Browsing by Subject "Functions"

Now showing 1 - 20 of 32

Open Access
Bessel functions-based reconstruction of non-uniformly sampled diffraction fields
(IEEE, 2007) Uzunov, V.; Esmer, G. Bora; Gotchev, A.; Onural, Levent; Özaktaş, Haldun M.
A discrete computational model for the diffraction process is essential in forward problems related to holographic TV. The model must be as general as possible, since the shape of the displayed objects does not bear any restrictions. We derive a discrete diffraction model which suits the problem of reconstruction of diffraction fields from a set of non-uniformly distributed samples. The only restriction of the model is the wave nature of the field. The derivation takes advantage of changing the spatial and frequency coordinates to polar form and ends up with a model stated in terms of Bessel functions. The model proves to be a separable orthogonal basis. It shows rapid convergence when evaluated in the framework of the non-uniform sampling problem.
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
Computationally efficient wavelet affine invariant functions for 2D object recognition
(IEEE, 2003) Bala, E.; Çetin, A. Enis
In this paper, an affine invariant function is presented for object recognition from wavelet coefficients of the object boundary. In previous works, undecimated wavelet transform was used for affine invariant functions. In this paper, an algorithm based on decimated wavelet transform is developed to compute the affine invariant function. As a result, computational complexity is significantly reduced without decreasing recognition performance. Experimental results are presented.
Open Access
Contact-free measurement of respiratory rate using infrared and vibration sensors
(Elsevier BV, 2015) Erden, F.; Alkar, A. Z.; Çetin, A. Enis
Respiratory rate is an essential parameter in many practical applications such as apnea detection, patient monitoring, and elderly people monitoring. In this paper, we describe a novel method and a contact-free multi-modal system which is capable of detecting human breathing activity. The multimodal system, which uses both differential pyro-electric infrared (PIR) and vibration sensors, can also estimate the respiratory rate. Vibration sensors pick up small vibrations due to the breathing activity. Similarly, PIR sensors pick up the thoracic movements. Sensor signals are sampled using a microprocessor board and analyzed on a laptop computer. Sensor signals are processed using wavelet analysis and empirical mode decomposition (EMD). Since breathing is almost periodic, a new multi-modal average magnitude difference function (AMDF) is used to detect the periodicity and the period in the processed signals. By fusing the data of two different types of sensors we achieve a more robust and reliable contact-free human breathing activity detection system compared to systems using only one specific type of sensors.
Open Access
Economic design of EWMA control charts based on loss function
(Elsevier, 2009) Serel, D. A.
For monitoring the stability of a process, various control charts based on exponentially weighted moving average (EWMA) statistics have been proposed in the literature. We study the economic design of EWMA-based mean and dispersion charts when a linear, quadratic, or exponential loss function is used for computing the costs arising from poor quality. The chart parameters (sample size, sampling interval, control limits and smoothing constant) minimizing the overall cost of the control scheme are determined via computational methods. Using numerical examples, we compare the performances of the EWMA charts with Shewhart over(X, -) and S charts, and investigate the sensitivity of the chart parameters to changes in process parameters and loss functions. Numerical results imply that rather than sample size or control limits, the users need to adjust the sampling interval in response to changes in the cost of poor quality.
Open Access
An efficient method for electromagnetic characterization of 2-D geometries in stratified media
(IEEE, 2002) Aksun, M. I.; Çalışkan, F.; Gürel, Levent
A numerically efficient technique, based on the spectral-domain method of moments (MoM) in conjunction with the generalized pencil-of-functions (GPOF) method, is developed for the characterization of two-dimensional geometries in multilayer planar media. This approach provides an analytic expression for all the entries of the MoM matrix, explicitly including the indexes of the basis and testing functions provided that the Galerkin's MoM is employed. This feature facilitates an efficient modification of the geometry without the necessity of recalculating the additional elements in the MoM matrix. To assess the efficiency of the approach, the results and the matrix fill times are compared to those obtained with two other efficient methods, namely, the spatial-domain MoM in conjunction with the closed-form Green's functions, and a fast Fourier transform algorithm to evaluate the MoM matrix entries. Among these, the spectral-domain MoM using the GPOF algorithm is the most efficient approach for printed multilayer geometries.
Open Access
Energetic efficient synthesis of general mutual intensity distribution
(Institute of Physics Publishing, 2000) Zalevsky, Z.; Medlovic, D.; Özaktaş, Haldun M.
The mutual intensity distribution of a light beam may contain available information. The task of encoding a given mutual intensity distribution is addressed in this paper. Various approaches for encoding the mutual intensity function have been previously proposed. However, all of them provide low energetic efficiency and commonly require sophisticated production methods. The idea of using a phase-only filter for performing this synthesis is hereby investigated. The proposed method is numerically examined for the case of placing the mutual intensity generating filter in the fractional Fourier domain.
Open Access
Exact calculation of blocking probabilities for bufferless optical burst switched links with partial wavelength conversion
(IEEE, 2004-10) Akar, Nail; Karasan, Ezhan
In this paper, we study the blocking probabilities in a wavelength division multiplexing-based asynchronous bufferless optical burst switch equipped with a bank of tuneable wavelength converters that is shared per output link. The size of this bank is generally chosen to be less than the number of wavelengths on the link because of the relatively high cost of wavelength converters using current technologies; this case is referred to as partial wavelength conversion in the literature. We present a probabilistic framework for exactly calculating the blocking probabilities. Burst durations are assumed to be exponentially distributed. Burst arrivals are first assumed to be Poisson and later generalized to the more general phase-type distribution. Unlike existing literature based on approximations and/or simulations, we formulate the problem as one of finding the steadystate solution of a continuous-time Markov chain with a block tridiagonal infinitesimal generator. We propose a numerically efficient and stable solution technique based on block tridiagonal LU factorizations. We show that blocking probabilities can exactly and efficiently be found even for very large systems and rare blocking probabilities. Based on the results of this solution technique, we also show how this analysis can be used for provisioning wavelength channels and converters. © 2004 IEEE.
Open Access
The fractional fourier transform and its applications to image representation and beamforming
(ASME, 2003-09) Yetik, I. Ş; Kutay, M. A.; Özaktaş, Haldun. M.
The ath order fractional Fourier transform operator is the ath power of the ordinary Fourier transform operator. We provide a brief introduction to the fractional Fourier transform, discuss some of its more important properties, and concentrate on its applications to image representation and compression, and beamforming. We show that improved performance can be obtained by employing the fractional Fourier transform instead of the ordinary Fourier transform in these applications.
Open Access
General Conclusions
(Palgrave Pivot, 2021-10-07) Zavagno, Luca
This chapter will sum up the nature and characteristics of the changes in urbanism in Byzantium show variations (in regional and sub-regional terms) which allow us to sketch different trajectories of development for the cities of the Byzantine empire. They should be pitted against each other to understand how different local needs produced different multifunctional real “urban” answers to the problems and challenges which presented themselves along with the ebbs and flows of the history of an Empire that would not die and indeed managed to navigate through streams of gold and rivers of blood until it fell (but not for the last time) with the Fourth Crusade and the sack of Constantinople.
Open Access
Guessing subject to distortion
(Institute of Electrical and Electronics Engineers, 1998-05) Arikan, E.; Merhav, N.
We investigate the problem of guessing a random vector X within distortion level D. Our aim is to characterize the best attainable performance in the sense of minimizing, in some probabilistic sense, the number of required guesses G(X) until the error falls below D. The underlying motivation is that G(X) is the number of candidate codewords to be examined by a rate-distortion block encoder until a satisfactory codeword is found. In particular, for memoryless sources, we provide a single-letter characterization of the least achievable exponential growth rate of the ρth moment of G(X) as the dimension of the random vector X grows without bound. In this context, we propose an asymptotically optimal guessing scheme that is universal both with respect to the information source and the value of ρ. We then study some properties of the exponent function E(D, ρ) along with its relation to the source-coding exponents. Finally, we provide extensions of our main results to the Gaussian case, guessing with side information, and sources with memory.
Open Access
Improving the accuracy of the MFIE with the choice of basis functions
(IEEE, 2004-06) Ergül, Özgür; Gürel, Levent
The accuracy of the magnetic-field integral equation (MFIE) for the Method of Moments (MOM) and fast-multiple-method (FMM) solutions of the electromagnetic scattering problems modeled by abitrary planar triangulations is improved by the choice of basis functions. The four different basis functions, Rao-Wilton-Glisson (RWG), TL, n × RWG and n × TL are used to define the planar triangles. The current distribution and the radar cross section (RCS) results are found to be more accurate for the TL and n × TL functions. TL and n × TL functions are used to improve the efficiency inspite of the increased computational cost.
Open Access
Influence function based Gaussianity tests for detection of microcalcifications in mammogram images
(IEEE, 1999-10) Gürcan, M. Nafi; Yardımcı, Y.; Çetin, A. Enis
In this paper, computer-aided diagnosis of microcalcifications in mammogram images is considered. Microcalcification clusters are an early sign of breast cancer. Microcalcifications appear as single bright spots in mammogram images. We propose an effective method for the detection of these abnormalities. The first step of this method is two-dimensional adaptive filtering. The filtering produces an error image which is divided into overlapping square regions. In each square region, a Gaussianity test is applied. Since microcalcifications have an impulsive appearance, they are treated as outliers. In regions with no microcalcifications, the distribution of the error image is almost Gaussian, on the other hand, in regions containing microcalcification clusters, the distribution deviates from Gaussianity. Using the theory of the influence function and sensitivity curves, we develop a Gaussianity test. Microcalcification clusters are detected using the Gaussianity test. Computer simulation studies are presented.
Open Access
An inventory problem with two randomly available suppliers
(Institute for Operations Research and the Management Sciences, 1997) Gürler, Ü.; Parlar, M.
This paper considers a stochastic inventory model in which supply availability is subject to random fluctuations that may arise due to machine breakdowns, strikes, embargoes, etc. It is assumed that the inventory manager deals with two suppliers who may be either individually ON (available) or OFF (unavailable). Each supplier's availability is modeled as a semi-Markov (alternating renewal) process. We assume that the durations of the ON periods for the two suppliers are distributed as Erlang random variables. The OFF periods for each supplier have a general distribution. In analogy with queuing notation, we call this an Es1[Es2]/G1[G2] system. Since the resulting stochastic process is non-Markovian, we employ the "method of stages" to transform the process into a Markovian one, albeit at the cost of enlarging the state space. We identify the regenerative cycles of the inventory level process and use the renewal reward theorem to form the long-run average cost objective function. Finite time transition functions for the semi-Markov process are computed numerically using a direct method of solving a system of integral equations representing these functions. A detailed numerical example is presented for the E2[E2]/M[M] case. Analytic solutions are obtained for the particular case of "large" (asymptotic) order quantity, in which case the objective function assumes a very simple form that can be used to analyze the optimality conditions. The paper concludes with the discussion of an alternative inventory policy for modeling the random supply availability problem.
Open Access
Investigation of the inaccuracy of the MFIE discretized with the RWG basis functions
(IEEE, 2004-06) Ergül, Özgür; Gürel, Levent
The inaccuracy of the magnetic-field integral equation (MFIE) discretized with the Rao-Wilton-Glisson (RWG) basis functions is discussed. The electric-field integral equation (EFIE) gives accurate results with the usage of RWG basis functions for the conducting surfaces with arbitrary planar triangulations. Two reasons i.e., logarithmic singularity in the field integration and solid angle expression in the MFIE, that lead to inaccuracy of the MFIE, are also discussed. It is found that the current distribution and the radar cross section (RCS) obtained by the MFIE does not perfectly match their counterparts obtained by the EFIE.
Open Access
Joint source-channel coding and guessing
(IEEE, 1997-06-07) Arıkan, Erdal; Merhav, N.
We consider the joint source-channel guessing problem, define measures of optimum performance, and give single-letter characterizations. As an application, sequential decoding is considered.
Open Access
Language evolution and information theory
(IEEE, 2004-06-07) Ahlswede, R.; Arıkan, Erdal; Bäumer, L.; Deppe, C.
The use of Nowak's model to study the language evolution and to settle a conjecture by Nowak was discussed. These models explained the ways by which natural selection can lead to the gradual emergence of human language. It was shown that the Nowak's conjecture is true for a class of spaces defined by a certain condition on the distance function. A connection between Nowak's model and standard information-theoretic models was indicated.
Open Access
Marginal allocation algorithm for nonseparable functions
(Taylor & Francis, 1999) Yüceer, Ü.
Marginal allocation algorithm is implemented to discrete allocation problems with nonseparable objective functions subject to a single linear constraint. A Lagrangian analysis shows that the algorithm generates a sequence of undominated allocations under the condition of discretely convex objective functions and Lagrangian functions. The case of separable functions is proven to be a special case. An application is provided to illustrate the method and various size randomly chosen problems are run to demonstrate the efficiency of the marginal allocation algorithm.
Open Access
Minimizing Lmax for the single machine scheduling problem with family set-ups
(Taylor & Francis, 2004) Schultz, S. R.; Hodgson, T. J.; King, R. E.; Taner, M. R.
A procedure for the single machine-scheduling problem of minimizing the maximum lateness for jobs with sequence independent set-ups is presented. The procedure provides optimal/near-optimal solutions over a wide range of problems. It performs well compared with other heuristics, and it is effective in finding solutions for large problems.
Open Access
New characterizations of ℓ1 solutions to overdetermined systems of linear equations
(Elsevier, 1994) Madsen, K.; Nielsen H. B.; Pınar, M. Ç.
New characterizations of the ℓ1 solutions to overdetermined system of linear equations are given. The first is a polyhedral characterization of the solution set in terms of a special sign vector using a simple property of the ℓ1 solutions. The second characterization is based on a smooth approximation of the ℓ1 function using a "Huber" function. This allows a description of the solution set of the ℓ1 problem from any solution to the approximating problem for sufficiently small positive values of an approximation parameter. A sign approximation property of the Huber problem is also considered and a characterization of this property is given. © 1994.