show that if T is the theory of the Fraïssé limit of finite metric spaces with integer distances, then Teq has more than one strict independence relation. This answers a question of Adler (J Math Log 9(1):1-20, , Question 1.7). [ABSTRACT FROM AUTHOR]

A number of philosophers think that grounding is, in some sense, well-founded. This thesis, however, is not always articulated precisely, nor is there a consensus in the literature as to how it should be characterized. In what follows, I consider several principles that one might have in mind when asserting that grounding is well-founded, and I argue that one of these principles, which I call 'full foundations', best captures the relevant claim. My argument is by the process of elimination. For each of the inadequate principles, I illustrate its inadequacy by showing either that it excludes cases that should not be ruled out by a well-foundedness axiom for grounding, or that it admits cases that should be ruled out. [ABSTRACT FROM AUTHOR]

The sports elimination problem asks whether a team participating in a competition still has a chance to win, given the current standings and the remaining matches to be played among the teams. This problem can be viewed as a graph labelling problem, where arcs receive labels that contribute to the score of both endpoints of the arc, and the aim is to label the arcs in a way that each vertex obtains a score not exceeding its capacity. We investigate the complexity of this problem in detail, using a multivariate approach to examine how various parameters of the input graph (such as the maximum degree, the feedback vertex/edge number, and different width parameters) influence the computational tractability. We obtain several efficient algorithms, as well as certain hardness results. [ABSTRACT FROM AUTHOR]

The inaccuracy and delay of speed feedback cause a vibration problem when the permanent magnet synchronous motor runs at low speed. As the low-speed smoothness is a key point of many applications of the permanent magnet synchronous motor, this article solves this problem by adding a real-time adjusted extended Kalman filter to low-precision-sensor vector control. In the mathematical model, the estimated speed of the extended kalman filter is significantly impacted by the deviations of the resistance and magnetic flux rather than other parameters. Thus, underid= 0 vector control, aRs-ψf-identifier is designed to calculate the values of the resistance and flux simultaneously with a small compensatingid. This algorithm runs on the platform in real time. Finally, the experiment results validate that when the velocity reaches as low as 1 r/min, the proposed method eliminates the vibration problem in the low-precision-sensor permanent magnet synchronous motor. [ABSTRACT FROM PUBLISHER]

We investigate incomplete symbols, i.e. definite descriptions with scope-operators. Russell famously introduced definite descriptions by contextual definitions; in this article definite descriptions are introduced by rules in a specific calculus that is very well suited for proof-theoretic investigations. That is to say, the phrase 'incomplete symbols' is formally interpreted as to the existence of an elimination procedure. The last section offers semantical tools for interpreting the phrase 'no meaning in isolation' in a formal way. [ABSTRACT FROM AUTHOR]

Underwater acoustic communications have found a growing interest because of its variety usages both in military and commercial applications. But, for ocean environment, the channel has an extended time varying multipath due to acoustic propagation. These phenomena cause pulse spreading and time varying inter-symbol interference (ISI). To overcome the interference caused by this harsh environment, equalizers with Passive Phase Conjugation (PPC) have been widely used in coherent communications. In this paper, we have proposed a combined scheme of PPC followed by an iteratively ISI cancelation algorithm to remove the residual ISI remained at the output of the PPC processor. By using a coarse estimation of the channel along with the ISI alleviated PPC output symbols; we can eliminate residual ISI from the received data signal. We have conducted extensive simulations and some experimental tests at the coastal environment of the Persian Gulf to investigate the performance of the proposed scheme. The advantages of the proposed combined scheme are using the channel probe signal for both frame synchronization and coarse estimation of the channel impulse response to using it in the iteratively ISI cancellation and the PPC processing block. The results showed the effectiveness of the combined method. [ABSTRACT FROM AUTHOR]

Quantifier elimination is a foundational issue in the field of algebraic and logic computation. In first-order logic, every formula is well composed of atomic formulas by negation, conjunction, disjunction, and introducing quantifiers. It is often made quite complicated by the occurrences of quantifiers and nonlinear functions in atomic formulas. In this paper, we study a class of quantified exponential polynomial formulas extending polynomial ones, which allows the exponential to appear in the first variable. We then design a quantifier elimination procedure for these formulas. It adopts the scheme of cylindrical decomposition that consists of four phases—projection, isolation, lifting, and solution formula construction. For the non-algebraic representation, the triangular systems are introduced to define transcendental coordinates of sample points. Based on that, our cylindrical decomposition produces projections for input variables only. Hence the procedure is direct and effective. [ABSTRACT FROM AUTHOR]

Vertex elimination is a graph operation that turns the neighborhood of a vertex into a clique and removes the vertex itself. It has widely known applications within sparse matrix computations. We define the Elimination problem as follows: given two graphs G and H, decide whether H can be obtained from G by | V( G)|−| V( H)| vertex eliminations. We show that Elimination is $\mathsf {W[1]} $-hard when parameterized by | V( H)|, even if both input graphs are split graphs, and $\mathsf {W[2]} $-hard when parameterized by | V( G)|−| V( H)|, even if H is a complete graph. On the positive side, we show that Elimination admits a kernel with at most 5| V( H)| vertices in the case when G is connected and H is a complete graph, which is in sharp contrast to the $\mathsf {W[1]} $-hardness of the related Clique problem. We also study the case when either G or H is tree. The computational complexity of the problem depends on which graph is assumed to be a tree: we show that Elimination can be solved in polynomial time when H is a tree, whereas it remains NP-complete when G is a tree. [ABSTRACT FROM AUTHOR]

This paper deals with the computational modeling and numerical simulation of contact problems at finite deformations using the finite element method. Quasi-static and dynamic problems are considered and two particular frictional conditions, full stick friction and frictionless cases, are addressed. Lagrange multipliers and regularized formulations of the contact problem, such as penalty or augmented Lagrangian methods, are avoided and a new direct elimination method is proposed. Conserving algorithms are also introduced for the proposed formulation for dynamic contact problems. An assessment of the performance of the resulting formulation is shown in a number of selected benchmark tests and numerical examples, including both quasi-static and dynamic contact problems under full stick friction and frictionless contact conditions. Conservation of key discrete properties exhibited by the time stepping algorithm used for dynamic contact problems is also shown in an example. [ABSTRACT FROM AUTHOR]

This paper presents an algorithm called “volume & neighbors” for finding elimination trees for multifrontal solver algorithm applied to three dimensional h -adaptive finite element method computations. The algorithm is described in a pseudo-code and explained on exemplary h -refined grids. The algorithm is implemented in three dimensional h -adaptive finite element method code and tested on a sequence of representative grids, namely uniform grid, grid with point singularity, grid with edge singularity and grid with face singularity. The number of floating point operations for the multifrontal solver algorithm working with the elimination trees generated by the volume & neighbors algorithm is compared with the number of floating-point operations resulting from execution of the state-of-the-art multifrontal direct solver MUMPS with state-of-the-art algorithms for constructing elimination trees like nested-dissection from METIS library and approximate minimum degree AMD algorithm as well as PORD algorithm. In all the cases the volume & neighbors algorithm outperforms other state-of-the art algorithms. The only exception is the case of the uniform grid, where the algorithm results in a similar number of FLOPs than nested dissection algorithm. [ABSTRACT FROM AUTHOR]

Given a variety X over a perfect field, we study the partition defined on X by the multiplicity (into equimultiple points), and the effect of blowing up at smooth equimultiple centers. Over fields of characteristic zero we prove resolution of singularities by using the multiplicity as an invariant, instead of the Hilbert Samuel function. [ABSTRACT FROM AUTHOR]

Abstract: Perfect vertex elimination schemes are part of the characterizations for several classes of graphs, including chordal and cop-win. Partial elimination schemes reduce a graph to an important subgraph, for example, -cores and robber-win graphs. We are interested in those partial elimination schemes, in which once a vertex is ready to be eliminated, it stays in that state regardless of which other vertices are eliminated. We show that in such a scheme, the sets of subsets of eliminated vertices, when ordered by inclusion, form an upper locally distributed lattice. We also show that (a) unless they contain a specific induced subgraph, the cop-win orderings have this property, and that (b) the process of cleaning graphs also leads to upper locally distributed lattices. Finally, we ask for an elimination scheme, which graphs are associated with distributive lattices? [Copyright &y& Elsevier]

Abstract: Video surveillance on highway is a hot topic and a great challenge in Intelligent Transportation Systems. In such applications requiring objects extraction, cast shadows induce shape distortions and object fusions interfering performance of high level algorithms. Shadow elimination allows to improve the performances of video object extraction, classification and tracking. In other hand, it is very important to recognize the type of a detected object in order to track reliably and estimate traffic parameters correctly. This paper presents two approaches to enhance automatic traffic surveillance systems. The first deals with the elimination of shadows and the second concerns the classification of vehicles, based on robust vision and image processing. For moving shadow elimination, a contrast model is proposed to describe and remove dynamic shadows based on the idea that a shadow transformation is a change in contrast. For vehicles classification, Hu moments are calculated in a manner to reduce the perspective effects and used to describe vehicles in knowledge base. Experimental results on the various challenging video sequences show that the proposed approach outperforms classification methods of related works (with a classification accuracy of 96.96%), and that the shadow elimination approach performs better than compared works (with detection rate of 95–99% and discrimination rate of 85.7–89%). [Copyright &y& Elsevier]

It needs much computation to develop a contact state graph and find an assembly sequence because polyhedral objects consist of a lot of vertices, edges, and faces. In this paper, we propose a new method to eliminate unnecessary contact states in the contact state graph corresponding to a robotic assembly task. In our method, the faces of polyhedral objects are triangulated, and the adjacency of each vertex, edge, and triangle between an initial contact state and a target contact state is defined. Then, this adjacency is used to create contact state graphs at different priorities. When a contact state graph is finished at a higher priority, a lot of unnecessary contact states can be eliminated because the contact state graph already includes at least one realizable assembly sequence. Our priority-based method is compared with a face-based method through statistically analyzing the contact state graphs obtained from different assembly tasks. Finally, our method results in a significant improvement in the final performance. [ABSTRACT FROM AUTHOR]

ABSTRACT A compact I-shaped λ/2 resonator is introduced in order to reduce the mutual coupling between antenna elements and eliminate the scan blindness in a microstrip array. The proposed λ/2 resonator is inserted between the adjacent E-shaped microstrip antenna elements separated by 0.45 λ, as a technique to suppress the occurrence of radiation in the horizontal direction. Simulated and measured results show that a reduction in mutual coupling of 35 dB is obtained between elements at the operation frequency of 3.94 GHz of the array. The scan properties of microstrip array with and without resonator have been studied and the result indicates that the scan blindness of the array can be well eliminated because of the effect of the resonator. We have developed experimental models that have proved this concept of scan blindness elimination. Finally, the influence of other antenna parameters at the presence of resonator in the array system has been studied. Prototype antennas of two-element and four-element array with and without resonator have been fabricated, measured, and the idea has been verified. © 2014 Wiley Periodicals, Inc. Microwave Opt Technol Lett 56:334-338, 2014 [ABSTRACT FROM AUTHOR]

This paper shows that for any given polynomial ideal the collection of Gröbner cones corresponding to -specific elimination orders forms a star-shaped region which contrary to first intuition in general is not convex. Moreover we show that the corresponding region may contain Gröbner cones intersecting in the boundary of the Gröbner fan in the origin only. This implies that Gröbner walks aiming for the elimination of variables from a polynomial ideal can be terminated earlier than previously known. We provide a slightly improved stopping criterion for a known Gröbner walk algorithm for the elimination of variables. [ABSTRACT FROM AUTHOR]

In an asymmetric rendezvous system, such as an unfair synchronous queue or an elimination array, threads of two types, consumers and producers, show up and are matched each with a unique thread of the other type. Here we present new highly scalable, high throughput asymmetric rendezvous systems that outperform prior synchronous queue and elimination array implementations under both symmetric and asymmetric workloads (more operations of one type than the other). Based on this rendezvous system, we also construct a highly scalable and competitive stack implementation. [ABSTRACT FROM AUTHOR]

By a sequence of rollings without slipping or twisting along segments of a straight line of the plane, a spherical ball of unit radius has to be transferred from an initial state to an arbitrary final state taking into account the orientation of the ball. We provide a new proof that with at most 3 moves, we can go from a given initial state to an arbitrary final state. The first proof of this result is due to Hammersley ( ). His proof is more algebraic than ours which is more geometric. We also showed that 'generically' no one of the three moves, in any elimination of the spin discrepancy, may have length equal to an integral multiple of 2π. [ABSTRACT FROM AUTHOR]

Abstract: In Gaussian elimination it is often desirable to preserve existing zeros (sparsity). This is closely related to perfect elimination schemes on graphs. Such schemes can be found in polynomial time. Gaussian elimination uses a pivot for each column, so opportunities for preserving sparsity can be missed. In this paper we consider a more flexible process that selects a pivot for each nonzero to be eliminated and show that recognizing matrices that allow such perfect partial elimination schemes is NP-hard. [Copyright &y& Elsevier]

The elimination tree model for sparse unsymmetric matrices and an algorithm for constructing it have been recently proposed by Eisenstat and Liu [SIAM J. Matrix Anal. Appl., 26 (2005), pp. 686-705] and [SIAM J. Matrix Anal. Appl., 29 (2008), pp. 1363-1381]. The construction algorithm has a worst-case time complexity of Θ(mn) for an n X n unsymmetric matrix having m off-diagonal nonzeros. We propose another algorithm that has a worst-case time complexity of ...(mlogn). We compare the two algorithms experimentally and show that both algorithms are efficient in general. The algorithm of Eisenstat and Liu is faster in many practical cases, yet there are instances in which there is a significant difference between the running time of the two algorithms in favor of the one proposed here. [ABSTRACT FROM AUTHOR]

This work addresses the inverse problems of expanded motion and path generation for the spatial (revolute–revolute–spherical–spherical, RRSS) linkage and the 4R spherical linkage with order and branch elimination. Two constrained non-linear equation systems are presented in this work for RRSS and 4R spherical motion and path generation with order and branching constraints. Both equation systems include the spatial four-link displacement model (by Suh and Radcliffe) as an objective function along with order and branching inequality constraints. As examples, both a branch defect-free and order defect-free RRSS linkage 4R spherical linkage are synthesized to approximate expanded groups of precision positions. [ABSTRACT FROM PUBLISHER]

Abstract: We present an alternative explicit expression for the Moore–Penrose inverse of a matrix. Based on this expression, we propose a Gauss–Jordan elimination method for the computation of . Its computational complexity indicates that this method is more efficient than the existing Gauss–Jordan elimination method in the literature for a large class of problems. An example is included to illustrate the new method. [Copyright &y& Elsevier]

We give a purely syntactic proof (from scratch) of the subject equality property of the BCD intersection type system through a reformulation of the subtyping relation having a 'cut-elimination' property. [ABSTRACT FROM AUTHOR]

Abstract: Neville elimination is a direct method for the solution of linear systems of equations with advantages for some classes of matrices and in the context of pivoting strategies for parallel implementations. The growth factor is an indicator of the numerical stability of an algorithm. In the literature, bounds for the growth factor of Neville elimination with some pivoting strategies have appeared. In this work, we determine all the matrices such that the minimal upper bound of the growth factor of Neville elimination with those pivoting strategies is reached. [Copyright &y& Elsevier]

Abstract: Partial Granger causality was introduced by who showed that it could better eliminate the influence of latent variables and exogenous inputs than conditional G-causality. In the recent literature we can find some reviews and applications of this type of Granger causality (e.g. ). These articles apparently do not take into account a serious flaw in the original work on partial G-causality, being the negative F values that were reported and even proven to be plausible. In our opinion, this undermines the credibility of the obtained results and thus the validity of the approach. Our study is aimed to further validate partial G-causality and to find an answer why negative partial Granger causality estimates were reported. Time series were simulated from the same toy model as used in the original paper and partial and conditional causal measures were compared in the presence of confounding variables. Inference was done parametrically and using non-parametric block bootstrapping. We counter the proof that partial Granger F values can be negative, but the main conclusion of the original article remains. In the presence of unknown latent and exogenous influences, it appears that partial G-causality will better eliminate their influence than conditional G-causality, at least when non-parametric inference is used. [Copyright &y& Elsevier]

The minimum edge count (MEC) and optimal Jacobian accumulation problems in linearized directed acyclic graphs (DAGs) result from the combinatorics induced by the associativity of the chain rule of differential calculus. This paper discusses a suitable graph formalism followed by proving a number of results that yield a considerable search space reduction for both problems. An algorithmic link between numerical analysis and theoretical computer science is established. Although both problems are believed to be NP-hard in general, a linear-time algorithm is presented solving the MEC problem for a specified subclass of l-DAGs. [ABSTRACT FROM AUTHOR]

This work presents a model-theoretic approach to the study of the amalgamation property for varieties of semilinear commutative residuated lattices. It is well-known that if a first-order theory T enjoys quantifier elimination in some language L, the class of models of the set of its universal consequences $${\rm T_\forall}$$ has the amalgamation property. Let $${{\rm Th}(\mathbb{K})}$$ be the theory of an elementary subclass $${\mathbb{K}}$$ of the linearly ordered members of a variety $${\mathbb{V}}$$ of semilinear commutative residuated lattices. We show that whenever $${{\rm Th}(\mathbb{K})}$$ has elimination of quantifiers, and every linearly ordered structure in $${\mathbb{V}}$$ is a model of $${{\rm Th}_\forall(\mathbb{K})}$$, then $${\mathbb{V}}$$ has the amalgamation property. We exploit this fact to provide a purely model-theoretic proof of amalgamation for particular varieties of semilinear commutative residuated lattices. [ABSTRACT FROM AUTHOR]

We introduce a method of reducing the q-Member p-Committee Problem for an arbitrary finite system of sets to the same problem for a system of sets of smaller size and with a smaller number of subsystems with nonempty intersection maximal with respect to inclusion. For p = 1/2, for an infeasible system of linear inequalities in ℝ we give an efficient implementation of this method with complexity polynomial in the number of inequalities and the number of committee elements, but exponential in the dimension of the space. For this implementation, we give experimental results for n = 2, 3. [ABSTRACT FROM AUTHOR]

This paper analyses the performance of several versions of a block parallel algorithm in order to apply Neville elimination in a distributed memory parallel computer. Neville elimination is a procedure to transform a square matrix A into an upper triangular one. This analysis must take into account the algorithm behaviour as far as execution time, efficiency and scalability are concerned. Special attention has been paid to the study of the scalability of the algorithms trying to establish the relationship existing between the size of the block and the performance obtained in this metric. It is important to emphasize the high efficiency achieved in the studied cases and that the experimental results confirm the theoretical approximation. Therefore, we have obtained a high predicting ability tool of analysis. Finally, we will present the elimination of Neville as an efficient tool in detecting point sources in cosmic microwave background maps. [ABSTRACT FROM AUTHOR]

Abstract: The paper discusses a general methodology to the design of recursive Gaussian filters to be used for separating the form, waviness and roughness components of the surface texture. By selecting appropriate initial values for the filter difference equations, it is possible to eliminate the so-called edge effect and evaluate the whole registered profile. Two ways of filter implementation were considered: series and parallel. The incremental difference operator is applied in place of the usual shift operator z to describe the filter transfer function. This increases the accuracy of the representation of filter parameters and decreases the number of rounding errors. The results of the analysis were illustrated using 2D and 3D roughness profiles of a ball bearing race. The data show that the mean line and the mean surface were correctly determined for the whole area of the measured profile. [Copyright &y& Elsevier]

Abstract: We present a method for finding optimal controlled variables, which are polynomial combinations of measurements. Controlling these variables gives optimal steady state operation. Our work extends the concept of self-optimizing control; starting from the first-order necessary optimality conditions, any unknown variables are eliminated using elimination theory for polynomial systems to obtain invariant variable combinations, which contain only known variables (measurements). If a disturbance causes the active constraints to change, the invariants may be used to identify, and switch to the right region. This makes the method applicable over a wide disturbance range with changing active sets. The procedure is applied to two case studies of continuous stirred tank reactors. [Copyright &y& Elsevier]

Abstract: In this paper we present two new algorithmic variants to compute the Neville elimination, with and without pivoting, which improve data locality and cast most of the computations in terms of high-performance Level 3 BLAS. The experimental evaluation on a state-of-the-art multi-core processor demonstrates that the new blocked algorithms exhibit a much higher degree of concurrency and better cache usage, yielding higher performance while offering numerical accuracy akin to that of the traditional columnwise variant in most cases. [Copyright &y& Elsevier]

This paper describes several parallel algorithmic variations of the Neville elimination. This elimination solves a system of linear equations making zeros in a matrix column by adding to each row an adequate multiple of the preceding one. The parallel algorithms are run and compared on different multi- and many-core platforms using parallel programming techniques as MPI, OpenMP and CUDA. [ABSTRACT FROM AUTHOR]

Abstract: Elimination methods are highly effective for the solution of linear and nonlinear systems of equations, but reversal of the elimination principle can be beneficial as well: competent incorporation of additional independent constraints and variables or more generally immersion of the original computational problem into a larger task, defined by a larger number of independent constraints and variables can improve global convergence of iterative algorithms, that is their convergence from the start. A well known example is the dual linear and nonlinear programming, which enhances the power of optimization algorithms. We believe that this is just an ad hoc application of general Principle of Expansion with Independent Constraints; it should be explored systematically for devising iterative algorithms for the solution of equations and systems of equations and for optimization. At the end of this paper we comment on other applications and extensions of this principle. Presently we show it at work for the approximation of a single zero of a univariate polynomial of a degree . Empirical global convergence of the known algorithms for this task is much weaker than that of the algorithms for all zeros, such as Weierstrass–Durand–Kerner’s root-finder, which reduces its root-finding task to Viète’s (Vieta’s) system of polynomial equations with unknowns. We adjust this root-finder to the approximation of a single zero of , preserve its fast global convergence and decrease the number of arithmetic operations per iteration from quadratic to linear. Together with computing a zero of a polynomial , the algorithm deflates this polynomial as by-product, and then could be reapplied to the quotient to approximate the next zero of . Alternatively by using processors that exchange no data, one can concurrently approximate up to zeros of . Our tests confirm the efficiency of the proposed algorithms. Technically our root-finding boils down to computations with structured matrices, polynomials and partial fraction decompositions. Our study of these links can be of independent interest; e.g., as by-product we express the inverse of a Sylvester matrix via its last column, thus extending the celebrated result of Gohberg and Sementsul (1972) from Toeplitz to Sylvester matrix inverses. [Copyright &y& Elsevier]

Abstract: In this paper we show that the intuitionistic theory for finitely many iterations of strictly positive operators is a conservative extension of Heyting arithmetic. The proof is inspired by the quick cut-elimination due to G. Mints. This technique is also applied to fragments of Heyting arithmetic. [Copyright &y& Elsevier]

Coordinated experimental and orthogonal space random walk (OSRW) molecular dynamics simulation studies were performed to understand the exceptionally low temperature required for thermal conversion of a poly(phenylenevinylene) (PPV) precursor containing the macromolecular counterion poly(ethylene glycol)-4-nonylphenyl-3-sulfopropyl ether (PEGNOPS). Simulations of this solvent-free system converged for starting points where the backbone was artificially expanded or compressed. In this example of a polymer organized by a polymer, the simulations revealed the ability of PEGNOPS to partially preorder the precursor chain in a conformation that favors the E2 elimination pathway. [ABSTRACT FROM AUTHOR]

In this paper we study the termination behavior of Russell’s description elimination rewrite system. We discuss certain claims made by Kripke (2005) in his paper concerning the possible nontermination of elimination of descriptions. [ABSTRACT FROM AUTHOR]

Abstract: Newton, in notes that he would rather not have seen published, described a process for solving simultaneous equations that later authors applied specifically to linear equations. This method — which Euler did not recommend, which Legendre called “ordinary,” and which Gauss called “common” — is now named after Gauss: “Gaussian” elimination. Gauss’s name became associated with elimination through the adoption, by professional computers, of a specialized notation that Gauss devised for his own least-squares calculations. The notation allowed elimination to be viewed as a sequence of arithmetic operations that were repeatedly optimized for hand computing and eventually were described by matrices. [Copyright &y& Elsevier]