Non-kissing complexes and tau-tilting for gentle algebras

We interpret the support τ \tau -tilting complex of any gentle bound quiver as the non-kissing complex of walks on its blossoming quiver. Particularly relevant examples were previously studied for quivers defined by a subset of the grid or by a dissection of a polygon. We then focus on the case when the non-kissing complex is finite. We show that the graph of increasing flips on its facets is the Hasse diagram of a congruence-uniform lattice. Finally, we study its g \mathbf {g} -vector fan and prove that it is the normal fan of a non-kissing associahedron.

Cybersecurity against the Loopholes in Industrial Control Systems Using Interval-Valued Complex Intuitionistic Fuzzy Relations

Technology is rapidly advancing and every aspect of life is being digitalized. Since technology has made life much better and easier, so organizations, such as businesses, industries, companies and educational institutes, etc., are using it. Despite the many benefits of technology, several risks and serious threats, called cyberattacks, are associated with it. The method of neutralizing these cyberattacks is known as cybersecurity. Sometimes, there are uncertainties in recognizing a cyberattack and nullifying its effects using righteous cybersecurity. For that reason, this article introduces interval-valued complex intuitionistic fuzzy relations (IVCIFRs). For the first time in the theory of fuzzy sets, we investigated the relationships among different types of cybersecurity and the sources of cyberattacks. Moreover, the Hasse diagram for the interval-valued complex intuitionistic partial order set and relation is defined. The concepts of the Hasse diagram are used to inspect different cybersecurity techniques and practices. Then, using the properties of Hasse diagrams, the most beneficial technique is identified. Furthermore, the best possible selection of types of cybersecurity is made after putting some restrictions on the selection. Lastly, the advantages of the proposed methods are illuminated through comparison tests.

MANAGEMENT ORGANIZATION ACCESS TO MEDICAL INFORMATION SYSTEMS USING THE METHODS SEMANTIC PROXIMITY

На основе анализа применения моделей управления доступом с использованием тематических иерархических классификаторов в медицинских информационных системах с применением мобильных систем в качестве элементов предложены методы формирования доверительных прав на доступ к объектам. При использовании традиционных тематически иерархических моделей управления доступа логическая информационная архитектура ресурсов медицинских информационных систем формирует собой тематический иерархический классификатор (рубрикатор). Диаграмма Хассе вводит отношения порядка в тематическом классификаторе на решетке безопасности для формирования доверительно - тематических полномочий пользователей медицинских информационных систем. Построение диаграмм Хассе на решетке безопасности включающей несколько уровней безопасности достаточно сложная алгоритмическая задача. При построении доверительно - тематических полномочий пользователей для избегания неопределенности при неполноте построенной диаграммы Хассе и завышения предоставленных полномочий при формировании прав доступа предлагается использовать семантическую близость запроса на доступ пользователя и тематической рубрики иерархического классификатора. Анализ существующих подходов к формированию метрик семантической близости показал, что в качестве наилучшей метрики для задания доверительных полномочий пользователя может использоваться меры близости, основанные на иерархии понятий Based on the analysis of the application of access control models using thematically hierarchical classifiers in medical information systems using mobile technologies (MS), methods of forming access rights to objects are proposed. When using traditional thematically hierarchical access control models, the logical information architecture of the medical information systems resources forms a thematic hierarchical classifier (rubricator). The Hasse diagram introduces order relations into the thematic classifier on the security grid to form the trust-thematic powers of the medical information systems users. The construction of Hasse diagrams on a security grid that includes several security levels is a rather complex algorithmic task. When constructing trust-thematic user powers to avoid ambiguity in the case of incompleteness of the constructed Hasse diagram and overestimation of the granted powers when forming access rights, it is proposed to use the semantic proximity of the user's access request and the thematic heading of the hierarchical classifier. An analysis of existing approaches to the formation of semantic proximity metrics showed that proximity measures based on a hierarchy of concepts can be used as the best metric for setting the user's trust authority

Diamond Subgraphs in the Reduction Graph of a One-Rule String Rewriting System

In this paper, we study a certain case of a subgraph isomorphism problem. We consider the Hasse diagram of the lattice Mk (the unique lattice with k + 2 elements and one anti-chain of length k) and find the maximal k for which it is isomorphic to a subgraph of the reduction graph of a given one-rule string rewriting system. We obtain a complete characterization for this problem and show that there is a dichotomy. There are one-rule string rewriting systems for which the maximal such k is 2 and there are cases where there is no maximum. No other intermediate option is possible.

Hasse diagrams for 3d $$ \mathcal{N} $$ = 4 quiver gauge theories — Inversion and the full moduli space

We study Hasse diagrams of moduli spaces of 3d $$ \mathcal{N} $$ N = 4 quiver gauge theories. The goal of this work is twofold: 1) We introduce the notion of inverting a Hasse diagram and conjecture that the Coulomb branch and Higgs branch Hasse diagrams of certain theories are related through this operation. 2) We introduce a Hasse diagram to map out the entire moduli space of the theory, including the Coulomb, Higgs and mixed branches. For theories whose Higgs and Coulomb branch Hasse diagrams are related by inversion it is straight forward to generate the Hasse diagram of the entire moduli space. We apply inversion of the Higgs branch Hasse diagram in order to obtain the Coulomb branch Hasse diagram for bad theories and obtain results consistent with the literature. For theories whose Higgs and Coulomb branch Hasse diagrams are not related by inversion it is nevertheless possible to produce the Hasse diagram of the full moduli space using different methods. We give examples for Hasse diagrams of the entire moduli space of theories with enhanced Coulomb branches.

Quantum Spectral Curve of γ-Twisted 𝒩 = 4 SYM Theory and Fishnet CFT

We review the quantum spectral curve (QSC) formalism for the spectrum of anomalous dimensions of [Formula: see text] SYM, including its [Formula: see text]-deformation. Leaving aside its derivation, we concentrate on the formulation of the “final product” in its most general form: a minimal set of assumptions about the algebraic structure and the analyticity of the [Formula: see text]-system — the full system of Baxter [Formula: see text]-functions of the underlying integrable model. The algebraic structure of the [Formula: see text]-system is entirely based on (super)symmetry of the model and is efficiently described by Wronskian formulas for [Formula: see text]-functions organized into the Hasse diagram. When supplemented with analyticity conditions on [Formula: see text]-functions, it fixes completely the set of physical solutions for the spectrum of an integrable model. First, we demonstrate the spectral equations on the example of [Formula: see text] and [Formula: see text] Heisenberg (super)spin chains. Supersymmetry [Formula: see text] occurs as a simple “rotation” of the Hasse diagram for a [Formula: see text] system. Then we apply this method to the spectral problem of [Formula: see text]/CFT4-duality, describing the QSC formalism. The main difference with the spin chains consists in more complicated analyticity constraints on [Formula: see text]-functions which involve an infinitely branching Riemann surface and a set of Riemann–Hilbert conditions. As an example of application of QSC, we consider a special double scaling limit of [Formula: see text]-twisted [Formula: see text] SYM, combining weak coupling and strong imaginary twist. This leads to a new type of non-unitary CFT dominated by particular integrable, and often computable, 4D fishnet Feynman graphs. For the simplest of such models — the bi-scalar theory — the QSC degenerates into the [Formula: see text]-system for integrable non-compact Heisenberg spin chain with conformal, [Formula: see text] symmetry. We describe the QSC derivation of Baxter equation and the quantization condition for particular fishnet graphs — wheel graphs, and review numerical and analytic results for them.

Assessing and Grouping Chemicals Applying Partial Ordering Alkyl Anilines as an Illustrative Example

Aim and Objective: In chemistry, there is a long tradition in classification. Usually, methods are adopted from the wide field of cluster analysis. The present study focusses on the application of partial ordering methodology for the classification of 21 alkyl substituted anilines. Materials and Methods: The analyses are based on the concepts from partial order methodology and cluster analyses. Here, with the example of 21 alkyl anilines, we show that concepts taken out from the mathematical discipline of partially ordered sets may be applied for classification. The chemical compounds are described by a multi-indicator system. For the present study four indicators, mainly taken from the field of environmental chemistry were applied and a graph of the ordering (Hasse diagram) was constructed. Results: A Hasse diagram is an acyclic, transitively reduced, triangle-free graph that may have several graph-theoretical components. The Hasse diagram has been directed from a structural chemical point of view. Two cluster analysis methods are applied (K-means and a hierarchical cluster method) and compared with the results from the Hasse diagram. In both cases, the partitioning of the set of 21 compounds by the component structure of the Hasse diagram appears to be better interpretable. Conclusion: It is shown that the partial ordering approach indeed can be used for classification in the present case. However, it must be clearly stated that a guarantee for meaningful results, in general, cannot be given. For that, further theoretical work is needed.

Graphs models and algorithms for reliability assessment of coherent and non-coherent systems

In this article, we propose new models and algorithms for the reliability assessment of systems relying on concepts of graphs theory. These developments exploit the order relation on the set of system components’ states which is graphically represented by the Hasse diagram. The monotony property of the reliability structure function of coherent systems allows us to obtain an ordered graph from the Hasse diagram. This ordered graph represents all the system states and it can be obtained from only the knowledge of the system tie-sets. First of all, this model gives a new way for the research of a minimal disjoint Boolean polynomial, and, second, it is able to directly find the system reliability without resorting to an intermediate Boolean polynomial. Browsing the paths from the minimal tie-sets to the maxima of the ordered graph and using a weight associated with each node, we are able to propose a new algorithm to directly obtain the reliability polynomial by the research of sub-graphs representing eligible monomials. This approach is then extended to non-coherent systems thanks to the introduction of a new concept of terminal tie-sets. These algorithms are applied to some case studies, for both coherent and non-coherent real systems, and the results compared with those computed using standard reliability block diagram or fault tree models validate the proposed approach. Formal definitions of used graphs and of developed algorithms are also given, making their software implementation easy and efficient.