Business Information Management - Closed

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    A method of systematic search for optimal multipliers in congruential random number generators
    (Springer Netherlands, 2004) Sezgin, F.
    This paper presents a method of systematic search for optimal multipliers for congruential random number generators. The word-size of computers is a limiting factor for development of random numbers. The generators for computers up to 32 bit word-size are already investigated in detail by several authors. Some partial works are also carried out for moduli of 248 and higher sizes. Rapid advances in computer technology introduced recently 64 bit architecture in computers. There are considerable efforts to provide appropriate parameters for 64 and 128 bit moduli. Although combined generators are equivalent to huge modulus linear congruential generators, for computational efficiency, it is still advisable to choose the maximum moduli for the component generators. Due to enormous computational price of present algorithms, there is a great need for guidelines and rules for systematic search techniques. Here we propose a search method which provides 'fertile' areas of multipliers of perfect quality for spectral test in two dimensions. The method may be generalized to higher dimensions. Since figures of merit are extremely variable in dimensions higher than two, it is possible to find similar intervals if the modulus is very large.
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    Distribution of lattice points
    (Springer Wien, 2006) Sezgin, F.
    We discuss the lattice structure of congruential random number generators and examine figures of merit. Distribution properties of lattice measures in various dimensions are demonstrated by using large numerical data. Systematic search methods are introduced to diagnose multiplier areas exhibiting good, bad and worst lattice structures. We present two formulae to express multipliers producing worst and bad laice points. The conventional criterion of normalised lattice rule is also questioned and it is shown that this measure used with a fixed threshold is not suitable for an effective discrimination of lattice structures. Usage of percentiles represents different dimensions in a fair fashion and provides consistency for different figures of merits.
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    Density of Western loan-words in Turkish
    (Harvard University * Near Eastern Languages and Civilizations, 2006) Sezgin, F.
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    On the statistical Analysis of Feigenbaum Constants
    (Elsevier, 2006-11) Sezgin, F.; Sezgin, T. M.
    We present statistical analysis of blocks in the binary expansions of Feigenbaum constants a and d for the logistic map. The analysis is carried out on both 1016 and 3400 bit expansions. A w2 test is applied for lumping data and a serial test is applied on gliding data. Contrary to a previous research by Karamanos and Kotsireas, our test results did not indicate any evidence to reject randomness of these constants. Additional 25 randomness tests also support the conjecture of randomness of these constants having transcendental character.
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    ItemOpen Access
    E-Öğrenme güncesi: dil öğreniminde öğrencinin inisiyatif kullanmasını arttırmaya yönelik bir araç
    (Türk Eğitim Derneği İktisadi İşletmesi, 2007) Yumuk-Şengül, Ayşe
    This study aims to explore the extent to which e-learning journals stimulate learner control over the language learning process through critical reflection on the process itself. The study involved 71 first-year non-native English-speaking students taking a two-semester “Text and Composition” course at the Department of Translation and Interpretation (English-French-Turkish) at a four-year English medium university in Turkey. The data were collected through e-learning journals, post-course interviews and post-course questionnaires. The results indicated that e-learning journals encouraged learners to reflect critically on their learning, resulting in increased learner control over the language learning process. Moreover, e-learning journals promoted positive change in the attitudes of the learners towards using more ICT (Information and Communication Technologies) in the language learning process.
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    Geometric random inner product test and randomness of π
    (World Scientific Publishing Co. Pte. Ltd., 2009) Sezgin, F.
    The Geometric Random Inner Product (GRIP) is a recently developed test method for randomness. As a relatively new method, its properties, weaknesses, and strengths are not well documented. In this paper, we provide a rigorous discussion of what the GRIP test measures, and point out specific classes of defects that it is able to diagnose. Our findings show that the GRIP test successfully detects series that have regularities in their first- or second-order differences, such as the Weyl and nested Weyl sequences. We compare and contrast the GRIP test to some of the existing conventional methods and show that it is particularly successful in diagnosing deficient random number generators with bad lattice structures and short periods. We also present an application of the GRIP test to the decimal digits of π.
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    Number guessing
    (Australian Association of Mathematics Teachers Inc., 2009) Sezin, F.; Sezgin, F.
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    Finding the best portable congruential random number generators
    (Elsevier, 2013-08) Sezgin, F.; Sezgin, T. M.
    Linear congruential random number generators must have large moduli to attain maximum periods, but this creates integer overflow during calculations. Several methods have been suggested to remedy this problem while obtaining portability. Approximate factoring is the most common method in portable implementations, but there is no systematic technique for finding appropriate multipliers and an exhaustive search is prohibitively expensive. We offer a very efficient method for finding all portable multipliers of any given modulus value. Letting M = AB+C, the multiplier A gives a portable result if B-C is positive. If it is negative, the portable multiplier can be defined as A = left perpendicularM/Brightperpendicular. We also suggest a method for discovering the most fertile search region for spectral top-quality multipliers in a two-dimensional space. The method is extremely promising for best generator searches in very large moduli: 64-bit sizes and above. As an application to an important and challenging problem, we examined the prime modulus 2(63)-25, suitable for 64-bit register size, and determined 12 high quality portable generators successfully passing stringent spectral and empirical tests.