Inclusion Relations Research Articles

Max-Tree Computation on GPUs

In Mathematical Morphology, the max-tree is a region-based representation that encodes the inclusion relationship of the threshold sets of an image. This tree has proved useful in numerous image processing applications. For the last decade, work has led to improving the construction time of this structure; mixing algorithmic optimizations, parallel and distributed computing. Nevertheless, there is still no algorithm that benefits from the computing power of the massively parallel architectures. In this work, we propose the first GPU algorithm to compute the max-tree. The proposed approach leads to significant speed-ups, and is up to one order of magnitude faster than the current State-of-the-Art parallel CPU algorithms. This work paves the way for a max-tree integration in image processing GPU pipelines and real-time image processing based on Mathematical Morphology. It is also a foundation for porting other image representations from Mathematical Morphology on GPUs.

Noise-resistant multilabel fuzzy neighborhood rough sets for feature subset selection

Feature selection attempts to capture the more discriminative features and plays a significant role in multilabel learning. As an efficient mathematical tool to handle incomplete and uncertain information, fuzzy rough set theory has been widely used in feature selection. However, there are two pivotal issues to be addressed when adopting fuzzy rough sets for multilabel data analysis. One is how to effectively characterize the discriminative ability of the features to multilabel samples. Another one is how to alleviate the effect of data noise on feature selection. For these reasons, this study mainly studies the noise-tolerant fuzzy neighborhood rough set model for multilabel learning and its feature selection strategy. Firstly, a parameterized hybrid fuzzy similarity relation is introduced to granulate multilabel data, and the parameterized fuzzy decision is extended to multilabel learning. Then, a noise-resistant multilabel fuzzy neighborhood rough set model using inclusion relation is constructed for describing the discriminative ability of the features to multilabel samples. Furthermore, a noise-resistant heuristic feature selection algorithm titled NRFSFN is designed. Besides, motivated by local sampling and ensemble strategy, an efficient extended version of NRFSFN is designed from the perspective of data distribution, named ENFSFN. Finally, a series of comparison experiments on sixteen multilabel datasets demonstrate the effectiveness of the proposed two algorithms.

Some Study on the Topological Structure on Semigroups

Some studies related to the topological structure of semigroups are provided. In, [3], considering and investigating the properties of the collection A of all the proper uniformly strongly prime ideals of a Γ - semigroup S, such study starts by constructing a topology τA on A using a closure operator defined in terms of the intersection and inclusion relation among these ideals of Γ-semigroup S, which is a generalization of the semigroup. In this paper, we introduce three other classes of ideals in semigroups called maximal ideals, prime ideals and strongly irreducible ideals, respectively. Investigating properties of the collection M, B and S of all proper maximal ideals, prime ideals and strongly irreducible ideals, respectively, of a semigroup S, we construct the respective topologies on them. The respective obtained topological spaces are called the structure spaces of the semigroup S. We study several principal topological axioms and properties in those structure spaces of semigroup such as separation axioms, compactness and connectedness, etc.

New Class Up and Down 
 λ-Convex Fuzzy-Number Valued Mappings and Related Fuzzy Fractional Inequalities

The fuzzy-number valued up and down λ-convex mapping is originally proposed as an intriguing generalization of the convex mappings. The newly suggested mappings are then used to create certain Hermite–Hadamard- and Pachpatte-type integral fuzzy inclusion relations in fuzzy fractional calculus. It is also suggested to revise the Hermite–Hadamard integral fuzzy inclusions with regard to the up and down λ-convex fuzzy-number valued mappings (U∙D λ-convex F-N∙V∙Ms). Moreover, Hermite–Hadamard–Fejér has been proven, and some examples are given to demonstrate the validation of our main results. The new and exceptional cases are presented in terms of the change of the parameters “i” and “α” in order to assess the accuracy of the obtained fuzzy inclusion relations in this study.

On q-Limaçon Functions

Very recently, functions that map the open unit disc U onto a limaçon domain, which is symmetric with respect to the real axis in the right-half plane, were initiated in the literature. The analytic characterization, geometric properties, and Hankel determinants of these families of functions were also demonstrated. In this article, we present a q-analogue of these functions and use it to establish the classes of starlike and convex limaçon functions that are correlated with q-calculus. Furthermore, the coefficient bounds, as well as the third Hankel determinants, for these novel classes are established. Moreover, at some stages, the radius of the inclusion relationship for a particular case of these subclasses with the Janowski families of functions are obtained. It is worth noting that many of our results are sharp.

On generalized double almost statistical convergence of weight $g$

The purpose of this paper is to introduce the concept of $\lambda$-double almost statistical convergence of weight $g$, which emerges naturally from the concept of the double almost convergence and $\lambda$-statistical convergence. Some interesting inclusion relations have been considered.

Diversity, Equity, Inclusion, and Internationalization: Past, Present, and Future of STP

Introduction: As an organization with a 75-year history of supporting the teaching of psychology, the Society for the Teaching of Psychology (STP), which also operates as Division 2 of the American Psychological Association, has a significant influence on psychology learning and teaching. Statement of the Problem: In this article, four former STP Vice Presidents for Diversity and International Relations explore STP’s history through the lenses of diversity, equity/social justice, inclusion, and international relations. Literature Review: The paper explores the relevant history of STP and incorporates scholarship of teaching and learning literature through an international and social justice lens. Teaching Implications: The authors discussed ways to support BIPOC and underrepresented instructors of psychology. Conclusion: STP and teachers of psychology play a pivotal role in changing the cultural, structural, and institutional processes representing ongoing barriers to diversity, equity, and inclusion, and social justice within the organization and the teaching of psychology. Instructors of psychology are well positioned to promote systemic and structural changes and advocate for social justice for Black, Indigenous, and People of Color (BIPOC) and other underrepresented teachers of psychology.

New Class Up and Down Pre-Invex Fuzzy Number Valued Mappings and Related Inequalities via Fuzzy Riemann Integrals

Numerous applications of the theory of convex and nonconvex mapping exist in the fields of applied mathematics and engineering. In this paper, we have defined a new class of nonconvex functions which is known as up and down pre-invex (pre-incave) fuzzy number valued mappings (F-N-V∙Ms). The well-known fuzzy Hermite–Hadamard (

On bundles of matrix pencils under strict equivalence

Bundles of matrix pencils (under strict equivalence) are sets of pencils having the same Kronecker canonical form, up to the eigenvalues (namely, they are an infinite union of orbits under strict equivalence). The notion of bundle for matrix pencils was introduced in the 1990's, following the same notion for matrices under similarity, introduced by Arnold in 1971, and it has been extensively used since then. Despite the amount of literature devoted to describing the topology of bundles of matrix pencils, some relevant questions remain still open in this context. For example, the following two: (a) provide a characterization for the inclusion relation between the closures (in the standard topology) of bundles; and (b) are the bundles open in their closure? The main goal of this paper is providing an explicit answer to these two questions. In order to get this answer, we also review and/or formalize some notions and results already existing in the literature. We also prove that bundles of matrices under similarity, as well as bundles of matrix polynomials (defined as the set of m×n matrix polynomials of the same grade having the same spectral information, up to the eigenvalues) are open in their closure.

Some Fixed Point Results in Bicomplex Valued Metric Spaces

Fixed points are also called as invariant points. Invariant point theorems are very essential tools in solving problems arising in different branches of mathematical analysis. In the present paper, we establish three unique common invariant point theorems using two self-mappings, four self-mappings and six self-mappings in the bicomplex valued metric space. In the first theorem, we generate a common invariant point theorem for four self-mappings by using weaker conditions such as weakly compatible, generalized contraction and <img src=image/13428832_01.gif> property. Then, in the second theorem, we generate a common invariant point theorem for six self-mappings by using inclusion relation, generalized contraction, weakly compatible and commuting maps. Further, in the third theorem, we generate a common coupled invariant point for two self mappings using different contractions in the bicomplex valued metric space. The above results are the extention and generalization of the results of [11] in the Bicomplex metric space. Moreover, we provide an example which supports the results.

“Bodyheartminding” (xin 心): Reconceiving the Inner Self and the Outer World in the Language of Holographic Focus and Field

“Bodyheartminding” (<i>xin</i> 心): Reconceiving the Inner Self and the Outer World in the Language of Holographic Focus and Field

Multivalent harmonic functions Involving multiplier transformation

In the present investigation we study a subclass of multivalent harmonic functions involving multiplier transformation. An equivalent convolution class condition and a sufficient coefficient condition for this class is acquired. We also show that this coefficient condition is necessary for functions belonging to its subclass. As an application of coefficient condition, a necessary and sufficient hypergeometric inequality is also given. Further, results on bounds, inclusion relation, extreme points, a convolution property and a result based on the integral operator are obtained.

Efficient algorithms for mining closed and maximal high utility itemsets

Closed high utility itemsets (CHUIs) and maximal high utility itemsets (MaxHUIs) are two important concise representations of HUIs. Discovering these itemsets is important because they are lossless and compact, i.e., they provide a concise summary of all HUIs that can be orders of magnitude smaller. In addition, it can be more efficient to extract these representations than it would be to extract all HUIs. Mining the concise representations of HUIs is also an important step toward the generation of nonredundant high utility association rules that can reveal meaningful information to decision-makers. However, although several algorithms have been designed to mine these representations, such as EFIM-Closed, HMiner-Closed, and CHUI-Miner(Max), they have long runtimes, high memory usage, and scalability issues, especially for dense and large datasets. To address this issue, this paper proposes two efficient algorithms named C-HUIM and MaxC-HUIM for mining CHUIs, and simultaneously mining both CHUIs and MaxHUIs, respectively. These algorithms use a novel weak upper bound on the utility, which is strictly tighter than traditional upper bounds, and a corresponding pruning strategy called SPWUB to quickly eliminate low utility itemsets. The algorithms also include two novel search space reduction strategies named PSNonCHUB and LPSNonCHUB. The PSNonCHUB strategy only requires checking the inclusion relationship among a small number of itemsets, while LPSNonCHUB does not perform any inclusion check. In addition, the algorithms adopt a structure named MPUN-list to efficiently store and calculate information about each itemset’s utility and support. Experimental results show that the proposed algorithms can be more than 100 times faster, are more memory efficient, and have better scalability than the state-of-the-art algorithms.

Some new concepts related to fuzzy fractional calculus for up and down convex fuzzy-number valued functions and inequalities

The theory of convex mapping has a lot of applications in the field of applied mathematics and engineering. The fuzzy Riemann-Liouville fractional integrals are the most significant operator of fractional theory which permits to generalize the classical theory of integrals. This study considers the well-known Hermite-Hadamard type and associated inequalities. To full fill this mileage, some new versions of fuzzy Hermite-Hadamard type and Hermite-Hadamard-Fejér type inequalities for up and down convex fuzzy-number valued mappings have been obtained. Some new related fuzzy Hermite-Hadamard type inequalities are also obtained with the help of product of two up and down convex fuzzy-number valued mappings. Moreover, we have introduced some new important classes of fuzzy numbered valued convexity which are known as lower up and down convex (concave) and, upper up and down convex (concave) fuzzy numbered valued mappings by applying some mild restrictions on up and down convex (concave) fuzzy numbered valued mappings. By using these definitions, we have acquired many classical and new exceptional cases which can be viewed as applications of the main results. We also present three examples of fuzzy numbered valued convexity to demonstrate the validity of the fuzzy inclusion relations proposed in this paper.

On Certain Subclass of Analytic Functions

In the present investigation, a new general subclass $M_{\alpha ,\beta }\left( \phi \right) $ of analytic functions is defined. Some subordination relations, inclusion relations, integral preserving properties, convolution properties and some other interesting properties are studied.

Properties of Meromorphic Spiral-Like Functions Associated with Symmetric Functions

To consolidate or adapt to many studies on meromorphic functions, we define a new subclass of meromorphic functions of complex order involving a differential operator. The defined function class combines the concept of spiral-like functions with other studies pertaining to subclasses of multivalent meromorphic functions. Inclusion relations, integral representation, geometrical interpretation, coefficient estimates and solution to the Fekete-Szegö problem of the defined classes are the highlights of this present study. Further to keep up with the present direction of research, we extend the study using quantum calculus. Applications of our main results are given as corollaries.

Some Subclasses of Spirallike Multivalent Functions Associated with a Differential Operator

In this paper we study convolution properties of spirallike multivalent functions defined by using a differential operator and higher order derivatives. Using convolution product relations we determine necessary and sufficient conditions for multivalent functions to belong to these classes, and our results generalized many previous results obtained by different authors. We obtain convolution and inclusion properties for new subclasses of multivalent functions defined by using the Dziok-Srivatava operator. Moreover, using a result connected with the Briot-Bouquet differential subordination, we obtain an inclusion relation between some of these classes of functions.

Some New Types of Convergence Definitions for Random Variable Sequences

In this paper, we introduce the concepts of invariant convergence in probability, statistically invariant convergence in probability, invariant convergence almost surely, invariant convergence in distribution and invariant convergence in Lp-norm for sequences of random variables. Also, we investigate some inclusion relations.

Artificial Intelligence Synergetic Opportunities in Services: Conversational Systems Perspective

The importance of this paper is its discovery of the unused synergetic potential of integration between several AI techniques into an orchestrated effort to improve service. Special emphasis is given to the conversational capabilities of AI systems. The paper shows that the literature related to the use of AI in service is divided into independent knowledge domains (silos) that are either related to the technology under consideration, or to a small group of technologies related to a certain application; it then discusses the reasons for the isolation of these silos, and reveals the barriers and the traps for their integration. Two case studies of service systems are presented to illustrate the importance of synergy. A special focus is given to the conversation part of these service systems: the first case presents an application with high potential for integrating new AI technologies into its AI portfolio, while the second case illustrates the advantages of a mature application that has already integrated many technologies into its AI portfolio. Finally, the paper discusses the two case studies and presents inclusion relationships between AI capabilities to facilitate generating a roadmap for extending AI capabilities with synergetic opportunities.

MAXIMAL TOWERS AND ULTRAFILTER BASES IN COMPUTABILITY THEORY

AbstractThe tower number ${\mathfrak t}$ and the ultrafilter number $\mathfrak {u}$ are cardinal characteristics from set theory. They are based on combinatorial properties of classes of subsets of $\omega $ and the almost inclusion relation $\subseteq ^*$ between such subsets. We consider analogs of these cardinal characteristics in computability theory.We say that a sequence $(G_n)_{n \in {\mathbb N}}$ of computable sets is a tower if $G_0 = {\mathbb N}$ , $G_{n+1} \subseteq ^* G_n$ , and $G_n\smallsetminus G_{n+1}$ is infinite for each n. A tower is maximal if there is no infinite computable set contained in all $G_n$ . A tower ${\left \langle {G_n}\right \rangle }_{n\in \omega }$ is an ultrafilter base if for each computable R, there is n such that $G_n \subseteq ^* R$ or $G_n \subseteq ^* \overline R$ ; this property implies maximality of the tower. A sequence $(G_n)_{n \in {\mathbb N}}$ of sets can be encoded as the “columns” of a set $G\subseteq \mathbb N$ . Our analogs of ${\mathfrak t}$ and ${\mathfrak u}$ are the mass problems of sets encoding maximal towers, and of sets encoding towers that are ultrafilter bases, respectively. The relative position of a cardinal characteristic broadly corresponds to the relative computational complexity of the mass problem. We use Medvedev reducibility to formalize relative computational complexity, and thus to compare such mass problems to known ones.We show that the mass problem of ultrafilter bases is equivalent to the mass problem of computing a function that dominates all computable functions, and hence, by Martin’s characterization, it captures highness. On the other hand, the mass problem for maximal towers is below the mass problem of computing a non-low set. We also show that some, but not all, noncomputable low sets compute maximal towers: Every noncomputable (low) c.e. set computes a maximal tower but no 1-generic $\Delta ^0_2$ -set does so.We finally consider the mass problems of maximal almost disjoint, and of maximal independent families. We show that they are Medvedev equivalent to maximal towers, and to ultrafilter bases, respectively.