This thesis aims to predict the probable undiscovered geothermal systems through investigation of spatial relation between geothermal occurrences and its surrounding geological phenomenon in Western Anatolia. In this context, four different public data, which are epicenter map, lineament map, Bouger gravity anomaly and magnetic anomaly maps, are utilized. In order to extract the necessary information for each map layer the raw public data is converted to a synthetic data which are directly used in the analysis. Synthetic data employed during the investigation process include Gutenberg-Richter b-value map, distance to lineaments map and distance to major grabens present in the area. Thus, these three layers including directly used magnetic anomaly maps are combined by means of Boolean logic model and Weights of Evidence method (WofE), which are multicriteria decision methods, in a Geographical Information System (GIS) environment. Boolean logic model is based on the simple logic of Boolean operators, while the WofE model depends on the Bayesian probability. Both of the methods use binary maps for their analysis. Thus, the binary map classification is the key point of the analysis. In this study three different binary map classification techniques are applied and thus three output maps were obtained for each of the method. The all resultant maps are evaluated within and among the methods by means of success indices. The findings reveal that the WofE method is better predictor than the Boolean logic model and that the third binarization approach, which is named as optimization procedure in this study, is the best estimator of binary classes due to obtained success indices. Finally, three output maps of each method are combined and the favorable areas in terms of geothermal potential are produced. According to the final maps the potential sites appear to be Aydin, Denizli and Manisa, of which first two have been greatly explored and exploited since today and thus not surprisingly found as potential in the output maps, while Manisa when compared to first two is nearly virgin.

This dissertation deals with some crucial building blocks of cryptosystems in symmetric cryptography / namely the Boolean functions that produce a single-bit result for each possible value of the m-bit input vector, where m&gt / 1. Objectives in this study are two-fold / the first objective is to develop relations between cryptographic properties of Boolean functions, and the second one is to form new concepts that associate coding theory with cryptology. For the first objective, we concentrate on the cryptographic properties of Boolean functions such as balancedness, correlation immunity, nonlinearity, resiliency and propagation characteristics / many of which are depending on the Walsh spectrum that gives components of the Boolean function along the direction of linear functions. Another efficient tool to study Boolean functions is the subject of covering sequences introduced by Carlet and Tarannikov in 2000. Covering sequences are defined in terms of the derivatives of the Boolean function. Carlet and Tarannikov relate the correlation immunity and balancedness properties of the Boolean function to its covering sequences. We find further relations between the covering sequence and the Walsh spectrum, and present two theorems for the calculation of covering sequences associated with each null frequency of the Walsh spectrum. As for the second objective of this thesis, we have studied linear codes over the rings Z4 and Z8 and their binary images in the Galois field GF(2). We have investigated the best-known examples of nonlinear binary error-correcting codes such as Kerdock, Preperata and Nordstrom-Robinson, which are -linear codes. We have then reviewed Tokareva&rsquo / s studies on Z4-linear codes and extended them to Z8-linear codes. We have defined a new classes of bent functions. Next, we have shown that the newly defined classes of bent, namely Tokareva&rsquo / s k-bent and our t,k-bent functions are affine equivalent to the well-known Maiorana McFarland class of bent functions. As a cryptological application, we have described the method of cubic cryptanalysis, as a generalization of the linear cryptanalysis given by Matsui in 1993. We conjecture that the newly introduced t,k-bent functions are also strong against cubic cryptanalysis, because they are as far as possible to t,k-bent functions.

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In this dissertation, three different microfluidic devices with bioanalytical applications are presented. From chapter to chapter, the bioanalytical focus will gradually become the development of a point-of-care sensor platform able to yield a reliable and quantitative response in the presence of the desired target. The first device consists of photolithographically-patterned gold on glass bipolar electrodes and PDMS Y-shaped microchannels for the controlled enrichment, separation from a mixture, and delivery of two charged dyes into separate receiving microchannels. The principle for the permanent separation of these dyes is based on the concept of bipolar electrochemistry and depended on the balancing/unbalancing of convective and electromigrating forces caused by the application of a potential bias, as well as the activation/deactivation of the bipolar electrodes. Two different bipolar electrode configurations are described and fluorescence is used to optimize their efficiency, speed, and cleanliness of delivery. The second device is a DNA sensor fabricated on paper by wax printing and folding to form 3D channels. DNA is detected by strand-displacement induced fluorescence of a single-stranded DNA. A multiplexed version of this sensor is also shown where the experiment results in “OR” and “AND” Boolean logic gate operations. In addition, the nonspecific adsorption of the reagents to cellulose is studied, demonstrating that significant reduction of nonspecific adsorption and increased sensitivity can be achieved by pre-treating the substrate with bovine serum albumin and by preparing all analyte solutions with spectator DNA. The third device, also made of paper, has a novel design and uses a versatile electrochemical detection method for the indirect detection of analytes via the direct detection of AgNP labels. A proof-of-concept experiment is shown where streptavidin-coated magnetic microbeads and biotin-coated AgNPs are used to form a composite model analyte. The paper device, called oSlip, and electrochemical method used are easily coupled so the resulting sensor has a simple user-device interface. LODs of 767 fM are achieved while retaining high reproducibility and efficiency. The fourth device is the updated version of the oSlip. In this case, the objective is to show the current progress and limitations in the detection of real analytes using the oSlip device. A sandwich-type immunoassay approach is used to detect human chorionic gonadotrophin (pregnancy hormone) present in human urine. Various optimization steps are performed to obtain the ideal reagent concentrations and incubation time necessary to form the immunocomposite in one step, that is, by mixing all reagents at the same time in the oSlip. Additionally, improvements to the electrochemical detection step are demonstrated. / text

Pattern discovery in large binary relations has been extensively studied. An emblematic success in this area concerns frequent itemset mining and its post-processing that derives association rules. In this case, we mine binary relations that encode whether some properties are satisfied or not by some objects. It is however clear that many datasets correspond to n-ary relations where n > 2. For example, adding spatial and/or temporal dimensions (location and/or time when the properties are satisfied by the objects) leads to the 4-ary relation Objects x Properties x Places x Times. Therefore, we study the generalization of association rule mining within arbitrary n-ary relations: the datasets are now Boolean tensors and not only Boolean matrices. Unlike standard rules that involve subsets of only one domain of the relation, in our setting, the head and the body of a rule can include arbitrary subsets of some selected domains. A significant contribution of this thesis concerns the design of interestingness measures for such generalized rules: besides a frequency measures, two different views on rule confidence are considered. The concept of non-redundant rules and the efficient extraction of the non-redundant rules satisfying the minimal frequency and minimal confidence constraints are also studied. To increase the subjective interestingness of rules, we then introduce disjunctions in their heads. It requires to redefine the interestingness measures again and to revisit the redundancy issues. Finally, we apply our new rule discovery techniques to dynamic relational graph analysis. Such graphs can be encoded into n-ary relations (n ≥ 3). Our use case concerns bicycle renting in the Vélo'v system (self-service bicycle renting in Lyon). It illustrates the added-value of some rules that can be computed thanks to our software prototypes.

Boolean functions are accepted to be cryptographically strong if they satisfy some common pre-determined criteria. It is expected that any design criteria should remain invariant under a large group of transformations due to the theory of similarity of secrecy systems proposed by Shannon. One of the most important design criteria for cryptographically strong Boolean functions is the nonlinearity criterion. Meier and Staffelbach studied nonlinearity preserving transformations, by considering the invertible transformations acting on the arguments of Boolean functions, namely the pre-transformations. In this thesis, first, the results obtained by Meier and Staffelbach are presented. Then, the invertible transformations acting on the truth tables of Boolean functions, namely the post-transformations, are studied in order to determine whether they keep the nonlinearity criterion invariant. The equivalent counterparts of Meier and Staffelbach&rsquo / s results are obtained in terms of the post-transformations. In addition, the existence of nonlinearity preserving post-transformations, which are not equivalent to pre-transformations, is proved. The necessary and sufficient conditions for an affine post-transformation to preserve nonlinearity are proposed and proved. Moreover, the sufficient conditions for an non-affine post-transformation to keep nonlinearity invariant are proposed. Furthermore, it is proved that the smart hill climbing method, which is introduced to improve nonlinearity of Boolean functions by Millan et. al., is equivalent to applying a post-transformation to a single Boolean function. Finally, the necessary and sufficient condition for an affine pre-transformation to preserve the strict avalanche criterion is proposed and proved.

A Boolean function can be represented in several different forms. These different representation have advantages and disadvantages of their own. The Algebraic Normal Form, truth table, and Walsh spectrum representations are widely studied in literature. In 1999, Claude Carlet and Phillippe Guillot introduced the Numerical Normal Form. NumericalNormal Form(NNF) of a Boolean function is similar to Algebraic Normal Form, with integer coefficients instead of coefficients from the two element field. Using NNF representation, just like the Walsh spectrum, characterization of several cryptographically important functions, such as resilient and bent functions, is possible. In 2002, Carlet had shown several divisibility results concerning resilient and correlation-immune functions using NNF. With these divisibility results, Carlet is able to give bounds concerning nonlinearity of resilient and correlation immune functions. In this thesis, following Carlet and Guillot, we introduce the Numerical Normal Form and derive the pairwise relations between the mentioned representations. Characterization of Boolean, resilient and bent functions using NNF is also given. We then review the divisibility results of Carlet, which will be linked to some results on the nonlinearity of resilient and correlation immune functions. We show the M&ouml / bius inversion properties of NNF of a Boolean function, using Gian-Carlo Rota&rsquo / s work as a guide. Finally, using a lot of the mentioned results, we prove a necessary condition on theWalsh spectrum of Boolean functions with given degree.

In cryptography especially in block cipher design, Boolean functions are the basic elements. A cryptographic function should have high nonlinearity as it can be attacked by linear attack. In this thesis the highest possible nonlinear boolean functions in the even dimension, that is bent functions, basic properties and construction methods of bent functions are studied. Also normal bent functions and generalized bent functions are presented.

The aim of the research presented in this thesis is to investigate the use of various optimisation heuristics in the fields of automated cryptanalysis and automated cryptographic function generation. These techniques were found to provide a successful method of automated cryptanalysis of a variety of the classical ciphers. Also, they were found to enhance existing fast correlation attacks on certain stream ciphers. A previously proposed attack of the knapsack cipher is shown to be flawed due to the absence of a suitable solution evaluation mechanism. Finally, a new approach for finding highly nonlinear Boolean functions is introduced.

This thesis is divided into two parts. In the first part we describe a new Monte Carlo algorithm for the consistent and unbiased estimation of multidimensional integrals and the efficient sampling from multidimensional densities. The algorithm is inspired by the classical splitting method and can be applied to general static simulation models. We provide examples from rare-event probability estimation, counting, optimization, and sampling, demonstrating that the proposed method can outperform existing Markov chain sampling methods in terms of convergence speed and accuracy. In the second part we present a new adaptive kernel density estimator based on linear diffusion processes. The proposed estimator builds on existing ideas for adaptive smoothing by incorporating information from a pilot density estimate. In addition, we propose a new plug-in bandwidth selection method that is free from the arbitrary normal reference rules used by existing methods. We present simulation examples in which the proposed approach outperforms existing methods in terms of accuracy and reliability.