Study shows existence and uniqueness of solutions for porous medium equation on curved manifolds.
problem Existence and uniqueness of solutions for porous medium equation on curved manifolds.
method Very weak solutions, Cauchy problem, Cartan-Hadamard manifolds, Ricci curvature bounds, sectional curvature bounds.
result Sharp growth rate of initial data for existence, maximal existence time estimate, blow-up for specific manifolds and data.
Deep learning models brain deformations based on atrophy and growth data.
problem Simulating brain deformations due to atrophy and growth.
method Differentiable biomechanical model using deep learning.
result Trained model can rapidly simulate new brain deformations with minimal residuals.
Simple math predicts growth trends.
problem Complex growth projections are hard to understand.
method Direct or indirect analysis of growth rates.
result Simple assumptions lead to understandable growth predictions.
Paper proves positivity of energy function on Riemannian manifolds.
problem Investigating positivity of energy function on Riemannian manifolds.
method Using energy function to prove positivity of initial energy.
result Simple method to obtain growth of eigen-solutions.
Ricci flow shows PIC1 manifolds with maximal volume growth are like Euclidean space.
problem Characterizing complete PIC1 manifolds with maximal volume growth.
method Ricci flow with local curvature estimates.
result PIC1 manifolds with maximal volume growth are diffeomorphic to \(\mathbb{R}^n\).
Bayesian Causal Forests model assesses part-time work's impact on student growth.
problem Estimating causal effects of part-time work on student growth in mathematics achievement.
method Longitudinal Bayesian Causal Forests model combining non-parametric and difference-in-differences methods.
result Negative impact of part-time work for most students, potential benefits for those with low school belonging, widening achievement gap identified.
New theory explains signal propagation in normalization-free transformers.
problem Understanding signal propagation in normalization-free transformers.
method Deriving recurrence relations for activation statistics and APJNs across layers.
result Transformers with elementwise tanh-like nonlinearities exhibit subcritical signal propagation.
Study shows GDP and CPI predict CCC funding, highlighting need for economic forecasting.
problem Challenges in aligning CCC funding with DEI initiatives.
method Quantitative correlational design, analyzing 30 years of economic data.
result Strong positive correlation between GDP growth and CCC funding levels, and between CPI and funding levels.
P.W. Anderson proposed the concept of complexity in order to describe the emergence and growth of macroscopic collective patterns out of the simple interactions of many microscopic agents. In the physical sciences this paradigm was implemented systematically and confirmed repeatedly by successful confrontation with rea…
TMLE improves IPM estimation for ecological population dynamics.
problem Estimating key demographic properties from IPM data.
method Targeted Maximum Likelihood Estimation (TMLE) for IPMs.
result Robust and efficient estimators for IPM properties.
Study on uniqueness of Ricci flow on noncompact manifolds.
problem Uniqueness of Ricci flow on complete noncompact manifolds.
method Curvature bounded above by C/t, polynomial growth initial curvature, relatively small Ricci curvature of the flow.
result Proved uniqueness under specified conditions.
Proves global existence of maps with curvature term on expanding spacetimes.
problem Global existence of Dirac-wave maps with curvature term on expanding spacetimes.
method Proves global existence with small initial data on globally hyperbolic manifolds with growth condition.
result Global existence of maps proved for small initial data.
Global existence of Yamabe flow on non-compact manifolds with unbounded initial curvature.
problem Global existence of Yamabe flow on non-compact manifolds with unbounded initial curvature.
method Assumption of conformally equivalent initial metric to a complete background metric with bounded scalar curvature and positive Yamabe invariant.
result Global existence of Yamabe flow without requiring initial curvature bounds.
Framework generates realistic crop images for growth modeling.
problem Modeling crop growth over time with precision and detail.
method Two-stage framework: image prediction and growth estimation models.
result Framework accurately predicts crop images with varying conditions.
A bipartite producer-consumer network is constructed to describe the industrial structure. The edges from consumer to producer represent the choices of the consumer for the final products and the degree of producer can represent its market share. So the size distribution of firms can be characterized by producer's degr…
The note shows equivalence between polynomial growth and polynomial containment for certain groups.
problem Equivalence between polynomial growth and polynomial containment for Cayley graphs of groups.
method Analyzes results from the literature on Cayley graphs of groups.
result Equivalence holds for elementary amenable groups and non-amenable groups.
We introduce and systematically study the concept of a growth tight action. This generalizes growth tightness for word metrics as initiated by Grigorchuk and de la Harpe. Given a finitely generated, non-elementary group G acting on a G--space X, we prove that if G contains a strongly contracting eleme…
Paper bounds mass of 3D Einstein data using spacetime harmonic functions.
problem Calculating the mass of 3D asymptotically flat initial data for the Einstein equations.
method Uses spacetime harmonic functions to give a lower bound for the ADM mass.
result New proof of spacetime positive mass theorem and rigidity statement.
Boundary-induced apparent risk aversion in non-ergodic growth models.
problem Risk aversion in multiplicative growth systems with absorbing boundaries.
method Exact lattice propagation and analysis of binary multiplicative processes.
result Optimal exposure is compressed near absorbing boundaries, mimicking risk aversion.
In many recent applications, data is plentiful. By now, we have a rather clear understanding of how more data can be used to improve the accuracy of learning algorithms. Recently, there has been a growing interest in understanding how more data can be leveraged to reduce the required training runtime. In this paper, we…
Cryptocurrency market capitalizations follow power-law distributions with distinct exponents.
problem Characterizing the dynamics of cryptocurrency coins and tokens.
method Proportional growth model applied to coin and token distributions.
result The power-law exponents for coins and tokens are distinct and converge to 1 for tokens in the future.
Neural IVP solves IVPs with neural networks, overcoming scaling and conditioning issues.
problem Solving initial value PDEs with neural networks is challenging due to numerical errors and limited scalability.
method Developed an ODE-based approach to solve IVPs with neural networks, preventing ill-conditioning and scaling issues.
result Neural IVP solves challenging PDEs with neural networks efficiently and accurately.
Unified Growth Theory contradicted by Latin American economic data.
problem Unified Growth Theory fails to explain Latin American economic growth.
method Analysis of historical economic growth data from Maddison.
result Unified Growth Theory is inconsistent with Latin American data.
Willmore flow preserves low energy surfaces to planes.
problem Preserving low energy surfaces to planes under Willmore flow.
method Willmore flow equation for complete, properly immersed surfaces in Rn.
result Complete Willmore surfaces with low energy converge to planes.
New method stabilizes deep neural networks by setting Lyapunov exponent to zero.
problem Stability issues in deep neural networks with low width.
method Lyapunov initialization method to set Lyapunov exponent to zero.
result Lyapunov exponent governs stability of deep networks; standard methods fail for low width.
Improved LLM pre-training performance through better weight and variance control.
problem Improper weight and variance control in LLM pre-training affects downstream task performance.
method Introduced Layer Index Rescaling (LIR) and Target Variance Rescaling (TVR) techniques.
result Substantial improvements in downstream task performance (up to 4.6%) and reduced extreme activation values.
Unified Growth Theory debunked: economic growth is insecure and unsustainable.
problem The mystery of the great divergence in income per capita.
method Analysis of economic data to show that growth trajectories are increasing vertically over time.
result Unified Growth Theory is incorrect and promotes misleading concepts.
Study on how neural network weights evolve and form structures.
problem Understanding the structure and evolution of neural network weights during training.
method Applied topological data analysis to monitor and analyze the weights of neural networks.
result Weights evolve to form trees or smooth surfaces, revealing important factors of variation.
The model predicts economic growth with high accuracy using physical principles.
problem Forecasting future economic growth and energy consumption.
method A purely physical economic model initialized with 1950s data.
result The model accurately predicts economic growth with >90% skill score.
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…
This paper presents a general solution for a recent model by Keen for endogenous money creation. The solution provides an analytic framework that explains all significant dynamical features of Keen's model and their parametric dependence, including an exact result for both the period and subsidence rate of the Great Mo…
Labor productivity in developed countries is analyzed and modeled. Modeling is based on our previous finding that the rate of labor force participation is a unique function of GDP per capita. Therefore, labor productivity is fully determined by the rate of economic growth, and thus, is a secondary economic variable. In…
Unified Growth Theory disproved by lack of economic takeoffs.
problem The absence of economic takeoffs from stagnation to growth.
method Analysis of historical economic growth data.
result Takeoffs from stagnation to growth never occurred.
DIVI clusters noisy high-dimensional data with stable feature gating.
problem Challenging clustering in high-dimensional noisy data.
method Data-informed variational clustering framework combining global feature gating and adaptive structure growth.
result DIVI performs competitively under severe feature noise and remains computationally feasible.
Research activities of Kyoto Econophysics Group is reviewed. Strong emphasis has been placed on real economy. While the initial stage of research was a first high-definition data analysis on personal income, it soon progressed to firm dynamics, growth rate distribution and establishment of Pareto's law and Gibrat's law…
Study optimizes natural resource harvesting under model uncertainty using risk measures.
problem Optimal harvesting policy selection for natural resources under model uncertainty.
method Investigated using neoclassical growth model dynamics and convex risk measures, specifically Fréchet risk measures.
result Robust harvesting strategies quantifying operational and marginal risk under model uncertainty.
Incremental training method for deep neural networks.
problem Training deep neural networks efficiently and with incremental growth.
method Partitioning the network into sub-networks, gradually incorporating them, and using look-ahead initialization.
result Incremental approach reaches baseline accuracy and identifies smaller network partitions.
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…
Galor's mysterious income growth rate is debunked, revealing data manipulation.
problem Mysterious sudden spurt in income per capita growth rate.
method Mathematical analysis of historical world economic growth data.
result The sudden spurt in income per capita growth rate is an artifact of data presentation.
Boundary-induced risk aversion in non-ergodic growth models.
problem Tension between expected-utility curvature and observed risk-taking behavior.
method Study of a finite-horizon binary multiplicative process with absorbing boundaries.
result Boundary-induced compression of optimal exposure below the Kelly fraction, leading to apparent risk aversion.
Study inverse mean curvature flow on entire graphs, proving finite time existence for certain asymptotic cases.
problem Analyzing the evolution of entire graphs under inverse mean curvature flow.
method Global existence for starshaped graphs, critical case analysis for asymptotically conical graphs.
result Existence of a finite time \( T \) for certain asymptotically conical graphs, convergence to a flat plane as \( t o T \).
Historical income per capita data follow hyperbolic growth patterns.
problem Economic stagnation and Malthusian traps in historical data.
method Fitting hyperbolic distributions to GDP/capita and population data.
result Income per capita growth was monotonic and without transitions.
Modeling tech transfer to explain convergence in Central and Eastern Europe.
problem Understanding mechanisms of technological diffusion in developing economies.
method Introducing a herding-based mechanism to model technological adoption and productivity growth.
result Explicit analytical solution showing nonlinear convergence to a moving frontier.
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…
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…
We present a simple dynamical model of stock index returns which is grounded on the ability of the Cyclically Adjusted Price Earning (CAPE) valuation ratio devised by Robert Shiller to predict long-horizon performances of the market. More precisely, we discuss a discrete time dynamics in which the return growth depends…
Existence criteria for Chern-Ricci flows on noncompact manifolds established.
problem Existence and properties of Chern-Ricci flows on noncompact complex manifolds.
method Generalization of results for Kahler-Ricci flows to Chern-Ricci flows, existence criteria established.
result Existence of complete Kahler metrics with nonnegative and bounded bisectional curvature on noncompact complex manifolds.
Public debt is one of the important economic variables that quantitatively describes a nation's economy. Because bankruptcy is a risk faced even by institutions as large as governments (e.g. Iceland), national debt should be strictly controlled with respect to national wealth. Also, the problem of eliminating extreme p…