A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Develops geometry for Lotka-Volterra model of species competition.
The study examines stability of Hamiltonian Poisson integrators on both integrable and non-integrable systems.
Study measures inequality in social-economic systems using Fokker-Planck equations and Lotka-Volterra dynamics.
Study uses machine learning to predict predator-prey dynamics without prior knowledge.
The paper improves SBI for BHMs by diagnosing misspecification and inferring parameters.
The paper adapts results for Reeb flows and Hamiltonian flows, showing all orbits are closed have identical periods.
In this paper we try to establish a connection between a three-dimensional Lotka--Volterra dynamical system and two-dimensional topological surgery. There are many physical phenomena exhibiting two-dimensional topological surgery through a `hole drilling' process. By our connection, such phenomena may be modelled mathe…
In this article three models of firms interaction on the market are described. One of these models is described by using a differential equation and by Lotka-Volterra model, where the equation has a different form. Also, there are models of non-competing and competing firms. The article presents an algorithm for solvin…
We analyse four consecutive cycles observed in the USA for employment and inflation. They are driven by three oil price shocks and an intended interest rate shock. Non-linear coupling between the rate equations for consumer products as prey and consumers as predators provides the required instability, but its natural d…
The dynamics of generalized Lotka-Volterra systems is studied by theoretical techniques and computer simulations. These systems describe the time evolution of the wealth distribution of individuals in a society, as well as of the market values of firms in the stock market. The individual wealths or market values are gi…
This paper combines ideas from classical economics and modern finance with the general Lotka-Volterra models of Levy & Solomon to provide straightforward explanations of wealth and income distributions. Using a simple and realistic economic formulation, the distributions of both wealth and income are fully explained. B…
At the heart of technology transitions lie complex processes of social and industrial dynamics. The quantitative study of sustainability transitions requires modelling work, which necessitates a theory of technology substitution. Many, if not most, contemporary modelling approaches for future technology pathways overlo…
Generalized Lotka-Volterra (GLV) models extending the (70 year old) logistic equation to stochastic systems consisting of a multitude of competing auto-catalytic components lead to power distribution laws of the (100 year old) Pareto-Zipf type. In particular, when applied to economic systems, GLV leads to power laws in…
Variational inference has had great success in scaling approximate Bayesian inference to big data by exploiting mini-batch training. To date, however, this strategy has been most applicable to models of independent data. We propose an extension to state space models of time series data based on a novel generative model…
We aim to identify the generating, ordinary differential equation (ODE) from a set of trajectories of a partially observed system. Our approach does not need prescribed basis functions to learn the ODE model, but only a rich set of Neural Arithmetic Units. For maximal explainability of the learnt model, we minimise the…
VISA improves inference efficiency for complex models.
Examines WENDy-IRLS algorithm's noise robustness and efficiency in various differential equations.
Parameter inference for stochastic differential equations is challenging due to the presence of a latent diffusion process. Working with an Euler-Maruyama discretisation for the diffusion, we use variational inference to jointly learn the parameters and the diffusion paths. We use a standard mean-field variational appr…
This paper presents a general theory that aims at explaining timescales observed empirically in technology transitions and predicting those of future transitions. This framework is used further to derive a theory for exploring the dynamics that underlie the complex phenomenon of irreversible and path dependent price or…
This paper highlights the size-dependency of income distributions, i.e. the income distribution curves versus the population of a country systematically. By using the generalized Lotka-Volterra model to fit the empirical income data in the United States during 1996-2007, we found an important parameter can scale wi…
Two simulation-based methods improve optimal sampling design in systems biology.
Many studies in Economics and other disciplines have been reporting distributions following power-law behavior (i.e distributions of incomes (Pareto's law), city sizes (Zipf's law), frequencies of words in long sequences of text etc.)[1, 6, 7]. This widespread observed regularity has been explained in many ways: genera…
Bayesian symbolic regression uncovers missing physics from data with uncertainty quantification.
A new machine learning method calculates failure probability efficiently and accurately.
This paper learns state, dynamics, and filtering algorithms together for data assimilation.
New insights into optimal portfolios and ecological equilibria reveal surprising complexity.
BLADE uses Bayesian methods to discover complex systems from scarce data.
The moments of spatial probabilistic systems are often given by an infinite hierarchy of coupled differential equations. Moment closure methods are used to approximate a subset of low order moments by terminating the hierarchy at some order and replacing higher order terms with functions of lower order ones. For a give…
Using the Generalised Lotka Volterra (GLV) model adapted to deal with muti agent systems we can investigate economic systems from a general viewpoint and obtain generic features common to most economies. Assuming only weak generic assumptions on capital dynamics, we are able to obtain very specific predictions for the …
Paper corrects and expands stochastic Lie systems theory.
Polynomial chaos expansions on Grassmannian submanifolds for high-dimensional stochastic systems.
New method stabilizes model selection with theoretical guarantees.
Using a model based on generalised Lotka Volterra dynamics together with some recent results for the solution of generalised Langevin equations, we show that the equilibrium solution for the probability distribution of wealth has two characteristic regimes. For large values of wealth it takes the form of a Pareto style…
CODE learns ODE dynamics from sparse data, outperforming neural and kernel methods.
PASTIS method selects simple models from noisy data.
SIP framework discovers governing equations in uncertain systems.
Unified framework detects change-points and estimates parameters in nonlinear systems with regime switching.
We give a microscopic representation of the stock-market in which the microscopic agents are the individual traders and their capital. Their basic dynamics consists in the auto-catalysis of the individual capital and in the global competition/cooperation between the agents mediated by the total wealth invested in the s…
This work presents an empirical study of the evolution of the personal income distribution in Brazil. Yearly samples available from 1978 to 2005 were studied and evidence was found that the complementary cumulative distribution of personal income for 99% of the economically less favorable population is well represented…