On a lower estimate of the growth function for the Grigorchuk group

2000 ◽  
Vol 67 (3) ◽  
pp. 403-405 ◽  
Author(s):  
Yu. G. Leonov
Keyword(s):  
Lower Estimate ◽  
Growth Function ◽  
Grigorchuk Group

LOWER BOUNDS ON THE GROWTH OF A GROUP ACTING ON THE BINARY ROOTED TREE

2001 ◽  
Vol 11 (01) ◽  
pp. 73-88 ◽  
Author(s):  
LAURENT BARTHOLDI
Keyword(s):  
Lower Bound ◽  
Lower Bounds ◽  
Rooted Tree ◽  
Growth Function ◽  
Finitely Generated ◽  
Grigorchuk Group ◽  
Intermediate Growth

In 1980, Rostislav Grigorchuk constructed an infinite finitely generated torsion 2-group G, called the first Grigorchuk group, and in 1983 showed that it is of intermediate growth, with the following estimates on its growth function γ (See [6]): [Formula: see text] where β= log 32(31)≈ 0.991. He conjectured that the lower bound is actually tight. In this paper we improve the lower bound to [Formula: see text] where α≈0.5157, and thus disproves the conjecture.

Conjugacy growth and width of certain branch groups

2014 ◽  
Vol 24 (08) ◽  
pp. 1213-1231 ◽  
Author(s):  
Elisabeth Fink
Keyword(s):  
Lower Bound ◽  
Growth Function ◽  
Conjugacy Classes ◽  
Grigorchuk Group ◽  
Intermediate Growth ◽  
Algebraic Properties

The conjugacy growth function counts the number of distinct conjugacy classes in a ball of radius n. We give a lower bound for the conjugacy growth of certain branch groups, among them the Grigorchuk group. This bound is a function of intermediate growth. We further prove that certain branch groups have the property that every element can be expressed as a product of uniformly boundedly many conjugates of the generators. We call this property bounded conjugacy width. We also show how bounded conjugacy width relates to other algebraic properties of groups and apply these results to study the palindromic width of some branch groups.

On Uniqueness of the Wulff Shape for Cellular Automata

1991 ◽  
Vol 14 (1) ◽  
pp. 75-89
Author(s):  
Paweł Wlaź
Keyword(s):  
Cellular Automata ◽  
Large Class ◽  
Growth Function ◽  
Wulff Shape ◽  
Transition Rules

In this paper, ordered transition rules are investigated. Such rules describe an increment of mono-crystals and for every rule one can calculate so called Wulff Shape. It is shown that for some large class of these rules, there exists at most one growth function which generates a given Wulff Shape.

scholarly journals Alterations in intestinal microbiota diversity, composition, and function in patients with sarcopenia

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Lin Kang ◽  
Pengtao Li ◽  
Danyang Wang ◽  
Taihao Wang ◽  
Dong Hao ◽  
...  
Keyword(s):  
Skeletal Muscle ◽  
16S Rrna ◽  
Intestinal Microbiota ◽  
Muscle Growth ◽  
Growth Function ◽  
16S Rrna Sequencing ◽  
Fecal Samples ◽  
Lipopolysaccharide Biosynthesis ◽  
Rrna Sequencing ◽  
And Function

Abstract16S rRNA sequencing of human fecal samples has been tremendously successful in identifying microbiome changes associated with both aging and disease. A number of studies have described microbial alterations corresponding to physical frailty and nursing home residence among aging individuals. A gut-muscle axis through which the microbiome influences skeletal muscle growth/function has been hypothesized. However, the microbiome has yet to be examined in sarcopenia. Here, we collected fecal samples of 60 healthy controls (CON) and 27 sarcopenic (Case)/possibly sarcopenic (preCase) individuals and analyzed the intestinal microbiota using 16S rRNA sequencing. We observed an overall reduction in microbial diversity in Case and preCase samples. The genera Lachnospira, Fusicantenibacter, Roseburia, Eubacterium, and Lachnoclostridium—known butyrate producers—were significantly less abundant in Case and preCase subjects while Lactobacillus was more abundant. Functional pathways underrepresented in Case subjects included numerous transporters and phenylalanine, tyrosine, and tryptophan biosynthesis suggesting that protein processing and nutrient transport may be impaired. In contrast, lipopolysaccharide biosynthesis was overrepresented in Case and PreCase subjects suggesting that sarcopenia is associated with a pro-inflammatory metagenome. These analyses demonstrate structural and functional alterations in the intestinal microbiota that may contribute to loss of skeletal muscle mass and function in sarcopenia.

scholarly journals Ekstrak Etanol Kulit Buah Naga Menurunkan Indikasi Neoplasia Mammae Tikus Putih Berdasarkan Histopatologi dan Inhibitor Siklooksigenase-2

2018 ◽  
Vol 19 (1) ◽  
pp. 23
Author(s):  
Muhammad Thohawi Elziyad Purnama ◽  
Ragil Angga Prastiya ◽  
Faisal Fikri ◽  
Amung Logam Saputro ◽  
Bodhi Agustono
Keyword(s):  
Mammary Gland ◽  
Ethanolic Extract ◽  
Ethanol Extract ◽  
Growth Function ◽  
Histopathological Features ◽  
White Rats ◽  
Fruit Skin ◽  
Dragon Fruit ◽  
Cox 2 ◽  
Dermal Injection

Cancer caused uncontrolled cell proliferation and triggered by changes on cell information that regulate growth function. Each cell has different potential so many cancer prevalence such as endometrial cancer, lymph node cancer, lung cancer, skin and mammary gland cancer. The aims of this study were to assess the potential of dragon fruit skin ethanolic extract on white rats (Rattus norvegicus) exposed 7,12- Dimethylbenz(á)antrasena (DMBA) on mammary gland based on histopathological features and cyclooxygenase-2 (Cox-2) intensity. This study were used 20 of rats randomly divided into five group and each groups consisted of four rats, i.e: K+ weren’t treated DMBA and extract; K- were treated with DMBA; P1 were treated with DMBA and extract 10 mg/kg BW; P2 were treated with DMBA and extract 15 mg/kg BW; P3 were treated with DMBA and extract 20 mg/kg BW. The DMBA was given by intra dermal injection during twice a week for five weeks and the extracts with gastric tube everyday till 14 days. The data was analyzed by Anova test and continued with Duncan test. The result showed that the histopathological features were decrease significantly on P3. The variables of Cox-2 intensity were decrease significantly on P1, P2 and P3. Conclusion of this study was ethanol extract of dragon fruit skin can decrease neoplastic indication of mammary gland on white rats (R. norvegicus) based on histopathological features and Cox-2 inhibitors.

On the closure of the first Grigorchuk group

2011 ◽  
Vol 173 (4) ◽  
pp. 371-377
Author(s):  
Yuriy G. Leonov
Keyword(s):  
Grigorchuk Group

Growth and spatiotemporal distribution of juvenile shortfin mako (Isurus oxyrinchus) in the western and central North Pacific

2015 ◽  
Vol 66 (12) ◽  
pp. 1176 ◽  
Author(s):  
M. Kai ◽  
K. Shiozaki ◽  
S. Ohshimo ◽  
K. Yokawa
Keyword(s):  
North Pacific ◽  
Linear Models ◽  
North Pacific Ocean ◽  
Age Groups ◽  
Growth Curves ◽  
Growth Function ◽  
Gaussian Mixture ◽  
Isurus Oxyrinchus ◽  
Shortfin Mako ◽  
Central North Pacific

This paper presents an estimation of growth curves and spatiotemporal distributions of juvenile shortfin mako shark (Isurus oxyrinchus) in the western and central North Pacific Ocean using port sampling data collected from 2005 to 2013. The monthly length compositions show a clear transition of three modes in the size range of smaller than 150-cm precaudal length (PCL), which were believed to represent the growth of age-0 to age-2 classes, and they were then decomposed into age groups by fitting a Gaussian mixture distribution. Simulation data of lengths at monthly ages were generated from the mean and standard deviation of each distribution, and fit with a von Bertalanffy growth function. Parameters of the estimated growth curves for males and females were 274.4 and 239.4cm PCL for the asymptotic length and 0.19 and 0.25 year–1 for the growth coefficient indicating apparently faster growth than previously reported. Generalised linear models were applied to age-0 to explore the seasonal changes of PCL by area. They were born during late autumn and winter off the coast of north-eastern Japan, an area known to have relatively high productivity compared with other pelagic areas, and gradually expanded their habitat eastward and northward with the seasons as they grew.

An Antarctic shelf population of the deep-sea, Pacific brachiopod Neorhynchia strebeli

1997 ◽  
Vol 77 (2) ◽  
pp. 399-407 ◽  
Author(s):  
David K.A. Barnes ◽  
Lloyd S. Peck
Keyword(s):  
Deep Sea ◽  
Growth Function ◽  
Weddell Sea ◽  
Von Bertalanffy ◽  
Growth Rings ◽  
Von Bertalanffy Growth Function ◽  
Annual Periodicity ◽  
A Site ◽  
The Antarctic ◽  
Order Rhynchonellida

Thirty-five specimens of the articulate brachiopod Neorhynchia strebeli were collected from a site at 814 m in the Weddell Sea. This was only the second species of the order Rhynchonellida to be found in Antarctica. Formerly N. strebeli was known solely from abyssal Pacific Ocean localities. A circumantarctic distribution is suggested in addition to the known deep-sea Pacific range. The specimens of this collection showed considerable commissure variation, suggesting that the previously proposed erection of two subspecies on the basis of this character is erroneous, and emphasises the phenotypic plasticity of some articulate brachiopods. The valve lengths and the number of alpha growth rings in the sample showed a normal distribution and a von Bertalanffy growth function was fitted to the data: Lt = 23 (1-exp[-0·228t]). If the alpha growth rings were of annual periodicity, the ages attained by the Antarctic N. strebeli of 11 y would be substantially lower than those reported for other Weddell Sea brachiopods. The epibiotic communities occurring on the valves of N. strebeli were impoverished, which is characteristic of deep water Antarctic brachiopods. The few specimens collected with their substratum were attached to small pebbles, but the typical attachment substrata may be different.

A description of the growth of sheep

1998 ◽  
Vol 1998 ◽  
pp. 47-47
Author(s):  
R.M. Lewis ◽  
G.C. Emmans ◽  
G. Simm ◽  
W.S. Dingwall ◽  
J. FitzSimons
Keyword(s):  
Growth Curves ◽  
Growth Function ◽  
Single Equation ◽  
Rate Parameter ◽  
Growth Functions ◽  
Gompertz Equation ◽  
Lumped Parameter ◽  
Highly Correlated ◽  
Mature Size

The idea that an animal of a given kind has, and grows to, a final or mature size is a useful one and several equations have been proposed that describe such growth to maturity (Winsor, 1932; Parks, 1982; Taylor, 1982). The Gompertz is one of these growth functions and describes in a comparatively simple, single equation the sigmoidal pattern of growth. It has 3 parameters, only 2 of which are important - mature size A and the rate parameter B. Estimates of A and B, however, are highly correlated. Considering A and B as a lumped parameter (AB) may overcome this problem. A Gompertz, or any other, growth function is not expected to describe all growth curves. When the environment (e.g., feed, housing) is non-limiting, it may provide a useful and succinct description of growth. The objectives of this study were to examine: (i) if the Gompertz equation adequately describes the growth of two genotypes of sheep under conditions designed to be non-limiting; and, (ii) if the lumped parameter AB has more desirable properties for estimation than A and B separately.

Sign in / Sign up

Export Citation Format

Share Document