arXiv research

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

Method reconstructs aneurysm growth history from patient parameters using physics-informed autoencoder.

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 …

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…

We study the volume growth of hyperkaehler manifolds of type $A_{\infty}$ constructed by Anderson-Kronheimer-LeBrun and Goto. These are noncompact complete 4-dimensional hyperkaehler manifolds of infinite topological type. These manifolds have the same topology but the hyperkaehler metrics are depends on the choice of …

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…

We introduce the logistic model of consumption growth, which captures a negative feedback loop preventing an unlimited growth of consumption due to finite biophysical resources of our planet. This simple dynamic model allows for derivation of the expression describing the declining long-term tail of a social discount c…

Neural networks cannot approximate certain functions in Sobolev spaces, leading to unbounded parameter growth.

The paper introduces a method for forecasting corporate sales growth using multiple reference variables.

Consider the one-parameter generalizations of the logarithmic and exponential functions which are obtained from the integration of non-symmetrical hyperboles. These generalizations coincide to the one obtained in the context of non-extensive thermostatistics. We show that these functions are suitable to describe and un…

We study the growth dynamics of the size of manufacturing firms considering competition and normal distribution of competency. We start with the fact that all components of the system struggle with each other for growth as happened in real competitive bussiness world. The detailed quantitative agreement of the theory w…

This paper considers the growth in the length of one-dimensional trajectories as they are passed through deep ReLU neural networks, which, among other things, is one measure of the expressivity of deep networks. We generalise existing results, providing an alternative, simpler method for lower bounding expected traject…

Atlas-type models are constant-parameter models of uncorrelated stocks for equity markets with a stable capital distribution, in which the growth rates and variances depend on rank. The simplest such model assigns the same, constant variance to all stocks; zero rate of growth to all stocks but the smallest; and positiv…

Study on colored Jones polynomial of figure-eight knot for complex parameters.

Understanding the dynamics of brain tumor progression is essential for optimal treatment planning. Cast in a mathematical formulation, it is typically viewed as evaluation of a system of partial differential equations, wherein the physiological processes that govern the growth of the tumor are considered. To personaliz…

This paper explains how low-precision arithmetic causes loss spikes in deep learning models.

The paper gauges AGI's impact on GDP growth using mathematical metrics.

Effective plant growth and yield prediction is an essential task for greenhouse growers and for agriculture in general. Developing models which can effectively model growth and yield can help growers improve the environmental control for better production, match supply and market demand and lower costs. Recent developm…

Investment strategy using fractional Kelly portfolios for better growth expectations.

In the preceding paper we presented empirical results describing the growth of publicly-traded United States manufacturing firms within the years 1974--1993. Our results suggest that the data can be described by a scaling approach. Here, we propose models that may lead to some insight into these phenomena. First, we st…

Proposes efficient model for continual learning that grows model over task-specific parameters.

We provide an analytically treatable model that describes in a unified manner income distribution for all income categories. The approach is based on a master equation with growth and reset terms. The model assumptions on the growth and reset rates are tested on an exhaustive database with incomes on individual level s…

We calculate the optimal solutions of the fully heterogeneous Von Neumann expansion problem with $N$ processes and $P$ goods in the limit $N\to\infty$. 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 $N$ in…

For a stochastic factor model we maximize the long-term growth rate of robust expected power utility with parameter $λ\in(0,1)$. Using duality methods the problem is reformulated as an infinite time horizon, risk-sensitive control problem. Our results characterize the optimal growth rate, an optimal long-term trading s…

Paper characterizes DLN distribution, its properties, and estimation methods.

Evolution of planar curves under a nonlocal geometric equation is investigated. It models the simultaneous contraction and growth of carbonate particles called ooids in geosciences. Using classical ODE results and a bijective mapping we demonstrate that the steady parameters associated with the physical environment det…

SSRCA simplifies ABM sensitivity analysis using machine learning.

Paper tackles robust control of SDEs with ambiguity, proving value function existence and applying to investment problems.

New approach finds solutions to games with unbounded controls.

Weibull weight-scale parameter $λ$ evolves during AdamW training, with alignment, injection, and decay forces driving its growth and relaxation.

Firm foundation theory estimates a security's firm fundamental value based on four determinants: expected growth rate, expected dividend payout, the market interest rate and the degree of risk. In contrast, other views of decision-making in the stock market, using alternatives such as human psychology and behavior, bou…

Recent research in economic theory attempts to study optimal economic growth and spatial location of economic activity in a unified framework. So far, the key result of this literature - asymptotic convergence, even in the absence of decreasing returns to capital - relies on specific assumptions about the objective of …

An array system of coupled maps is proposed as a model for economy evolution. The local dynamics of each map or agent is controlled by two parameters. One of them represents the growth capacity of the agent and the other one is a control term representing the local environmental pressure which avoids an exponential gro…

Method improves microbial biomass yield estimation from noisy data.

We consider the problem of finding optimal strategies that maximize the average growth-rate of multiplicative stochastic processes. For a geometric Brownian motion the problem is solved through the so-called Kelly criterion, according to which the optimal growth rate is achieved by investing a constant given fraction o…

We prove existence and uniqueness for a two-parameter family of translators for mean curvature flow. We get additional examples by taking limits at the boundary of the parameter space. Some of the translators resemble well-known minimal surfaces (Scherk's doubly periodic minimal surfaces, helicoids), but others have no…

Economic growth is unpredictable unless demand is quantified. We solve this problem by introducing the demand for unpaid spare time and a user quantity named human capacity. It organizes and amplifies spare time required for enjoying affluence like physical capital, the technical infrastructure for production, organize…

Paper reduces sample complexity for bilinear systems identification to nearly constant.

This paper studies the long-term growth rate of expected utility from holding a leveraged exchanged-traded fund (LETF), which is a constant proportion portfolio of the reference asset. Working with the power utility function, we develop an analytical approach that employs martingale extraction and involves finding the …

Model shows how capital accumulation can lead to poverty traps and well-being states.

Given for instance a finite volume negatively curved Riemannian manifold $M$, we give a precise relation between the logarithmic growth rates of the excursions into cusps neighborhoods of the strong unstable leaves of negatively recurrent unit vectors of $M$ and their linear divergence rates under the geodesic flow. As…

We consider the classic Kelly gambling problem with general distribution of outcomes, and an additional risk constraint that limits the probability of a drawdown of wealth to a given undesirable level. We develop a bound on the drawdown probability; using this bound instead of the original risk constraint yields a conv…

A deterministic system of coupled maps is proposed as a model for economic activity among interacting agents. The values of the maps represent the wealth of the agents. The dynamics of the system is controlled by two parameters. One parameter expresses the growth capacity of the agents and the other describes the local…

TLRF improves timely COVID-19 outbreak detection with small sample size counties.

In this paper, we propose an active learning method for an inverse problem that aims to find an input that achieves a desired structured-output. The proposed method provides new acquisition functions for minimizing the error between the desired structured-output and the prediction of a Gaussian process model, by effect…

A novel model-selection method for dynamic networks using synthetic data.

The relationship between the size and the variance of firm growth rates is known to follow an approximate power-law behavior $σ(S) \sim S^{-β(S)}$ where $S$ is the firm size and $β(S)\approx 0.2$ is an exponent weakly dependent on $S$. Here we show how a model of proportional growth which treats firms as classes compos…

New method improves regression estimates, reducing bias.