Browsing by Subject "Function evaluation"
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Item Open Access Bilgisayarlı iyonosfer tomografisinde açılım işlevlerinin ve yeniden yapılandırma algoritmalarının model üzerinden karşılaştırılması(IEEE, 2005-05) Yavuz, E.; Arıkan, F.; Arıkan, Orhan; Erol, C. B.Bilgisayarlı İyonosfer Tomografisi (BİT), iyonosfer elektron yoğunluğunun iki boyutlu veya üç boyutlu olarak görüntülenmesi için kullanılan bir yöntemdir. Bu yöntem özellikle iyonosfer fiziği veya uydu haberleşmesi gibi alanlar için iyonosferin incelenmesine olanak sağlamaktadır. Bu yöntemde Küresel Yer Belirleme (KYB) uyduları ve bu uydulardan gelen ışınları toplamak üzere yeryüzüne belirli bir geometride yerleştirilen alıcılar kullanılır. Alıcılar KYB uydularından aldıkları sinyaller ile iyonosfere ait olan Toplam Elektron İçeriği (TEİ) verisinin hesaplanmasına olanak sağlar. TEİ verileri ve tomografik yeniden yapılandırma algoritmaları kullanılarak, iyonosfer elektron yoğunluğu görüntülerinin elde edilmesi sağlanır. Gerçekleştirilen bu çalışmada tek bir GPS uydusu ve bu uyduyu izlemek üzere yeryüzünde belirli bir enlem noktasına yerleştirilmiş bir alıcı senaryosu canlandırıldı. Alıcıda oluşan hatalar ve model hataları bu çalışmada ihmal edildi. Bu senaryo içerisinde değişik açılım işlevleri ve yeniden yapılandırma algoritmaları kullanılarak, iyonosfer elektron yoğunluğunun iki boyutlu olarak elde edilmesi gerçekleştirildi. Sonuçların başarım analizleri ileri model olarak kullanılan IRI-95 ile karşılaştırılarak verildi.Item Open Access Decentralized control and periodic feedback(IEEE, 1994) Khargonekar P. P.; Özgüler, A. B.The decentralized stabilization problem for linear, discretetime, periodically time-varying plants using periodic controllers is considered. The main tool used is the technique of lifting a periodic system to a time-invariant one via extensions of the input and output spaces. It is shown that a periodically time-varying system of fundamental period N can be stabilized by a decentralized periodic controller if and only if: 1) the system is stabilizable and detectable, and 2) the N-lifting of each complementary subsystem of identically zero input-output map is free of unstable input-output decoupling zeros. In the special case of N = 1, this yields and clarifies all the major existing results on decentralized stabilization of time-invariant plants by periodically time-varying controllers. © 1994 IEEEItem Open Access Efficient use of closed-form Green's functions for three-dimensional problems involving multilayered media(IEEE, 1994-06) Aksun, M. Irsadi; Mittra, R.With the use of casting the spatial domain Green's functions into closed forms approach, it was demonstrated that the computational efficiency of the method of moments (MoM) for the solution of the mixed potential integral equations can be improved significantly for planar microstrip geometries. However, this approach is not effective in the improvement in the computational efficiency achieved for three-dimensional geometries in planar layered media. In this paper, discussed are the difficulties involved in using the spatial domain, closed-form Green's functions in the Method of Moments formulation for three-dimensional geometries and proposed a technique to improve the computational efficiency of the MoM.Item Open Access Fast and accurate solutions of scattering problems involving dielectric objects with moderate and low contrasts(IEEE, 2007-08) Ergül, Özgür; Gürel, LeventWe consider the solution of electromagnetic scattering problems involving relatively large dielectric objects with moderate and low contrasts. Three-dimensional objects are discretized with Rao-Wilton-Glisson functions and the scattering problems are formulated with surface integral equations. The resulting dense matrix equations are solved iteratively by employing the multilevel fast multipole algorithm. We compare the accuracy and efficiency of the results obtained by employing various integral equations for the formulation of the problem. If the problem size is large, we show that a combined formulation, namely, electric-magnetic current combined-field integral equation, provides faster iterative convergence compared to other formulations, when it is accelerated with an efficient block preconditioner. For low-contrast problems, we introduce various stabilization procedures in order to avoid the numerical breakdown encountered in the conventional surface formulations. © 2007 IEEE.Item Open Access GPS/TEC estimation with IONOLAB method(IEEE, 2007) Nayir, H.; Arıkan, F.; Arıkan, Orhan; Erol, C. B.Total Electron Content (TEC) is a key variable to measure the ionospheric characteristics and disturbances. The Global Positioning System (GPS) can be used for TEC estimation making use of the recorded signals at the GPS receiver. Reg-Est method that is developed by F.Arikan, C.B. Erol and O. Arikan can be used to estimate high resolution, robust TEC values combining GPS measurements of 30 s resolution obtained from the satellites which are above the 10° elevation limit. Using this method, it is possible to estimate TEC values for a whole day or a desired time period both for quiet and disturbed days of the ionosphere. Reg-Est provides robust TEC estimates for high-latitude, mid-latitude and equatorial stations. In this study, some important parameters of Reg-Est such as ionospheric thin shell height, weighting function and receiver-satellite biases are investigated. By incorporating the results of the investigation, Reg-Est algorithm is developed into IONOLAB method. Thin shell model height is an important parameter for Single Layer Ionosphere Model (SLIM). In this study, it is shown that IONOLAB provides reliable and robust TEC estimates independent of the choice of the maximum ionization height. Signals from the low elevation satellites are prone to multipath effects. In order to reduce the distortion due to multipath signals, the optimum weighting function is implemented in IONOLAB, minimizing the non-ionospheric noise effects. GPS receivers record both pseudorange and phase data of signals. IONOLAB can input absolute TEC computed from the pseudorange measurements or phase-corrected low-noise TEC. The TEC estimates for both of these inputs are in good accordance with each other. Thus, taking either pseoudorange or phase-corrected measurement data as input, high resolution, robust TEC estimates can be obtained from IONOLAB. Another important parameter for TEC estimation is satellite-receiver instrumental biases. The biases are the frequency dependent delays due to satellite and receiver hardware. In order to compute TEC, satellite and receiver biases should be removed from GPS measurements correctly. However, the proper procedure of how to include them in the TEC computation is generally vaguely defined. IONOLAB suggests a technique for inclusion of the hardware biases obtained from the web for TEC estimates that are consistent with the results from the IGS analysis centers.Item Open Access Improving AWE accuracy using multipoint Pade approximation(IEEE, 1994-05-06) Çelik, Mustafa; Ocali, Ogan; Tan, Mehmet Ali; Atalar, AbdullahA new method is proposed for dominant pole-zero analysis of large linear circuits containing both lumped and distributed elements. This method is based on a multipoint Pade approximation. It finds a reduced order s-domain transfer function using a data set obtained by solving the circuit at only a few frequency points. The proposed method yields more accurate computation of transient and frequency responses with respect to the AWE-type techniques.Item Open Access Large deviations of probability rank(IEEE, 2000) Arıkan, ErdalConsider a pair of random variables (X,Y) with distribution P. The probability rank function is defined so that G(x|y) = 1 for the most probable outcome x conditional on Y = y, G(x|y) = 2 for the second most probable outcome, and so on, resolving ties between elements with equal probabilities arbitrarily. The function G was considered in [1] in the context of finding the unknown outcome of a random experience by asking question of the form 'Is the outcome equal to x?' sequentially until the actual outcome is determined. The primary focus in [1], and the subsequent works [2], [3], was to find tight bounds on the moments E[G(X|Y)θ]. The present work is closely related to these works but focuses more directly on the large deviations properties of the probability rank function.Item Open Access Levy walk evolution for global optimization(ACM, 2008-07) Urfalıoğlu, Onay; Çetin, A. Enis; Kuruoğlu, E. E.A novel evolutionary global optimization approach based on adaptive covariance estimation is proposed. The proposed method samples from a multivariate Levy Skew Alpha-Stable distribution with the estimated covariance matrix to realize a random walk and so to generate new solution candidates in the mutation step. The proposed method is compared to the popular Differential Evolution method, which is one of the best general evolutionary global optimizers available. Experimental results indicate that the proposed approach yields a general improvement in the required number of function evaluations to solve global optimization problems. Especially, as shown in experiments, the underlying heavy tailed alpha-stable distribution enables a considerably more effective global search in more complex problems. Track: Evolution Strategies.Item Open Access Memory-efficient multilevel physical optics algorithm for fast computation of scattering from three-dimensional complex targets(IEEE, 2007) Manyas, Alp; Gürel, LeventMultilevel physical optics (MLPO) algorithm provides a speed-up for computing the physical-optics integral over complex bodies for a range of aspect angles and frequencies. On the other hand, when computation of the RCS pattern as a function of θ, φ, and frequency is desired, the O N3 memory complexity of the algorithm may prevent the solution of electrically large problems. In this paper, we propose an improved version of the MLPO algorithm, for which the memory complexity is reduced to O N2 log N . The algorithm is based on the aggregation of only some portion of the scattering patterns at each aggregation step. This way, memory growth in each step is prevented, and a significant amount of saving is achieved.Item Open Access New identities for 7-cores with prescribed BG-rank(Elsevier BV * North-Holland, 2008) Berkovich, A.; Yesilyurt, H.Let π be a partition. BG-rank(π) is defined as an alternating sum of parities of parts of π [A. Berkovich, F.G. Garvan, On the Andrews-Stanley refinement of Ramanujan's partition congruence modulo 5 and generalizations, Trans. Amer. Math. Soc. 358 (2006) 703-726. [1]]. Berkovich and Garvan [The BG-rank of a partition and its applications, Adv. in Appl. Math., to appear in 〈http://arxiv.org/abs/math/0602362〉] found theta series representations for the t-core generating functions ∑n ≥ 0 at, j (n) qn, where at, j (n) denotes the number of t-cores of n with BG-rank = j. In addition, they found positive eta-quotient representations for odd t-core generating functions with extreme values of BG-rank. In this paper we discuss representations of this type for all 7-cores with prescribed BG-rank. We make an essential use of the Ramanujan modular equations of degree seven [B.C. Berndt, Ramanujan's Notebooks, Part III, Springer, New York, 1991] to prove a variety of new formulas for the 7-core generating functionunder(∏, j ≥ 1) frac((1 - q7 j)7, (1 - qj)) .These formulas enable us to establish a number of striking inequalities for a7, j (n) with j = - 1, 0, 1, 2 and a7 (n), such asa7 (2 n + 2) ≥ 2 a7 (n), a7 (4 n + 6) ≥ 10 a7 (n) . Here a7 (n) denotes a number of unrestricted 7-cores of n. Our techniques are elementary and require creative imagination only. © 2007 Elsevier B.V. All rights reserved.Item Open Access Self Fourier functions and fractional Fourier transforms(Elsevier, 1994) Mendlovic, D.; Özaktaş, Haldun M.; Lohmann, A. W.Self Fourier functions and fractional Fourier transforms are two concepts that have been discussed recently. Investigated is the combination of these two concepts: self fractional Fourier functions and the fractional Fourier transform of a self Fourier function. © 1994.Item Open Access Synthetic TEC mapping with ordinary and universal kriging(IEEE, 2007-06) Sayın, I.; Arıkan, F.; Arıkan, OrhanSpatiotemporal variations in the ionosphere affects the HF and satellite communications and navigation systems. Total Electron Content (TEC) is an important parameter since it can be used to analyze the spatial and temporal variability of the ionosphere. In this study, the performance of the two widely used Kriging algorithms, namely Ordinary Kriging (OrK) and Universal Kriging (UnK), is compared over the synthetic data set. In order to represent various ionospheric states, such as quiet and disturbed days, spatially correlated residual synthetic TEC data with different variances is generated and added to trend functions. Synthetic data sampled with various type of sampling patterns and for a wide range of sampling point numbers. It is observed that for small sampling numbers and with higher variability, OrK gives smaller errors. As the sample number increases, UnK errors decrease faster. For smaller variances in the synthetic surfaces, UnK gives better results. For increasing variance and decreasing range values, usually, the errors increase for both OrK and UnK. © 2007 IEEE.