scholarly journals Classification of δ-invariant amalgamation classes

1999 ◽  
Vol 64 (4) ◽  
pp. 1743-1750 ◽  
Author(s):  
Roman D. Aref'ev ◽  
John T. Baldwin ◽  
Marco Mazzucco
Keyword(s):  
Finite Graph ◽  
Theory Model ◽  
Dimension Function ◽  
Model Completeness ◽  
Minimal Set ◽  
Generic Structure ◽  
Finite Graphs ◽  
Generic Models ◽  
Random Graph Theory

Hrushovski's generalization of the Fraisse construction has provided a rich source of examples in model theory, model theoretic algebra and random graph theory. The construction assigns to a dimension function δ and a class K of finite (finitely generated) models a countable ‘generic’ structure. We investigate here some of the simplest possible cases of this construction. The class K will be a class of finite graphs; the dimension, δ(A), of a finite graph A will be the cardinality of A minus the number of edges of A. Finally and significantly we restrict to classes which are δ-invariant. A class of finite graphs is δ-invariant if membership of a graph in the class is determined (as specified below) by the dimension and cardinality of the graph, and dimension and cardinality of all its subgraphs. Note that a generic graph constructed as in Hrushovski's example of a new strongly minimal set does not arise from a δ-invariant class.We show there are countably many δ-invariant (strong) amalgamation classes of finite graphs which are closed under subgraph and describe the countable generic models for these classes. This analysis provides ω-stable generic graphs with an array of saturation and model completeness properties which belies the similarity of their construction. In particular, we answer a question of Baizhanov (unpublished) and Baldwin [5] and show that this construction can yield an ω-stable generic which is not saturated. Further, we exhibit some ω-stable generic graphs that are not model complete.

Classification of cultivated barley (Hordeum vulgare). 1. Historical aspects, and phenetic character analysis of some characters by information theory and by spatial autocorrelation

1986 ◽  
Vol 64 (11) ◽  
pp. 2769-2773
Author(s):  
Bernard B. Baum
Keyword(s):  
Information Theory ◽  
Hordeum Vulgare ◽  
Spatial Autocorrelation ◽  
Theory Model ◽  
Kernel Weight ◽  
Hordeum Vulgare L ◽  
Department Of Agriculture ◽  
Character Analysis ◽  
Barley Cultivars

A brief historical sketch of the classification of barley (Hordeum vulgare L.) cultivars is presented along with reference to key reviews on this subject. Characters, utilized in the comprehensive study on the barley cultivars of North America by Aberg and Wiebe (U.S. Department of Agriculture Technical Bulletin 942), were subjected to a series of phenetic character analyses using an information theory model and a spatial autocorrelation model. The ranking of the 48 characters in order of their importance (for classification and identification purposes) from the character analysis by information theory was compared with the previous rating of characters made by Aberg and Wiebe and was found to differ significantly. Numerous trials of character analysis by spatial autocorrelation using various Minkowski distances, setting various values among three parameters, never yielded results comparable with those obtained by Aberg and Wiebe. Among those trials, a few combinations of values for the three parameters (X, Y, and Z) yielded results comparable with those obtained with character analysis by information theory. Those same combinations of values were found by Estabrook and Gates (Taxon, 33: 13–25) in their study of Banisteriopsis in 1984, where they also developed the method of character analysis by spatial autocorrelation. Kernel weight was found to be the most important character.

The Investigation of the First Order Size Effect in Micro-Plastic Forming

2011 ◽  
Vol 464 ◽  
pp. 592-595
Author(s):  
Yun Wang ◽  
Jing Jing Wang ◽  
Jia Xi Wang ◽  
Zhen Ying Xu ◽  
Pei Long Dong
Keyword(s):  
Size Effects ◽  
Rapid Development ◽  
Theory Model ◽  
Electronic Industry ◽  
Layer Model ◽  
Micro Forming ◽  
First Order ◽  
Micro Parts ◽  
Plastic Forming

With the rapid development of MEMS and electronic industry, the demands for micro-parts are increasing gradually. However, size effects make the traditional forming theories and deformation mechanism not suitable in micro forming field. In this paper, we introduced the classification of the size effects. It pointed out that the size effects can be divided into the first order and the second order size effects in the micro-forming. For the first order size effects, the theory model was established based on the surface layer model. It also clarified the phenomenon that flow stress of the blank reduced with the increase of the ratio of grain size and thickness (t decreases or d increases). Finally, the model was verified with the experimental results of the first order size effects in the references, confirming the effectiveness of the theoretical model. It provides a method to theoretically and experimentally study the micro-plastic forming.

Matchings in Arbitrary Graphs

1971 ◽  
Vol 69 (3) ◽  
pp. 401-407 ◽  
Author(s):  
R. A. Brualdi
Keyword(s):  
Perfect Matching ◽  
Sufficient Conditions ◽  
Finite Graph ◽  
Maximum Cardinality ◽  
Original Proof ◽  
Locally Finite ◽  
Finite Graphs ◽  
Locally Finite Graphs ◽  
Arbitrary Graphs ◽  
Necessary And Sufficient

1. Tutte(10) has given necessary and sufficient conditions in order that a finite graph have a perfect matching. A different proof was given by Gallai(4). Berge(1) (and Ore (7)) generalized Tutte's result by determining the maximum cardinality of a matching in a finite graph. In his original proof Tutte used the method of skew symmetric determinants (or pfaffians) while Gallai and Berge used the much exploited method of alternating paths. Another proof of Berge's theorem, along with an efficient algorithm for constructing a matching of maximum cardinality, was given by Edmonds (2). In another paper (12) Tutte extended his conditions for a perfect matching to locally finite graphs.

scholarly journals Geodetic Topological Cycles in Locally Finite Graphs

10.37236/233 ◽  
2009 ◽  
Vol 16 (1) ◽  
Author(s):  
Agelos Georgakopoulos ◽  
Philipp Sprüssel
Keyword(s):  
Finite Graph ◽  
Cycle Space ◽  
Locally Finite ◽  
Finite Graphs ◽  
Locally Finite Graph ◽  
Locally Finite Graphs

We prove that the topological cycle space ${\cal C}(G)$ of a locally finite graph $G$ is generated by its geodetic topological circles. We further show that, although the finite cycles of $G$ generate ${\cal C}(G)$, its finite geodetic cycles need not generate ${\cal C}(G)$.

scholarly journals DEVELOPMENT OF ALGORITHMS TO DETERMINE WHEN TO USE GENERIC MODELS OF THE SENSORS

2019 ◽  
Vol 22 (6) ◽  
pp. 118-126
Author(s):  
R. W. Stativko ◽  
E. P. Kolomytseva
Keyword(s):  
Preliminary Analysis ◽  
Smart Home ◽  
Control Center ◽  
Lighting Control ◽  
Generic Models ◽  
Correct Placement ◽  
Standard Models ◽  
Main Components ◽  
Control Modules

The aim of this work is to develop approaches to automate the process of installing sensors for monitoring "smart home". The article briefly describes the emergence of the smart home system and the further spread of this system in Russia. “Smart Home” is a home control system that provides automatic and well-coordinated operation of a whole complex of systems, in particular, lighting control, which requires the use of correct placement of sensors. Such a system can provide benefits for people with disabilities. The sensor layout will optimize energy consumption. The paper gives a brief description of the classic sensor sets for a smart home. A classic set for a smart home are: control center, cameras, modules in the socket, wall switches, control modules and various sensors. The classification of sensors according to various characteristics and the method of connection is given. The article focuses on the placement of motion and light sensors, which are often the basis of a “smart home” and are used to control various devices. This paper describes the classic smart home circuit and lists its main components. An algorithm is proposed for determining the need for using standard models of motion and illumination sensors and their quantitative ratio from the room analysis, namely: the type of room (residential, non-residential), the size of the room, the presence of window and door openings. The presented algorithm contains the following steps: preliminary analysis of the room in which it is necessary to install motion and light sensors, take into account the characteristics of the sensors. Brief results of testing are given. This work shows that it is quite possible to arrange a “smart home” complex in an individual residential structure.

The Ramsey Property for Families of Graphs Which Exclude a Given Graph

1992 ◽  
Vol 44 (5) ◽  
pp. 1050-1060 ◽  
Author(s):  
V. Rödl ◽  
N. Sauer
Keyword(s):  
Positive Integer ◽  
Finite Graph ◽  
Ramsey Property ◽  
Finite Graphs ◽  
Cut Point

AbstractFor graphs A, B and a positive integer r, the relation means that whenever Δ is an r-colouring of the vertices of A, then there is an embedding ϕ of B into A such that Δ ∘ ϕ is constant. A class of graphs has the Ramsey property if, for every , there is an such that . For a given finite graph G, let Forb(G) denote the class of all finite graphs which do not embed G. It is known that, if G is 2-connected, then Forb() has the Ramsey property, and Forb(G) has the Ramsey property if and only if Forb(G) also has the Ramsey property. In this paper we show that if neither G nor its complement is 2-connected, then either (i) G has a cut point adjacent to every other vertex, or (ii) G has a cut point adjacent to every other vertex except one. We show that Forb(G) has the Ramsey property if G is a path of length 2 or 3, but that Forb(G) does not have the Ramsey property if (i) holds and G is not the path of length 2.

The Therapeutic Community and the Mental Institution: A New Perspective

1970 ◽  
Vol 26 (1) ◽  
pp. 79-82
Author(s):  
Louis H. Muzekari
Keyword(s):  
Broad Spectrum ◽  
Organizational Context ◽  
Therapeutic Community ◽  
Total Institution ◽  
Therapeutic Communities ◽  
Generic Models ◽  
New Perspective ◽  
Mental Institution ◽  
Agent Of Change

The therapeutic community construct has been applied to a broad spectrum of extant institutional programs. However, little attention has been devoted to the nature of the therapeutic community as a system or subsystem within an organizational context and its role as an agent of change. Four generic models of a therapeutic community are presented as a basis for the analysis and classification of existing therapeutic communities in relation to the total institution within which they function as well as the extramural community.

Automatic classification of plants based on information content

1970 ◽  
Vol 48 (4) ◽  
pp. 793-802 ◽  
Author(s):  
Laszlo Orloci
Keyword(s):  
Information Theory ◽  
Cluster Analysis ◽  
Information Content ◽  
Random Sample ◽  
Nearest Neighbor ◽  
Theory Model ◽  
Second Stage ◽  
Large Samples ◽  
Two Stages

An information theory model is described and its application is illustrated by an actual example. Classification is accomplished in two stages. The first stage includes cluster analysis of a random sample by an agglomerative method. Cluster analysis is followed by nearest neighbor sorting in the second stage whereby the clustering results are imposed on a second random sample of the same collection. The advantage of the procedure resides in the fact that large samples can be handled, and also, the classification produced in the second stage can be used, under specific restrictive assumptions, for unbiased prediction of different population properties. While the present paper is principally concerned with the technique itself, some taxonomic conclusions are also given.

Random Colourings and Automorphism Breaking in Locally Finite Graphs

2013 ◽  
Vol 22 (6) ◽  
pp. 885-909 ◽  
Author(s):  
FLORIAN LEHNER
Keyword(s):  
Automorphism Group ◽  
Haar Measure ◽  
Finite Graph ◽  
Locally Finite ◽  
Finite Graphs ◽  
Locally Finite Graph ◽  
Locally Finite Graphs ◽  
Null Set

A colouring of a graphGis called distinguishing if its stabilizer in AutGis trivial. It has been conjectured that, if every automorphism of a locally finite graph moves infinitely many vertices, then there is a distinguishing 2-colouring. We study properties of random 2-colourings of locally finite graphs and show that the stabilizer of such a colouring is almost surely nowhere dense in AutGand a null set with respect to the Haar measure on the automorphism group. We also investigate random 2-colourings in several classes of locally finite graphs where the existence of a distinguishing 2-colouring has already been established. It turns out that in all of these cases a random 2-colouring is almost surely distinguishing.

scholarly journals Topological entropy for the canonical completely positive maps on graph C*-Algebras

2004 ◽  
Vol 70 (1) ◽  
pp. 101-116 ◽  
Author(s):  
Ja A. Jeong ◽  
Gi Hyun Park
Keyword(s):  
Topological Entropy ◽  
Finite Graph ◽  
Infinite Graph ◽  
Completely Positive Map ◽  
Completely Positive Maps ◽  
Completely Positive ◽  
Locally Finite ◽  
Finite Graphs ◽  
C Algebras ◽  
Positive Maps

Let C*(E) = C*(se, pv) be the graph C*-algebra of a directed graph E = (E0, E1) with the vertices E0 and the edges E1. We prove that if E is a finite graph (possibly with sinks) and φE: C*(E) → C*(E) is the canonical completely positive map defined by then Voiculescu's topological entropy ht(φE) of φE is log r(AE), where r(AE) is the spectral radius of the edge matrix AE of E. This extends the same result known for finite graphs with no sinks. We also consider the map φE when E is a locally finite irreducible infinite graph and prove that , where the supremum is taken over the set of all finite subgraphs of E.

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