Browsing by Subject "Polynomials"

Now showing 1 - 20 of 27

Open Access
Comparison of surface-modeling techniques
(IEEE, 1997-07) Sertel, Kubilay; Gürel, Levent
Solution techniques based on surface integral equations are widely used in computational electromagnetics. The accurate surface models increase the accuracy solutions by using exact and flat-triangulation models for a sphere. For a required solution accuracy, the problem size is significantly reduced by using geometry models for the scatterers. The dependence of the accuracy of the solution on the geometry modeling is investigated.
Open Access
Composite regions of feasibility for certain classes of distance constrained network location problems
(INFORMS, 1996) Tansel, B. Ç.; Yeşilkökçen, G. N.
Distance constrained network location involves locating m new facilities on a transport network G so as to satisfy upper bounds on distances between pairs of new facilities and pairs of new and existing facilities. The problem is script N sign℘-complete in general, but polynomially solvable for certain classes. While it is possible to give a consistency characterization for these classes, it does not seem possible to give a global description of the feasible set. However, substantial geometrical insights can be obtained on the feasible set by studying its projections onto the network. The j-th projection defines the j-th composite region which is the set of all points in G at which new facility j can be feasibly placed without violating consistency. We give efficient methods to construct these regions for solvable classes without having to know the feasible set and discuss implications on consistency characterization, what if analysis, and recursive solution constructions.
Open Access
Compound poisson disorder problems with nonlinear detection delay penalty cost functions
(2010) Dayanik, S.
The quickest detection of the unknown and unobservable disorder time, when the arrival rate and mark distribution of a compound Poisson process suddenly changes, is formulated in a Bayesian setting, where the detection delay penalty is a general smooth function of the detection delay time. Under suitable conditions, the problem is shown to be equivalent to the optimal stopping of a finite-dimensional piecewise-deterministic strongly Markov sufficient statistic. The solution of the optimal stopping problem is described in detail for the compound Poisson disorder problem with polynomial detection delay penalty function of arbitrary but fixed degree. The results are illustrated for the case of the quadratic detection delay penalty function. © Taylor & Francis Group, LLC.
Open Access
Constructing convex directions for stable polynomials
(IEEE, 2000) Özgüler, A. B.
The constructions of convex directions based on phase-derivative interpretations were obtained for Hurwitz-stable polynomials. The phase-derivative conditions were based on the sensitivity of root-locus associated with the even and odd parts of a polynomial. The phase-growth condition directly established anti-Hurwitz polynomials, polynomials of degree one, even polynomials and odd polynomials for the entire set of Hurwitz polynomials.
Open Access
Customer order scheduling on a single machine with family setup times: complexity and algorithms
(Elsevier, 2007) Erel, E.; Ghosh, J. B.
We consider a situation where C customers each order various quantities (possibly zero in some cases) of products from P different families, which can be produced on a continuously available machine in any sequence (requiring a setup whenever production switches from one family to another). We assume that the time needed for a setup depends only on the family to be produced immediately after it, and we follow the item availability model (which implies that all units are ready for dispatch as soon as they are produced). However, an order is shipped only when all units required by a customer are ready. The time from the start (time zero) to the completion of a customer order is called the order lead time. The problem, which restates the original description of the customer order scheduling problem, entails finding a production schedule that will minimize the total order lead time. While this problem has received some attention in the literature, its complexity status has remained vexingly open. In this note, we show for the first time that the problem is strongly NP-hard. We proceed to give dynamic programming based exact solution algorithms for the general problem and a special case (where C is fixed). These algorithms allow us to solve small instances of the problem and understand the problem complexity more fully. In particular, the solution of the special case shows that the problem is solvable in polynomial time when C is fixed.
Open Access
Efficient evaluation of spatial-domain MoM matrix entries in the analysis of planar stratified geometries
(IEEE, 2000) Kinayman, N.; Aksun, M. I
An efficient hybrid method for evaluation of spatial-domain method-of-moments (MoM) matrix entries is presented in this paper. It has already been demonstrated that the introduction of the closed-form Green's functions into the MoM formulation results in a significant computational improvement in filling up MoM matrices and, consequently, in the analysis of planar geometries. To achieve further improvement in the computational efficiency of the MoM matrix entries, a hybrid method is proposed in this paper and, through some examples, it is demonstrated that it provides significant acceleration in filling up MoM matrices while preserving the accuracy of the results.
Open Access
Exact expression and tight bound on pairwise error probability for performance analysis of turbo codes over Nakagami-m fading channels
(IEEE, 2007) Ali, S. A.; Kambo, N. S.; İnce, E. A.
This letter presents derivation for an exact and efficient expression on pairwise error probability over fully interleaved Nakagami-m fading channels under ideal channel state information at the decoder. As an outcome, this derivation also leads to a tight upper bound on pairwise error probability which is close to the exact expression. Pairwise error probability plots for different values of Nakagami parameter m along with an already existing numerically computable expression are provided. As an application of pairwise error probability, average union upper bounds for turbo codes having (1, 7/5, 7/5) and (1, 5/7, 5/7) generator polynomials employing transfer function approach are presented to illustrate the usefulness of the new efficient results. © 2007 IEEE.
Open Access
Fibre products of superelliptic curves and codes therefrom
(IEEE, 1997) Stepanov, Serguei A.; Özbudak, Ferruh
A method of constructing long geometric Goppa codes coming from fiber products of superelliptic curves is presented. A family of smooth projective curves with a lot of Fq-rational points are needed to produce a family of asymptotically good geometric Goppa codes. The genus in every such family is considerably less than the number of rational points, so the corresponding geometric Goppa codes have rather good parameters. Examples of such families are provided by modular curves, by Drinfeld modular curves, and by Artin-Schreier coverings of the projective line.
Open Access
A general theory on spectral properties of state-homogeneous finite-state quasi-birth-death processes
(Elsevier, 2001) Fadıloğlu, M. M.; Yeralan, S.
In this paper a spectral theory pertaining to Quasi-Birth–Death Processes (QBDs) is presented. The QBD, which is a generalization of the birth–death process, is a powerful tool that can be utilized in modeling many stochastic phenomena. Our theory is based on the application of a matrix polynomial method to obtain the steady-state probabilities in state-homogeneous finite-state QBDs. The method is based on finding the eigenvalue–eigenvector pairs that solve a matrix polynomial equation. Since the computational effort in the solution procedure is independent of the cardinality of the counting set, it has an immediate advantage over other solution procedures. We present and prove different properties relating the quantities that arise in the solution procedure. By also compiling and formalizing the previously known properties, we present a formal unified theory on the spectral properties of QBDs, which furnishes a formal framework to embody much of the previous work. This framework carries the prospect of furthering our understanding of the behavior the modeled systems manifest.
Open Access
A gPC-based approach to uncertain transonic aerodynamics
(2010) Simon F.; Guillen P.; Sagaut P.; Lucor, D.
The present paper focus on the stochastic response of a two-dimensional transonic airfoil to parametric uncertainties. Both the freestream Mach number and the angle of attack are considered as random parameters and the generalized Polynomial Chaos (gPC) theory is coupled with standard deterministic numerical simulations through a spectral collocation projection methodology. The results allow for a better understanding of the flow sensitivity to such uncertainties and underline the coupling process between the stochastic parameters. Two kinds of non-linearities are critical with respect to the skin-friction uncertainties: on one hand, the leeward shock movement characteristic of the supercritical profile and on the other hand, the boundary-layer separation on the aft part of the airfoil downstream the shock. The sensitivity analysis, thanks to the Sobol' decomposition, shows that a strong non-linear coupling exists between the uncertain parameters. Comparisons with the one-dimensional cases demonstrate that the multi-dimensional parametric study is required to get the correct shape and magnitude of the standard deviation distributions of the flow quantities such as pressure and skin-friction. © 2009 Elsevier B.V.
Open Access
Interframe differential vector coding of line spectrum frequencies
(IEEE, 1993-04) Erzin, Engin; Çetin, A. Enis
Line Spectrum Frequencies (LSF's) uniquely represent the Linear Predictive Coding (LPC) filter of a speech frame. In many vocoders LSF's are used to encode the LPC parameters. In this paper, an interframe differential coding scheme is presented for the LSF's. The LSF's of the current speech frame are predicted by using both the LSF's of the previous frame and some of the LSF's of the current frame. Then, the difference vector resulting from prediction is vector quantized.
Open Access
A joint production and transportation planning problem with heterogeneous vehicles
(2014) Toptal, A.; Koc, U.; Sabuncuoglu, I.
We consider a manufacturer's planning problem to schedule order production and transportation to respective destinations. The manufacturer in this setting can use two vehicle types for outbound shipments. The first type is available in unlimited numbers. The availability of the second type, which is less expensive, changes over time. Motivated by some industry practices, we present formulations for three different solution approaches: the myopic solution, the hierarchical solution and the coordinated solution. These approaches vary in how the underlying production and transportation subproblems are solved, that is, sequentially versus jointly or heuristically versus optimally. We provide intractability proofs or polynomial-time exact solution procedures for the sub-problems and their special cases. We also compare the three solution approaches over a numerical study to quantify the savings from integration and explicit consideration of transportation availabilities. Our analytical and numerical results set a foundation and a need for a heuristic to solve the integrated problem. We thus propose a tabu search heuristic, which quickly generates near-optimal solutions.
Open Access
Local convex directions for Hurwitz stable polynomials
(IEEE, 2002) Özgüler, A. B.; Saadaoui, K.
A new condition for a polynomial p(s) to be a local convex direction for a Hurwitz stable polynomial q(s) is derived. The condition is in terms of polynomials associated with the even and odd parts of p(s) and q(s), and constitutes a generalization of Rantzer's phase-growth condition for global convex directions. It is used to determine convex directions for certain subsets of Hurwitz stable polynomials.
Open Access
Matrix-geometric solutions of M/G/1-type Markov chains: A unifying generalized state-space approach
(1998) Akar, N.; Oǧuz, N.C.; Sohraby, K.
In this paper, we present an algorithmic approach to find the stationary probability distribution of M/G/1-type Markov chains which arise frequently in performance analysis of computer and communication networ ks. The approach unifies finite- and infinite-level Markov chains of this type through a generalized state-space representation for the probability generating function of the stationary solution. When the underlying probability generating matrices are rational, the solution vector for level k, x k, is shown to be in the matrix-geometric form x k+1 = gF k H, k ≥ 0, for the infinite-level case, whereas it takes the modified form x k+1 = g 1F 1 kH 1 + g 2F 2 K-k-1 H 2, 0 ≤ k < K, for the finite-level case. The matrix parameters in the above two expressions can be obtained by decomposing the generalized system into forward and backward subsystems, or, equivalently, by finding bases for certain generalized invariant subspaces of a regular pencil λE - A. We note that the computation of such bases can efficiently be carried out using advanced numerical linear algebra techniques including matrix-sign function iterations with quadratic convergence rates or ordered generalized Schur decomposition. The simplicity of the matrix-geometric form of the solution allows one to obtain various performance measures of interest easily, e.g., overflow probabilities and the moments of the level distribution, which is a significant advantage over conventional recursive methods.
Open Access
A model-based scheme for anticontrol of some chaotic systems
(World Scientific Publishing, 2003) Morgül, Ö.
We consider a model-based approach for the anticontrol of some continuous time systems. We assume the existence of a chaotic model in an appropriate form. By using a suitable input, we match the dynamics of the controlled system and the chaotic model. We show that controllable systems can be chaotifled with the proposed method. We give a procedure to generate such chaotic models. We also apply an observer-based synchronization scheme to compute the required input.
Open Access
Network-aware virtual machine placement in cloud data centers with multiple traffic-intensive components
(Elsevier BV, 2015) Ilkhechi, A. R.; Korpeoglu, I.; Ulusoy, Özgür
Following a shift from computing as a purchasable product to computing as a deliverable service to consumers over the Internet, cloud computing has emerged as a novel paradigm with an unprecedented success in turning utility computing into a reality. Like any emerging technology, with its advent, it also brought new challenges to be addressed. This work studies network and traffic aware virtual machine (VM) placement in a special cloud computing scenario from a provider's perspective, where certain infrastructure components have a predisposition to be the endpoints of a large number of intensive flows whose other endpoints are VMs located in physical machines (PMs). In the scenarios of interest, the performance of any VM is strictly dependent on the infrastructure's ability to meet their intensive traffic demands. We first introduce and attempt to maximize the total value of a metric named "satisfaction" that reflects the performance of a VM when placed on a particular PM. The problem of finding a perfect assignment for a set of given VMs is NP-hard and there is no polynomial time algorithm that can yield optimal solutions for large problems. Therefore, we introduce several off-line heuristic-based algorithms that yield nearly optimal solutions given the communication pattern and flow demand profiles of subject VMs. With extensive simulation experiments we evaluate and compare the effectiveness of our proposed algorithms against each other and also against naïve approaches.
Open Access
Non-local, non-commutative picture in quantum mechanics and distinguished continuous canonical maps
(IOP Science, 2002) Hakioglu, T.
It is shown that continuous classical nonlinear canonical (Poisson) maps have a distinguished role in quantum mechanics. They act unitarily on the quantum phase space and generate h-independent quantum nonlinear canonical maps. It is also shown that such maps act in the non-commutative phase space under the classical covariance. A crucial result of the work is that under the action of Poisson maps a local quantum mechanical picture is converted onto a non-local picture which is then represented in a non-local Hilbert space. On the other hand, it is known that a non-local picture is equivalent by the Weyl map to a non-commutative picture which, in the context of this work, corresponds to a phase space formulation of the theory. As a result of this equivalence, a phase space Schrödinger picture can be formulated. In particular, we obtain the *-genvalue equation of Fairlie [Proc. Camb. Phil. Soc., 60, 581 (1964)] and Curtright, Fairlie and Zachos [Phys. Rev., D 58, 025002 (1998)]. In a non-local picture entanglement becomes a crucial concept. The connection between the entanglement and non-locality is explored in the context of Poisson maps and specific examples of the generation of entanglement from a local wavefunction are provided by using the concept of generalized Bell states. The results obtained are also relevant for the non-commutative soliton picture in the non-commutative field theories. We elaborate on this in the context of the scalar non-commutative field theory.
Open Access
On algebraic properties of general proper decentralized systems
(Elsevier, 1993) Yu, R.; Sezer, M. E.; Gao, W.
The new concepts of the decentralized output feedback variable polynomial, the decentralized output feedback cycle index of general proper systems, and the geometric multiplicities of decentralized fixed modes are introduced. Their computational methods and some algebraic properties are presented. It is shown that the decentralized output feedback cycle index of a general proper system is equal to one when the system has no fixed modes or equal to the maximum of the geometric multiplicities of its decentralized fixed modes. It is also shown that almost all decentralized output feedback can be used to make the zeros of the decentralized variable polynomial distinct, and disjoint from any given finite set of points on the complex plane.
Open Access
On the analyticity of functions approximated by their q-Bernstein polynomials when q > 1
(2010) Ostrovskii I.; Ostrovska, S.
Since in the case q > 1 the q-Bernstein polynomials Bn,q are not positive linear operators on C[0, 1], the investigation of their convergence properties for q > 1 turns out to be much harder than the one for 0 < q < 1. What is more, the fast increase of the norms ∥Bn,q∥ as n → ∞, along with the sign oscillations of the q-Bernstein basic polynomials when q > 1, create a serious obstacle for the numerical experiments with the q-Bernstein polynomials. Despite the intensive research conducted in the area lately, the class of functions which are uniformly approximated by their q-Bernstein polynomials on [0, 1] is yet to be described. In this paper, we prove that if f:[0,1]→C is analytic at 0 and can be uniformly approximated by its q-Bernstein polynomials (q > 1) on [0, 1], then f admits an analytic continuation from [0, 1] into {z: z < 1}. © 2010 Elsevier Inc. All rights reserved.
Open Access
On the Lagrange interpolation in multilevel fast multipole algorithm
(IEEE, 2006) Ergül, Özgür; Gürel, Levent
We consider the Lagrange interpolation employed in the multilevel fast multipole algorithm (MLFMA) as part of our efforts to obtain faster and more efficient solutions for large problems of computational electromagnetics. For the translation operator, we present the choice of the parameters for optimal interpolation. For the aggregation and dissaggregation processes, we discuss the interpolation matrices and introduce an efficient way of improving the accuracy by employing the poles.