LANGUAGES WITH A FINITE ANTIDICTIONARY: SOME GROWTH QUESTIONS

2014 ◽  
Vol 25 (08) ◽  
pp. 937-953
Author(s):  
ARSENY M. SHUR
Keyword(s):  
Growth Rate ◽  
Structural Properties ◽  
Exponential Growth ◽  
Regular Languages ◽  
The Other ◽  
Exponential Growth Rate ◽  
Strong Component ◽  
Order Of Growth ◽  
Finite Sets ◽  
Complex Order

We study FAD-languages, which are regular languages defined by finite sets of forbidden factors, together with their “canonical” recognizing automata. We are mainly interested in the possible asymptotic orders of growth for such languages. We analyze certain simplifications of sets of forbidden factors and show that they “almost” preserve the canonical automata. Using this result and structural properties of canonical automata, we describe an algorithm that effectively lists all canonical automata having a sink strong component isomorphic to a given digraph, or reports that no such automata exist. This algorithm can be used, in particular, to prove the existence of a FAD-language over a given alphabet with a given exponential growth rate. On the other hand, we give an example showing that the algorithm cannot prove non-existence of a FAD-language having a given growth rate. Finally, we provide some examples of canonical automata with a nontrivial condensation graph and of FAD-languages with a “complex” order of growth.

scholarly journals Optimal Strategies for Prudent Investors

1998 ◽  
Vol 01 (04) ◽  
pp. 473-486 ◽  
Author(s):  
Roberto Baviera ◽  
Michele Pasquini ◽  
Maurizio Serva ◽  
Angelo Vulpiani
Keyword(s):  
Growth Rate ◽  
Random Walk ◽  
Exponential Growth ◽  
Optimal Strategies ◽  
Maximum Amount ◽  
Exponential Growth Rate ◽  
One Dimensional ◽  
Economic Level ◽  
Random Walk With Drift ◽  
Analytical Expressions

We consider a stochastic model of investment on an asset in a stock market for a prudent investor. she decides to buy permanent goods with a fraction α of the maximum amount of money owned in her life in order that her economic level never decreases. The optimal strategy is obtained by maximizing the exponential growth rate for a fixed α. We derive analytical expressions for the typical exponential growth rate of the capital and its fluctuations by solving an one-dimensional random walk with drift.

Validation and Analysis of Modeled Predictions of Growth of Bacillus cereus Spores in Boiled Rice

2000 ◽  
Vol 63 (2) ◽  
pp. 268-272 ◽  
Author(s):  
DANA M. McELROY ◽  
LEE-ANN JAYKUS ◽  
PEGGY M. FOEGEDING
Keyword(s):  
Growth Rate ◽  
Bacillus Cereus ◽  
Exponential Growth ◽  
Generation Time ◽  
Time Lag ◽  
Lag Phase ◽  
Exponential Growth Rate ◽  
Phase Duration ◽  
Margin Of Safety ◽  
Fail Safe

The growth of psychrotrophic Bacillus cereus 404 from spores in boiled rice was examined experimentally at 15, 20, and 30°C. Using the Gompertz function, observed growth was modeled, and these kinetic values were compared with kinetic values for the growth of mesophilic vegetative cells as predicted by the U.S. Department of Agriculture's Pathogen Modeling Program, version 5.1. An analysis of variance indicated no statistically significant difference between observed and predicted values. A graphical comparison of kinetic values demonstrated that modeled predictions were “fail safe” for generation time and exponential growth rate at all temperatures. The model also was fail safe for lag-phase duration at 20 and 30°C but not at l5°C. Bias factors of 0.55, 0.82, and 1.82 for generation time, lag-phase duration, and exponential growth rate, respectively, indicated that the model generally was fail safe and hence provided a margin of safety in its growth predictions. Accuracy factors of 1.82, 1.60, and 1.82 for generation time, lag-phase duration, and exponential growth rate, respectively, quantitatively demonstrated the degree of difference between predicted and observed values. Although the Pathogen Modeling Program produced reasonably accurate predictions of the growth of psychrotrophic B. cereus from spores in boiled rice, the margin of safety provided by the model may be more conservative than desired for some applications. It is recommended that if microbial growth modeling is to be applied to any food safety or processing situation, it is best to validate the model before use. Once experimental data are gathered, graphical and quantitative methods of analysis can be useful tools for evaluating specific trends in model prediction and identifying important deviations between predicted and observed data.

scholarly journals Determination of collected porcini and chanterelle quantities depending on different climate change scenarios

2016 ◽  
pp. 77-98
Author(s):  
Nenad Rankovic ◽  
Jelena Nedeljkovic ◽  
Zoran Poduska ◽  
Dragan Nonic
Keyword(s):  
Climate Change ◽  
Growth Rate ◽  
Regression Models ◽  
The Other ◽  
Climate Change Scenarios ◽  
Exponential Growth Rate ◽  
Scientific Methods ◽  
Exponential Regression ◽  
Modelling Methods

This study examines the influence of some climate elements on the collected quantities of two commercially most significant types of mushrooms in Serbia (porcini and chanterelle). The main objective of the research is to determine the extent of the collected quantity of porcini and chanterelle, which can be expected in different scenarios of climate change (?1Bmin, ?1Bmax, A2min ? A2max), based on forecasts of temperature and rainfall changes. The general (dialectical) and specific (modelling methods) are used in the research, as well as the classical scientific methods of reasoning. The calculation of the average annual exponential growth rate (IS) was carried out by forming exponential regression models of the trend of porcini and chanterelle collected quantities. In the research it was found that, according to the data related to the period up to 2014, one can expect a decrease in the movement of both porcini and chanterelle IS, and thus a decrease in the collected quantities. On the other hand, according to the data related to the period up to 2040, in both cases one can expect some fluctuation (increase and decrease) in the movement of IS. According to the data related to periods after 2041 (especially for the period until 2100), in both cases, one can expect a decrease in the collected quantities, as a result of changes in T and P, caused by the assumed climate change.

TOPOLOGICAL ENTROPY VERSUS GEODESIC ENTROPY

1994 ◽  
Vol 05 (02) ◽  
pp. 213-218 ◽  
Author(s):  
GABRIEL P. PATERNAIN ◽  
MIGUEL PATERNAIN
Keyword(s):  
Growth Rate ◽  
Topological Entropy ◽  
Exponential Growth ◽  
Geodesic Flow ◽  
Compact Riemannian Manifold ◽  
Betti Numbers ◽  
Exponential Growth Rate ◽  
Sphere Bundle ◽  
Space Of Paths ◽  
Simply Connected

Using Yomdin's Theorem [8], we show that for a compact Riemannian manifold M, the geodesic entropy — defined as the exponential growth rate of the average number of geodesic segments between two points — is ≤ the topological entropy of the geodesic flow of M. We also show that if M is simply connected and N ⊂ M is a compact simply connected submanifold, then the exponential growth rate of the sequence given by the Betti numbers of the space of paths starting in N and ending in a fixed point of M, is bounded above by the topological entropy of the geodesic flow on the normal sphere bundle of N.

scholarly journals A Study to Understand the Factors that Play Major Role in Influencing the Loyalty Behaviour of Shoppers towards Department Based Brick-and-Mortar Fashion Retailers with Special Reference to Pune City, India

2016 ◽  
Vol 5 (1) ◽  
pp. 159
Author(s):  
Sarita Karangutkar ◽  
Prashant Chaudhary ◽  
Siddhant Shah
Keyword(s):  
Growth Rate ◽  
Special Reference ◽  
Influencing Factors ◽  
Exponential Growth ◽  
Consumer Behaviour ◽  
Exponential Growth Rate ◽  
Major Objective ◽  
Fashion Products ◽  
Brick And Mortar ◽  
Loyalty Programme

<div><p><em>The major objective of this study is to understanding the factors that influence the loyalty behaviour of customers towards brick-and-mortar departmental fashion retailers in Pune city. The study has been conducted by keeping one of the leading departmental stores in reference, but the findings of the study are generalized and can be applied to other fashion retailers of similar or non-similar formats. Fashion is one of the fastest growing categories and continues to grow at exponential growth rate due to increased fashion awareness and aspirations. Today we can see that fashion products account for a substantial percentage of the products sold across a broad range of merchandise categories. </em></p><p><em>Research on fashion retailing has been based on varying conceptual definitions of the construct and has focused primarily on in-store retailing. A number of researchers have made important contributions to understanding of loyalty behaviour of shoppers towards fashion retailers.  Therefore, the consumer behaviour of an important sector of the millennials is worth to be researched. Here the researchers are trying to understand the variables that influence shoppers' loyalty behaviour which is nothing but the “preferential” behaviour of the shoppers towards a specific retailer’s stores. During this research the researchers found that, some of the major influencing factors are shopping atmosphere-ambience, fashion image of the retailer (retailer as a brand), fashion image of the Private Labels, and the effectiveness of the loyalty programme offered by the retailer.</em></p></div>

scholarly journals Epidemic Potential of COVID-19 in Omsk Region during Anti-Epidemic Measures

2020 ◽  
pp. 36-42
Author(s):  
A. I. Blokh ◽  
N. A. Pen’evskaya ◽  
N. V. Rudakov ◽  
I. I. Lazarev ◽  
O. A. Mikhailova ◽  
...  
Keyword(s):  
Growth Rate ◽  
Exponential Growth ◽  
Reproduction Number ◽  
Herd Immunity ◽  
Case Fatality ◽  
Community Acquired Pneumonia ◽  
Cumulative Number ◽  
Exponential Growth Rate ◽  
Epidemic Size ◽  
Threshold Data

Aim. To study the spread of COVID-19 among the population of the Omsk Region during 24 weeks of the epidemic on the background of anti-epidemic measures.Materials and methods. A descriptive epidemiological study was carried out based on publically available data и data from the Center for Hygiene and Epidemiology in the Omsk Region on the official registration and epidemiological investigation of detected COVID-19 cases in the Omsk Region for the period from March 27 to September 10, 2020. To assess the potential of COVID-19 to spread, the following indicators were calculated: exponential growth rate (r), basic reproduction number (R0), effective reproduction number (Rt), expected natural epidemic size and herd immunity threshold. Data processing was performed using MS Excel 2010. The cartogram was built using the QGIS 3.12-Bukuresti application in the EPSG: 3576 coordinate system.Results and discussion. For the period from March 27 to September 10, 2020, a total of 9779 cases of COVID-19 were registered in the Omsk Region, the cumulative incidence was 507,6 per 100000 (95 % CI 497,5÷517,6), the case-fatality rate for completed cases was 2.9 %, for identified cases – 2.4 %. The most active spread of COVID-19 was noted in Omsk and 4 out of 32 districts of the region (Moskalensky, Azov German National, Mariyanovsky, Novovarshavsky). During the ongoing anti-epidemic measures, the exponential growth rate of the cumulative number of COVID-19 cases was 4.5 % per day, R0 – 1.4–1.5, Rt – 1.10, herd immunity threshold – 28.6 %. The expected size of the epidemic in case of sustained anti-epidemic measures can reach 58.0 % of the recovered population. A decrease in the number of detected virus carriers, incomplete detection of COVID-19 among patients with community-acquired pneumonia introduced additional risks for the latent spread of infection and complications of the epidemic situation. Maintaining restrictive  measures and increasing the proportion of the immune population (over 28.6 %) may significantly reduce the risks of increasing the spread of COVID-19 in the Omsk Region. 

Publish or perish

2018 ◽  
Author(s):  
Gianfranco Pacchioni
Keyword(s):  
Growth Rate ◽  
Exponential Growth ◽  
Quantitative Data ◽  
Constant Pressure ◽  
Exponential Growth Rate ◽  
Publish Or Perish

How many new papers are published each year? Based on the analysis of De Solla Price, from 1960 till more recent evaluations, an exponential growth rate has led to 2–2.4 million new publications annually. According to the latest estimates, the total number of existing articles doubles every 8–9 years. Why is this? There are various reasons, some positive, some not. One is the increased number of collaborations between scientists, as well as the case of hyper-collaborations, where some papers list thousands of authors. But the main reason is the constant pressure to produce papers, leading to the notion of ‘publish or perish’. This chapter also discusses cases of misconduct, stories of plagiarism, and some quantitative data about how diffuse plagiarism is.

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