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We study the tandem duplication distance between binary sequences and their roots. In other words, the quantity of interest is the number of tandem duplication operations of the form $ {x}_{} = {a}_{} {b}_{} {c}_{} \to {y}_{} = {a}_{} {b}_{} {b}_{} {c}_{}$ , where $ {x}_{}$ and $ {y}_{}$ are sequences and $ {a}_{}$ , $ {b}_{}$ , and $ {c}_{}$ are their substrings, needed to generate a binary...
Graph matching is the task of computing the resemblance of graphs. While in exact matching, a strict one-to-one correspondence should exist between two graphs or among their subgraphs, on the other hand in error-tolerant matching a strict correspondence is not necessary, and some similarity measure should be exhibited between two graphs or their subgraph depending on some tolerance value or noise...
In the paper a novelty fractional-order backward difference is proposed. On the basis of the classical first-order backward difference and its generalization into the fractional-order case we introduce a constant parameter a which essentially influences the differentiation action. This novelty fractional-order backward difference will be further named as a-difference. Its fundamental properties are...
Eye movement detection is one of the most developed technologies in the field of human and computer interaction especially as a control instrument of an automatic device. Eye movement of user can provide an easy input source, natural and high-bandwidth. By tracking the user's point of view, the ease of communication from the user to the automatic device can be improved. In general, the process of...
The paper considers a class of symmetric Boolean functions called Reed-Muller type Fundamental Symmetric Functions, it reviews some of their properties and presents some new ones. The main contribution of the paper is a proof that the Reed-Muller transform of a symmetric Boolean function is also symmetric and that of a rotation symmetric Boolean function is also rotation symmetric. Since symmetric...
A cyclic proof system, called CLKID-omega, gives us another way of representing inductive definitions and efficient proof search. The 2011 paper by Brotherston and Simpson showed that the provability of CLKID-omega includes the provability of the classical system of Martin-Lof's inductive definitions, called LKID, and conjectured the equivalence. By this year the equivalence has been left an open...
System of symmetric ternary functions was brought to the new forms. Several systems of functions based on symmetric ternary functions were developed. All developed systems of functions were tested for possibility of being applied for representation of information flows using orthogonal transforms. An orthogonal system of functions based on symmetric ternary functions was developed and proved to be...
This paper highlights a fixed point theorem on the subset constructed by growing d-dimensional Apollonian graph sequence, for any d from N\{0, 1}. We base our paper on a weighted graph edit distance constructing a metric space on the set of high dimensional Apollonian networks. The main result of this paper shows that we can select a subset of a growing graph sequence on the set of d-dimensional Apollonian...
The Reed-Muller-Fourier transform, defined in a q-valued domain, is applied to obtain two-sided spectra of classes of matrices, which may be interpreted as representing pixels of pictures or patterns. Operations on matrices, representing operations on pictures are considered, and their effect in the spectral domain is analyzed. It is shown that the transform is very effective to calculate the spectrum...
It has long been known that some transformationsof the Boolean functions affect only the permutation of somesubset of coefficients in the Walsh-Hadamard spectrum or justchange the sign of some coefficients. These operations are knownas spectral invariant operations. It exists a generalization of theseinvariant operations for multi-valued functions and Vilenkin-Chrestenson spectrum. Here some new spectral...
Bent functions generalized to the alphabet Zq, the ring of integers modulo q, are interesting not just in the realm of multiple-valued functions, but have some applications in the binary environment. The case q = 4, i.e., quaternary bent functions, are of a particular interest due to a simple relationship to binary functions. We consider the possibilities for characterization of quaternary bent functions...
Applications of pattern recognition, design of faulttolerant systems and communications have key problems that arenaturally described by partially defined (incompletely defined)discrete functions. Such partially defined functions arising frompractical demands usually have a large number of variables andso their direct implementations require complex systems. Thusit is important to have at hand an...
The operations ofexpansion and refinement on non-deterministic matrices(Nmatrices) are composed to form a new operation called rexpansion. Properties of this operation are investigated, together with their effects on the induced consequence relations. A semantic method for obtaining conservative extensions of matrix-defined logics is introduced and applied to fragments of the classical two-valued...
Relevance measure in both homogeneous and heterogeneous networks has been extensively studied. However, how to measure the relevance among different-typed objects in weighted signed heterogeneous information networks remains an open problem. It is challenging to incorporate both positive and negative multi-typed relationships simultaneously in signed heterogeneous networks due to the opposite opinions...
To better exploit spatial correlations in a video frame, the HEVC video coding standard has introduced many intra prediction modes and a recursive quadtree-based coding unit (CU) structure. As a result, the complexity of Rate-distortion optimized (RDO) HEVC intra mode selection is significantly higher. Many techniques have been proposed to expedite the intra mode selection process to achieve a good...
A new spatial domain steganography method for the grayscale image is presented in this paper. The method has used neighboring pixel pair difference value and Least Significant Bit (LSB) substitution, which provides enhanced embedding capacity. This method uses a 3×3 block structure to divide the cover image into some non-overlapping blocks horizontally. k-LSBs of the center pixel of the cover image...
Traditional password conversion scheme for user authentication is to transform the passwords into hash values. These hash-based password schemes are comparatively simple and fast because those are based on text and famed cryptography. However, those can be exposed to cyber-attacks utilizing password by cracking tool or hash-cracking online sites. Attackers can thoroughly figure out an original password...
In this paper, a novel local relative phase binary pattern (LRPBP) method is proposed based on LBP and relative phase for extracting texture features. In LRPBP, an image will be firstly processed through Gabor transform. And then the relative phase information of the image is extracted in the complex transform domain of Gabor. Finally, the texture feature of the image is constructed via calculating...
Cluster Deletion (CD) problem asks to transform a given graph into a cluster graph by at most k edge deletions. CD is a combinatorial problem arising in the field of classification. In this paper, we introduce a graph transformation which enabled the identification of new polynomially solvable classes of CD problem. We show that if a graph is K3-free or (diamond, kite, house, xbanner)-free then cluster...
Geometrical warp model for alignment is a key issue in image stitching. For robustness, most of the commercial tools for stitching use global parametric warps to bring image into alignment, which is suitable for ideal imaging conditions that the images to be stitched differ purely by rotation or the imaged scene is purely planar. When such conditions are violated alignment artifacts or “ghosting”...
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