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Concept: Exponential growth


In recent years there has been an exponential increase in tungsten demand, potentially increasing human exposure to the metal. Currently, the toxicology of tungsten is poorly understood, but mounting evidence suggests that both the elemental metal and its alloys have cytotoxic effects. Here, we investigate the association between tungsten and cardiovascular disease (CVD) or stroke using six waves of the National Health and Nutrition Examination Survey (NHANES).

Concepts: Medicine, Health, Disease, Iron, Chemical element, Carbon, The Association, Exponential growth


Next-generation sequencing (NGS) is increasingly being adopted as the backbone of biomedical research. With the commercialization of various affordable desktop sequencers, NGS will be reached by increasing numbers of cellular and molecular biologists, necessitating community consensus on bioinformatics protocols to tackle the exponential increase in quantity of sequence data. The current resources for NGS informatics are extremely fragmented. Finding a centralized synthesis is difficult. A multitude of tools exist for NGS data analysis; however, none of these satisfies all possible uses and needs. This gap in functionality could be filled by integrating different methods in customized pipelines, an approach helped by the open-source nature of many NGS programmes. Drawing from community spirit and with the use of the Wikipedia framework, we have initiated a collaborative NGS resource: The NGS WikiBook. We have collected a sufficient amount of text to incentivize a broader community to contribute to it. Users can search, browse, edit and create new content, so as to facilitate self-learning and feedback to the community. The overall structure and style for this dynamic material is designed for the bench biologists and non-bioinformaticians. The flexibility of online material allows the readers to ignore details in a first read, yet have immediate access to the information they need. Each chapter comes with practical exercises so readers may familiarize themselves with each step. The NGS WikiBook aims to create a collective laboratory book and protocol that explains the key concepts and describes best practices in this fast-evolving field.

Concepts: Molecular biology, Biology, Sequence, Medical research, Sustainability, Bench, Exponential growth, Wikipedia


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.

Concepts: European Union, Radioactive decay, Probability theory, Derivative, Exponential growth, Exponential function, Competitiveness, Global Competitiveness Report


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.

Concepts: Language, Exponential growth, Exponential function, Zipf's law, Historical linguistics, Exponentials, Language family, Indo-European languages


MOTIVATION: BLAST remains one of the most widely used tools in computational biology. The rate at which new sequence data is available continues to grow exponentially, driving the emergence of new fields of biological research. At the same time multicore systems and conventional clusters are more accessible. ScalaBLAST has been designed to run on conventional multiprocessor systems with an eye to extreme parallelism, enabling parallel BLAST calculations using over 16,000 processing cores with a portable, robust, fault-resilient design that introduces little to no overhead with respect to serial BLAST. ScalaBLAST 2.0 source code can be freely downloaded from

Concepts: Bioinformatics, Biology, Parallel computing, Computer program, Computational biology, C, Source code, Exponential growth


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.

Concepts: Scientific method, Prediction, Futurology, Hypothesis, Exponential growth, Exponential function, Technological singularity, Moore's law


Recent years have seen an exponential increase in people with long-term conditions using the Internet for information and support. Prior research has examined support for long-term condition self-management through the provision of illness, everyday, and emotional work in the context of traditional offline communities. However, less is known about how communities hosted in digital spaces contribute through the creation of social ties and the mobilization of an online illness “workforce.”

Concepts: Internet, Exponential growth, Online and offline


Claims of extreme survival of DNA have emphasized the need for reliable models of DNA degradation through time. By analysing mitochondrial DNA (mtDNA) from 158 radiocarbon-dated bones of the extinct New Zealand moa, we confirm empirically a long-hypothesized exponential decay relationship. The average DNA half-life within this geographically constrained fossil assemblage was estimated to be 521 years for a 242 bp mtDNA sequence, corresponding to a per nucleotide fragmentation rate (k) of 5.50 × 10(-6) per year. With an effective burial temperature of 13.1°C, the rate is almost 400 times slower than predicted from published kinetic data of in vitro DNA depurination at pH 5. Although best described by an exponential model (R(2) = 0.39), considerable sample-to-sample variance in DNA preservation could not be accounted for by geologic age. This variation likely derives from differences in taphonomy and bone diagenesis, which have confounded previous, less spatially constrained attempts to study DNA decay kinetics. Lastly, by calculating DNA fragmentation rates on Illumina HiSeq data, we show that nuclear DNA has degraded at least twice as fast as mtDNA. These results provide a baseline for predicting long-term DNA survival in bone.

Concepts: DNA, Mitochondrion, Mitochondrial DNA, Radioactive decay, Fossil, Exponential growth, Nuclear DNA, Moa


“Publish or perish” is the time-honored “principle” for academicians who race to accumulate lines under the “publications” section of a curriculum vitae. The original intent of publication-to inform others of findings and further scientific knowledge-has been corrupted by factors including (1) exponential growth of journals and the journal industry, fueled in part by intrusion of the Internet into all aspects of academic life; and (2) adoption of journal metrics (rather than written content) as the measure of scientific quality. The proprietary Thomson Reuters Impact Factor is the most pernicious metric, having caused editors and publishers to change editorial practices to boost the number. At the same time, gullible administrators and government agencies have been persuaded that metrics for the journal in which materials are published can be used as a measure of the worth of individual investigators (and institutions) and their research efforts: simple numbers can be substituted for the burdensome effort required to read and assess research quality. Thus, granting of research funds, awarding of academic rank and tenure, and determination of salaries (including bonus payments) have become tied to manipulable journal metrics rather than the significance or quality of reported research. Therefore, it is no wonder that the integrity of science is more often being questioned. How should a young investigator approach the “publish or perish” dilemma? Performing sound research and preparing optimal materials for publication must remain the overriding goals: properly articulate the question addressed by the study; thoroughly document all methods and case information; carefully describe results including any conflicting or negative findings; discuss the importance of the findings along with how the results address the initial question and whether findings refute or confirm previous studies; prepare properly cited bibliographic references; list all author contributions, potential conflicts of interest, financial support, and required ethical approvals; and provide a catchy title and an abstract containing sufficient information that other investigators perusing scientific indices will be enticed to read the published article. Submit the completed manuscript to the most appropriate journal based on that journal’s previously published content and relevance to the field of study regardless of journal metrics. On publication, notify investigators in the same field to ask for their comments on the work. Thus, an individual will become known for the quality of his or her work product and the worshiping of publication metrics will be unnecessary.

Concepts: Academic publishing, Impact factor, Publishing, Exponential growth, Tenure, Publication, Publish or perish, Thomson Reuters


Background- The Sprint Fidelis implantable cardioverter-defibrillator lead was recalled in 2007 because of an elevated risk of lead fracture. Several studies have demonstrated an accelerating risk of lead failure over time. We sought to identify predictors and characterize trends of Fidelis lead failure. Methods and Results- We evaluated 604 Fidelis leads with ≥90 days of follow-up implanted at our institution. Fidelis lead survival was analyzed by the Kaplan-Meier method. Analysis of log-log plots of cumulative hazard plots was performed to assess changes in lead failure rate over time. During follow-up of 3.3±1.7 years, 51 (8.4%) Fidelis lead failures were identified. The 3-year and 5-year Fidelis lead survival rates were 93.5% and 85.3%, respectively. Female sex was the only significant predictor of lead failure (heart rate, 2.1; 95% CI, 1.1-3.9; P<0.0001). The rate of lead failure initially increased exponentially with a power of 2.3 (95% CI, 2.22-2.43; P<0.0001). However, log-log analysis of cumulative hazard for leads functioning at 2 and 4 years revealed a stable rate of failure of 4.5%/year. Mathematical modeling of the Fidelis lead failure demonstrated a transition from an exponential to linear pattern of lead failure at 2.9 years. Conclusions- After 3 years, failure rates of Fidelis leads stabilize but at a significantly elevated rate. Female sex is associated with a doubling of the risk of Fidelis lead failure. These findings have implications for Fidelis lead management decisions that are based on the prediction of lead failure risk.

Concepts: Decision making, Implantable cardioverter-defibrillator, Failure, Failure rate, Exponential growth, Weibull distribution, Annualized failure rate, Exponential distribution