An Algorithm for the Enumeration of Serial and/or Parallel Combinations of Kinematic Building Blocks

2004 ◽  
Author(s):  
Hong-Sen Yan ◽  
Feng-Ming Ou ◽  
Ming-Feng Tang
Keyword(s):  
Graph Theory ◽  
Building Blocks ◽  
Power Source ◽  
Cam Follower ◽  
Tree Representations ◽  
The Given

An algorithm is presented, based on graph theory, for enumerating all feasible serial and/or parallel combined mechanisms from the given rotary or translational power source and specific kinematic building blocks. Through the labeled out-tree representations for the configurations of combined mechanisms, the enumeration procedure is developed by adapting the algorithm for the enumeration of trees. A rotary power source and four kinematic building blocks: a crank-rocker linkage, a rack-pinion, a double-slider mechanism, and a cam-follower mechanism, are chosen as the combination to illustrate the algorithm. And, two examples are provided to validate the algorithm.

Pattern Recognition in Histo-Pathology: Basic Considerations

1982 ◽  
Vol 21 (01) ◽  
pp. 15-22 ◽  
Author(s):  
W. Schlegel ◽  
K. Kayser
Keyword(s):  
Pattern Recognition ◽  
Graph Theory ◽  
Normal Tissue ◽  
Diagnostic Procedures ◽  
Minimal Distance ◽  
Malignant Growth ◽  
Colon Tissue ◽  
First Results ◽  
Tissue Structures ◽  
The Given

A basic concept for the automatic diagnosis of histo-pathological specimen is presented. The algorithm is based on tissue structures of the original organ. Low power magnification was used to inspect the specimens. The form of the given tissue structures, e. g. diameter, distance, shape factor and number of neighbours, is measured. Graph theory is applied by using the center of structures as vertices and the shortest connection of neighbours as edges. The algorithm leads to two independent sets of parameters which can be used for diagnostic procedures. First results with colon tissue show significant differences between normal tissue, benign and malignant growth. Polyps form glands that are twice as wide as normal and carcinomatous tissue. Carcinomas can be separated by the minimal distance of the glands formed. First results of pattern recognition using graph theory are discussed.

scholarly journals Graph Theoretic Techniques in the Analysis of Uniquely Localizable Sensor Networks

2009 ◽  
pp. 146-173 ◽  
Author(s):  
Bill Jackson ◽  
Tibor Jordán
Keyword(s):  
Graph Theory ◽  
Sensor Networks ◽  
Optimization Problems ◽  
Partial Information ◽  
Two Dimensions ◽  
Localization Problem ◽  
Graph Theoretic ◽  
Network Localization ◽  
Exact Location ◽  
The Given

In the network localization problem the goal is to determine the location of all nodes by using only partial information on the pairwise distances (and by computing the exact location of some nodes, called anchors). The network is said to be uniquely localizable if there is a unique set of locations consistent with the given data. Recent results from graph theory and combinatorial rigidity made it possible to characterize uniquely localizable networks in two dimensions. Based on these developments, extensions, related optimization problems, algorithms, and constructions also became tractable. This chapter gives a detailed survey of these new results from the graph theorist’s viewpoint.

scholarly journals Cryptosystem using double vertex graph

2020 ◽  
Vol 13 (44) ◽  
pp. 4483-4489
Author(s):  
C Beaula ◽  
Keyword(s):  
Graph Theory ◽  
Secure Communication ◽  
System Method ◽  
Encryption And Decryption ◽  
Vertex Graph ◽  
Private And Public ◽  
Almost All ◽  
Encryption Method ◽  
The Given ◽  
Edge Labeling

Background/Objective: The Coronavirus Covid-19 has affected almost all the countries and millions of people got infected and more deaths have been reported everywhere. The uncertainty and fear created by the pandemic can be used by hackers to steal the data from both private and public systems. Hence, there is an urgent need to improve the security of the systems. This can be done only by building a strong cryptosystem. So many researchers started embedding different topics of mathematics like algebra, number theory, and so on in cryptography to keep the system, safe and secure. In this study, a cryptosystem using graph theory has been attempted, to strengthen the security of the system. Method: A new graph is constructed from the given graph, known as a double vertex graph. The edge labeling of this double vertex graph is used in encryption and decryption. Findings: A new cryptosystem using the amalgamation of the path, its double vertex graph and edge labeling has been proposed. From the double vertex graph of a path, we have given a method to find the original path. To hack such an encrypted key, the knowledge of graph theory is important, which makes the system stronger. Applications:The one-word encryption method will be useful in every security system that needs a password for secure communication or storage or authentication. Keywords: Double vertex graphs; path; adjacency matrix; encryption; cryptography

scholarly journals A weapon in the battle of definitions: a special rhetorical strategy in Hánfēizǐ

2014 ◽  
Vol 68 (4) ◽  
pp. 969-999
Author(s):  
Lukáš Zádrapa
Keyword(s):  
Textual Analysis ◽  
Building Blocks ◽  
Warring States Period ◽  
Rhetorical Strategy ◽  
Semantic Relationships ◽  
Lexical Semantic ◽  
Warring States ◽  
Structural Relationships ◽  
Textual Strategies ◽  
The Given

Abstract Regardless of the actual views on the art of embellished speech of the author(s) presented by the collection of essays known as Hánfēizǐ, the work is well known for its formal intricacy and refinement. The composition of several chapters appears unique against the background of other transmitted texts of the Warring States period, and the same is true of some textual strategies serving to convey the presented ideas with intensified rhetorical appeal. In this study, I aim to identify one of these strategies, showing, on the basis of thorough textual analysis, how the sections in which it is employed are structured and how the given devices contribute to the construction of meaning. Relevant parts of the chapters 45 (“Guǐshǐ” 詭使), 46 (“Liùfǎn” 六反) and 47 (“Bāshuō” 八說) are analyzed here both with regard to their formal features, such as various arrangements of basic building blocks or transformations of metalinguistic formulae, and to their semantics, including the systematic lexical-semantic relationships of synonymy and antonymy. It is argued that not only overt interventions by the author in favour of “correct” definitions of selected terms, but also the very inventory of the terms itself and their deeper structural relationships and tensions reveal much about the author's intentions and opinions.

New Developments in Quasigroup-Based Cryptography

2014 ◽  
pp. 286-317 ◽  
Author(s):  
Aleksandra Mileva
Keyword(s):  
Building Blocks ◽  
Block Ciphers ◽  
Public Key ◽  
Message Authentication ◽  
Authentication Codes ◽  
New Developments ◽  
Identification Schemes ◽  
Public Key Cryptosystems ◽  
Research Activities ◽  
The Given

This chapter offers an overview of new developments in quasigroup-based cryptography, especially of new defined quasigroup-based block ciphers and stream ciphers, hash functions and message authentication codes, PRNGs, public key cryptosystems, etc. Special attention is given to Multivariate Quadratic Quasigroups (MQQs) and MQQ public key schemes, because of their potential to become one of the most efficient pubic key algorithms today. There are also directions of using MQQs for building Zero knowledge ID-based identification schemes. Recent research activities show that some existing non-quasigroup block ciphers or their building blocks can be represented by quasigroup string transformations. There is a method for generating optimal 4x4 S-boxes by quasigroups of order 4, by which a more optimized hardware implementation of the given S-box can be obtained. Even some block ciphers' modes of operations can be represented by quasigroup string transformations, which leads to finding weaknesses in the interchanged use of these modes.

Which Elasticity Tensors are Realizable?

1995 ◽  
Vol 117 (4) ◽  
pp. 483-493 ◽  
Author(s):  
Graeme W. Milton ◽  
Andrej V. Cherkaev
Keyword(s):  
Building Blocks ◽  
Elasticity Tensor ◽  
Isotropic Phase ◽  
Order Tensor ◽  
Two Phase ◽  
Effective Elasticity ◽  
Elasticity Tensors ◽  
Two Phases ◽  
The Given ◽  
Fourth Order Tensor

It is shown that any given positive definite fourth order tensor satisfying the usual symmetries of elasticity tensors can be realized as the effective elasticity tensor of a two-phase composite comprised of a sufficiently compliant isotropic phase and a sufficiently rigid isotropic phase configured in an suitable microstructure. The building blocks for constructing this composite are what we call extremal materials. These are composites of the two phases which are extremely stiff to a set of arbitrary given stresses and, at the same time, are extremely compliant to any orthogonal stress. An appropriately chosen subset of the extremal materials are layered together to form the composite with elasticity tensor matching the given tensor.

Portable Pneumatic Power-Harvesting Ankle-Foot-Orthosis

2008 ◽  
Author(s):  
Robin Chin ◽  
Elizabeth T. Hsiao-Wecksler ◽  
Eric Loth ◽  
Andrew Alleyne ◽  
Scott Manwaring ◽  
...  
Keyword(s):  
Power Source ◽  
Power Harvesting ◽  
Ankle Motion ◽  
Ankle Foot Orthosis ◽  
Locking Mechanism ◽  
External Power Source ◽  
Cam Follower ◽  
External Power ◽  
Pneumatic Power ◽  
Foot Orthosis

In this paper, we present a novel ankle-foot-orthosis (AFO) design that controls ankle motion by providing a plantarflexion stop with free dorsiflexion during gait. The biomechanical controls are accomplished with a unique application of a cam-follower design that uses pneumatic power harvested via an air bellow embedded into the insole of the AFO (Figure 1). This portable design is self-contained and does not require any external power source to provide for the plantarflexion stop locking mechanism. It is the first step in a series of untethered fluid-powered orthotic devices.

scholarly journals Sun Toughness Conditions for P 2 and P 3 Factor Uniform and Factor Critical Avoidable Graphs

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Shu Gong ◽  
Haci Mehmet Baskonus ◽  
Wei Gao
Keyword(s):  
Graph Theory ◽  
Computer Networks ◽  
The Sun ◽  
Graph Structure ◽  
Network Graph ◽  
The Given ◽  
Path Factor

The security of a network is closely related to the structure of the network graph. The denser the network graph structure is, the better it can resist attacks. Toughness and isolated toughness are used to characterize the vulnerable programs of the network which have been paid attention from mathematics and computer scholars. On this basis, considering the particularity of the sun component structures, sun toughness was introduced in mathematics and applied to computer networks. From the perspective of modern graph theory, this paper presents the sun toughness conditions of the path factor uniform graph and the path factor critical avoidable graph in P ≥ 2 -factor and P ≥ 3 -factor settings. Furthermore, examples show that the given boundaries are sharp.

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 Application of Reverse Vertex Magic Labeling of a Graph

2019 ◽  
Vol 8 (11) ◽  
pp. 12-14
Keyword(s):  
Graph Theory ◽  
Graph Labeling ◽  
The Given ◽  
Positive Integers ◽  
A Company

Graph labeling is a currently emerging area in the research of graph theory. A graph labeling is an assignment of integers to the vertices or edges or both subject to certain conditions. If the labels of edges are distinct positive integers and for each vertex the sum of the labels of all edges incident with is the same for every vertex in the given graph, then the labeling of the graph is called magic labeling. There are several types of magic labeling defined on graphs. In this paper we consider vertex magic labeling and group magic labeling of graphs as an application of magic labeling. We solve a problem of finding number of computers/workstations to be allocated to each department in a company under certain conditions.

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