Browsing by Subject "Boolean functions"

Now showing 1 - 9 of 9

Open Access
Automatic detection of geospatial objects using multiple hierarchical segmentations
(Institute of Electrical and Electronics Engineers, 2008-07) Akçay, H. G.; Aksoy, S.
The object-based analysis of remotely sensed imagery provides valuable spatial and structural information that is complementary to pixel-based spectral information in classification. In this paper, we present novel methods for automatic object detection in high-resolution images by combining spectral information with structural information exploited by using image segmentation. The proposed segmentation algorithm uses morphological operations applied to individual spectral bands using structuring elements in increasing sizes. These operations produce a set of connected components forming a hierarchy of segments for each band. A generic algorithm is designed to select meaningful segments that maximize a measure consisting of spectral homogeneity and neighborhood connectivity. Given the observation that different structures appear more clearly at different scales in different spectral bands, we describe a new algorithm for unsupervised grouping of candidate segments belonging to multiple hierarchical segmentations to find coherent sets of segments that correspond to actual objects. The segments are modeled by using their spectral and textural content, and the grouping problem is solved by using the probabilistic latent semantic analysis algorithm that builds object models by learning the object-conditional probability distributions. The automatic labeling of a segment is done by computing the similarity of its feature distribution to the distribution of the learned object models using the Kullback-Leibler divergence. The performances of the unsupervised segmentation and object detection algorithms are evaluated qualitatively and quantitatively using three different data sets with comparative experiments, and the results show that the proposed methods are able to automatically detect, group, and label segments belonging to the same object classes. © 2008 IEEE.
Open Access
Boolean normal forms, shellability, and reliability computations
(Society for Industrial and Applied Mathematics, 2000) Borgs, E.; Crama, Y.; Ekin, O.; Hammer, P.L.; Ibaraki, T.; Kogan, A.
Orthogonal forms of positive Boolean functions play an important role in reliability theory, since the probability that they take value 1 can be easily computed. However, few classes of disjunctive normal forms are known for which orthogonalization can be efficiently performed. An interesting class with this property is the class of shellable disjunctive normal forms (DNFs). In this paper, we present some new results about shellability. We establish that every positive Boolean function can be represented by a shellable DNF, we propose a polynomial procedure to compute the dual of a shellable DNF, and we prove that testing the so-called lexico-exchange (LE) property (a strengthening of shellability) is NP-complete.
Open Access
Design and fabrication of CSWAP gate based on nano-electromechanical systems
(Springer, Cham, 2016) Yüksel, Mert; Erbil, Selçuk Oğuz; Arı, Atakan B.; Hanay, M. Selim
In order to reduce undesired heat dissipation, reversible logic offers a promising solution where the erasure of information can be avoided to overcome the Landauer limit. Among the reversible logic gates, Fredkin (CSWAP) gate can be used to compute any Boolean function in a reversible manner. To realize reversible computation gates, Nano-electromechanical Systems (NEMS) offer a viable platform, since NEMS can be produced en masse using microfabrication technology and controlled electronically at high-speeds. In this work-in-progress paper, design and fabrication of a NEMS-based implementation of a CSWAP gate is presented. In the design, the binary information is stored by the buckling direction of nanomechanical beams and CSWAP operation is accomplished through a mechanism which can selectively allow/block the forces from input stages to the output stages. The gate design is realized by fabricating NEMS devices on a Silicon-on-Insulator substrate. © Springer International Publishing Switzerland 2016.
Open Access
Downlink beamforming under individual SINR and per antenna power constraints
(IEEE, 2007-08) Yazarel, Y. K.; Aktaş, Defne
In this paper we consider the problem of finding the optimum beamforming vectors for the downlink of a multiuser system, where there are individual signal to interference plus noise ratio (SINR) targets for each user. Majority of the previous work on this problem assumed a total power constraint on the base stations. However, since each transmit antenna is limited by the amount of power it can transmit due to the limited linear region of the power amplifliers, a more realistic constraint is to place a limit on the per antenna power. In a recent work, Yu and Lan proposed an iterative algorithm for computing the optimum beamforming vectors minimizing the power margin over all antennas under individual SINR and per antenna power constraints. However, from a system designer point of view, it may be more desirable to minimize the total transmit power rather than minimizing the power margin, especially when the system is not symmetric. Reformulating the transmitter optimization problem to minimize the total transmit power subject to individual SINR constraints on the users and per antenna power constraints on the base stations, the algorithm proposed by Yu and Lan is modified. Performance of the modified algorithm is compared with existing methods for various cellular array scenarios. ©2007 IEEE.
Open Access
Efficient solution of the combined-field integral equation with the parallel multilevel fast multipole algorithm
(IEEE, 2007-08) Gürel, Levent; Ergül, Özgür
We present fast and accurate solutions of large-scale scattering problems formulated with the combined-field integral equation. Using the multilevel fast multipole algorithm (MLFMA) parallelized on a cluster of computers, we easily solve scattering problems that are discretized with tens of millions of unknowns. For the efficient parallelization of MLFMA, we propose a hierarchical partitioning scheme based on distributing the multilevel tree among the processors with an improved load-balancing. The accuracy of the solutions is demonstrated on scattering problems involving spheres of various radii from 80λ to 110λ. In addition to canonical problems, we also present the solution of real-life problems involving complicated targets with large dimensions. © 2007 IEEE.
Open Access
Exploiting linearity of modular multiplication
(Springer, 2020) Yıldırım, Hamdi Murat
The XOR Open image in new window and the addition ⊞⊞ operations have been widely used as building blocks for many cryptographic primitives. These operations and the multiplication ⊙⊙ operation are successively used in the design of IDEA and the MESH block ciphers. This work presents several interesting algebraic properties of the multiplication operation. By fixing one operand, we obtain vector valued function ggZggZ on Zn2Z2n, associated with ⊙⊙. In this paper we show that the nonlinearity of ggZggZ remains the same under some transformations of Z and moreover we give an upper bound for the nonlinearity of ggZggZ when Z is a power of 2. Under weak-key assumptions, we furthermore present a list of new linear relations for 1-round IDEA cipher, some of directly derived and others algorithmically generated using these relations and known ones. We extend the largest linear weak key class for IDEA cipher with size 223223 to derive such a class with sizes 224224. Under the independent key subblocks (subkeys) and weak-key assumptions we derive many linear relations for IDEA cipher using linear relations for 1-round IDEA cipher.
Open Access
FPTAS for half-products minimization with scheduling applications
(Elsevier, 2008) Erel, E.; Ghosh, J. B.
A special class of quadratic pseudo-boolean functions called "half-products" (HP) has recently been introduced. It has been shown that HP minimization, while NP-hard, admits a fully polynomial time approximation scheme (FPTAS). In this note, we provide a more efficient FPTAS. We further show how an FPTAS can also be derived for the general case where the HP function is augmented by a problem-dependent constant and can justifiably be assumed to be nonnegative. This leads to an FPTAS for certain partitioning type problems, including many from the field of scheduling.
Open Access
Memory-efficient multilevel physical optics algorithm for fast computation of scattering from three-dimensional complex targets
(IEEE, 2007) Manyas, Alp; Gürel, Levent
Multilevel 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.
Open Access
Solution of large-scale scattering problems with the multilevel fast multipole algorithm parallelized on distributed-memory architectures
(IEEE, 2007) Ergül, Özgür; Gürel, Levent
We present the solution of large-scale scattering problems involving three-dimensional closed conducting objects with arbitrary shapes. With an efficient parallelization of the multilevel fast multipole algorithm on relatively inexpensive computational platforms using distributed-memory architectures, we perform the iterative solution of integral-equation formulations that are discretized with tens of millions of unknowns. In addition to canonical problems, we also present the solution of real-life problems involving complicated targets with large dimensions.