scholarly journals The combinatorics of minimal unsatisfiability: connecting to graph theory

2021 ◽  
Author(s):  
◽  
Hoda Abbasizanjani
Keyword(s):  
Graph Theory ◽  
Building Blocks ◽  
Point Of View ◽  
New Class ◽  
Strongly Connected ◽  
Combinatorial Point ◽  
Minimal Unsatisfiability ◽  
Full Classification ◽  
New Framework

Minimally Unsatisfiable CNFs (MUs) are unsatisfiable CNFs where removing any clause destroys unsatisfiability. MUs are the building blocks of unsatisfia-bility, and our understanding of them can be very helpful in answering various algorithmic and structural questions relating to unsatisfiability. In this thesis we study MUs from a combinatorial point of view, with the aim of extending the understanding of the structure of MUs. We show that some important classes of MUs are very closely related to known classes of digraphs, and using arguments from logic and graph theory we characterise these MUs.Two main concepts in this thesis are isomorphism of CNFs and the implica-tion digraph of 2-CNFs (at most two literals per disjunction). Isomorphism of CNFs involves renaming the variables, and flipping the literals. The implication digraph of a 2-CNF F has both arcs (¬a → b) and (¬b → a) for every binary clause (a ∨ b) in F .In the first part we introduce a novel connection between MUs and Minimal Strong Digraphs (MSDs), strongly connected digraphs, where removing any arc destroys the strong connectedness. We introduce the new class DFM of special MUs, which are in close correspondence to MSDs. The known relation between 2-CNFs and implication digraphs is used, but in a simpler and more direct way, namely that we have a canonical choice of one of the two arcs. As an application of this new framework we provide short and intuitive new proofs for two im-portant but isolated characterisations for nonsingular MUs (every literal occurs at least twice), both with ingenious but complicated proofs: Characterising 2-MUs (minimally unsatisfiable 2-CNFs), and characterising MUs with deficiency 2 (two more clauses than variables).In the second part, we provide a fundamental addition to the study of 2-CNFs which have efficient algorithms for many interesting problems, namely that we provide a full classification of 2-MUs and a polytime isomorphism de-cision of this class. We show that implication digraphs of 2-MUs are “Weak Double Cycles” (WDCs), big cycles of small cycles (with possible overlaps). Combining logical and graph-theoretical methods, we prove that WDCs have at most one skew-symmetry (a self-inverse fixed-point free anti-symmetry, re-versing the direction of arcs). It follows that the isomorphisms between 2-MUs are exactly the isomorphisms between their implication digraphs (since digraphs with given skew-symmetry are the same as 2-CNFs). This reduces the classifi-cation of 2-MUs to the classification of a nice class of digraphs.Finally in the outlook we discuss further applications, including an alter-native framework for enumerating some special Minimally Unsatisfiable Sub-clause-sets (MUSs).

scholarly journals On topological sequence entropy of piecewise monotonic mappings

2000 ◽  
Vol 62 (1) ◽  
pp. 21-28 ◽  
Author(s):  
Jose S. Cánovas
Keyword(s):  
Point Of View ◽  
Sequence Entropy ◽  
Piecewise Monotonic ◽  
Topological Sequence Entropy ◽  
Full Classification

In this paper a full classification of piecewise monotonic maps from the point of view of the topological sequence entropy is established.

RHYNCHOLITES AND THE PROBLEM OF NARROW AND BROAD CONCEPTION OF TAXONS

2018 ◽  
pp. 12-17 ◽  
Author(s):  
I. R. Khuzina ◽  
V. N. Komarov
Keyword(s):  
Sexual Dimorphism ◽  
Morphological Characteristics ◽  
Mass Scale ◽  
Individual Variability ◽  
Point Of View ◽  
The Other ◽  
New Taxon ◽  
Artificial System ◽  
Broad Understanding

The paper considers a point of view, based on the conception of the broad understanding of taxons. According to this point of view, rhyncholites of the subgenus Dentatobeccus and Microbeccus are accepted to be synonymous with the genus Rhynchoteuthis, and subgenus Romanovichella is considered to be synonymous with the genus Palaeoteuthis. The criteria, exercising influence on the different approaches to the classification of rhyncholites, have been analyzed (such as age and individual variability, sexual dimorphism, pathological and teratological features, degree of disintegration of material), underestimation of which can lead to inaccuracy. Divestment of the subgenuses Dentatobeccus, Microbeccus and Romanovichella, possessing very bright morphological characteristics, to have an independent status and denomination to their synonyms, has been noted to be unjustified. An artificial system (any suggested variant) with all its minuses is a single probable system for rhyncholites. The main criteria, minimizing its negative sides and proving the separation of the new taxon, is an available mass-scale material. The narrow understanding of the genus, used in sensible limits, has been underlined to simplify the problem of the passing the view about the genus to the other investigators and recognition of rhyncholites for the practical tasks.

LEGAL, MORAL AND ETHICAL SIDE OF THE OFFENSE, DISCREDITING HONOR EMPLOYEE THE PENAL SYSTEM

2020 ◽  
Vol 10 (2) ◽  
pp. 213-218
Author(s):  
OKSANA KOCHKINA ◽  
◽  
OLGA MARCHUK ◽  
Keyword(s):  
Point Of View ◽  
Professional Activity ◽  
Penal System ◽  
Moral Norms ◽  
Ethical Aspects ◽  
Self Assessment ◽  
Personal Qualities ◽  
Executive System ◽  
Correction System

The article examines the legal and moral and ethical aspects of a misdemeanor that discredits the honor of an employee of the criminal Executive system. The considered reason for dismissal has the main feature associated with the integration of legal and moral norms, which often raises a lot of questions about the attribution of a particular offense to this basis. Using the analysis of normative legal acts, the authors attempt to identify the signs that contribute to the separation of the studied grounds for dismissal from all their diversity. The classification of offenses that discredit the honor of an employee of the criminal Executive system is presented, which allows to systematize and organize the knowledge obtained about the considered grounds for dismissal. The analysis of a misdemeanor that defames the honor of an employee of the penal system from a moral and ethical position gives an understanding, first of all, that it does not have a clear regulation from the point of view of the law, but the consequences of committing such a misdemeanor are clearly legal. The concepts of “honor” and “dignity” are considered as ethical categories and are analyzed as personal qualities that are manifested in an employee of the penal correction system during the period of service. These categories in the behavior of a person or employee are manifested both externally (assessment from the outside) and internally (self-assessment). The article describes the value orientation of an employee of the criminal Executive system to ethical standards in professional activity, which is an integral part of the moral and ethical side of a misdemeanor that discredits the honor of an employee.

A Bottom-Up Approach to Solution-Processed, Atomically Precise Graphitic Cylinders on Surfaces

2018 ◽  
Author(s):  
Erik Leonhardt ◽  
Jeff M. Van Raden ◽  
David Miller ◽  
Lev N. Zakharov ◽  
Benjamin Aleman ◽  
...  
Keyword(s):  
Self Assembly ◽  
Carbon Nanostructures ◽  
Carbon Nanomaterials ◽  
Circle Packing ◽  
Pyrolytic Graphite ◽  
Building Blocks ◽  
Bottom Up ◽  
Casting Technique ◽  
New Class ◽  
Solution Casting Technique

Extended carbon nanostructures, such as carbon nanotubes (CNTs), exhibit remarkable properties but are difficult to synthesize uniformly. Herein, we present a new class of carbon nanomaterials constructed via the bottom-up self-assembly of cylindrical, atomically-precise small molecules. Guided by supramolecular design principles and circle packing theory, we have designed and synthesized a fluorinated nanohoop that, in the solid-state, self-assembles into nanotube-like arrays with channel diameters of precisely 1.63 nm. A mild solution-casting technique is then used to construct vertical “forests” of these arrays on a highly-ordered pyrolytic graphite (HOPG) surface through epitaxial growth. Furthermore, we show that a basic property of nanohoops, fluorescence, is readily transferred to the bulk phase, implying that the properties of these materials can be directly altered via precise functionalization of their nanohoop building blocks. The strategy presented is expected to have broader applications in the development of new graphitic nanomaterials with π-rich cavities reminiscent of CNTs.

REFLECTION OF THE CURRENT STATE OF PUBLICISTIC JOURNALISM GENRES IN THE SLOVAK MEDIA ENVIRONMENT

2020 ◽  
Author(s):  
Zuzana Kvetanová
Keyword(s):  
Discourse Analysis ◽  
Point Of View ◽  
Media Theory ◽  
Logical Analysis ◽  
Periodical Press ◽  
Media Environment ◽  
Current State ◽  
Journalistic Practice ◽  
Opinion Journalism

The submitted study addresses the topic of the current state of the opinion journalism and its genres in the Slovak periodical press. The author draws attention to the question of classification of the opinion journalism of a rational and emotional type from the genre categorization point of view and, simultaneously, reflects on its application in the present journalistic practice. This brings a certain rate of confrontation between the defined theoretical premises and their subsequent practical (non-)implementation. The main objective of the study is to clarify the presence of genres of analytical and literary opinion journalism stated by media theory in the environment of the Slovak periodicals. Presentation of the basic terminological axis and the related explication of journalism genres included in the opinion journalism constitute the secondary objectives of the paper. For the purposes of achieving the set objectives, the author uses methods of logical analysis of text in combination with discourse analysis. Similarly, she predicts the evident presence of the phenomenon of hybridization in the Slovak journalistic practice.

Reductionism and holism in the philosophy of medicine

2020 ◽  
pp. 66-74
Author(s):  
E. Zakablukovskiy
Keyword(s):  
Philosophy Of Medicine ◽  
Point Of View ◽  
Social Model ◽  
Macro Level ◽  
New Classification

The article highlights certain aspects of the discussion on the topic of reductionism vs. holism in the philosophy of medicine. Classic radical reductionism is defeated by the concept of emergence. The s.c. bio-medical point of view on a malady, despite its relevance and clear benefit, is not recognized as universal as its adherents may claim, and it yields to an integral psycho-bio-social model. The author introduces a new classification of holism (vitalistic, social and individualistic) and makes appropriate recommendations to clinicians. It is social holism at the macro level that has proven effective in combating the spread of COVID-19.

To the Question of the Classification Patterns of Social Stratification in the Countries of the World (Brief Overview of Some Concepts and Author’s Comment)

2020 ◽  
pp. 65-75
Author(s):  
S. N. Smirnov
Keyword(s):  
Social Sciences ◽  
Social Stratification ◽  
Legal Status ◽  
Scientific Literature ◽  
Point Of View ◽  
The World

The author considers the problems of typification of society. Some concepts of typification of social stratification models in different countries formulated and justified in historical and legal, historical, sociological, and economic scientific literature are reviewed. The circumstances that make it difficult to formulate universal concepts designed for application in the complex of social Sciences are identified. These circumstances include insufficient consideration of legal factors, including the position of the legislator, the specifics of the corporate legal status, and the characteristics of the mechanism for changing individual legal status. The author offers a variant of classification of society types from the point of view of legal registration of their structure. The possibility of distinguishing types such as consolidated companies and segmented companies is justified.

scholarly journals Phylogenetic relationships among accessions in Citrus and related genera based on the insertion polymorphism of the CIRE1 retrotransposon

2020 ◽  
Vol 5 (1) ◽  
pp. 243-251
Author(s):  
Akira Horibata ◽  
Tsuneo Kato
Keyword(s):  
Phylogenetic Relationships ◽  
Sweet Orange ◽  
Point Of View ◽  
Insertion Polymorphism ◽  
Navel Orange ◽  
Citrus Germplasm ◽  
Outgroup Species ◽  
Blood Orange

AbstractA total of 145 accessions of the genus Citrus and related genera, maintained in the Conservation Garden for Citrus Germplasm at the Experimental Farm of Kindai University, Yuasa, Wakayama, Japan, were examined for their phylogenetic relationships. The present classification was conducted using an inter-retrotransposon amplified polymorphism (IRAP) method based on the insertion polymorphism of a retrotransposon, CIRE1, identified in C. sinensis. The objective of this study was to evaluate the applicability of the IRAP method for citrus classification. The constructed dendrogram showed that the 145 accessions and two outgroup species were successfully classified into five major clades. A large number of C. sinensis accessions were divided into three traditional groups, navel orange, sweet orange, and blood orange, almost corresponding to the sub-clades in the dendrogram. Several other accessions belonging to the same species, and also many hybrid cultivars from crossbreeding, were localized into the respective sub-clades or near positions in the dendrogram. Several unclassified accessions could also be located in the dendrogram, suggesting novel relationships with other accessions. It was concluded that the IRAP method based on CIRE1 insertion polymorphism was suitable for the classification of citrus from a molecular point of view.

Powerfully nilpotent groups of rank 2 or small order

2020 ◽  
Vol 23 (4) ◽  
pp. 641-658
Author(s):  
Gunnar Traustason ◽  
James Williams
Keyword(s):  
Detailed Analysis ◽  
Special Kind ◽  
Nilpotent Groups ◽  
Nilpotency Class ◽  
Central Series ◽  
Rank 2 ◽  
Full Classification

AbstractIn this paper, we continue the study of powerfully nilpotent groups. These are powerful p-groups possessing a central series of a special kind. To each such group, one can attach a powerful nilpotency class that leads naturally to the notion of a powerful coclass and classification in terms of an ancestry tree. In this paper, we will give a full classification of powerfully nilpotent groups of rank 2. The classification will then be used to arrive at a precise formula for the number of powerfully nilpotent groups of rank 2 and order {p^{n}}. We will also give a detailed analysis of the ancestry tree for these groups. The second part of the paper is then devoted to a full classification of powerfully nilpotent groups of order up to {p^{6}}.

scholarly journals Comparison of Quantitative Morphology of Layered and Arbitrary Patterns: Contrary to Visual Perception, Binary Arbitrary Patterns Are Layered from a Structural Point of View

2021 ◽  
Vol 11 (14) ◽  
pp. 6300
Author(s):  
Igor Smolyar ◽  
Daniel Smolyar
Keyword(s):  
Boolean Function ◽  
Layer Structure ◽  
Central Element ◽  
Morphological Characteristics ◽  
Building Blocks ◽  
Point Of View ◽  
Living Systems ◽  
Seismic Profiles ◽  
Contour Maps ◽  
Anisotropic Layers

Patterns found among both living systems, such as fish scales, bones, and tree rings, and non-living systems, such as terrestrial and extraterrestrial dunes, microstructures of alloys, and geological seismic profiles, are comprised of anisotropic layers of different thicknesses and lengths. These layered patterns form a record of internal and external factors that regulate pattern formation in their various systems, making it potentially possible to recognize events in the formation history of these systems. In our previous work, we developed an empirical model (EM) of anisotropic layered patterns using an N-partite graph, denoted as G(N), and a Boolean function to formalize the layer structure. The concept of isotropic and anisotropic layers was presented and described in terms of the G(N) and Boolean function. The central element of the present work is the justification that arbitrary binary patterns are made up of such layers. It has been shown that within the frame of the proposed model, it is the isotropic and anisotropic layers themselves that are the building blocks of binary layered and arbitrary patterns; pixels play no role. This is why the EM can be used to describe the morphological characteristics of such patterns. We present the parameters disorder of layer structure, disorder of layer size, and pattern complexity to describe the degree of deviation of the structure and size of an arbitrary anisotropic pattern being studied from the structure and size of a layered isotropic analog. Experiments with arbitrary patterns, such as regular geometric figures, convex and concave polygons, contour maps, the shape of island coastlines, river meanders, historic texts, and artistic drawings are presented to illustrate the spectrum of problems that it may be possible to solve by applying the EM. The differences and similarities between the proposed and existing morphological characteristics of patterns has been discussed, as well as the pros and cons of the suggested method.

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