Showing papers on "Logical matrix published in 2002"

A secure data hiding scheme for binary images

Abstract: This letter presents a novel steganography scheme capable of concealing a piece of critical information in a host message which is a binary image (e.g., a facsimile). A binary matrix and a weight matrix are used as secret keys to protect the hidden information. Given a host image of size m/spl times/n, the proposed scheme can conceal as many as /spl lfloor/log/sub 2/ (mn+1)/spl rfloor/ bits of data in the image by changing, at most, two bits in the host image. This scheme can provide a higher security, embed more information, and maintain a higher quality of the host image than available schemes.

On the complexity of generating maximal frequent and minimal infrequent sets

Abstract: Let A be an m x n binary matrix, t E {1,…,m} be a threshold, and e > 0 be a positive parameter. We show that given a family of O(n e ) maximal t-frequent column sets for A, it is NP-complete to decide whether A has any further maximal t-frequent sets, or not, even when the number of such additional maximal t-frequent column sets may be exponentially large. In contrast, all minimal t-infrequent sets of columns of A can be enumerated in incremental quasi-polynomial time. The proof of the latter result follows from the inequality a < (m-t+1)β, where a and β are respectively the numbers of all maximal t-frequent and all minimal t-infrequent sets of columns of the matrix A. We also discuss the complexity of generating all closed t-frequent column sets for a given binary matrix.

On the Complexity of Generating Maximal Frequent and Minimal Infrequent Sets

Abstract: Let A be an m × n binary matrix, t ? {1, ..., m} be a threshold, and ? > 0 be a positive parameter. We show that given a family of O(n?) maximal t-frequent column sets for A, it is NP-complete to decide whether A has any further maximal t-frequent sets, or not, even when the number of such additional maximal t-frequent column sets may be exponentially large. In contrast, all minimal t-infrequent sets of columns of A can be enumerated in incremental quasi-polynomial time. The proof of the latter result follows from the inequality ? ? (m-t+1)s, where ? and s are respectively the numbers of all maximal t-frequent and all minimal t-infrequent sets of columns of the matrix A. We also discuss the complexity of generating all closed t-frequent column sets for a given binary matrix.

Random binary matrices in biogeographical ecology—Instituting a good neighbor policy

Abstract: Binary matrices originating from presence/absence data on species (rows) distributed over sites (columns) have been a subject of much controversy in ecological biogeography Under the null hypothesis that every matrix is equally likely, the distributions of some test statistics measuring co-occurrences between species are sought, conditional on the row and column totals being fixed at the values observed for some particular matrix Many ad hoc methods have been proposed in the literature, but at least some of them do not provide uniform random samples of matrices In particular, some “swap” algorithms have not accounted for the number of neighbors each matrix has in the universe of matrices with a set of fixed row and column sums We provide a Monte-Carlo method using random walks on graphs that gives correct estimates for the distributions of statistics We exemplify its use with one statistic

LU-decomposition and numerical structure for solving large sparse nonsymmetric linear systems

Abstract: In this work, the solution of a large sparse linear system of equations with an arbitrary sparsity pattern is obtained by using LU -decomposition method as well as numerical structure approach. The LU -decomposition method is based on Doolittle's method while the numerical structure approach is based on Cramer's rule. The numerical structure approach produces direct solution without facing fill-in problems as encountered in LU -decomposition. In order to reduce the ‘fill-ins’ in the decomposition, the powers of a Boolean matrix, obtained from the coefficient matrix A are taken so that the ‘fill-ins’ in the structure of A can be known in advance. The position of fill-ins in A are thus determined in the best choice manner, that is, it is very effective and memory-wise cheap. We also outline a method by using numerical structure with reduced computation efforts. Finally, experiments are performed on eight examples to compare the efficiency of the proposed methods. The results obtained are reported in a table. It is found that the LU -decomposition method is much better than numerical structure. The usefulness of numerical structure approach is also discussed.

Exact minimisation of large multiple output FPRM functions

Abstract: The properties of the polarity for sum-of-products (SOP) expressions of Boolean functions are formally investigated. A transform matrix S is developed to convert SOP expressions from one polarity to another polarity. It is shown that the effect of SOP polarity is to reorder the on-set minterms of a Boolean function. Furthermore, the transform matrix P for fixed polarity Reed-Muller (FPRM) expressions for the conversion between two different polarities, based on the properties of SOP polarity, is achieved. Comparison of these two matrices shows that the Reed-Muller transform matrix P has a much more complex structure. Additionally, the best polarity of FPRM forms with the least on-set terms corresponds with the polarity of SOP forms with the best 'order' of the on-set minterms. Applying these algebraic properties of the transform matrix P, a fast algorithm is presented to obtain the best polarity of FPRM expressions for large multiple Output Boolean functions. The computation time is independent of the number of outputs. The developed program is tested oil common personal computers and the results for benchmark examples of up to 25 inputs and 29 outputs are presented.

A new approach to generate fixed-polarity Reed–Muller expansions for completely and incompletely specified functions

Abstract: Generally, the application of Exclusive-OR (ExOR) logic design suffers from a lack of straightforward methods. In this paper, based on the Boolean matrix representation, the author introduces a new approach associated with a fast, simple, straightforward and computationally effective algorithm to obtain the minimum Reed–Muller ExOR expansion with fixed polarity. The new algorithm can be applied to completely as well as incompletely specified functions and it applies no constraints on the number of variables within any given switching function. The proposed minimization approach is based on the Boolean matrix representation and minterm separation operation to generate a fixed polarity Reed–Muller expansion that has a minimum number of non-zero valued terms in the final expansion while having a minimum numberof total literals. This is done efficiently and directly without involving exhaustive search procedures. For the case of an incompletely specified function, the algorithm tries to deduce the best select...

Discrete Tomography: Reconstruction under Periodicity Constraints

Abstract: This paper studies the problem of reconstructing binary matrices that are only accessible through few evaluations of their discrete X-rays. Such question is prominently motivated by the demand in material science for developing a tool for the reconstruction of crystalline structures from their images obtained by high-resolution transmission electron microscopy. Various approaches have been suggested for solving the general problem of reconstructing binary matrices that are given by their discrete X-rays in a number of directions, but more work have to be done to handle the ill-posedness of the problem. We can tackle this ill-posedness by limiting the set of possible solutions, by using appropriate a priori information, to only those which are reasonably typical of the class of matrices which contains the unknown matrix that we wish to reconstruct. Mathematically, this information is modelled in terms of a class of binary matrices to which the solution must belong. Several papers study the problem on classes of binary matrices on which some connectivity and convexity constraints are imposed.We study the reconstruction problem on some new classes consisting of binary matrices with periodicity properties, and we propose a polynomial-time algorithm for reconstructing these binary matrices from their orthogonal discrete X-rays.

Mining WWW access sequence by matrix clustering

Abstract: Sequence pattern mining is one of the most important methods for mining WWW access log. The Apriori algorithm is well known as a typical algorithm for sequence pattern mining. However, it suffers from inherent difficulties in finding long sequential patterns and in extracting interesting patterns among a huge amount of results. This article proposes a new method for finding generalized sequence pattern by matrix clustering. This method decomposes a sequence into a set of sequence elements, each of which corresponds to an ordered pair of items. Then matrix clustering is applied to extract a cluster of similar sequences. The resulting sequence elements are composed into a generalized sequence. Our method is evaluated with practical WWW access log, which shows that it is practically useful in finding long sequences and in presenting the generalized sequence in a graph.

Logical measure: structure of logical formula

Abstract: The structure of logical and/or pseudo-logical formula is introduced. The structure of logical formula is its characteristic invariant to its functional realization ({0,1}-valued, many-valued and/or [0,1]-valued logical function). The Boolean algebra is defined on the set of all n-ary logical structures. The fundamental principle of structural functionality is introduced. A logical discrete Choquet integral is defined as [0,1]-valued logical and pseudo-logical function for AND operator defined as min function.

A Geometric Approach to Boolean Matrix Multiplication

Abstract: For a Boolean matrix D, let rD be the minimum number of rectangles sufficient to cover exactly the rectilinear region formed by the 1-entries in D. Next, let mD be the minimum of the number of 0-entries and the number of 1-entries in D.Suppose that the rectilinear regions formed by the 1-entries in two n × n Boolean matrices A and B totally with q edges are given. We show that in time O (q + min{rArB, n(n + rA), n(n + rB)}) one can construct a data structure which for any entry of the Boolean product of A and B reports whether or not it is equal to 1, and if so, reports also the so called witness of the entry, in time O(log q).As a corollary, we infer that if the matrices A and B are given as input, their product and the witnesses of the product can be computed in time O (n(n + min{rA, rB})). This implies in particular that the product of A and B and its witnesses can be computed in time Õ(n(n + min{mA, mB})).In contrast to the known sub-cubic algorithms for Boolean matrix multiplication based on arithmetic 0 - 1-matrix multiplication, our algorithms do not involve large hidden constants in their running time and are easy to implement.

CT3 as an Index of Knowledge Domain Structure: Distributions for Order Analysis and Information Hierarchies

Abstract: The problem with which this study is concerned is articulating all possible CT3 and KR21 reliability measures for every case of a 5x5 binary matrix (32,996,500 possible matrices). The study has three purposes. The first purpose is to calculate CT3 for every matrix and compare the results to the proposed optimum range of .3 to .5. The second purpose is to compare the results from the calculation of KR21 and CT3 reliability measures. The third purpose is to calculate CT3 and KR21 on every strand of a class test whose item set has been reduced using the difficulty strata identified by Order Analysis. The study was conducted by writing a computer program to articulate all possible 5 x 5 matrices. The program also calculated CT3 and KR21 reliability measures for each matrix. The nonparametric technique of Order Analysis was applied to two sections of test items to stratify the items into difficulty levels. The difficulty levels were used to reduce the item set from 22 to 9 items. All possible strands or chains of these items were identified so that both reliability measures (CT3 and KR21) could be calculated. One major finding of this study indicates that .3 to .5 is a desirable range for CT3 (cumulative p=.86 to p=.98) if cumulative frequencies are measured. A second major finding is that the KR21 reliability measure produced an invalid result more than half the time. The last major finding is that CT3, rescaled to range between 0 and 1, supports De Vellis' guidelines for reliability measures. The major conclusion is that CT3 is a better measure of reliability since it considers both inter- and intra-item variances.

The quantification of the relating degree of parts based on the fuzzy synthesizing evaluation method

Abstract: In the planning of a product's disassembly sequence, the difficulty of disassembly path analysis can be decreased extremely, when some components are disassembled as a sub-assembly at the same time. In order to decrease the complexity of disassembly analysis and achieve the auto-building of disassembly paths, the sub-assembly should be identified first. The concept of relating degree is put forward in this paper, and it is used as a measurement of sub-assemblies identification. The product relation matrix C/spl tilde/ is built based on the relating degree. It is possible for the sub-assemblies to be clustered according to the matrix by using a fuzzy clustering method. As some components are disassembled as a sub-assembly, the problem of combination explosion can also be solved efficiently.

Expansion in Terms of Power of a Small Parameter of the Maximum Rank Distribution of a Random Boolean Matrix

Abstract: The paper considers an N \times n matrix (N \ge n) over a field GF(2) that consists of random values with a distribution depending on a small parameter e. The expansion is found in terms of the power of the parameter e of the probability that the matrix rank is equal to n. Exact values of the first three coefficients are indicated.