Usual Operations Research Articles

Hirsch polytopes with exponentially long combinatorial segments

In their paper proving the Hirsch bound for flag normal simplicial complexes (Math. Oper.~Res.~2014) Adiprasito and Benedetti define the notion of~\emph{combinatorial segment}. The study of the maximal length of these objects provides the upper bound~$O(n2^d)$ for the diameter of any normal pure simplicial complex of dimension~$d$ with~$n$ vertices, and the Hirsch bound $n-d$ if the complexes are, moreover, flag. In the present article, we propose a formulation of combinatorial segments which is equivalent but more local, by introducing the notions of monotonicity and conservativeness of dual paths in pure simplicial complexes. We use this definition to investigate further properties of combinatorial segments. Besides recovering the two stated bounds, we show a refined bound for banner complexes, and study the behavior of the maximal length of combinatorial segments with respect to two usual operations, namely join and one-point suspension. Finally, we show the limitations of combinatorial segments by constructing pure normal simplicial complexes in which all combinatorial segments between two particular facets achieve the length $\Omega(n2^{d})$. This includes vertex-decomposable---therefore Hirsch---polytopes.

Norm equalities and inequalities for three circulant operator matrices

In this paper, three new circulant operator matrices, scaled circulant operator matrices, diag-circulant operator matrices and retrocirculant operator matrices, are given respectively. Several norm equalities and inequalities for these operator matrices are proved. We show the special cases for norm equalities and inequalities, such as the usual operator norm and the Schatten p-norm. Pinching type inequality is also given for weakly unitarily invariant norms. These results are closely related to the nice structure of these special operator matrices. Furthermore, some special cases and specific examples are also considered.

Subspace projection method for unstructured searches with noisy quantum oracles using a signal-based quantum emulation device

This paper describes a novel approach to solving unstructured search problems using a classical, signal-based emulation of a quantum computer. The classical nature of the representation allows one to perform subspace projections in addition to the usual unitary gate operations. Although bandwidth requirements will limit the scale of problems that can be solved by this method, it can nevertheless provide a significant computational advantage for problems of limited size. In particular, we find that, for the same number of noisy oracle calls, the proposed subspace projection method provides a higher probability of success for finding a solution than does an single application of Grover’s algorithm on the same device.

Periodic solutions of a semilinear elliptic equation with a fractional Laplacian

We consider periodic solutions of the following problem associated with the fractional Laplacian $$(-\partial _{xx})^s u(x) + F'(u(x))=0,\quad u(x)=u(x+T),\quad \text{ in } \, \mathbb {R}, $$ where \((-\partial _{xx})^s\) denotes the usual fractional Laplace operator with \(0<s<1\). The primitive function F of the nonlinear term is a smooth double-well potential. We prove the existence of periodic solutions with large period T using variational methods. An estimate of the energy of the periodic solutions is also established.

Introducing oriented Laplacian diffusion into a variational decomposition model.

The decomposition model proposed by Osher, Solé and Vese in 2003 (the OSV model) is known for its good denoising performance. This performance has been found to be due to its higher weighting of lower image frequencies in the H −1-norm modeling the noise component in the model. However, the OSV model tends to also move high-frequency texture into this noise component. Diffusion with an oriented Laplacian for oriented texture is introduced in this paper, in lieu of the usual Laplacian operator used to solve the OSV model, thereby significantly reducing the presence of such texture in the noise component. Results obtained from the proposed oriented Laplacian model for test images with oriented texture are given, and compared to those from the OSV model as well as the Mean Curvature model (MCM). In general, the proposed oriented Laplacian model yields higher signal-to-noise ratios and visually superior denoising results than either the OSV or the MCM models. We also compare the proposed method to a non-local means model and find that although the proposed method generally yields slightly lower signal-to-noise ratios, it generally gives results of better perceptual visual quality.

Spaces of Bessel Generators and Characterizations of Bessel Generator Multipliers for Unitary Systems

In this paper, we introduce a set of frame generators for a unitary system which is closed under linear combinations. Certain structural properties of the set are studied. Then we give several sufficient conditions such that an operator is a frame generator multiplier for certain unitary systems. Since there are two natural norms endowed with each Bessel multiplier, i.e., the usual operator norm and the Bessel norm, we compare these norms of Bessel multipliers for some cases.

PERFORMANCE OF TRAPEZOIDAL METHOD AND GAUSS-LEGENDRE METHOD IN SETTLEMENT OF CERTAIN INTEGRAL ASSISTED MATLAB

This study aimed to compare the performance of a particular integral calculation using the Trapezoid and Gauss-Legendre method in five integral cases to determine the accuracy of the integral results value of both methods which are based on the relative error percentage. This study is a literature research which formulate mathematical problem that can be solved with the usual arithmetic operations or calculations which are addition, subtraction, multiplication and division to obtain numeral with the best accuracy. Trapezoidal method formula used is while the Gauss-Legendre formula used is , This study shows that the Gauss-Legendre method has better performance by giving the percentage of error which is relatively better than Trapezoid method used in the five cases. Keywords: Numerical Methods, Trapezoid method, the method of Gauss-Legendre

Boolean operations on arbitrary polygonal and polyhedral meshes

A linearithmic floating-point arithmetic algorithm designed for solving usual boolean operations (intersection, union, and difference) on arbitrary polygonal and polyhedral meshes is described in this paper. This method does not dis-feature the inputs which can be two volume meshes, two surface meshes or one of each. It provides conformal meshes upon exit. It can be used in many pre- and post-processing applications in computational physics (e.g. cut-cell volume mesh generation or conservative remapping). The core idea is to consider any configuration as a polygonal cloud. The polygons are first triangulated, the intersections are solved, the polyhedral cells are then reconstructed from the conformal triangles cloud and finally their triangular faces are re-aggregated to polygons. This approach offers great flexibility regarding the admissible topologies: non-planar faces, concave faces or cells and some non-manifoldness are handled. The algorithm is described in detail and some current results are shown.

Szegedy’s quantum walk with queries

When searching for a marked vertex in a graph, Szegedy's usual search operator is defined by using the transition probability matrix of the random walk with absorbing barriers at the marked vertices. Instead of using this operator, we analyze searching with Szegedy's quantum walk by using reflections around the marked vertices, that is, the standard form of quantum query. We show we can boost the probability to 1 of finding a marked vertex in the complete graph. Numerical simulations suggest that the success probability can be improved for other graphs, like the two-dimensional grid. We also prove that, for a certain class of graphs, we can express Szegedy's search operator, obtained from the absorbing walk, using the standard query model.

Time, classical and quantum

We propose a new point of view regarding the problem of time in quantum mechanics, based on the idea of replacing the usual time operator T with a suitable real-valued function T on the space of physical states. The proper characterization of the function T relies on a particular relation with the dynamical evolution of the system rather than with the infinitesimal generator of the dynamics (Hamiltonian). We first consider the case of classical hamiltonian mechanics, where observables are functions on phase space and the tools of differential geometry can be applied. The idea is then extended to the case of the unitary evolution of pure states of finite-level quantum systems by means of the geometric formulation of quantum mechanics. It is found that T is a function on the space of pure states which is not associated with any self-adjoint operator. The link between T and the dynamical evolution is interpreted as defining a simultaneity relation for the states of the system with respect to the dynamical evolution itself. It turns out that different dynamical evolutions lead to different notions of simultaneity, i.e., the notion of simultaneity is a dynamical notion.

The impact of product returns and remanufacturing uncertainties on the dynamic performance of a multi-echelon closed-loop supply chain

We investigate a three-echelon manufacturing and remanufacturing closed-loop supply chain (CLSC) constituting of a retailer, a manufacturer and a supplier. Each echelon, apart from its usual operations in the forward SC (FSC), has its own reverse logistics (RL) operations. We assume that RL information is transparent to the FSC, and the same replenishment policies are used throughout the supply chain. We focus on the impact on dynamic performance of uncertainties in the return yield, RL lead time and the product consumption lead time. Two outcomes are studied: order rate and serviceable inventory. The results suggest that higher return yield improves dynamic performance in terms of overshoot and risk of stock-out with a unit step response as input. However, when the return yield reaches a certain level, the classic bullwhip propagation normally associated with the FSC does not always hold. The longer remanufacturing and product consumption lead times result in a higher overshoot and a longer time to recover inventory, as well as more oscillation in the step response at the upstream echelons. We also study bullwhip and inventory variance when demand is a random variable. Our analysis suggests that higher return yield contributes to reduced bullwhip and inventory variance at the echelon level but for the CLSC as a whole the level of bullwhip may decrease as well as increase as it propagates along the supply chain. The reason for such behaviour is due to the interaction of the various model parameters and should be the subject of further analytical research. Furthermore, by studying the three-echelon CLSC, we produce a general equation for eliminating inventory offsets in an n-echelon CLSC. This is helpful to managers who wish to maintain inventory service levels in multi-echelon CLSCs.

Collocational Restrictions of English Phrasal Verbs

Idioms and phrasal verbs constitute a highly considerable portion of the English vocabulary and their mastery is often indicated as a native like competence. They pose many difficulties to foreign learners because of their syntactic and semantic abnormalities. On semantic terms phrasal verbs, and idiomatic ones in particular, are viewed as phrases which do not correspond to their literal meanings. Syntactically they could be recognized by their idiosyncratic behavior which often defies the usual syntactic operations. The view of idioms and phrasal verbs as bits of frozen units provides only little possibility of syntactic and sematic flexibility. This paper attempts to trace the flexibility of the structure of phrasal verbs with reference to the collocational restrictions that govern their structures.

Collocational Restrictions of English Phrasal Verbs

Idioms and phrasal verbs constitute a highly considerable portion of the English vocabulary and their mastery is often indicated as a native like competence. They pose many difficulties to foreign learners because of their syntactic and semantic abnormalities. On semantic terms phrasal verbs, and idiomatic ones in particular, are viewed as phrases which do not correspond to their literal meanings. Syntactically they could be recognized by their idiosyncratic behavior which often defies the usual syntactic operations. The view of idioms and phrasal verbs as bits of frozen units provides only little possibility of syntactic and sematic flexibility. This paper attempts to trace the flexibility of the structure of phrasal verbs with reference to the collocational restrictions that govern their structures.

Configuration logics: Modeling architecture styles

We study a framework for the specification of architecture styles as families of architectures involving a common set of types of components and coordination mechanisms. The framework combines two logics: 1) interaction logics for the specification of architectures as generic coordination schemes involving a configuration of interactions between typed components; and 2) configuration logics for the specification of architecture styles as sets of interaction configurations. The presented results build on previous work on architecture modeling in BIP. We show how propositional interaction logic can be extended into a corresponding configuration logic by adding new operators on sets of interaction configurations. In addition to the usual set-theoretic operators, configuration logic is equipped with a coalescing operator + to express combination of configuration sets. We provide a complete axiomatization of propositional configuration logic as well as decision procedures for checking that an architecture satisfies given logical specifications. To allow genericity of specifications, we study first-order and second-order extensions of the propositional configuration logic. First-order logic formulas involve quantification over component variables. Second-order logic formulas involve additional quantification over sets of components. We provide several examples illustrating the application of the results to the characterization of various architecture styles. We also provide an experimental evaluation using the Maude rewriting system to implement the decision procedure for the propositional flavor of the logic.

Algorithm 960

The design and implementation of a Matlab object-oriented software library for working with polynomials is presented. The construction and evaluation of polynomials in Bernstein form are motivated and justified. Efficient constructions for the coefficients of a polynomial in Bernstein form when the polynomial is not given with this representation are provided. The presented adaptive evaluation algorithm uses the VS (Volk and Schumaker) algorithm, the de Casteljau algorithm, and a compensated VS algorithm. In addition, we have completed the library with other algorithms to perform other usual operations with polynomials in Bernstein form.

Pilot Mental Health: Expert Working Group Recommendations - Revised 2015.

In September 2012, the Aerospace Medical Association published and distributed recommendations from its Pilot Mental Health Working Group to improve awareness and identification of pilot mental health issues during the aeromedical assessment of pilots. Following the crash of Germanwings Flight 9525 in March 2015 with pilot suicide as the probable cause, the Pilot Mental Health Working Group reconvened to review their recommendations. As a result, the working group revised the recommendations which are provided here and which were distributed worldwide. The Working Group continues to emphasize the importance of assessing and optimizing pilot mental health, while providing additional recommendations on building trust and rapport between the aeromedical examiner and the pilot, on utilizing aviation mental health and aeromedical specialists, and on the balance between medical confidentiality and risk to public safety. The working group encourages all organizations involved in flight safety to review and consider implementing these recommendations within their usual operations.

A mathematical analysis of the GW0 method for computing electronic excited energies of molecules

This article is concerned with the GW method for finite electronic systems. In the first step, we provide a mathematical framework for the usual one-body operators that appear naturally in many-body perturbation theory. We then give a rigorous mathematical formulation of the [Formula: see text] equations, and study the well-posedness of these equations, proving the existence of a unique solution in a perturbative regime.

A New Weak Galerkin Finite Element Scheme for the Brinkman Model

AbstractThe Brinkman model describes flow of fluid in complex porous media with a high-contrast permeability coefficient such that the flow is dominated by Darcy in some regions and by Stokes in others. A weak Galerkin (WG) finite element method for solving the Brinkman equations in two or three dimensional spaces by using polynomials is developed and analyzed. The WG method is designed by using the generalized functions and their weak derivatives which are defined as generalized distributions. The variational form we considered in this paper is based on two gradient operators which is different from the usual gradient-divergence operators for Brinkman equations. The WG method is highly flexible by allowing the use of discontinuous functions on arbitrary polygons or polyhedra with certain shape regularity. Optimal-order error estimates are established for the corresponding WG finite element solutions in various norms. Some computational results are presented to demonstrate the robustness, reliability, accuracy, and flexibility of the WG method for the Brinkman equations.

Curvature on the integers, I

Starting with a symmetric/antisymmetric matrix with integer coefficients (which we view as an analogue of a metric/form on a principal bundle over the “manifold” SpecZ) we introduce arithmetic analogues of Chern connections and their curvature (in which usual partial derivative operators acting on functions are replaced by Fermat quotient operators acting on integer numbers); curvature is introduced via a formal patching technique. We prove various non-vanishing, respectively vanishing results for curvature; morally, SpecZ will appear as “intrinsically curved”. Along with [7–9], this theory can be viewed as taking first steps in developing a “differential geometry of SpecZ”.

Potential position node placement approach via oppositional gravitational search for fulfill coverage and connectivity in target based wireless sensor networks

Wireless Sensor Network (WSN) has appeared as a powerful technological platform with tremendous and novel applications. Now-a-days, monitoring and target tracking are the most major application in WSNs. In target based WSN, coverage and connectivity are the two most important issues for definite data forwarding from every target to a remote base station. An NP entire issue is to find least number of potential or possible locations to set sensor nodes gratifying both coverage and connectivity from a given a group of target points. In this article, we propose an Oppositional Gravitational Search algorithm (OGSA) based approach to solve this problem. This approach helps that the sensor nodes are prone to failure, the proposed system provides l-coverage to all targets and n-connectivity to each sensor node. This OGSA based system is presented with agent representation, derivation of efficient fitness function along with the usual Gravitational Search algorithm operators. The approach is simulated broadly with various scenarios of Wireless Sensor Network. The experimentation results are compared with some relevant existing algorithms to demonstrate the efficiency of the proposed approach.