Exponential Growth

Commensurate with this exponential growth in the depth and breadth of derivative markets and the range of financial products traded therein, there needs to be developed a comprehensive mathematical framework to support the, hitherto, empirically established features of trading strategies involving these instruments. It is the objective of this article, to provide a mathematical backup for the various properties of 'volatility trading' strategy using call options. Additionally, an attempt is made to elucidate the implications of behavior of various 'option Greeks' on volatility trading.

Growth kinetics of Thiobacillus ferrooxidans in batch cultures, containing prills of elementary sulfur as the sole energy source, were studied by measuring the incorporation of radioactive phosphorus in free and adsorbed bacteria. The data obtained indicate an initial exponential growth of the attached bacteria until saturation of the susceptible surface was reached, followed by a linear release of free bacteria due to successive replication of a constant number of adsorbed bacteria. These adsorbed bacteria could continue replication provided the colonized prills were transferred to fresh medium each time the stationary phase was reached. The bacteria released from the prills were unable to multiply, and in the medium employed they lost viability with a half-life of 3.5 days. The spreading of the progeny on the surface was followed by staining the bacteria on the prills with crystal violet; this spreading was not uniform but seemed to proceed through distortions present in the surfa...

The available mathematical models describing tumor growth and the effect of anticancer treatments on tumors in animals are of limited use within the drug industry. A simple and effective model would allow applying quantitative thinking to the preclinical development of oncology drugs. In this article, a minimal pharmacokinetic-pharmacodynamic model is presented, based on a system of ordinary differential equations that link the dosing regimen of a compound to the tumor growth in animal models. The growth of tumors in nontreated animals is described by an exponential growth followed by a linear growth. In treated animals, the tumor growth rate is decreased by a factor proportional to both drug concentration and number of proliferating tumor cells. A transit compartmental system is used to model the process of cell death, which occurs at later times. The parameters of the pharmacodynamic model are related to the growth characteristics of the tumor, to the drug potency, and to the kinetics of the tumor cell death. Therefore, such parameters can be used for ranking compounds based on their potency and for evaluating potential differences in the tumor cell death process. The model was extensively tested on discovery candidates and known anticancer drugs. It fitted well the experimental data, providing reliable parameter estimates. On the basis of the parameters estimated in a first experiment, the model successfully predicted the response of tumors exposed to drugs given at different dose levels and/or schedules. It is, thus, possible to use the model prospectively, optimizing the design of new experiments.

Recent progress in genomics and experimental biology has brought exponential growth of the biological information available for computational analysis in public genomics databases. However, applying the potentially enormous scientific value of this information to the understanding of biological systems requires computing and data storage technology of an unprecedented scale. The grid, with its aggregated and distributed computational and storage infrastructure, offers an ideal platform for high-throughput bioinformatics analysis. ...

Growth curves were generated for Escherichia coli O157:H7 in brain±heart infusion broth incubated at 37 or158C in the presence of individual and combinations of competing micro£ora. Broths were inoculated with E. coli O157:H7 (log 10 3Á00 cfu ml 71) and competitors (log 10 4Á00 cfu ml 71) and the initial pH of the broth was either neutral (7Á0) or adjusted to 5Á8 and then sequentially reduced to 4Á8 over 10 h to simulate fermentation conditions. Growth curves were also generated for the competitors in these cultures, including Pseudomonas fragi, Hafnia alvei, Pediococcus acidilactici (pepperoni starter culture) and Brochothrix thermosphacta. Gompertz equations were ¢tted to the data and growth kinetics including lag phase duration, exponential growth rates and maximum population densities (MPD) calculated. In pure culture, the growth parameters for E. coli O157:H7 in neutral pH broths were signi¢cantly di¡erent from those recorded in simulated fermentation broths (P50Á05).The presence of competitors in the broth also had a signi¢cant e¡ect on the growth kinetics of the pathogen. H. alvei signi¢cantly inhibited the growth (lag phase, growth rate and MPD) of E. coli O157:H7 at 378C, neutral pH and outgrew the pathogen under these conditions. In neutral pH cultures, two other competitors, B. thermosphacta and P. acidilactici also inhibited the lag phase of the pathogen but had no e¡ect on the other growth parameters. In simulated fermentation broths, the growth rate of E. coli O157:H7 was consistently slower and the MPD lower in the presence of a competitive micro£ora than when grown individually. At158C, only one competitor, P. fragi signi¢cantly inhibited the lag phase of the pathogen. The implications of these ¢ndings for food safety are discussed.

If one goes backward in time, the number of ancestors of an individual doubles at each generation. This exponential growth very quickly exceeds the population size, when this size is finite. As a consequence, the ancestors of a given individual cannot be all different and most remote ancestors are repeated many times in any genealogical tree. The statistical properties of these repetitions in genealogical trees of individuals for a panmictic closed population of constant size N can be calculated. We show that the distribution of the repetitions of ancestors reaches a stationary shape after a small number G c ∝ log N of generations in the past, that only about 80% of the ancestral population belongs to the tree (due to coalescence of branches), and that two trees for individuals in the same population become identical after G c generations have elapsed. Our analysis is easy to extend to the case of exponentially growing population. We used the tree of Edward III which can be found at

Objective: The objective of this paper is to analyse and quantify the effects exerted on summer mortality by extremes of heat, particularly among persons aged 65–74 and 75 years and over, groups in which mortality is higher. Methods: The study included the period from 1 January 1986 to 31 December 1997, for all people aged over 65 years resident in Madrid, based on mortality due to all causes except accidents (ICD-9 codes 1–799), and circulatory (390–459) and respiratory (460–487) causes. Meteorological variables analysed were: daily maximum temperature, daily minimum temperature and relative humidity. To control the effect of air pollution on mortality we considered the daily mean values of sulphur dioxide (SO2), total suspended particulate (TSP), nitric oxides (NOx), nitrogen dioxide (NO2) and tropospheric ozone (O3). Univariate and multivariate ARIMA models were used. Box-Jenkins pre-whitening was performed. Results: The results yielded by this study indicate a mortality increase up to 28. 4% for every degree the temperature rises above 36.5 °C, with particular effect in women over the age of 75 years and circulatory-cause mortality. The first heat wave that leads to the greatest effects on mortality, due to the higher number of susceptible people and the duration of the heat wave, show an exponential growth in mortality. Furthermore, low relative humidity enhances the effects of high temperature, linking dryness to air pollutants, ozone in particular. Conclusions: Since a warmer climate is predicted in the future, the incidence of heat wave should increase, and more comprehensive measures, both medical and social, should be adopted to prevent the effects of extreme heat on the population, particularly the elderly.

Abstract-Backtracking search is frequently applied to solve a constraint-based search prob!em, but it often suffers from exponential growth of computing time. We present an alternative to backtracking search: local search with conflict minimization. We have applied this ...

The extension efficiency of PCR-driven DNA amplification was examined by step-controlled limiting dilution method using as internal controls 8E5 lymphocytes carrying a single copy of H~ genome. The results reveal that under standard conditions recommended by the PCR kit manufacturer the exponential growth of DNA template is approximately one third of the theoretical doubling rate, Index Entries: Amplification; efficiency; PCR; quantitation; HIV.

Globalization, free trade, and individualization have opened up a worldwide marketplace for trading goods. The fair trade movement and other political consumerist endeavours view consumers as important active holders of responsibility for global welfare. Civil society and governments strive to teach consumers how political consumerism can be used as a push factor to change market capitalism. The market itself can also create an interest in political consumerism and, thereby, teach consumers about the political responsibility embedded in their shopping choices. When this happens, the market works as a pull factor for securing human rights. Questions can be raised about the significance of political consumers as a way to solve complex global problems. Political consumerism may be a fair-weather option that loses its attractiveness in times of downward private and corporate economic spirals. Parts of the fair trade movement believe that there are problems with sole reliance on voluntary consumer choice and using personal money and private capital to solve human rights problems by shopping them away. The exponential growth of voluntary codes of corporate conduct and labelling schemes has also created contradictory practices, incoherence in efforts, and superficial changes or what activists call ''sweatwash.'' Increasingly, many actors call on international law to create new standards that apply direct human rights obligations on corporations.

The generation of Lagrangian chaos has been studied experimentally in a twisted duct flow, a configuration representing a three-dimensional steady open flow in which various signatures of Lagrangian chaos are documented. The twisted duct consists of four 90∘ bends of square cross-section; the plane of curvature of each bend is at 90∘ to that of its neighbors. Dean roll-cells, generated

Abstract. Ontology at the beginning was (and it is still usually) conceived as a defini-tely philosophical discipline, far from the world of technology. Nevertheless, in the last years, the exponential growth of communication through the net has favoured a new phenomenon: the ontological ...

The linear historic global crop yield trends found in this study, when extended, trace future rates of yield gain that are well below the recent growth in food demand. Fortunately for consumers, the population growth rates have also fallen after exponential growth, on average, for at least 2 centuries. Global food demand growth may exceed yield growth for several decades, bringing higher commodity prices that are necessary to draw land and other conventional resources into food production

Petri nets (PN) are useful for the modelling, analysis and control of hybrid dynamical systems (HDS) because PN combine in a comprehensive way discrete events and continuous behaviours. On one hand, PN are suitable for modelling the discrete part of HDS and for providing a discrete abstraction of continuous behaviours. On the other hand, continuous PN are suitable for modelling the continuous part of HDS and for working out a continuous approximation of the discrete part in order to avoid the complexity associated with the exponential growth of discrete states. This paper focuses on the advantages of PN as a modelling tool for HDS. Investigations of such models for diagnosis and control issues are detailed.

An estimate of the lag phase duration is an important component for predicting the growth of a bacterium and for creating process models and risk assessments. Most current research and data for predictive modeling programs initiated growth studies with cells grown to the stationary phase in a favorable pH, nutrient and temperature environment. In this work, Listeria monocytogenes Scott A cells were grown in brain heart infusion (BHI) broth at different temperatures from 4 to 37°C to the exponential growth or stationary phases. Additional cells were suspended in a dilute broth, desiccated or frozen. These cells were then transferred to BHI broth at various temperatures from 4 to 37°C and the lag phase durations were determined by enumerating cells at appropriate time intervals. Long lag phases were observed for cells initially grown at high temperatures and transferred to low temperatures. In general, exponential growth cells had the shortest lag phases, stationary phase and starved cells had longer, frozen cells had slightly longer and desiccated cells had the longest lag phases. These data were from immediate temperature transitions. When a computer-controlled water bath linearly changed the temperature from 37 to 5°C over a 3.0-or 6.0-h period, the cells had short lags and grew continuously with declining growth rates. Transitions of 0.75 or 1.0 h had 20-h lag phases, essentially that of immediate transitions. When the transition was 1.5 h, an intermediate pattern of less than 1 log of growth followed by no additional growth for 20 h occurred. Published by Elsevier Science B.V.

The last decade has witnessed an exponential growth of sequence information in the field of biological macromolecules such as proteins and nucleic acids and their interactions with other molecules. Computational analyses for structure-function predictions based on such information are increasingly becoming an essential and integral part of modern biology. With rapid advances in the area, there is a growing need to develop efficient versatile bioinformatics software packages, which are hypothesis driven. 'Gene to Drug' is an attempt in this pursuit and an integration of heterologous applications of different technologies developed in-house and their translation into in silico products that cater to a majority of bioinformatics applications. This paper briefly presents the science behind Gene to Drug and how grid services and high performance computing platforms can be harnessed to bridge the gap between biomolecular sequence, structure and function.

Episodes of population growth and decline leave characteristic signatures in the distribution of nucleotide (or restriction) site differences between pairs of individuals. These signatures appear in histograms showing the relative frequencies of pairs of individuals who differ by i sites, where i = 0, 1, . . . . In this distribution an episode of growth generates a wave that

Internet was designed for network services without any intention for secure communication. Exponential growth of internet and its users have developed an era of global competition and rivalry. Denial of service attack by multiple nodes is capable of disturbing the services of rival servers. The attack can be for multiple reasons e. g. extortion or to beat the rivals. Peer

Cell viability was improved by supplemental feeding of amino acids and vitamins in batch culture of hybridoma cells. Cells could be maintained over a 10 day period following exponential growth at a constant viable cell concentration of 2.1×106 cells/ml. Concentrations of monoclonal antibody (MAb) reached 140 mg/l, a value of nearly four times that found in typical batch culture. Lactate formation appeared to occur only during active exponential growth and not during the stationary phase.

A freshly-prepared yeast extract at 30 or 50 g/1 improved the growth of Bradyrhizobium japonicum SEMIA 587 in a 5-1 stirred fermenter. Monosodium glutamate or a commercial yeast extract at 2.0 g/1 almost doubled cell mass productivity and cell viability when added at the end of the first exponential growth phase.

The Solow growth model assumes that labor force grows exponentially. This is not a realistic assumption because, exponential growth implies that population increases to infinity as time tends to infinity. In this paper we propose replacing the exponential population growth with a simple and more realistic equation-the Von Bertalanffy model. This model utilizes three hypotheses about human population growth: (1) when population size is small, growth is exponential; (2) population is bounded; and (3) the rate of population growth decreases to zero as time tends toward infinity. After making this substitution, the generalized Solow model is then solved in closed form, demonstrating that the intrinsic rate of population growth does not influence the long-run equilibrium level of capital per worker. We also study the revised model's stability, comparing it with that of the classical model.

In this paper we compare two alternative theoretical approaches for simulating the growth of cell aggregates in vitro: individual cell (agent)-based models and continuum models. We show by a quantitative analysis of both a biophysical agent-based and a continuum mechanical model that for densely packed aggregates the expansion of the cell population is dominated by cell proliferation controlled by mechanical stress. The biophysical agent-based model introduced earlier (Drasdo and Hoehme in Phys Biol 2:133-147, 2005) approximates each cell as an isotropic, homogeneous, elastic, spherical object parameterised by measurable biophysical and cell-biological quantities and has been shown by comparison to experimental findings to explain the growth patterns of dense monolayers and multicellular spheroids. Both models exhibit the same growth kinetics, with initial exponential growth of the population size and aggregate diameter followed by linear growth of the diameter and power-law growth of the cell population size. Very sparse monolayers can be explained by a very small or absent cell-cell adhesion and large random cell migration. In this case the expansion speed is not controlled by mechanical stress but by random cell migration and can be modelled by the Fisher-Kolmogorov-Petrovskii-Piskounov (FKPP) reaction-diffusion equation. The growth kinetics differs from that of densely packed aggregates in that the initial spread, as quantified by the radius of gyration, is

AbstractÐIn the past decade, the exponential growth in commodity CPU's speed has far outpaced advances in memory latency. A second trend is that CPU performance advances are not only brought by increased clock rate, but also by increasing parallelism inside the CPU. Current database systems have not yet adapted to these trends and show poor utilization of both CPU and memory resources on current hardware. In this paper, we show how these resources can be optimized for large joins and translate these insights into guidelines for future database architectures, encompassing data structures, algorithms, cost modeling, and implementation. In particular, we discuss how vertically fragmented data structures optimize cache performance on sequential data access. On the algorithmic side, we refine the partitioned hash-join with a new partitioning algorithm called radix-cluster, which is specifically designed to optimize memory access. The performance of this algorithm is quantified using a detailed analytical model that incorporates memory access costs in terms of a limited number of parameters, such as cache sizes and miss penalties. We also present a calibration tool that extracts such parameters automatically from any computer hardware. The accuracy of our models is proven by exhaustive experiments conducted with the Monet database system on three different hardware platforms. Finally, we investigate the effect of implementation techniques that optimize CPU resource usage. Our experiments show that large joins can be accelerated almost an order of magnitude on modern RISC hardware when both memory and CPU resources are optimized.

Each technology transfer (TT) transaction takes place because of some motivation on the part of the respective participants. This paper attempts to create a generic taxonomy that lists such motivations and links them to the participants in the transfer. Although the past three decades have recorded an exponential growth in the literature of TT, this literature is highly fractionated. Yet, as the literature has grown several taxonomies have surfaced dealing with the various aspects of TT. Most, however, were designed to serve one of the many scientific disciplines or professions concerned with technology transfer. Zhao and Reisman (1992)provide a synthesis of these taxonomic efforts. Thispaper in turn addresses an aspect of TT not previousIy dealt with in this manner.

This chapter has two goals. The first goal is to compare Machine Learning (ML) and Knowledge Discovery in Data (KDD, also often called Data Mining, DM) insisting on how much they actually differ. In order to make my ideas somewhat easier to understand, and as an illustration, I will include a description of several research topics that I find relevant to KDD and to KDD only. The second goal is to show that the definition I give of KDD can be almost directly applied to text analysis, and that will lead us to a very restrictive definition of Knowledge Discovery in Texts (KDT). I will provide a compelling example of a real-life set of rules obtained by what I call KDT techniques.

The theory of autocatalytic binary ligation is reviewed within the context of a consistently applied Michaelis-Menten quasi-steady-state approximation to obtain explicit analytical results describing time-course data from experiments. A detailed protocol for the step-wise elucidation of a minimal set of experimental parameters is outlined. The kinetic equations are then generalized to cases of self-and cross-catalysis among an arbitrary number of di erent templates and applied to experiments involving just two templates. Depending on the values of various kinetic parameters such systems can display exclusionary Darwinian selection corresponding to an exponential growth law, selective coexistence or coexistence of all species characteristic of a parabolic growth law; the intermediate behaviour arises as a property of the full mechanism analysed here. Our results are applicable to the classical case of self-replicating nucleic acids and their analogues as well as to newly discovered self-replicating peptides.

Data Mining has become a buzzword in industry in recent years. It is something that everyone is talking about but few seem to understand. There are two reasons for this lack of understanding: First is the fact that Data Mining researchers have very diverse backgrounds such as machine learning, psychology and statistics. This means that the research is often based on different methodologies and communication links e.g. notation is often unique to a particular research area which hampers the exchange of ideas and the dissemination to the wider public. The second reason for the lack of understanding is that the main ideas behind Data Mining are often completely opposite to mainstream statistics and as many companies interested in Data Mining already employ statisticians, such a change of view can create opposition.

The identi¢ability properties of the Baranyi model for bacterial growth were investigated, both structurally and applied to real-life data. Using the Taylor-series approach, it was formally proven that the model is structurally identi¢able, i.e. it is now ascertained that it is certainly possible to give unique values to all parameters of the model, provided the bacterial growth data are of su¤ciently good quality. The model also has acceptable practical identi¢ability properties in the presence of realistic data, which means that the con¢dence intervals on the parameter values are reasonable. However, there was a relatively high correlation between the maximum speci¢c growth rate m mx and the suitability indicator h 0 . An optimal experimental design to improve parameter estimation uncertainty was worked out, using the sampling times of the microbial growth curve as experimental degree of freedom. Using a D-optimal design criterion, it could be shown that the optimal sampling times were concentrated in four time periods (initial, start and end of exponential growth, end of experiment), each providing maximum information on a particular parameter. Because the optimal experimental design requires a priori estimates of the parameters, the propagation of the parameter uncertainty into the experimental design was assessed with a Monte Carlo simulation. In this way, 95% con¢dence intervals could be established around the optimal sampling times to be used in the optimal experiment. Based on these intervals, a design was proposed and experimentally validated. The error on the parameter estimates was more than halved, their correlation diminished and the nonlinearity of the result improved.

In this brief discussion, we try to make understand what exponential growth
is and how it is related with SARS-CoV-2, with giving significant pathways of
remedy for India and many regions which are in the same situation as India
(We call the this as ‘Stage 2,3 intermediate’).

Exponential growth in storage requirements and an increasing number of heterogeneous devices and application policies are making enterprise storage management a nightmare for administrators. Back-of-the-envelope calculations, rules of thumb, and manual correlation of individual device data are too error prone for the day-to-day administrative tasks of resource provisioning, problem determination, performance management, and impact analysis. Storage management tools have evolved over the past several years from standardizing the data reported by storage subsystems to providing intelligent planners. In this paper, we describe that evolution in the context of the IBM TotalStoraget Productivity Center (TPC)-a suite of tools to assist administrators in the day-to-day tasks of monitoring, configuring, provisioning, managing change, analyzing configuration, managing performance, and determining problems. We describe our ongoing research to develop ways to simplify and automate these tasks by applying advanced analytics on the performance statistics and raw configuration and event data collected by TPC using the popular Storage Management Initiative-Specification (SMI-S). In addition, we provide details of SMART (storage management analytics and reasoning technology) as a library that provides a collection of data-aggregation functions and optimization algorithms.

Municipal solid waste (MSW) is the abridgment of the waste generated from domestic, commercial, and construction activities by natural persons that is collected and treated by municipalities. Exponential growth of population and urbanization, and the development of social economy, coupled with the improvement of living standard, have resulted in an increase in the amount of MSW generation throughout the world. On average the developed countries typically generate 521.95–759.2 kg per person per year (kpc) and 109.5–525.6 kpc typically by developing countries. Recent estimates suggest that the MSW generation globally exceeds 2 billion tons per year, which is a potential threat to environmental dilapidation. Therefore, MSW management (MSWM) seems to be one of the key topics for environmental protection in present days and also in the future. The authors have illustrated MSW generation and composition analysis and have provided a comprehensive review of MSWM in different countries throughout the world based on the available literatures. Some of the important aspects of waste management, such as composting, landfilling, and incineration, are illustrated.

Since its introduction by the Nuremberg Code and the Declaration of Helsinki, the place held by ethics in biomedical research has been continuously increasing in importance. The past 30 years have also seen exponential growth in the number of biomedical articles published. A systematic review of the literature is the scientific way of synthesising a plethora of information, by exhaustively searching out and objectively analysing the studies dealing with a given issue. However, the question of ethics in systematic reviews is rarely touched upon. This could lead to some drawbacks, as systematic reviews may contain studies with ethical insufficiencies, may be a possible way to publish unethical research and may also be prone to conflict of interest. Finally, informed consent given for an original study is not necessarily still valid at the systematic review level. There is no doubt that routine ethical assessment in systematic reviews would help to improve the ethical and methodological quality of studies in general. However, ethical issues change so much with time and location, and are so broad in scope and in context that it appears illusory to search for a universal, internationally accepted standard for ethical assessment in systematic reviews. Some simple suggestions could nevertheless be drawn from the present reflection and are discussed in the paper.