Applications of implicit parametrizations

We review several applications of the implicit parametrization theorem in optimization. In nonlinear programming, we discuss both new forms, with less multipliers, of the known optimality conditions, and new algorithms of global type. For optimal control problems, we analyze the case of mixed equality constraints and indicate an algorithm, while in shape optimization problems the emphasis is on the new penalization approach.

Breast Cancer Detection via Global and Local Features using Digital Histology Images

Globally, breast cancer (BC) is the prevailing cause of unusual deaths in women. Breast tumor (BT) is a primary symptom and may lead to BC. Digital histology (DH) image modality is a gold standard medical test for a definite diagnosis of BC. Traditionally, DH images are visually examined by two or more pathologists to come up with a consensus for authentic BC detection which may cause a high error rate. Therefore, researchers had developed automated BC detection models using a machine learning (ML) based approach. Thus, this study aims to develop a BC detection model through ten feature extraction methods which extract both local and global type features from publicly available breast histology dataset. The extracted features are sorted by their weights, which are computed by the neighborhood component analysis method. A feature selection algorithm is developed to find the minimum number of discriminating features, evaluated through seven heterogeneous traditional ML classifiers. The proposed ML-based BC detection model acquired 90% accuracy for the initial testing set using 51 Harris features. Whereas, for the extended testing set, only three Harris features is shown 93% accuracy. The proposed BC detection model can assist the doctor in giving a second opinion.

Semantic Analysis of Digital Destructive Content of School Shooting in the Social Network ‘VKontakte’

Since the middle 1970s, the public has been seriously concerned about cases of school shooting — an armed attack by students on educational organizations. The global type of activity of social networks, as well as the high potential for the dissemination of destructive information in cyberspace with the use of anonymization, assigns digital resources, in fact, unlimited freedom of action. In this study, an attempt to semantic content analysis of digital destructive content of school shooting is made. The purpose of the study is to determine the system of signs of destructive content suitable for its identification in cyberspace through semantic analysis of the text openly published by users on the social network ‘Vkontakte’, using neural networks. The conducted research allowed us to identify a number of important signs of destructive content of school shooting with the allocation of thematic groups: indirect content of school shooting; drug content; mental distress.

Content and methodological bases for studying global problems of humanity in the framework of the subject «Geography» based on the potential of extracurricular and extracurricular activities

Modern geographical education is undergoing a stage of updating its content. In the context of globalisation and constantly emerging problems and contradictions that have a universal character of manifestation, the key theme of school geographical education at the high school level can include global problems of humanity, the study of which will not only form a set of educational results, fixed by normative documents, but also help pupils to form a global type of thinking and behaviour, ensure the formation of a value attitude to the surrounding reality and understanding the significance of their own activities, aimed at ensuring the sustainability and balance of the development of all mankind. This article defines the content bases for studying global problems of humanity in six contexts that have a personal aspect for pupils. The article presents a methodological system for studying global problems of humanity in the process of both regular and extracurricular activities and represents a set of target (goal ideal and goal-means, correlated with the components of learning: cognitive, praxiological and axiological), content (contexts of studying global problems and levels of their consideration), procedural (forms, techniques, methods and technologies of learning that ensure the complex nature of the study of global problems of our time), performance-evaluation criteria, indicators and levels of mastering content about global problems of humanity) blocks.

Examples: A Pragmatic Approach

This study deals with a seemingly obvious topic to everyone – examples. Yet, on a closer perusal, the topic turns out to be interestingly perplexed. This can be justified by the amalgam of cognition and communication out of which such concept is delivered. This mixture gives a hand in texturizing examples. This work aims at pragmatically investigating the concept of ‘example’ as far as its definition, structure, types and functions are concerned. Furthermore, it aims at developing an eclectic model that will be utilized to pragmatically analyze the data of the work represented by four interviews with Donald Trump in 2018. Consequently, it hypothesizes the following: complex schema is more frequently used in the data; abductive inference is never employed in the data; faulty analogy is never made in the data; the interpersonal variant of the global type of examples is more frequently found in the data; explicit examples are more commonly given; and, finally, the argumentative function of examples prevails. Afterwards, the percentage equation is employed to statistically calculate the results of the analysis. The study has come up with many conclusions, out of which is that examples, once chosen meticulously, support the cogency of argumentation by means of strengthening and boosting one’s standpoints towards the alleged goals.

Ricci flow of warped Berger metrics on $${\mathbb {R}}^{4}$$

We study the Ricci flow on $${\mathbb {R}}^{4}$$ R 4 starting at an SU(2)-cohomogeneity 1 metric $$g_{0}$$ g 0 whose restriction to any hypersphere is a Berger metric. We prove that if $$g_{0}$$ g 0 has no necks and is bounded by a cylinder, then the solution develops a global Type-II singularity and converges to the Bryant soliton when suitably dilated at the origin. This is the first example in dimension $$n > 3$$ n > 3 of a non-rotationally symmetric Type-II flow converging to a rotationally symmetric singularity model. Next, we show that if instead $$g_{0}$$ g 0 has no necks, its curvature decays and the Hopf fibres are not collapsed, then the solution is immortal. Finally, we prove that if the flow is Type-I, then there exist minimal 3-spheres for times close to the maximal time.

Exploring Type-Level Bisimilarity towards More Expressive Multiparty Session Types

A key open problem with multiparty session types (MPST) concerns their expressiveness: current MPST have inflexible choice, no existential quantification over participants, and limited parallel composition. This precludes many real protocols to be represented by MPST. To overcome these bottlenecks of MPST, we explore a new technique using weak bisimilarity between global types and endpoint types, which guarantees deadlock-freedom and absence of protocol violations. Based on a process algebraic framework, we present well-formed conditions for global types that guarantee weak bisimilarity between a global type and its endpoint types and prove their check is decidable. Our main practical result, obtained through benchmarks, is that our well-formedness conditions can be checked orders of magnitude faster than directly checking weak bisimilarity using a state-of-the-art model checker.

Reduced norms of division algebras over complete discrete valuation fields of local-global type

Let [Formula: see text] be a complete discrete valuation field whose residue field [Formula: see text] is a global field of positive characteristic [Formula: see text]. Let [Formula: see text] be a central division [Formula: see text]-algebra of [Formula: see text]-power degree. We prove that the subgroup of [Formula: see text] consisting of reduced norms of [Formula: see text] is exactly the kernel of the cup product map [Formula: see text], if either [Formula: see text] is tamely ramified or of period [Formula: see text]. This gives a [Formula: see text]-torsion counterpart of a recent theorem of Parimala, Preeti and Suresh, where the same result is proved for division algebras of prime-to-[Formula: see text] degree.