Distance metric has a key role in many machine learning and computer vision algorithms so that choosing an appropriate distance metric has a direct effect on the performance of such algorithms. Recently, distance metric learning using labeled data or other available supervisory information has become a very active research area in machine learning applications. Studies in this area have shown that distance metric learning-based algorithms considerably outperform the commonly used distance metrics such as Euclidean distance. In the kernelized version of the metric learning algorithms, the data points are implicitly mapped into a new feature space using a non-linear kernel function. The associated distance metric is then learned in this new feature space. Utilizing kernel function improves the performance of pattern recognition algorithms, however choosing a proper kernel and tuning its parameter(s) are the main issues in such methods. Using of an appropriate composite kernel instead of a single kernel is one of the best solutions to this problem. In this research study, a multiple kernel is constructed using the weighted sum of a set of basis kernels. In this framework, we propose different learning approaches to determine the kernels weights. The proposed learning techniques arise from the distance metric learning concepts. These methods are performed within a semi supervised framework where different cost functions are considered and the learning process is performed using a limited amount of supervisory information. The supervisory information is in the form of a small set of SIMILARITY and/or disSIMILARITY PAIRS. We define four distance metric based cost functions in order to optimize the multiple kernel weight. In the first structure, the average distance between the SIMILARITY PAIRS is considered as the cost function. The cost function is minimized subject to maximizing of the average distance between the disSIMILARITY PAIRS. This is in fact, a commonly used goal in the distance metric learning problem. In the next structure, it is tried to preserve the topological structure of the data by using of the idea of graph Laplacian. For this purpose, we add a penalty term to the cost function which preserves the topological structure of the data. This penalty term is also used in the other two structures. In the third arrangement, the effect of each disSIMILARITY pair is considered as an independent constraint. Finally, in the last structure, maximization of the distance between the disSIMILARITY PAIRS is considered within the cost function not as a constraint. The proposed methods are examined in the clustering application using the kernel k-means clustering algorithm. Both synthetic (a XOR data set) and real data sets (the UCI data) used in the experiments and the performance of the clustering algorithm using single kernels, are considered as the baseline. Our experimental results confirm that using the multiple kernel not only improves the clustering result but also makes the algorithm independent of choosing the best kernel. The results also show that increasing of the number of constraints, as in the third structures, leads to instability of the algorithm which is expected.

Binary array PAIRS with optimal/ideal correlation values and their algebraic counterparts \difference set PAIRS" (DSPs) in abelian groups are studied. In addition to generalizing known 1-dimensional (sequences) examples, we provide four new recursive constructions, unifying previously obtained ones. Any further advancements in the construction of binary sequences/arrays with opti-mal/ideal correlation values (equivalently cyclic/abelian difference sets) would give rise to richer classes of DSPs (and hence binary perfect array PAIRS). Discrete signals arising from DSPs nd applications incryptography, CDMA systems, radar and wireless communications.

In this paper, we consider properties of weak extended order algebras with adjoint PAIRS and Galois PAIRS, and prove some new results. Moreover, we clarify the relation between these algebras and BCK-algebras, that is, the class of all normal weak extended order algebras with adjoint pair satisfying the condition $\top \to x=x$ is identical the class of all BCK-algebras with the condition (S).

Let v be a henselian valuation on a field K, and v ̃,be its unique extension to the algebraic closure K ̃,of K. An element α, ∈, K ̃, K has a distinguished pair if the corresponding set M(α, , K) (defined as the following) has a maximum element M(α, , K)={v ̃, (α,-β, )┤, β,in K ̃, , [K(β, ) ∶, K]<[K(α, ) ∶, K]}. In this case, a pair (α, , β, ) of elements of K ̃,is a distinguished pair for α,whenever β,is an element of smallest degree over K such that deg⁡, α, >deg⁡, β,and v ̃, (α,-β, )=supM(α, , K). In this paper, we first present some results about distinguished PAIRS of algebraic elements of arbitrary degree over henselian valued fields. Then considering the importance of algebraic elements of prime degree in the extensions of valued fields, we concentrate on such elements. In particular, for α, ∈, K ̃,of prime degree over K, we give a necessary and sufficient condition for the existence of the maximum of the corresponding set M(α, , K) by using the minimal polynomial of α,over K.

‎The Frobenius complement of a given Frobenius group acts on its kernel‎. The scheme which is arisen from the orbitals of this action is called Ferrero pair scheme‎. In this paper‎, ‎we show that the fibers of a Ferrero pair scheme consist of exactly one singleton fiber and every two fibers with more than one point have the same cardinality‎. Moreover‎, ‎it is shown that the restriction of a Ferrero pair scheme on each fiber is isomorphic to a regular scheme‎. Finally‎, ‎we prove that for any prime p‎, ‎there exists a Ferrero pair p-scheme‎, ‎and if p>2‎, ‎then the Ferrero pair p-schemes of the same rank are all isomorphic‎.

Let (G; N) be a pair of groups. In this paper,  rstly, we construct a relative central extension for the pair (G; N) such that special types of the covering pair of (G; N) are the homomor-phic image of it. Secondly, we show that every perfect pair admits at least one covering pair. Finally, among extending some proper-ties of perfect groups to perfect PAIRS, we characterize the covering PAIRS of a perfect pair (G; N) under some extra assumptions.

In this paper, we determine the structure of the nilpotent multipliers of all PAIRS (G,N) of finitely generated abelian groups where N admits a complement in G. Moreover, some inequalities for the nilpotent multipliers of PAIRS of finite groups and their factor groups are given.

Recognition and prediction of biological function of proteins based on amino acid sequences is a simple method employed in so many software and operators. However, the sequence SIMILARITY does not always imply to SIMILARITY of biological function. The aim of this study was to determine the semantic SIMILARITY of gene ontology (GO) of six pluripotency factors, Oct4, Sox2, C-Myc, Klf-4, Lin28 and Nanog in six species and evaluate their conformity with their protein sequence SIMILARITY and phylogenetic distance. C-myc factor exhibited a significant correlation between phylogenetic distance and protein SIMILARITY. The other factors like Sox2, Klf-4 and Lin-28 showed the correct changes of phylogenetic distance and protein SIMILARITY, but Nanog and Oct4 factors did not display a correct correlation between two indices because, the increase of protein SIMILARITY was not followed with the decrease of phylogenetic distance. Following the study, the protein or nucleotide SIMILARITY was assumed as dependent variable and GO SIMILARITY in three categories of biological process (BP), molecular function (MF) and, cell component (CC) were expected as the independent variables. With this assumption, regression analysis was accomplished to determine the best model for protein and nucleotide SIMILARITY estimation. The protein or nucleotide SIMILARITY also displayed a significant regression with GO SIMILARITY for C-myc factor and category of BP and CC were selected to estimate protein or nucleotide SIMILARITY by model, but a significant regression was not observed for other pluripotency factors for estimation of protein or nucleotide SIMILARITY. It means that except of C-myc, GO SIMILARITY of other studied pluripotency factors didn’ t reflect the protein or nucleotide SIMILARITY. It is suggested that related data for five pluripotency factors, including Oct-4, Sox2, Klf4, Lin28 and Nanog in the six studied species should be reviewed.