Search results for "symbolic"
showing 10 items of 449 documents
Matroid optimization problems with monotone monomials in the objective
2022
Abstract In this paper we investigate non-linear matroid optimization problems with polynomial objective functions where the monomials satisfy certain monotonicity properties. Indeed, we study problems where the set of non-linear monomials consists of all non-linear monomials that can be built from a given subset of the variables. Linearizing all non-linear monomials we study the respective polytope. We present a complete description of this polytope. Apart from linearization constraints one needs appropriately strengthened rank inequalities. The separation problem for these inequalities reduces to a submodular function minimization problem. These polyhedral results give rise to a new hiera…
A Characterization of Quintic Helices
2005
A polynomial curve of degree 5, @a, is a helix if and only if both @[email protected]^'@? and @[email protected]^'@[email protected]^''@? are polynomial functions.
A New Set of Quartic Trivariate Polynomial Equations for Stratified Camera Self-calibration under Zero-Skew and Constant Parameters Assumptions
2012
This paper deals with the problem of self-calibrating a moving camera with constant parameters. We propose a new set of quartic trivariate polynomial equations in the unknown coordinates of the plane at infinity derived under the no-skew assumption. Our new equations allow to further enforce the constancy of the principal point across all images while retrieving the plane at infinity. Six such polynomials, four of which are independent, are obtained for each triplet of images. The proposed equations can be solved along with the so-called modulus constraints and allow to improve the performance of existing methods.
Exact Voronoi diagram of smooth convex pseudo-circles: General predicates, and implementation for ellipses
2013
International audience; We examine the problem of computing exactly the Voronoi diagram (via the dual Delaunay graph) of a set of, possibly intersecting, smooth convex \pc in the Euclidean plane, given in parametric form. Pseudo-circles are (convex) sites, every pair of which has at most two intersecting points. The Voronoi diagram is constructed incrementally. Our first contribution is to propose robust and efficient algorithms, under the exact computation paradigm, for all required predicates, thus generalizing earlier algorithms for non-intersecting ellipses. Second, we focus on \kcn, which is the hardest predicate, and express it by a simple sparse $5\times 5$ polynomial system, which a…
A Perturbation Approach to Continuous-Time Portfolio Selection Under Stochastic Investment Opportunities
2013
This paper studies portfolio selection in continuous-time models with stochastic investment opportunities. We consider asset allocation problems where preferences are specified as power utility derived from terminal wealth as well as consumption-savings problems with recursive utility Epstein-Zin preferences. The paper approximates the associated dynamic programming problem by perturbing the coefficients of the stochastic dynamics. We represent the Hamilton-Jacobi-Bellman equation as a series of partial differential equations that can be solved iteratively in closed-form through computer algebra software, at any desired accuracy.
Neural network approach to solving fuzzy nonlinear equations using Z-numbers
2020
In this article, the fuzzy property is described by means of the Z-number as the coefficients and variables of the fuzzy equations. This alteration for the fuzzy equation is appropriate for system modeling with Z-number parameters. In this article, the fuzzy equation with Z-number coefficients and variables is tended to be used as the models for the uncertain systems. The modeling issue related to the uncertain system is to obtain the Z-number coefficients and variables of the fuzzy equation. Nevertheless, it is extremely hard to get the Z-number coefficients of the fuzzy equations. In this article, in order to model the uncertain nonlinear systems, a novel structure of the multilayer neura…
Quantum Dual Adversary for Hidden Subgroups and Beyond
2019
An explicit quantum dual adversary for the S-isomorphism problem is constructed. As a consequence, this gives an alternative proof that the query complexity of the dihedral hidden subgroup problem is polynomial.
Virtual and arrow Temperley–Lieb algebras, Markov traces, and virtual link invariants
2021
Let [Formula: see text] be the algebra of Laurent polynomials in the variable [Formula: see text] and let [Formula: see text] be the algebra of Laurent polynomials in the variable [Formula: see text] and standard polynomials in the variables [Formula: see text] For [Formula: see text] we denote by [Formula: see text] the virtual braid group on [Formula: see text] strands. We define two towers of algebras [Formula: see text] and [Formula: see text] in terms of diagrams. For each [Formula: see text] we determine presentations for both, [Formula: see text] and [Formula: see text]. We determine sequences of homomorphisms [Formula: see text] and [Formula: see text], we determine Markov traces […
Special arrangements of lines: Codimension 2 ACM varieties in P 1 × P 1 × P 1
2019
In this paper, we investigate special arrangements of lines in multiprojective spaces. In particular, we characterize codimension 2 arithmetically Cohen–Macaulay (ACM) varieties in [Formula: see text], called varieties of lines. We also describe their ACM property from a combinatorial algebra point of view.
On a generalisation of Krein's example
2017
We generalise a classical example given by Krein in 1953. We compute the difference of the resolvents and the difference of the spectral projections explicitly. We further give a full description of the unitary invariants, i.e., of the spectrum and the multiplicity. Moreover, we observe a link between the difference of the spectral projections and Hankel operators.