Abstract:
In this work, we propose an original approach of semi-vectorial hybrid morphological segmentation for multicomponent images or multidimensional data by analyzing compact multidimensional histograms based on different orders. Its principle consists first of segment marginally each component of the multicomponent image into different numbers of classes fixed at K. The segmentation of each component of the image uses a scalar segmentation strategy by histogram analysis; we mainly count the methods by searching for peaks or modes of the histogram and those based on a multi-thresholding of the histogram. It is the latter that we have used in this paper, it relies particularly on the multi-thresholding method of OTSU. Then, in the case where i) each component of the image admits exactly K classes, K vector thresholds are constructed by an optimal pairing of which each component of the vector thresholds are those resulting from the marginal segmentations. In addition, the multidimensional compact histogram of the multicomponent image is computed and the attribute tuples or ‘colors’ of the histogram are ordered relative to the threshold vectors to produce (K + 1) intervals in the partial order giving rise to a segmentation of the multidimensional histogram into K classes. The remaining colors of the histogram are assigned to the closest class relative to their center of gravity. ii) In the contrary case, a vectorial spatial matching between the classes of the scalar components of the image is produced to obtain an over-segmentation, then an interclass fusion is performed to obtain a maximum of K classes. Indeed, the relevance of our segmentation method has been highlighted in relation to other methods, such as K-means, using unsupervised and supervised quantitative segmentation evaluation criteria. So the robustness of our method relatively to noise has been tested.

Abstract:
This paper will propose a novel star schema attribute induction as a new attribute induction paradigm and as improving from current attribute oriented induction. A novel star schema attribute induction will be examined with current attribute oriented induction based on characteristic rule and using non rule based concept hierarchy by implementing both of approaches. In novel star schema attribute induction some improvements have been implemented like elimination threshold number as maximum tuples control for generalization result, there is no ANY as the most general concept, replacement the role concept hierarchy with concept tree, simplification for the generalization strategy steps and elimination attribute oriented induction algorithm. Novel star schema attribute induction is more powerful than the current attribute oriented induction since can produce small number final generalization tuples and there is no ANY in the results.

Abstract:
This paper will propose a novel star schema attribute induction as a new attributeinduction paradigm and as improving from current attribute oriented induction. A novelstar schema attribute induction will be examined with current attribute oriented inductionbased on characteristic rule and using non rule based concept hierarchy by implementingboth of approaches. In novel star schema attribute induction some improvements havebeen implemented like elimination threshold number as maximum tuples control forgeneralization result, there is no ANY as the most general concept, replacement the roleconcept hierarchy with concept tree, simplification for the generalization strategy stepsand elimination attribute oriented induction algorithm. Novel star schema attributeinduction is more powerful than the current attribute oriented induction since can producesmall number final generalization tuples and there is no ANY in the results.

Abstract:
We introduce the defect sequence for a contractive tuple of Hilbert space operators and investigate its properties. The defect sequence is a sequence of numbers, called defect dimensions associated with a contractive tuple. We show that there are upper bounds for the defect dimensions. The tuples for which these upper bounds are obtained, are called maximal contractive tuples. The upper bounds are different in the non-commutative and in the com- mutative case. We show that the creation operators on the full Fock space and the co ordinate multipliers on the Drury-Arveson space are maximal. We also study pure tuples and see how the defect dimensions play a role in their irreducibility.

Abstract:
In this article we answer a question raised by N. Feldman in \cite{Feldman} concerning the dynamics of tuples of operators on $\mathbb{R}^n$. In particular, we prove that for every positive integer $n\geq 2$ there exist $n$ tuples $(A_1, A_2, ..., A_n)$ of $n\times n$ matrices over $\mathbb{R}$ such that $(A_1, A_2, ..., A_n)$ is hypercyclic. We also establish related results for tuples of $2\times 2$ matrices over $\mathbb{R}$ or $\mathbb{C}$ being in Jordan form.

Abstract:
Attribute-based access control (ABAC) provides a high level of flexibility that promotes security and information sharing. ABAC policy mining algorithms have potential to significantly reduce the cost of migration to ABAC, by partially automating the development of an ABAC policy from an access control list (ACL) policy or role-based access control (RBAC) policy with accompanying attribute data. This paper presents an ABAC policy mining algorithm. To the best of our knowledge, it is the first ABAC policy mining algorithm. Our algorithm iterates over tuples in the given user-permission relation, uses selected tuples as seeds for constructing candidate rules, and attempts to generalize each candidate rule to cover additional tuples in the user-permission relation by replacing conjuncts in attribute expressions with constraints. Our algorithm attempts to improve the policy by merging and simplifying candidate rules, and then it selects the highest-quality candidate rules for inclusion in the generated policy.

Abstract:
In this work we address the classical problem of classifying tuples of linear operators and linear functions on a finite dimensional vector space up to base change. Having adopted for the situation considered a construction of framed moduli spaces of quivers, we develop an explicit classification of tuples belonging to a Zariski open subset. For such tuples we provide a finite family of normal forms and a procedure allowing to determine whether two tuples are equivalent.

Abstract:
Starting with Zhang's theorem on the infinitude of prime doubles, we give an inductive argument that there exists an infinite number of prime $k$-tuples for at least one admissible set $\mathcal{H}_k=\{h_1,\ldots,h_k\}$ for each $k$.

Abstract:
Motivated by a result on weak Markov dilations, we define a notion of characteristic function for ergodic and coisometric row contractions with a one-dimensional invariant subspace for the adjoints. This extends a definition given by G. Popescu. We prove that our characteristic function is a complete unitary invariant for such tuples and show how it can be computed.

Abstract:
The paper contains examples of Fredholm n-tuples of operators that are of index 0 but cannot be perturbed by compact operators to n-tuples with exact Koszul complex.