Related papers: Mathematics of Predicting Growth
This is an evolving document. It is devoted to summarizing patterns and laws of knowledge growth. By examining a variety of parameters in data sources such as Wikipedia and Microsoft Academic Graph, we can get deeper insights of how…
This overview article highlights the critical role of mathematics in artificial intelligence (AI), emphasizing that mathematics provides tools to better understand and enhance AI systems. Conversely, AI raises new problems and drives the…
Politics today is largely about the art of messaging to influence the public, but the mathematical theory of messaging -- information and communication theory -- can turn this art into a precise analysis, both qualitative and quantitative,…
The possibility of using mathematics to model church growth is investigated using ideas from population modeling. It is proposed that a major mechanism of growth is through contact between religious enthusiasts and unbelievers, where the…
Quantifying the improvement in human living standard, as well as the city growth in developing countries, is a challenging problem due to the lack of reliable economic data. Therefore, there is a fundamental need for alternate, largely…
This paper presents a statistically sound method for measuring the accuracy with which a probabilistic model reflects the growth of a network, and a method for optimising parameters in such a model. The technique is data-driven, and can be…
The purpose of this essay is to bring out the unique role of Mathematics in providing a base to the diverse sciences which conform to its rigid structure. Of these the physical and economic sciences are so intimately linked with…
The problem of error growth due to the incomplete knowledge of the evolution law which rules the dynamics of a given physical system is addressed. Major interest is devoted to the analysis of error amplification in systems with many…
Social norms and conventions are commonly accepted and adopted behaviors and practices within a social group that guide interactions -- e.g., how to spell a word or how to greet people -- and are central to a group's culture and identity.…
Mathematical theory of selection is developed within the frameworks of general models of inhomogeneous populations with continuous time. Methods that allow us to study the distribution dynamics under natural selection and to construct…
A hypothesis of singleness of the growth equation for biological objects on different organizational levels and dimensional analysis are used in order to substantiate Schmalhausen's model of ontogenetic growth (the mass of a growing…
Economic growth is measured as the rate of relative change in gross domestic product (GDP) per capita. Yet, when incomes follow random multiplicative growth, the ensemble-average (GDP per capita) growth rate is higher than the time-average…
There are various approaches to the problem of how one is supposed to conduct a statistical analysis. Different analyses can lead to contradictory conclusions in some problems so this is not a satisfactory state of affairs. It seems that…
We study size and growth distributions of products and business firms in the context of a given industry. Firm size growth is analyzed in terms of two basic mechanisms, i.e. the increase of the number of new elementary business units and…
The Bayesian statistical paradigm provides a principled and coherent approach to probabilistic forecasting. Uncertainty about all unknowns that characterize any forecasting problem -- model, parameters, latent states -- is able to be…
Accurate predictions and representations of plant growth patterns in simulated and controlled environments are important for addressing various challenges in plant phenomics research. This review explores various works on state-of-the-art…
We introduce a predictive algorithm for the smart growth of cities with populations upward of 100,000, allowing for extensive simulations of growth plans and their effects upon an urban populous. A smart growth metric is calculated to…
In stochastic analysis, the flow of information through time is typically modelled using a filtration. We introduce some of the basic ideas involving enlargements of filtration. Here, we focus mainly on initial enlargements, where a given…
In this article, a new mathematical model of human population growth as an autonomous non-Markov queuing system with an unlimited number of servers and two types of applications is proposed. The research of this system was carried out a…
Predicting dynamic behaviors is one of the goals of science in general as well as essential to many specific applications of human knowledge to real world systems. Here we introduce an analytic approach using the sigmoid growth curve to…