Effective Reduction Algorithm Research Articles

A method for solving the open-pit mine production scheduling problem using the constraint programming paradigm

A method is developed to solve the problem of open-pit mine production scheduling, which is based on Constraint Programming and is used in working out an optimal plan of mining operations, taking into account heterogeneous economical, technological and some others requirements imposed by the customer. An original model is proposed to represent the problem considered as a constraint satisfaction problem. As the customer may verify the requirements, the domain model should enable addition of the new constraints and/or eliminate the existing ones. With the domain model being developed, the method proposed makes it possible to reach accurate solutions at the expense of highly effective reduction algorithms for each type of constraints and at the expense of specialized heuristics for non-perspective alternatives reduction in a search tree. The approach proposed enables addition of different constraints, even those for which it is difficult to find an analytical expression.

TripleK: A Mathematica package for evaluating triple-K integrals and conformal correlation functions

I present a Mathematica package designed for manipulations and evaluations of triple-K integrals and conformal correlation functions in momentum space. Additionally, the program provides tools for evaluation of a large class of 2- and 3-point massless multi-loop Feynman integrals with generalized propagators. The package is accompanied by five Mathematica notebooks containing detailed calculations of numerous conformal 3-point functions in momentum space. Program summaryProgram Title: TripleKCPC Library link to program files:http://dx.doi.org/10.17632/5sz4bt28vr.1Developer’s repository link:https://triplek.hepforge.org/Licensing provisions: GNU General Public License v3.0Programming language: Wolfram Language [1] (Mathematica 10.0 or higher)Supplementary material: The package includes five Mathematica notebooks containing bulk of the results regarding the structure of conformal 3-point functions.Nature of problem: Triple-K integrals were introduced in [2] as a convenient tool for the analysis of conformal 3-point functions in momentum space. All 3-point functions of scalar operators, conserved currents and stress tensor can be expressed in terms of triple-K integrals. Furthermore, a large class of 2- and 3-point massless multi-loop Feynman integrals with generalized propagators is expressible in terms of triple-K integrals as well. Since the expressions are usually long and unwieldy, an automated tool is essential for efficient manipulations.Solution method: In [3] an effective reduction algorithm was provided for expressing a large class of triple-K integrals in terms of master integrals. The presented package implements this reduction scheme. As far as the multi-loop Feynman integrals are concerned, the conversion to multiple-K integrals proceeds by means of Schwinger parameterization.Additional comments including restrictions and unusual features: Despite extensive testing, this package is a one man job, therefore bugs are unavoidable. Please, report all issues at adam.bzowski@physics.uu.se or abzowski@gmail.com. [1] Wolfram Research Inc., Mathematica, Version 11.2, 12.0, Champaign, IL, 2020 [2] A. Bzowski, P. McFadden, K. Skenderis, Implications of conformal invariance in momentum space, JHEP 03 (2014) 111. http://arxiv.org/abs/1304.7760arXiv:1304.7760, https://doi.org/10.1007/JHEP03(2014)111doi:10.1007/JHEP03(2014)111 [3] A. Bzowski, P. McFadden, K. Skenderis, Evaluation of conformal integrals, JHEP 02 (2016) 068. http://arxiv.org/abs/1511.02357arXiv:1511.02357, https://doi.org/10.1007/JHEP02(2016)068doi:10.1007/JHEP02(2016)068

Addition of Divisors on Hyperelliptic Curves via Interpolation Polynomials

Two problems are addressed: reduction of an arbitrary degree non-special divisor to the equivalent divisor of the degree equal to genus of a curve, and addition of divisors of arbitrary degrees. The hyperelliptic case is considered as the simplest model. Explicit formulas defining reduced divisors for some particular cases are found. The reduced divisors are obtained in the form of solution of the Jacobi inversion problem which provides the way of computing Abelian functions on arbitrary non-special divisors. An effective reduction algorithm is proposed, which has the advantage that it involves only arithmetic operations on polynomials. The proposed addition algorithm contains more details comparing with the known in cryptography, and is extended to divisors of arbitrary degrees comparing with the known in the theory of hyperelliptic functions.

A general reduction algorithm for relation decision systems and its applications

This paper studies the attribute reduction problem for general relation decision systems. We propose a new discernibility matrix to solve this problem. Combining the discernibility matrix and a recently proposed fast algorithm, we propose a simple and unified attribute reduction algorithm for relation decision systems that is not contingent on the consistency of relation decision systems. We derive the reduction algorithm for the special cases of complete, incomplete, and numerical decision tables. As an application, we transform the attribute reduction of relation decision systems into one for covering decision systems. This gives a convenient and effective reduction algorithm for covering decision systems. The reduction results obtained using University of California Irvine data sets show that the proposed algorithm is simple and efficient. Moreover, the proposed algorithm enables the results of classical attribute reduction approaches to be reinterpreted, giving them far greater unification and generality.

Extended rank reduction formulas containing Wedderburn and Abaffy–Broyden–Spedicato rank reducing processes

The Wedderburn rank reduction formula and the Abaffy–Broyden–Spedicato (ABS) algorithms are powerful methods for developing matrix factorizations and many fundamental numerical linear algebra processes such as Gram–Schmidt, conjugate direction and Lanczos methods. We present a rank reduction formula for transforming the rows and columns of A, extending the Wedderburn rank reduction formula and the ABS approach. By repeatedly applying the formula to reduce the rank, an extended rank reducing process is derived. The biconjugation process associated with the Wedderburn rank reduction process and the scaled extended ABS class of algorithms are shown to be in our proposed rank reducing process, while the process is more general to produce several other effective reduction algorithms to compute various structured factorizations. The process provides a general finite iterative approach for constructing factorizations of A and AT under a common framework of a general decomposition VTAP=Ω. We also show that the biconjugation process associated with the Wedderburn rank reduction process can be derived from the scaled ABS class of algorithms applied to A or AT. Finally, we provide a list of some well-known reduction procedures as special cases of our extended rank reducing process. The approach is general enough to produce various structured decompositions as well.

Can a partial volume edge effect reduction algorithm improve the repeatability of subject-specific finite element models of femurs obtained from CT data?

The reliability of patient-specific finite element (FE) modelling is dependent on the ability to provide repeatable analyses. Differences of inter-operator generated grids can produce variability in strain and stress readings at a desired location, which are magnified at the surface of the model as a result of the partial volume edge effects (PVEEs). In this study, a new approach is introduced based on an in-house developed algorithm which adjusts the location of the model's surface nodes to a consistent predefined threshold Hounsfield unit value. Three cadaveric human femora specimens were CT scanned, and surface models were created after a semi-automatic segmentation by three different experienced operators. A FE analysis was conducted for each model, with and without applying the surface-adjustment algorithm (a total of 18 models), implementing identical boundary conditions. Maximum principal strain and stress and spatial coordinates were probed at six equivalent surface nodes from the six generated models for each of the three specimens at locations commonly utilised for experimental strain guage measurement validation. A Wilcoxon signed-ranks test was conducted to determine inter-operator variability and the impact of the PVEE-adjustment algorithm. The average inter-operator difference in stress values was significantly reduced after applying the adjustment algorithm (before: 3.32 ± 4.35 MPa, after: 1.47 ± 1.77 MPa, p = 0.025). Strain values were found to be less sensitive to inter-operative variability (p = 0.286). In summary, the new approach as presented in this study may provide a means to improve the repeatability of subject-specific FE models of bone obtained from CT data.