Hyperbolic Growth Research Articles

Unified Growth Theory Contradicted by the Absence of Takeoffs in the Gross Domestic Product

Abstract. Data describing historical economic growth are analysed. They demonstrate convincingly that the take offs from stagnation to growth, claimed in the Unified Growth Theory, never happened. This theory is again contradicted by the same data which were used, but never properly analysed, during its formulation. The absence of the claimed takeoffs demonstrates that the postulate of the differential takeoffs is also contradicted by data. Furthermore, this analysis demonstrates that the mathematically-analysable data contradict the concept of the prolonged Malthusian stagnation, its effects on the economic growth as well as the concept of a dramatic escape from the Malthusian trap. Keywords. Historical economic growth, regimes of growth, Malthusian stagnation, takeoffs, Malthusian trap, hyperbolic growth. JEL. A10, B10, B22, F01, N10.

Leaf Dynamics of Panicum maximum under Future Climatic Changes.

Panicum maximum Jacq. ‘Mombaça’ (C4) was grown in field conditions with sufficient water and nutrients to examine the effects of warming and elevated CO2 concentrations during the winter. Plants were exposed to either the ambient temperature and regular atmospheric CO2 (Control); elevated CO2 (600 ppm, eC); canopy warming (+2°C above regular canopy temperature, eT); or elevated CO2 and canopy warming (eC+eT). The temperatures and CO2 in the field were controlled by temperature free-air controlled enhancement (T-FACE) and mini free-air CO2 enrichment (miniFACE) facilities. The most green, expanding, and expanded leaves and the highest leaf appearance rate (LAR, leaves day-1) and leaf elongation rate (LER, cm day-1) were observed under eT. Leaf area and leaf biomass were higher in the eT and eC+eT treatments. The higher LER and LAR without significant differences in the number of senescent leaves could explain why tillers had higher foliage area and leaf biomass in the eT treatment. The eC treatment had the lowest LER and the fewest expanded and green leaves, similar to Control. The inhibitory effect of eC on foliage development in winter was indicated by the fewer green, expanded, and expanding leaves under eC+eT than eT. The stimulatory and inhibitory effects of the eT and eC treatments, respectively, on foliage raised and lowered, respectively, the foliar nitrogen concentration. The inhibition of foliage by eC was confirmed by the eC treatment having the lowest leaf/stem biomass ratio and by the change in leaf biomass-area relationships from linear or exponential growth to rectangular hyperbolic growth under eC. Besides, eC+eT had a synergist effect, speeding up leaf maturation. Therefore, with sufficient water and nutrients in winter, the inhibitory effect of elevated CO2 on foliage could be partially offset by elevated temperatures and relatively high P. maximum foliage production could be achieved under future climatic change.

Knowledge production and world population dynamics

Three laws of knowledge production explaining the empirically observed hyperbolic growth of world population are formulated. Knowledge and demographic dynamics are developed on the basis of the least action principle to describe deviations from the hyperbolic growth. The efficiency of knowledge production defined as the share of technological knowledge in total knowledge production is introduced. It is proven that a monotonic population growth with reaching a plateau is possible only when efficiency is 1. At a lower efficiency, population reaches a maximum and then declines. The estimated efficiency is currently not more than 0.1. The calculations show that if efficiency remains constant, population will peak at 9 billion in the mid-21st century and then decline to 5 billion or lower over several centuries. To keep population at a level of not less than 90% of maximum, it is necessary to raise efficiency of up to 0.31.

The Polygon of Progress in the Epoch of Retardation: Architecture of universities within the context of global stabilization

In the 1970s the period of global development in the context of the hyperbolic growth of the key indicators came to its end. The demographic, economic, scientific and technical growth decelerated. Against the background of the reduced flow of innovations the social image of universities changes, while approaching the image of medieval monasteries. The architecture of universities evolves accordingly. It tends to isolate campuses from the city structure and aspires to international and supranational stylistics, which is common for universities of the whole world.

Boundary asymptotics of the relative Bergman kernel metric for elliptic curves

For a family of compact Riemann surfaces, we study the asymptotic behaviors of the relative Bergman kernel metric near the boundaries of the moduli spaces. We have shown that the relative Bergman kernel metric on a family of elliptic curves has hyperbolic growth at the node. The proof relies largely on the elliptic function theory.

On Hyperbolic Monomolecular growth model in Height/Diameter growth of PINES

Abstract This paper proposed a hyperbolic monomolecular growth model (HMMGM). it came as a solution to the improved monomolecular growth equation which was developed by injecting an allometric parameter θ into the intrinsic rate of growth of the monomolecular growth equation using a hyperbolic sine function. Its ability in model prediction was compared with the classical monomolecular growth model an approach which mimicked the natural variability of height/diameter increment with respect to age and therefore provides a more realistic height/diameter predictions using goodness of fit tests and model selection criteria. The Kolmogorov Smirnov test and Shapiro-Wilk test was also used to test the compliance of the error term to normality assumptions while using testing the independence of the error term using the runs test . The mean function of top height/Dbh over age using the two models under study predicted closely the observed values of top height/Dbh in the hyperbolic monomolecular nonlinear growth models better than the source model (classical monomolecular growth model) while the results of R2, Adj. R2, MSE and AIC confirmed the predictive power of the Hyperbolic Monomolecular growth models over its source model.

Network Mapping by Replaying Hyperbolic Growth

Recent years have shown a promising progress in understanding geometric underpinnings behind the structure, function, and dynamics of many complex networks in nature and society. However these promises cannot be readily fulfilled and lead to important practical applications, without a simple, reliable, and fast network mapping method to infer the latent geometric coordinates of nodes in a real network. Here we present HyperMap, a simple method to map a given real network to its hyperbolic space. The method utilizes a recent geometric theory of complex networks modeled as random geometric graphs in hyperbolic spaces. The method replays the network's geometric growth, estimating at each time step the hyperbolic coordinates of new nodes in a growing network by maximizing the likelihood of the network snapshot in the model. We apply HyperMap to the AS Internet, and find that: 1) the method produces meaningful results, identifying soft communities of ASs belonging to the same geographic region; 2) the method has a remarkable predictive power: using the resulting map, we can predict missing links in the Internet with high precision, outperforming popular existing methods; and 3) the resulting map is highly navigable, meaning that a vast majority of greedy geometric routing paths are successful and low-stretch. Even though the method is not without limitations, and is open for improvement, it occupies a unique attractive position in the space of trade-offs between simplicity, accuracy, and computational complexity.

Statistical analysis of an alternative von Bertalanffy model for tree growth

This paper proposed an alternative von Bertalanffy nonlinear growth equation by introducing a growth rate stabilizing parameter using hyperbolic sine function. The ability of the integral solution of the alternative von Bertalanffy growth equation in model prediction was compared with the classical von Bertalanffy growth model, an approach which mimicked the natural variability of heights/diameter increment with respect to age and therefore provides a more realistic height/diameter predictions using the coefficient of determination (R 2 ), Mean Square Error (MSE) and Akaike Information Criterion (AIC) results. The “Kolmogorov-Smirnov” test, “Shapiro-Wilk” test and runs test were also used to test the compliance of the error term to the underlying assumptions. The mean function of top “height/diameter” over age using the two models under study predicted closely the observed values of top height/Dbh in the hyperbolic von Bertalanffy nonlinear growth models better than the classical von Bertalanffy growth model while the assumptions of the error term were maintained.

TRANSDISCIPLINARY – MODERN EDUCATIONAL TECHNOLOGY INTEGRATION OF KNOWLEDGE

The article is concerned with the new educational technology, based on the principle of transdisciplinarity aimed at implementing the strategy of “efficient pedagogics” in the era of the hyperbolic growth of information. The essence of transdisciplinarity is the idea of methodological knowledge acquisition, invariable for a number of disciplines. The authors advocate a view that one of the transdisciplinarity central concepts is the concept of “subjectivity” of modern scientific knowledge in general and pedagogy in particular. Based on provided examples of use of transdisciplinary knowledge in engineering and pedagogical disciplines the paper shows that transdisciplinarity technology can be successfully used in any discipline.

Development of Agro-industrial Clusters in Russia: Synergetic Approach

Based on the analysis of objective statistical data authors identified a global megatrend of the XXI century and the related growth of knowledge-intensive clustering, which provides high efficiency and competitiveness of the world economy. Based on the study of synergy, the self-organization theory and the eastern philosophy on original principles of synergy, the synergetic approach to the cluster development is elaborated. Article shows an artificial and rapid creation and development of clusters that uses the achievements of synergy, in particular ultrafast processes of the hyperbolic growth. The proposed model of clustering considers these processes.

On Differential Growth Equation to Stochastic Growth Model Using Hyperbolic Sine Function in Height/Diameter Modeling of Pines

Richrads growth equation being a generalized logistic growth equation was improved upon by introducing an allometric parameter using the hyperbolic sine function. The integral solution to this was called hyperbolic Richards growth model having transformed the solution from deterministic to a stochastic growth model. Its ability in model prediction was compared with the classical Richards growth model an approach which mimicked the natural variability of heights/diameter increment with respect to age and therefore provides a more realistic height/diameter predictions using the coefficient of determination (R2), Mean Absolute Error (MAE) and Mean Square Error (MSE) results. The Kolmogorov Smirnov test and Shapiro-Wilk test was also used to test the behavior of the error term for possible violations. The mean function of top height/Dbh over age using the two models under study predicted closely the observed values of top height/Dbh in the hyperbolic Richards nonlinear growth models better than the classical Richards growth model.

Semi-empirical description and projections of Internet traffic trends using a hyperbolic compound annual growth rate

For the purpose of projecting future macroscopic Internet traffic, we have analyzed historical U.S. and global Internet traffic volumes previously reported for 1990 to the present. The empirical long-term traffic trends are characterized by growth rates that have generally been decreasing over time, and so are not adequately described as exponential growth. Based on regression analyses, we also conclude that the decreasing growth rates are not well represented by the saturation characteristic of the logistic function alone. However, we find the observed traffic data are well reproduced over ranges spanning more than six orders of magnitude of traffic volume and a period of 17 years by a hyperbolic dependence of the compound annual growth rate on time. Using a semi-empirical hyperbolic function to model the growth rate we have carried out linearized regression analyses of a combination of historical and near-term traffic forecasts to project macroscopic Internet traffic to 2020 for several geo-economic regions, market segments, and application categories. In contrast to the decade of 2000–2010 when global Internet traffic grew more than 100-fold, the projections indicate that over the decade 2010–2020 the global wireline Internet traffic will grow approximately 16 times larger to approach 250 exabytes per month and the global mobile Internet traffic will grow approximately 150 times larger to approach 40 exabytes per month. The projections also indicate that over the decade the compound annual growth rate of global wireline Internet traffic will decrease from approximately 45 percent to 25 percent per year and the growth rate of global mobility Internet traffic will decrease from approximately 170 percent to 30 percent per year. By considering both the historical trends and near-term forecasts, our analyses and projections call attention to those traffic categories for which estimates of future Internet traffic may carry lesser or greater uncertainty.

On Comparison of Exponential and Hyperbolic Exponential Growth Models in Height/Diameter Increment of PINES (Pinus caribaea)

A new tree growth model called the hyperbolic exponential nonlinear growth model is suggested. Its ability in model prediction was compared with the Malthus or exponential growth model an approach which mimicked the natural variability of heights/diameter increment with respect to age and therefore provides more realistic height/diameter predictions as demonstrated by the results of the Kolmogorov Smirnov test and Shapiro-Wilk test. The mean function of top height/Dbh over age using the two models under study predicted closely the observed values of top height/Dbh in the Hyperbolic exponential nonlinear growth models better than the ordinary exponential growth model without violating most of the assumptions about the error term.

Becoming the Second City: Chicago’s Mass News Media, 1833-1898

Becoming the Second City: Chicago's Mass News Media, 1833-1898. By Richard Junger (University of Illinois Press, 2010. Pp. 235; notes, index. Cloth $69.97. Paper $15.00). In Becoming the Second City: Chicago's Mass News Media, 1833-1898, Richard Junger seeks to answer the question that Chicagoans themselves asked from the time of incorporation 1833 until today: why can Chicago not be the biggest, most populace and prosperous city in the United States. Why does Chicago have to be the second city in all things of importance to New York? Junger's answer to the question of why Chicago became second class to New York lies in the way mass media - mainly newspapers like the Chicago Tribune and Chicago Times - influenced Chicago's growth. For Junger, the media acted as a accelerant (x) to Chicago's rapid urbanization and population boom. As discussed in chapter one, titled From Zero to 29,963 in Just Fifty Years, the rate at which Chicago grew demographically indeed resembled that of a rapid, chemical chain reaction. unbridled boosterism of Chicago's mass media and the sensational reporting of not only Chicagoans on their own city but other city's newspapers did much for the city. This kind of journalism acted congruently with the thousands of people migrating to Chicago throughout the nineteenth century to nearly make the city into the powerhouse media visionaries wanted it to be. At the same time, those same newspapers both in Chicago and elsewhere helped regulate the flow of people into Chicago by their sensational reporting of events like the 1871 fire (chapter three) and violent instances of labor unrest as in 1886 with the Haymarket Riot and in 1894 with the Pullman Strike (chapter four). Thus the media helped to both give Chicago its prominence while also ensuring that it could never rise above its main competitor in New York. Junger warns his readers, however, of the dangers of using the sensational journalism en vogue in the nineteenth century as documents to demonstrate Chicago place as the nation's second city to New York. Too often historians take historical newspapers at their word and extrapolate broad conclusions without reading them with a critical eye. As a trained journalist and professor of communications and English, Junger possesses the training to use the Chicago Tribune, for instance, as a source more in the way nineteenth century journalists did: to prove a point rather than any strict fidelity to strict, objective reporting. Comparing Junger's use of historical newspapers to nineteenth century journalism is not to accuse Junger of yellow journalism since Junger knows of the kind of journalistic practices common in the nineteenth century where newspapers were often a promotional tool rather than solely a record of daily events. Newspapers thus help to prove his point for him. For Junger, the penultimate promotional event for Chicago media came with the 1893 Chicago's World Fair covered in chapter five, titled The Beauty. By the 1880s, as related in preceding chapters, newspapers around the country and in Chicago contributed to the city's hyperbolic urban growth. Yet for all of Chicago's enthusiasm for demographic and geographic enlargement, it still could not match the size and population of New York City. And when it came time for the United States to host the World's Fair (originally scheduled for 1892), New York thought itself the natural host for such a global event. Meanwhile, Chicagoans saw the fair as an opportunity to put aside the city's rampant corruption, pollution, social disorder, disease, and poverty (126) and show the world that Chicago could outdo not only pretender hosts like New York, but also Paris which held the 1888 World's Fair that featured the Eiffel Tower. …

Generation of high-current electron beam in a wide-aperture open discharge

In the present study, it was examined generation of nanosecond-duration electron-beam (EB) pulses by a wide-aperture open discharge burning in helium or in a mixture of helium with nitrogen and water vapor. In the experiments, a discharge cell with coaxial electrode geometry, permitting radial injection of the electron beam into operating lasing medium, was used, with the cathode having radius 2.5 cm and length 12 cm. It was shown possible to achieve an efficient generation of a high-intensity electron beam (EB pulse power ∼250 MW and EB pulse energy up to 4 J) in the kiloampere range of discharge currents (up to 26 kA at ∼12 kV discharge voltage). The current-voltage characteristics of the discharge proved to be independent of the working-gas pressure. The existence of an unstable dynamic state of EB, conditioned by the presence of an uncompensated space charge accumulated in the discharge cell due to the exponential growth of the current in time during discharge initiation and the hyperbolic growth of current density in the direction towards the tube axis, was revealed. The obtained pulsed electron beam was used to excite the self-terminated laser on He 21P10-21S0 transition. The oscillations developing in the discharge cell at high discharge currents put limit to the pumping energy and emissive power of the laser excited with the radially converging electron beam.

Things in Themselves

We have been confronted in the last hundred years with a rapidly changing technological environment. This environment has brought with it great wealth and prosperity, and there is no doubt that emerging concepts and applications of intellectual property (IP) have aided our scientific, technological, and economic expansion. Copyrights and patents offer monopolistic rights to authors and inventors over their creations, ensuring profits for fixed terms, and providing fortune as well as fame for the most successful inventors and authors. Monopoly rights are strong incentives to create both utilitarian and aesthetic works.Recently, emerging technologies have challenged traditional IP theory and practice. Consider the rise of computerized phenomena, and the proliferation of software and instantaneous communications through the Internet. Software has been considered a kind of hybrid, treated both as a patentable invention and as copyrightable expressions. In my first book, The Ontology of Cyberspace, I consider how software has revealed that our distinctions between copyrightable and patentable objects are artificial and illogical. I argue that all intentionally produced, man-made objects are expressions, and that computerization has merely revealed how one expression is very much like another. More recently, I have considered the question of patenting un-modified genes. In the course of that discussion, I further criticize the application of existing IP to genomics and genetics, at least where patents have issued for unmodified genes or l ife-forms. In all of my work, I have sought to uncover the ontologies (descriptions of the objects and relations involved) of the underlying objects. I have done this believing that once we reveal the nature of things (like expressions, machines, software, and genes, as well as relations and social objects like property, ownership, and intentions) we could then sensibly sort out logical errors and inefficiencies in public policies.We are now on the cusp of a new engineering breakthrough that will once again challenge our relation to our technological world, and likely pose new challenges to the application of traditional IP. Nanotechnology involves the construction of materials and objects at the ?nano-scale,? beginning at the molecular level. Theoretically, this will mean cheap and abundant objects of any size and shape, more-or-less instantly created, with little-to-no waste, and constructed anywhere and at any time. The science-fiction notion of simply dialing up an object and having it constructed on the spot, molecule-by-molecule, may well be decades away or further, but it is the end-goal of many who pursue nanotechnology research. Even so, we will begin facing unique challenges about the nature of intellectual property as the dividing lines between ideas and expressions further blur, and matter itself becomes programmable.Intellectual property has become a major force economically and culturally, impelling in part our hyperbolic economic and technological growth in the past century, and influencing both cultures and economies world-wide. Historically, the emergence of intellectual property as a class of objects is relatively new. This class of objects, which includes things that are patentable, copyrightable, and trademarkable, has evolved since its inception both significantly and rapidly. Let's look briefly at the evolution, form, and purposes of intellectual property law, and then consider how and to what extent new material technologies will challenge current notions of IP.The Emergence of Intellectual PropertyIntellectual property is often mistakenly thought to protect ideas in much the same way that ordinary property law protects things. In fact, there never has been any legally-recognized protection for ideas themselves, but only for various forms of expressions. Beginning around the time of the Renaissance, in Britain and Italy, the first legally-sanctioned monopolies over inventions and works of authorship were created. …

Symmetry in Motion in Euler's Formula and its Breakdown in Hyperbolic Function and Growth Function

Symmetry in Motion in Euler's Formula and its Breakdown in Hyperbolic Function and Growth Function

Acoustic emission for fatigue damage characterization in metal plates

Acoustic emission (AE) supplies information on the fracturing behavior of different materials. In this study, AE activity was recorded during fatigue experiments in metal coupons. The plates were characterized by a symmetric V-shape notch and were loaded in tension–tension fatigue until final failure with concurrent AE activity monitoring. The relatively broad bandwidth of the sensors enabled the recording of a wide range of frequencies up to 1 MHz. AE parameters like energy and duration exhibited a certain increase with the accumulation of damage although the hit rate was not significantly influenced. Furthermore the behavior of RA value (ratio of rise time to amplitude of the waveforms) which quantifies the shape of the first part of the AE signals and has been used for characterization of the cracking mode, showed a certain shift indicating the transition from tensile mode to shear which can be confirmed by the visual observation of the crack geometry after the experiment. The time history of RA is similar to the crack propagation rate (d a/d N) curve but exhibits the rapid hyperbolic growth consistently about 1000 cycles earlier than final failure. Therefore, the use of acoustic emission parameters is discussed both in terms of characterization of the damage mechanisms, as well as a tool for the prediction of ultimate life of the material under fatigue.

Аналоги фазовых переходов в экономике и демографии

Crises in social systems are considered by analogy with phase transitions and the corresponding critical phenomena in «non-living» many-particle physical systems. We present two qualitative physical models: (i) a histori- cal and demographic progress as a gradual condensation of economical domains with an improvement of living condi- tions, and (ii) the modern economical crisis as a result of a spontaneous «condensation» of assets in a free expansion of the U.S. economy in 1990th and 2000th, reducing a control over large business enterprises formed in this process. The first model explains the observed hyperbolic growth of world population in the I-XX centuries A.D. without any addi- tional assumption while the second model points to the analogy between the economic expansion with a drop of com- petition, and the expansion of gas into vacuum with a drop of temperature.

On the reasons of hyperbolic growth in the biological and human world systems

Macroevolution of the biological and human world systems in the aspect of time-dependence of their sizes is studied. These systems are considered as ‘civilizations’, which are defined here in a generalized sense as the systems having memory and producing knowledge (vital information) necessary for survival. Sizes of three types of memory – genetic, neural, and external – are estimated. Dominating one of them leads to the development of an appropriate type of civilization. The rise and development of the genetic memory was accompanied with the formation of the biota (which can be tractable as a biological civilization) and a hyperbolic growth of its biodiversity. The prevailing development of the neural memory in one of the taxa of biota led to the rise of the human civilization and to a hyperbolic growth of its population. The development of the external memory will probably lead to the extraction of a taxon (probably, a pool of countries) from the human world community, with a hyperbolic growth of the taxon's memory and fund of knowledge but without a pronounced growth of its population.