Random 3-manifolds have exponential growth of torsion in covers.
problem Exponential growth of torsion in random 3-manifolds.
method Study of random 3-manifolds with positive first Betti number.
result Exponential growth of torsion in cyclic covers.
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48 results for “random growth”
This paper calculates the stock price covariance with correlated growth rates.
problem Determining the covariance of stock prices with correlated growth rates.
method Developed a formula for the covariance of random stock prices with correlated growth rates of dividends.
result A formula for the covariance of stock prices with correlated growth rates of dividends.
Effects of Randomness on Power Law Tails in Multiplicatively Interacting Stochastic Processescond-mat.stat-mech
Effects of randomness on non-integer power law tails in multiplicatively interacting stochastic processes are investigated theoretically. Generally, randomness causes decrease of the exponent of tails and the growth rate of processes. Explicit calculations are performed for two examples: uniformly distributed and two p…
Study shows exponential growth of Laplacian determinant on random hyperbolic surfaces.
problem Understanding the behavior of Laplacian determinants on random hyperbolic surfaces.
method Investigated various models of random hyperbolic surfaces and their Laplacian determinants as genus increases.
result For all popular models, the determinant grows exponentially with a universal exponent as the genus goes to infinity.
Random walks on hyperbolic spaces show linear growth in translation lengths.
problem Investigate the growth of translation lengths in random walks on hyperbolic spaces.
method Prove linear growth without moment conditions and apply to Teichmüller spaces.
result Linear growth of translation lengths in random walks on hyperbolic spaces.
Dynamical Stationarity as a Result of Sustained Random Growthcond-mat.stat-mech
New approach models sustained growth leading to stationary distributions.
problem Understanding stationary distributions in fast-growing systems.
method Applied discrete and continuous master equations, derived rates from stationary distributions.
result Reconstructed distributions for various growing systems.
The paper improves lower bounds on deep neural network trajectories.
problem Understanding the expressivity of deep neural networks.
method Generalized method for lower bounding trajectory growth in random sparse deep ReLU networks.
result Trajectory growth can remain exponential in depth with sparse variants of random nets.
The study connects Kleinian group divergence to random walk recurrence.
problem Understanding the recurrence of random walks on Schreier graphs of Kleinian groups.
method Connecting growth rates of orbits, volume, and Schreier graphs.
result Constructing Kleinian groups of divergence type.
Trading excess volatility for growth in random return dynamics.
problem Trading excess volatility for growth in random return dynamics.
method Studied binomial and Gaussian return dynamics in discrete time.
result Excess volatility can be traded to create growth.
Random quotients of hyperbolic cubulated groups remain cubulated.
problem Understanding properties of random quotients of hyperbolic cubulated groups.
method Cubical small-cancellation theory, exponential growth of conjugacy classes, and hyperplane stabilizers' growth.
result Low-density random quotients of cubulated hyperbolic groups are cubulated and hyperbolic.
Random surfaces' diameter grows logarithmically with size.
problem Estimating the diameter of random hyperbolic surfaces.
method Uniform gluing of triangles, compactification, asymptotic analysis.
result The diameter is asymptotic to .
The paper shows subexponential growth and displacement bounds for random walks on graphs with bounded degrees and non-negative curvature.
problem Analyzing subexponential growth and displacement bounds for random walks on graphs with bounded degrees and non-negative curvature.
method Proving bounds on the continuous-time random walk displacement and log-volume growth using Ollivier--Ricci curvature.
result The paper establishes subexponential growth and displacement bounds for random walks on graphs with bounded degrees and non-negative curvature.
Deep-SITAR uses autoencoders to predict growth patterns.
problem Predicting individual growth trajectories from population data.
method Deep learning framework integrating autoencoders and B-spline models.
result Deep-SITAR predicts individual growth without full model re-estimation.
Graphs with bounded degrees and non-negative Ollivier-Ricci curvature have subexponential growth and diffusive random walk.
problem Understanding geometric properties of graphs with non-negative Ollivier-Ricci curvature.
method Analyzing the geometric properties of graphs with non-negative Ollivier-Ricci curvature, proving subexponential growth and diffusive random walk.
result For graphs with bounded degrees and non-negative Ollivier-Ricci curvature, the average log-volume growth and random walk displacement are subexponential.
New model generates clusters with sublinear growth, useful for sparse multigraphs.
problem Cluster sizes grow linearly with sample size, limiting applicability in some cases.
method Non-exchangeable random partition models based on completely random measures and Poisson embedding.
result Model generates partitions with sublinearly growing cluster sizes, controlled by parameters.
Directly proves logarithmic systolic growth for all hyperbolic surfaces.
problem Proving logarithmic systolic growth for all hyperbolic surfaces.
method Using original Brooks/Buser-Sarnak surfaces through a direct approach.
result Directly proves logarithmic systolic growth for all hyperbolic surfaces.
The study establishes spectral theorems for random walks on mapping class groups and Out(FN).
problem Analyzing random walks on mapping class groups and Out(FN) to understand their asymptotic behavior.
method Relating the stretching factor to the Lyapunov exponent, using contraction properties of Teichmüller geodesics and outer space.
result Established spectral theorems linking random walk properties to Lyapunov exponents and growth rates.
TLRF improves timely COVID-19 outbreak detection with small sample size counties.
problem Balancing accuracy and speed in estimating COVID-19 case growth rates.
method Transfer Learning Random Forest (TLRF) framework for growth rate estimation.
result TLRF outperforms existing methods in predicting case growth rates and timely outbreak detection.
Study extreme values of stable random fields on geometric spaces.
problem Understanding extreme values of stable random fields on various geometric spaces.
method Analyzing extreme values through Patterson-Sullivan measures and extremal cocycle growth.
result Established a dichotomy for the growth-rate of maxima sequences of stable random fields.
Let Mod(S) denote the mapping class group of a compact, orientable surface S. We prove that finitely generated subgroups of Mod(S) which are not virtually abelian have uniform exponential growth with minimal growth rate bounded below by a constant depending only, and necessarily, on S. For the proof, we find in any suc…
Simple, non-optimized portfolios beat capitalization-weighted indexes due to excess growth, not individual stock growth.
problem Simple investment strategies outperform capitalization-weighted indexes over long periods.
method Decomposed portfolio log-returns into average and excess growth components, using rank-based empirical study.
result Excess growth component, not individual stock growth, explains outperformance of naive portfolios.
Uniform models for random 3-manifolds with controlled metrics.
problem Understanding the geometric properties of random 3-manifolds.
method Two constructions of hyperbolic metrics on 3-manifolds with Heegaard splittings.
result The diameter of a random Heegaard splitting grows coarsely linearly in the length of the associated random walk.
Solves consumption-investment problem with random horizon under Epstein-Zin preferences.
problem Maximizing consumption and investment under random time horizons with Epstein-Zin utility.
method Backward stochastic differential equations with superlinear growth on unbounded random horizons.
result Optimal strategies differ significantly when moving from fixed to random time horizons.
The paper examines linking numbers in grid models and finds polynomial moments.
problem Analyzing linking numbers in grid models.
method Examined linking numbers as a random variable on isotopy classes of 2-component links, computed moments and limits.
result The th moment of the linking number is a polynomial in the grid size with degree , and all odd moments vanish.
We investigate the relation between economic growth and equality in a modified version of the agent-based asset exchange model (AEM). The modified model is a driven system that for a range of parameter space is effectively ergodic in the limit of an infinite system. We find that the belief that "a rising tide lifts all…
Study shows a central limit theorem for random coverings of manifolds with nilpotent groups.
problem Understanding the distribution of connected components in random coverings of manifolds with nilpotent fundamental groups.
method Used sampling homomorphisms from the fundamental group into the symmetric group and subgroup growth zeta functions of nilpotent groups.
result Proved a central limit theorem for the number of connected components of these random coverings.
New CRM models for sparse networks with linear edge growth.
problem Modeling extremely sparse networks with tractable properties.
method Introduced a new class of CRMs with index of variation α∈(0,1] based on mixtures of stable or generalized gamma processes.
result Models produce networks with near-linear edge growth, aligning with empirical evidence.
Study growth patterns in random networks using i.i.d. perturbations.
problem Understanding the growth of affine regions in random piecewise-linear networks.
method Analyzes a random compositional model with i.i.d. perturbations of the tent map, proving submultiplicative pressure and using finite-state defect process for upper-tail lower bounds.
result Proves the existence of a submultiplicative pressure for \(N_n\) and gives exponential upper bounds for \(n^{-1}\log N_n\).
Random surfaces with long systoles created from graph theory ideas.
problem Finding surfaces with long systoles.
method Two constructions inspired by graph theory.
result Proved a new lower bound on systole length.
The paper studies random covers of torus knot complements and their statistical properties.
problem Understanding the statistical behavior of finite covers of torus knot complements.
method Asymptotic subgroup growth analysis and Benjamini-Schramm limit theorems.
result Determination of the linear growth rate of Betti numbers for random covers of torus knot complements.
Random walks on groups yield infinitely many normal subgroups and exponential growth rates.
problem Understanding normal subgroups and growth rates in random walks on groups.
method Analyzing random walks on groups of isometries of non-proper delta-hyperbolic spaces under WPD condition.
result The probability that the normal closure of random elements is free tends to 1, and the dynamical degree of random Cremona transformations grows exponentially.
The paper explains how speculative supply and demand amplify financial market fluctuations.
problem The wild fluctuations of financial prices.
method Formally, the paper shows that asset returns follow a multiplicative random growth with exogenous input.
result The theory explains the power-law distribution of returns and related variables.
The growth dynamics of German business firmscond-mat.stat-mech
We determine the distribution of size and growthrates of German business firms in 1987-1997. We find a log-normal size distribution. The distribution of growth rates has fat tails. It can be fitted to an exponential in a narrow central region and is dominated by finite-sample-size effects far in its wings. We study the…
Minimal hyperbolic surface diameter grows logarithmically with genus.
problem Finding the smallest possible diameter of hyperbolic surfaces.
method Random construction, lattice point counting, and exploration of random trivalent graphs.
result Minimal diameter is asymptotic to log(g) as genus g approaches infinity.
This paper refines bounds on random walk speed in Teichmüller space.
problem Understanding the speed of random walks on Teichmüller space.
method Analyzing Jenkins-Strebel directions and Lebesgue geodesics.
result The drift of random walks grows exponentially for typical geodesics and oscillates between linear and exponential for some geodesics.
Study optimal healthcare spending under Epstein-Zin preferences for longevity.
problem Optimizing healthcare spending to extend longevity under Epstein-Zin preferences.
method Formulated Epstein-Zin utilities over a controllable random horizon using backward stochastic differential equations and HJB equations.
result Calibrated model accurately reflects actual mortality data and compares healthcare efficacy between countries.
We revisit a recently introduced agent model[ACS {\bf 11}, 99 (2008)], where economic growth is a consequence of education (human capital formation) and innovation, and investigate the influence of the agents' social network, both on an agent's decision to pursue education and on the output of new ideas. Regular and ra…
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.
Deep learning predicts plant growth and yield in greenhouses.
problem Predicting plant growth and yield for better greenhouse management.
method Utilized a new deep recurrent neural network (RNN) with LSTM neurons to model growth parameters.
result Deep learning models outperformed traditional ML methods in predicting plant growth and yield.
A novel model-selection method for dynamic networks using synthetic data.
problem Classifying and understanding the growth mechanisms of dynamic networks.
method Training a classifier on synthetic network data generated by nine random graph models, using dynamic features that count new links.
result Achieves near-perfect classification of synthetic networks, outperforming state-of-the-art methods.
A new growth model for dynamic networks using Markovian latent points.
problem Modeling temporal dynamic networks with latent points and distances.
method Markovian latent space dynamic with Euclidean Sphere sampling and connection probabilities based on geodesic distances.
result Theoretical guarantees for non-parametric estimation of the latitude and envelope functions.
Study shows convergence rate for empirical minimizer of unbounded functions with fast growth.
problem Convergence rate of empirical minimizer for unbounded functions with fast growth.
method Analyzes -distance convergence rate of the empiric minimizer for coercive functions sampled with noise.
result Convergence rate is bounded above by , where is the dimension and for every .
Is the large influence that mutual funds assert on the U.S. financial system spread across many funds, or is it is concentrated in only a few? We argue that the dominant economic factor that determines this is market efficiency, which dictates that fund performance is size independent and fund growth is essentially ran…
We investigate the ergodic problem of growth-rate maximization under a class of risk constraints in the context of incomplete, Itô-process models of financial markets with random ergodic coefficients. Including {\em value-at-risk} (VaR), {\em tail-value-at-risk} (TVaR), and {\em limited expected loss} (LEL), these cons…
Near-Interpolators: Rapid Norm Growth and the Trade-Off between Interpolation and Generalizationstat.ML
Near-interpolating models grow norms quickly, affecting generalization.
problem Understanding the trade-off between interpolation and generalization in near-interpolating models.
method Random matrix theory and eigendecay analysis of data covariance matrix.
result Near-interpolating models exhibit rapid norm growth and worse generalization trade-offs.
Optimal Strategies for Prudent Investorscond-mat.dis-nn
We consider a stochastic model of investment on an asset of a stock market for a prudent investor. She decides to buy permanent goods with a fraction $\a$ of the maximum amount of money owned in her life in order that her economic level never decreases. The optimal strategy is obtained by maximizing the exponential gro…
Typical properties of optimal growth in the Von Neumann expanding model for large random economiesphysics.soc-ph
We calculate the optimal solutions of the fully heterogeneous Von Neumann expansion problem with processes and goods in the limit . This model provides an elementary description of the growth of a production economy in the long run. The system turns from a contracting to an expanding phase as in…
A theoretical approach for Pareto-Zipf lawphysics.soc-ph
We suggest an analytical approach for Pareto-Zipf law, where we assume random multiplicative noise and fragmentation processes for the growth of the number of citizens of each city and the number of the cities, respectively.