Concept: Exponential function
Politicians world-wide frequently promise a better life for their citizens. We find that the probability that a country will increase its per capita GDP (gdp) rank within a decade follows an exponential distribution with decay constant λ = 0.12. We use the Corruption Perceptions Index (CPI) and the Global Competitiveness Index (GCI) and find that the distribution of change in CPI (GCI) rank follows exponential functions with approximately the same exponent as λ, suggesting that the dynamics of gdp, CPI, and GCI may share the same origin. Using the GCI, we develop a new measure, which we call relative competitiveness, to evaluate an economy’s competitiveness relative to its gdp. For all European and EU countries during the 2008-2011 economic downturn we find that the drop in gdp in more competitve countries relative to gdp was substantially smaller than in relatively less competitive countries, which is valuable information for policymakers.
Zipf’s law on word frequency and Heaps' law on the growth of distinct words are observed in Indo-European language family, but it does not hold for languages like Chinese, Japanese and Korean. These languages consist of characters, and are of very limited dictionary sizes. Extensive experiments show that: (i) The character frequency distribution follows a power law with exponent close to one, at which the corresponding Zipf’s exponent diverges. Indeed, the character frequency decays exponentially in the Zipf’s plot. (ii) The number of distinct characters grows with the text length in three stages: It grows linearly in the beginning, then turns to a logarithmical form, and eventually saturates. A theoretical model for writing process is proposed, which embodies the rich-get-richer mechanism and the effects of limited dictionary size. Experiments, simulations and analytical solutions agree well with each other. This work refines the understanding about Zipf’s and Heaps' laws in human language systems.
Forecasting technological progress is of great interest to engineers, policy makers, and private investors. Several models have been proposed for predicting technological improvement, but how well do these models perform? An early hypothesis made by Theodore Wright in 1936 is that cost decreases as a power law of cumulative production. An alternative hypothesis is Moore’s law, which can be generalized to say that technologies improve exponentially with time. Other alternatives were proposed by Goddard, Sinclair et al., and Nordhaus. These hypotheses have not previously been rigorously tested. Using a new database on the cost and production of 62 different technologies, which is the most expansive of its kind, we test the ability of six different postulated laws to predict future costs. Our approach involves hindcasting and developing a statistical model to rank the performance of the postulated laws. Wright’s law produces the best forecasts, but Moore’s law is not far behind. We discover a previously unobserved regularity that production tends to increase exponentially. A combination of an exponential decrease in cost and an exponential increase in production would make Moore’s law and Wright’s law indistinguishable, as originally pointed out by Sahal. We show for the first time that these regularities are observed in data to such a degree that the performance of these two laws is nearly the same. Our results show that technological progress is forecastable, with the square root of the logarithmic error growing linearly with the forecasting horizon at a typical rate of 2.5% per year. These results have implications for theories of technological change, and assessments of candidate technologies and policies for climate change mitigation.
As the hardware of FLIM technique becomes mature, the most important criterion for FLIM application is the correct interpretation of its data. In this research, first of all, a more orthogonal phasor approach, called as Modified Phasor Approach (MPA), is put forward. It is a way to calculate the lifetime of the complex fluorescent process, and a rule to measure how much the fluorescence process deviates from single exponential decay. Secondly, MPA is used to analysis the time-resolved fluorescence processes of the transfected CHO-K1 Cell lines expressing adenosine receptor A1R tagged by CYP and YFP, measured in the channel of the acceptor. The image of the fluorescence lifetime and the multiplication of the fluorescence lifetime and deviation from single exponential decay reveal the details of the Homo-FRET. In one word, MPA provides the physical meaning in its whole modified phasor space, and broadens the way for the application of the fluorescence lifetime imaging.
The reliable assessment of the biological activity of a minor component embedded in a complex matrix of several hundred compounds is a difficult but common task in the search for natural product-based antibiotics, for example, by bioassay-guided fractionation. To quantify the antibiotic properties, it is necessary to assess the cell viability. Direct measurements use CFU counts, OD measurements or detection via fluorescent or reducible dyes. However, natural extracts often already possess intrinsic dye, fluorescent, reducing or protein denaturing properties, or they contain insoluble compounds or general protein-binding (tanning) polyphenols as disturbing features, while at the same time very little of the selective antibiotic sought after is present. A promising alternative is provided by intrinsically produced bright fluorescent proteins. In this paper, a rapid, robust and concentration-dependent assay for screening antibiotics with genetically modified mutants of Bacillus subtilis 168 (PabrB-iyfp) is presented. The Gram-positive bacteria exhibit a native fluorescence during their exponential growth phase due to the expression of improved yellow fluorescent protein. To demonstrate the applicability in the field of natural product research, several compounds and extracts were screened for antibacterial activity, with an emphasis on those from the fungal genus Hygrophorus (waxy caps).The Journal of Antibiotics advance online publication, 8 July 2015; doi:10.1038/ja.2015.71.
In order for the promise of terahertz (THz) wireless communications to become a reality, many new devices need to be developed, such as those for routing THz waves. We demonstrate a power splitting router based on a parallel-plate waveguide (PPWG) T-junction excited by the TE1 waveguide mode. By integrating a small triangular septum into the waveguide plate, we are able to direct the THz light down either one of the two output channels with precise control over the ratio between waveguide outputs. We find good agreement between experiment and simulation in both amplitude and phase. We show that the ratio between waveguide outputs varies exponentially with septum translation offset and that nearly 100% transmission can be achieved. The splitter operates over almost the entire range in which the waveguide is single mode, providing a sensitive and broadband method for THz power splitting.
- Proceedings of the National Academy of Sciences of the United States of America
- Published almost 7 years ago
The ability to implant electronic systems in the human body has led to many medical advances. Progress in semiconductor technology paved the way for devices at the scale of a millimeter or less (“microimplants”), but the miniaturization of the power source remains challenging. Although wireless powering has been demonstrated, energy transfer beyond superficial depths in tissue has so far been limited by large coils (at least a centimeter in diameter) unsuitable for a microimplant. Here, we show that this limitation can be overcome by a method, termed midfield powering, to create a high-energy density region deep in tissue inside of which the power-harvesting structure can be made extremely small. Unlike conventional near-field (inductively coupled) coils, for which coupling is limited by exponential field decay, a patterned metal plate is used to induce spatially confined and adaptive energy transport through propagating modes in tissue. We use this method to power a microimplant (2 mm, 70 mg) capable of closed-chest wireless control of the heart that is orders of magnitude smaller than conventional pacemakers. With exposure levels below human safety thresholds, milliwatt levels of power can be transferred to a deep-tissue (>5 cm) microimplant for both complex electronic function and physiological stimulation. The approach developed here should enable new generations of implantable systems that can be integrated into the body at minimal cost and risk.
Background Sports drinks intended to improve performance and hydrate athletes taking part in endurance sport are being marketed to children, for whom these products are not intended. Popularity among children has grown exponentially. Worryingly they consume them socially, as well as during physical activity. Sports drinks are high in sugar and are acidic. Product marketing ignores the potential harmful effects of dental caries and erosion.Objective To investigate the use of sports drinks by children.Method One hundred and eighty-three self-complete questionnaires were distributed to four schools in South Wales. Children in high school years 8 and 9 (aged 12-14) were recruited to take part. Questions focused on use of sports drinks, type consumed, frequency of and reason for consumption and where drinks were purchased.Results One hundred and sixty children responded (87% response rate): 89.4% (143) claimed to drink sports drinks, half drinking them at least twice a week. Lucozade Sport(™) was the most popular brand. The main reason for consuming the drinks was attributed to the ‘nice taste’ (90%, 129/143). Most respondents purchased the drinks from local shops (80.4%, 115) or supermarkets (54.5%, 78). More boys claimed to drink sports drinks during physical activity (77.9% versus 48.6% girls, P <0.001). Whereas more girls claimed to drink them socially (51.4% versus 48.5% boys, NS).Conclusion A high proportion of children consumed sports drinks regularly and outside of sporting activity. Dental health professionals should be aware of the popularity of sports drinks with children when giving health education advice or designing health promotion initiatives.
In this paper, we apply an original scientometric analyses to a corpus comprising synthetic biology (SynBio) publications in Thomson Reuters Web of Science to characterize the emergence of this new scientific field. Three results were drawn from this empirical investigation. First, despite the exponential growth of publications, the study of population level statistics (newcomers proportion, collaboration network structure) shows that SynBio has entered a stabilization process since 2010. Second, the mapping of textual and citational networks shows that SynBio is characterized by high heterogeneity and four different approaches: the central approach, where biobrick engineering is the most widespread; genome engineering; protocell creation; and metabolic engineering. We suggest that synthetic biology acts as an umbrella term allowing for the mobilization of resources, and also serves to relate scientific content and promises of applications. Third, we observed a strong intertwinement between epistemic and socio-economic dynamics. Measuring scientific production and impact and using structural analysis data, we identified a core set of mostly American scientists. Biographical analysis shows that these central and influential scientists act as “boundary spanners,” meaning that their importance to the field lies not only in their academic contributions, but also in their capacity to interact with other social spaces that are outside the academic sphere.
The distribution of scientific citations for publications selected with different rules (author, topic, institution, country, journal, etc…) collapse on a single curve if one plots the citations relative to their mean value. We find that the distribution of “shares” for the Facebook posts rescale in the same manner to the very same curve with scientific citations. This finding suggests that citations are subjected to the same growth mechanism with Facebook popularity measures, being influenced by a statistically similar social environment and selection mechanism. In a simple master-equation approach the exponential growth of the number of publications and a preferential selection mechanism leads to a Tsallis-Pareto distribution offering an excellent description for the observed statistics. Based on our model and on the data derived from PubMed we predict that according to the present trend the average citations per scientific publications exponentially relaxes to about 4.