We present a quantitative characterisation of the fluctuations of the annualized growth rate of the real US GDP per capita growth at many scales, using a wavelet transform analysis of two data sets, quarterly data from 1947 to 2015 and annual data from 1800 to 2010. Our main finding is that the distribution of GDP grow…
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48 results for “data set growth”
The paper introduces a method for forecasting corporate sales growth using multiple reference variables.
problem Forecasting corporate sales growth with multiple reference variables.
method Reference class selection using rank-based algorithms and principal components analysis for data dimension reduction.
result Dimension reduced variables with past sales growth rates and operating margins perform well in forecasting.
Study uses web search data to analyze tech startups growth.
problem Analyzing growth dynamics of tech startups.
method Utilized Google Trends data for 241 US-based tech startups.
result Web search traffic correlates positively with tech startup growth.
Production networks amplify economic growth through technology diffusion.
problem Understanding how technology improvements propagate through production networks.
method Analyzing a production network model to study the effects of technological improvements.
result Longer production chains lead to faster price reduction and GDP growth.
Model predicts growth competition on curved surfaces.
problem Growth dynamics of two subsets on Riemannian manifolds.
method Modeling growth rates on spherically symmetric Riemannian manifolds.
result Conditions for bounded or unbounded growth on different manifolds.
Proves WPD elements are exponentially generic in acylindrically hyperbolic groups.
problem Growth rates of acylindrically hyperbolic groups.
method Analyzes exponential growth rates of non-WPD and WPD elements.
result WPD elements are exponentially generic in acylindrically hyperbolic groups.
Growth rates of geodesics on modular orbifolds are studied.
problem Understanding growth rates of geodesics on modular orbifolds.
method Exhaustion of modular orbifold by compact subsurfaces, analysis of low lying geodesics and reciprocal geodesics.
result Growth rates of low lying geodesics and reciprocal geodesics converge to the full set's growth rate.
New growth functions for mapping class sets discovered.
problem Growth of mapping class sets in terms of Lipschitz maps.
method Different mechanism to show variety of growth functions.
result Universe of possible growth functions is large.
Do firms share the same functional form of their growth rate distribution? A new statistical testphysics.data-an
We introduce a new statistical test of the hypothesis that a balanced panel of firms have the same growth rate distribution or, more generally, that they share the same functional form of growth rate distribution. We applied the test to European Union and US publicly quoted manufacturing firms data, considering functio…
Historical economic growth in countries of the former USSR is analysed. It is shown that Unified Growth Theory is contradicted by the data, which were used, but not analysed, during the formulation of this theory. Unified Growth Theory does not explain the mechanism of economic growth. It explains the mechanism of Malt…
Historical economic growth in Latin America is analysed using the data of Maddison. Unified Growth Theory is found to be contradicted by these data in the same way as it is contradicted by the economic growth in Africa, Asia, former USSR, Western Europe, Eastern Europe and by the world economic growth. Paradoxically, U…
Deep learning performance scales predictably with data and computation.
problem Understanding the relationship between training set size, computational scale, and model accuracy improvements.
method Empirical characterization of generalization error and model size growth across four domains: machine translation, language modeling, image processing, and speech recognition.
result Power-law generalization error scaling and sublinear model size growth with data size, with exponents not explained by theoretical work.
The paper proposes a method to determine the geometric priors of relational data.
problem Identifying geometric structure in heterogeneous, high-dimensional data.
method Combinatorial approach analyzing nearest-neighbor structures and local neighborhood growth rates.
result The method can identify the geometric priors of suitable embedding spaces for relational data.
The so-called great divergence in the income per capita is described in the Unified Growth Theory as the mind-boggling and unresolved mystery about the growth process. This mystery has now been solved: the great divergence never happened. It was created by the manipulation of data. Economic growth in various regions is…
Since non-compact RCD(0, N) spaces have at least linear volume growth, we study noncompact RCD(0, N) spaces with linear volume growth in this paper. One of the main results is that the diameter of level sets of a Busemann function grow at most linearly on a noncompact RCD(0, N) space satisfying the linear volume growth…
The Unified Growth Theory is a puzzling collection of myths based on illusions created by hyperbolic distributions. Some of these myths are discussed. The examination of data shows that the three stages of growth (Malthusian Regime, Post-Malthusian Regime and Modern Growth Regime) did not exist and that Industrial Revo…
This research develops efficient surrogate models for predicting crack growth in metal structures.
problem Accurately predicting crack growth in metal structures under uncertainty.
method Employing Gaussian Process (GP) regression models for latent variable modeling to create probabilistic surrogate models.
result Surrogate models successfully encode material and load-related uncertainties in stochastic crack growth processes.
On the geometry at infinity of manifolds with linear volume growth and nonnegative Ricci curvaturemath.DG
The study proves manifolds with specific curvature and volume properties always split off a line at infinity.
problem Understanding the geometry at infinity of manifolds with linear volume growth and nonnegative Ricci curvature.
method Analyzing properties of Busemann functions and constructing examples.
result Manifolds with the specified properties always split off a line at infinity, with bounded diameter of level sets of Busemann functions.
A general nonlinear logistic equation has been proposed to model long-time saturation in industrial growth. An integral solution of this equation has been derived for any arbitrary degree of nonlinearity. A time scale for the onset of nonlinear saturation in industrial growth can be estimated from an equipartition cond…
Finite distortion maps cannot have compact branch sets under growth conditions.
problem Understanding the structure of branch sets in mappings of finite distortion.
method Analyzing the asymptotic growth of distortion and constructing specific examples.
result The bound on the size of branch sets is strict and achievable.
Historical economic growth in Asia (excluding Japan) is analysed. It is shown that Unified Growth Theory is contradicted by the data, which were used (but not analysed) during the formulation of this theory. Unified Growth Theory does not explain the mechanism of economic growth. It explains the mechanism of Malthusian…
Data describing historical economic growth are analysed. They demonstrate convincingly that the takeoffs from stagnation to growth, claimed in the Unified Growth Theory, never happened. This theory is again contradicted by data, which were used, but never properly analysed, during its formulation. The absence of the cl…
Study of Anosov representations with Lipschitz limit set and applications to rigidity.
problem Characterizing Anosov representations with specific limit set properties.
method Introducing an unstable Jacobian and analyzing its orbit growth rate.
result Many higher rank representations belong to the studied class.
Data describing historical growth of income per capita [Gross Domestic Product per capita (GDP/cap)] for the world economic growth and for the growth in Western Europe, Eastern Europe, Asia, former USSR, Africa and Latin America are analysed. They follow closely the linearly-modulated hyperbolic distributions represent…
The paper examines perimeter minimizing sets in curved spaces and finds conditions for their boundary to match a specific structure.
problem Conditions for perimeter minimizing sets in curved spaces to have a boundary matching a product structure.
method Analyzes Riemannian manifolds with non-negative sectional curvature and quadratic volume growth.
result The boundary of a perimeter minimizing set in such manifolds is identified with a slice in the product structure.
Dividend discount models have been developed in a deterministic setting. Some authors (Hurley and Johnson, 1994 and 1998; Yao, 1997) have introduced randomness in terms of stochastic growth rates, delivering closed-form expressions for the expected value of stock prices. This paper extends such previous results by dete…
Mathematical properties of the historical GDP/cap distributions are discussed and explained. These distributions are frequently incorrectly interpreted and the Unified Growth Theory is an outstanding example of such common misconceptions. It is shown here that the fundamental postulates of this theory are contradicted …
Study on polynomial growth functions and forms on gradient Ricci solitons.
problem Estimating dimensions of polynomial growth holomorphic functions and forms.
method Relating to spectral data of the -Laplacian, proving estimates under curvature assumptions.
result Sharp dimension estimates and almost sharp frequency estimates for polynomial growth holomorphic functions.
New insights into groups with uniform exponential growth.
problem Uniform exponential growth in hierarchically hyperbolic groups.
method Quasi-isometric characterization and new insights into group structure.
result Uniform exponential growth for hierarchically hyperbolic groups.
Data describing historical economic growth are analysed. Included in the analysis is the world and regional economic growth. The analysis demonstrates that historical economic growth had a natural tendency to follow hyperbolic distributions. Parameters describing hyperbolic distributions have been determined. A search …
Predicting car sales using maximum entropy principle and proportional growth dynamics.
problem Predicting the sales of new cars over time.
method Analyzing 10 years of Spanish car sales data, applying Gibrat's law, and using the Maximum Entropy Principle.
result Car sales distribution follows predictions from the Maximum Entropy Principle for proportional growth systems.
Galor discovered many mysteries of the growth process. He lists them in his Unified Growth Theory and wonders how they can be explained. Close inspection of his mysteries reveals that they are of his own creation. They do not exist. He created them by his habitually distorted presentation of data. One of his self-creat…
Word metrics from large balls in injective spaces are exponentially generic and growth tight.
problem Understanding genericity and growth in word metrics from injective spaces.
method Geometric arguments and large ball considerations.
result Exponential genericity and growth tightness for word metrics.
Subgroup detection in linear growth curve models with generalized linear mixed model (GLMM) treesstat.ME
GLMM trees identify subgroups with different growth patterns in longitudinal data.
problem Identifying subgroups with distinct growth trajectories in longitudinal studies.
method Extended GLMM trees for longitudinal data.
result Extended GLMM trees outperform other methods in accuracy and speed.
One of the fundamental postulates of the Unified Growth Theory is the claimed existence of three distinctly different regimes of economic growth governed by three distinctly different mechanisms of growth. However, Galor also proposed that the timing of these regimes is different for developed countries and for less-de…
Study subgroup growth in RAAGs and RAAGs with Coxeter relations.
problem Understanding subgroup growth in RAAGs and RAAGs with Coxeter relations.
method Analyzing the independence number of defining graphs for RAAGs and conjecturing for RAAGs with Coxeter relations.
result Subgroup growth rate depends on the independence number of the defining graph for RAAGs and a conjecture for RAAGs with Coxeter relations.
Growth rate of the world Growth Domestic Product (GDP) is analysed to determine possible pathways of the future economic growth. The analysis is based on using the latest data of the World Bank and it reveals that the growth rate between 1960 and 2014 was following a trajectory approaching asymptotically a constant val…
Estimates tumor growth parameters from MRI data.
problem Personalizing brain tumor growth models for individual patients.
method Learning-based technique using a mixture-density network to estimate parameters from medical scans.
result Reduces the number of forward model integrations and relaxes functional form constraints.
Study ancient solutions on graphs with unbounded Laplacians, generalizing previous results.
problem Understanding ancient solutions on graphs with unbounded Laplacians.
method Generalizing Colding and Minicozzi's theorem and Hua's result to graphs with unbounded Laplacians.
result The dimension of the space of ancient solutions of polynomial growth is bounded by the dimension of harmonic functions with the same growth.
We derive a precise estimate on the volume growth of the level set of a potential function on a complete noncompact Riemannian manifold. As applications, we obtain the volume growth rate of a complete noncompact self-shrinker and a gradient shrinking Ricci soliton. We also prove the equivalence of weighted volume finit…
New approach uses satellite imagery to estimate economic growth.
problem Lack of reliable economic data in developing countries.
method Dynamic network and representation learning.
result Accurately predicts spatial gross economic expenditures.
Study volume growth and asymptotic cones of nonnegative Ricci curvature manifolds.
problem Whether the volume growth order of manifolds is greater than or equal to the dimension of their asymptotic cones.
method Analyzing asymptotic cones and volume growth conditions, extending Sormani's results.
result Existence of asymptotic cones with upper box dimension at most equal to the volume growth order.
The study of double coset growth in specific groups confirms a conjecture about generic 3-manifolds.
problem Understanding the growth of double cosets in specific groups.
method Generalizing previous work on hyperbolic groups, the study proves the growth of double cosets for certain subgroups.
result The double coset growth of certain subgroups is comparable to the orbital growth function.
This paper analyzes the robust growth rate of leveraged ETFs under uncertain parameters.
problem Analyzing the robust long-term growth rate of leveraged ETFs with uncertain parameters.
method Derive worst-case parameters using comparison principle and martingale extraction method.
result Explicitly obtain robust long-term growth rates under various models.
Study optimizes growth rate for investors with long-only constraints.
problem Maximizing growth rate under drift uncertainty and long-only constraints.
method Developed a finite dimensional approximation for concave functionally generated portfolios.
result Proved uniqueness and existence for optimal portfolios under long-only constraints.
Let be a finitely generated group with a finite generating set . For , let be the length of the shortest word over representing . The growth series of with respect to is the series , where is the number of elements of with . If…
New potential theory on minimal hypersurfaces shows stable growth of solutions near singularities.
problem Analyzing potential theory on minimal hypersurfaces.
method Introducing Hardy structures to study classical operators and showing stable growth of solutions.
result Minimal growth of positive solutions of Lw = 0 is stable and persists under perturbations or blow-ups.
Method reconstructs aneurysm growth history from patient parameters using physics-informed autoencoder.
problem Predicting arterial aneurysm rupture due to inaccessible growth time series.
method Physics-informed autoencoder combined with neural network for mapping patient parameters to aneurysm growth time history.
result Incorporating physical model constraints improves time series reconstruction, especially in noisy data.