arXiv research

New theory accelerates stochastic optimization by leveraging local growth rate.

Enhanced Gordon growth model for valuing financial products.

In an evolutionary system in which the rules of mutation are local in nature, the number of possible outcomes after $m$ mutations is an exponential function of $m$ but with a rate that depends only on the set of rules and not the size of the original object. We apply this principle to find a uniform upper bound for the…

New algorithms optimize private convex optimization with faster rates for functions with κ-growth.

Abstract Coxeter groups have growth rates that are Perron numbers.

The aim here is to address the origins of sustainability for the real growth rate in the United States. For over a century of observations on the real GDP per capita of the United States a sustainable two percent growth rate has been observed. To find an explanation for this observation I consider the impact of utility…

Exponential growth of stable subgroups in Morse geodesics.

The paper simplifies string topology computations using Hochschild chain models.

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…

Growth rates of geodesics on modular orbifolds are studied.

Study growth rates of subgroups in groups with a constricting element.

New proof shows not all Salem numbers are growth rates of Coxeter groups.

This paper analyzes the robust growth rate of leveraged ETFs under uncertain parameters.

Study projection in acylindrically hyperbolic groups, proving sublinear tracking and growth bounds.

World GDP growth is predicted to become unsustainable.

Study confined subgroups in groups with contracting elements, showing their growth rate is strictly greater than half of the ambient growth rate.

The US GDP per capita growth alternates between high and low rates, with an average growth rate of 1.6% since 1800.

Study growth rates of specific hyperbolic Coxeter groups with fixed dihedral angles.

The paper explores growth rates and Perron numbers in Coxeter systems with low-dimensional Davis complexes.

3D hyperbolic Coxeter groups' growth rates are Perron numbers.

Study bounds growth rate of irreducible meanders, showing proportion vanishes.

Mathematical study of excess growth rate connects info theory with finance.

Improved adaptive rates for Lipschitz bandit problem.

New infinite series of hyperbolic polytopes with special growth rates found.

New growth rate identified for quaternionic Heisenberg group filling functions.

This paper investigates the statistical properties of within-country GDP and industrial production (IP) growth rate distributions. Many empirical contributions have recently pointed out that cross-section growth rates of firms, industries and countries all follow Laplace distributions. In this work, we test whether als…

Bubbles are essential in certain economic models with high growth and low interest rates.

Study on Monge-Ampère equations with polynomial growth rates.

Early warning signs of Greece's economic crisis were present in GDP growth rate instability.

Investigates the relationship between US money supply and asset indices over 2001-2019.

We introduce a solvable model of randomly growing systems consisting of many independent subunits. Scaling relations and growth rate distributions in the limit of infinite subunits are analysed theoretically. Various types of scaling properties and distributions reported for growth rates of complex systems in a variety…

This paper calculates the stock price covariance with correlated growth rates.

Optimizes portfolio growth rate for a behavioral investor considering terminal relative growth rate.

Galor's mysterious income growth rate is debunked, revealing data manipulation.

We give a survey of the approaches to classifying foliations, starting with the Haefliger classifying spaces and the various results and examples about the secondary classes of foliations. Various dynamical properties of foliations are introduced and discussed, including expansion rate, local entropy, and orbit growth …

Study finds minimum growth rate for surface solutions.

In [6], Kellerhals and Perren conjectured that the growth rates of the reflection groups given by hyperbolic Coxeter polyhedra are always Perron numbers. We prove that this conjecture is always true for the case of ideal Coxeter polyhedra in $\mathbb{H}^3$. We also find out the ideal Coxeter polyhedron in $\mathbb{H}^3…

The study examines how automorphism growth rates of a group can be deduced from its simpler decompositions.

Study growth rates of harmonic functions on curved surfaces.

In a previous paper Kobayashi and Rieck defined the growth rate of the tunnel number of a knot $K$, a knot invariant that measures the asymptotic behavior of the tunnel number under iterated connected sum of $K$. We denote the growth rate by $\mbox{gr}_t(K)$. In this paper we construct, for any $ε> 0$, a hyperbolic kno…

In a previous paper the authors defined the growth rate of the tunnel number of knots, an invariant that measures that asymptotic behavior of the tunnel number under connected sum. In this paper we calculate the growth rate of the tunnel number of m-small knots in terms of their bridge indices.

Zipf's law states that the number of firms with size greater than S is inversely proportional to S. Most explanations start with Gibrat's rule of proportional growth but require additional constraints. We show that Gibrat's rule, at all firm levels, yields Zipf's law under a balance condition between the effective grow…

We provide a lower bound for the uniform exponential growth rate of closed nonflat nonpositively curved 3-manifold groups. A detailed study of the uniform exponential growth rate of closed 3-manifold groups is also presented.

Study local control of a specific mechanism with growth vector (4,7).

Analyzes long-term growth rate of leveraged ETFs using martingale extraction.

The paper discusses the role of monetary policy when potential output depends on the inflation rate. If the intention of the central bank is to maximize actual output growth, then it has to be credibly committed to a strict inflation targeting rule, and to take the MOGIR (the Maximizing Output Growth Inflation Rate) as…

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…

Model shows consumption growth slows due to finite planet resources.