SOME PROPERTIES OF BINARY SERIES-PARALLEL GRAPHS

2014 ◽  
Vol 28 (4) ◽  
pp. 565-572 ◽  
Author(s):  
Hosam M. Mahmoud
Keyword(s):  
Random Walk ◽  
Normal Distribution ◽  
Growth Model ◽  
Average Length ◽  
Golden Ratio ◽  
Coding Method ◽  
Incremental Growth

We introduce an incremental growth model for directed binary series-parallel (SP) graphs. The vertices of a directed binary SP graphs can only have outdgrees 1 or 2. We show that the number of vertices of outdegree 1 have a normal distribution (so, necessarily, the vertices of outdegree 2 have a normal distribution, too). Furthermore, we study the average length of a random walk between the poles of the graph. The asymptotic equivalent of the latter property includes the golden ratio. Pólya urns will systematically provide a coding method to initiate the studies.

scholarly journals Diamond aggregation

2010 ◽  
Vol 149 (2) ◽  
pp. 351-372
Author(s):  
WOUTER KAGER ◽  
LIONEL LEVINE
Keyword(s):  
Random Walk ◽  
Growth Model ◽  
Power Law ◽  
Simple Random Walk ◽  
Internal Diffusion ◽  
Diffusion Limited Aggregation ◽  
Directional Bias ◽  
Model Based ◽  
Diffusion Limited ◽  
Logarithmic Fluctuations

AbstractInternal diffusion-limited aggregation is a growth model based on random walk in ℤd. We study how the shape of the aggregate depends on the law of the underlying walk, focusing on a family of walks in ℤ2 for which the limiting shape is a diamond. Certain of these walks—those with a directional bias toward the origin—have at most logarithmic fluctuations around the limiting shape. This contrasts with the simple random walk, where the limiting shape is a disk and the best known bound on the fluctuations, due to Lawler, is a power law. Our walks enjoy a uniform layering property which simplifies many of the proofs.

SOME NODE DEGREE PROPERTIES OF SERIES–PARALLEL GRAPHS EVOLVING UNDER A STOCHASTIC GROWTH MODEL

2013 ◽  
Vol 27 (3) ◽  
pp. 297-307 ◽  
Author(s):  
Hosam M. Mahmoud
Keyword(s):  
Stochastic Model ◽  
Normal Distribution ◽  
Growth Model ◽  
Multivariate Normal Distribution ◽  
Exact Distribution ◽  
Node Degree ◽  
Natural Growth ◽  
Multivariate Normal ◽  
Stochastic Growth ◽  
Graph Properties

We introduce a natural growth model for directed series-parallel (SP) graphs and look at some of the graph properties under this stochastic model. Specifically, we look at the degrees of certain types of nodes in the random SP graph. We examine the degree of a pole and will find its exact distribution, given by a probability formula with alternating signs. We also prove that, for a fixed value s, the number of nodes of outdegree 1, …, s asymptotically has a joint multivariate normal distribution. Pólya urns will systematically provide a working tool.

PEOPLING OF OCEANIA: CLARIFYING AN INITIAL SETTLEMENT HORIZON IN THE MARIANA ISLANDS AT 1500 BC

Radiocarbon ◽  
2020 ◽  
pp. 1-22 ◽  
Author(s):  
Mike T Carson
Keyword(s):  
Growth Model ◽  
Mariana Islands ◽  
Long Distance ◽  
Crucial Step ◽  
Marine Samples ◽  
Oceanic Region ◽  
Initial Settlement ◽  
Incremental Growth

ABSTRACT Radiocarbon (14C) has been instrumental in clarifying how people came to inhabit the expanse of Pacific Oceania, now supporting an “incremental growth model” that shows a number of long-distance sea-crossing migrations over the last few millennia. A crucial step in this narrative involved the initial settlement of the remote-distance Oceanic region, in the case of the Mariana Islands around 1500 BC. The Marianas case can be demonstrated through delineation of stratigraphic layers, dating of individual points or features within those layers, redundant dating of samples in secure contexts, localized and taxon-specific corrections for marine samples, and cross-constraining dating of superimposed layer sequences. Based on the technical and methodological lessons from the Marianas example, the further steps of the incremental growth model will continue to be refined across Pacific Oceania. Many of these issues may be relevant for broader research of ancient settlement horizons in other regions.

ON THE COMBINATORICS OF BINARY SERIES-PARALLEL GRAPHS

2016 ◽  
Vol 30 (2) ◽  
pp. 244-260
Author(s):  
Micha Hofri ◽  
Chao Li ◽  
Hosam Mahmoud
Keyword(s):  
Random Walk ◽  
Structural Equation ◽  
Regular Expression ◽  
Average Length ◽  
Probability Model ◽  
Order Number ◽  
Systematic Method ◽  
Large Graphs ◽  
Combinatorial Properties ◽  
Transportation Modeling

Binary series-parallel (BSP) graphs have applications in transportation modeling, and exhibit interesting combinatorial properties. This work is limited to the second aspect. The BSP graphs of a given size – measured in edges – are enumerated. Under a uniform probability model, we investigate the asymptotic distribution of the order (number of vertices) and the asymptotic average length of a random walk (under different strategies) of large graphs of the same size. The systematic method throughout is to define the graphs, and the features we evaluate by a structural equation (equivalent to a regular expression). The structural equation is translated into an equation for a generating function, which is then analyzed.

scholarly journals Institutional Change in ASEAN: A Conceptual Analysis of the ASEAN Political-Security Community

2021 ◽  
pp. 58-77
Author(s):  
Kwei-Bo Huang
Keyword(s):  
Institutional Change ◽  
Growth Model ◽  
Analytical Framework ◽  
Security Cooperation ◽  
Security Community ◽  
Field Investigations ◽  
Making Choices ◽  
Incremental Growth ◽  
Political Security ◽  
Internal And External Factors

ObjectivesTo figure out whether adaptation – specifically, Ernst B. Hass’ incremental growth model – is able to account for institutional changes of ASEAN in the shape of the ASEAN Political-Security Community (APSC).MethodsUse Ernst Hass' theoretical arguments and propositions to examine some of ASEAN's internal and external factors that have an impact on the discussion, planning, and implementation of the APSC. Three variables -- the types of knowledge used by ASEAN leaders in making choices, their political objectives, as well as the manner in which issues being negotiated -- are found in historical documents and academic analyses and then operationalized in a simpler way.ResultsThe selection of the incremental growth model is justified and the incremental growth model can serve as an innovative analytical framework for the institutional change in ASEAN.ConclusionsASEAN is in a dynamic context where increased expectations and pressure from within and outside are taking place all at once. The institutionalization of ASEAN security arrangements, originally led by the initiation of the ASC/APSC, means that ASEAN has started facing these expectations and pressure and moved on to enhance security cooperation to a certain degree. It is time for students of international relations to apply again the previous finding of adaptation through incremental growth and conduct further field investigations into the current evolution of the APSC.

Growth model induced by a random walk of particles

2002 ◽  
Vol 35 (28) ◽  
pp. 5807-5814 ◽  
Author(s):  
S M D Queir$oacute$s ◽  
A L Ferreira
Keyword(s):  
Random Walk ◽  
Growth Model

One Eye is Usually Centred Horizontally (and near the Golden Section Vertically) in Portraits over the Past 500 Years

Perception ◽  
1997 ◽  
Vol 26 (1_suppl) ◽  
pp. 18-18
Author(s):  
C W Tyler
Keyword(s):  
Normal Distribution ◽  
Art Criticism ◽  
Golden Section ◽  
Golden Ratio ◽  
Bimodal Distribution ◽  
Eye Position ◽  
Height Distribution ◽  
The Past ◽  
Single Person

Although the eyes are a key feature of facial portraits, compositional rules for the placement of the eyes relative to the frame are obscure. Two hypotheses of eye position in the portrait frame were compared: that the pair of eyes were symmetrically placed or that one eye was centred in the frame. Portraits were defined as paintings of a single person from the waist up without other dominant objects or animals in the scene. From all artists represented in seven source-books on portraiture over the past five centuries (eg from van Eyck to Picasso), the first portrait in which both eyes were visible was analysed (170 portraits). Horizontal and vertical eye and mouth positions were measured as a proportion of frame width and height. The eyes in portraits tend to cluster horizontally around the centre vertical, with one eye centred in a normal distribution with a sigma of only ±5% of the frame width. The binocular mean had a bimodal distribution implying that one or other eye was usually centred. Conversely, the eye height distribution was not centred vertically but peaked close to the classic golden ratio of 0.618 (where the smaller portion has the same ratio to the larger as does the larger to the whole), with virtually no eyes below the vertical centre. The mouth distribution was much broader than that of the centred eye. The eye centring with an accuracy of ∼1 eye width seems not to be mentioned in art criticism, which suggests that unconscious functions operate in our aesthetic judgements.

Aminoguanidinium(1+) pentafluorozirconate: multiple redetermination and comparisons

2002 ◽  
Vol 58 (5) ◽  
pp. 841-848 ◽  
Author(s):  
C. R. Ross II ◽  
M. R. Bauer ◽  
R. M. Nielson ◽  
S. C. Abrahams
Keyword(s):  
Bond Length ◽  
Normal Distribution ◽  
Structural Changes ◽  
Average Length ◽  
Unit Cell ◽  
Unit Cell Parameters ◽  
Cell Parameters ◽  
Normal Probability ◽  
Radiation Induced ◽  
Atomic Coordinates

The structure of CN4H7ZrF5 reported by Bukvetskii et al. [Koord. Khim. (1992). 18, 576–579] has been independently redetermined on the basis of measurements on three different crystals. Assuming all four resulting structures are drawn from a normal distribution, normal probability analysis of the atomic coordinates taken in pairs reveals joint standard uncertainties that are underestimated by factors as large as 16.5 for the x(Zr) coordinate. Unit-cell parameters in the four crystals similarly have joint uncertainties, under the same assumption, that are underestimated by factors as large as 83.0 for the b axis. The variations in axial lengths from crystal to crystal and the declines in standard reflection intensities by 13–15% in at least two of the crystals measured are consistent with the inference that the distribution is not normal. Rather, the differences observed may be assumed to be caused by small but highly significant radiation-induced structural changes. The large underestimations hence reflect physical differences among the four irradiated crystals. The determinations show that the CN4H7 +1 cation is exactly planar except for the two H atoms bonded to the terminal N atom; the plane of this NH2 group is normal to that of the cation. The average length of the three independent C—N bonds is 1.318 (11) Å; the N—N bond length is 1.397 (3) Å. Distorted ZrF7 pentagonal bipyramids share edges, forming chains linked by N—H...F bonds to the CN4H7 +1 ions.

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