Related papers: Dynamic intersectoral models with power-law memory
We model a dynamic data economy with fully endogenous growth where agents generate data from consumption and share them with innovation and production firms. Different from other productive factors such as labor or capital, data are…
In artificial neural networks, the activation dynamics of non-trainable variables is strongly coupled to the learning dynamics of trainable variables. During the activation pass, the boundary neurons (e.g., input neurons) are mapped to the…
We introduce and solve a model which considers two coupled networks growing simultaneously. The dynamics of the networks is governed by the new arrival of network elements (nodes) making preferential attachments to pre-existing nodes in…
Many scientific areas, from computer science to the environmental sciences and finance, give rise to multivariate time series which exhibit long memory, or loosely put, a slow decay in their autocorrelation structure. Efficient modelling…
We numerically study the dynamics of elementary 1D cellular automata (CA), where the binary state $\sigma_i(t) \in \{0,1\}$ of a cell $i$ does not only depend on the states in its local neighborhood at time $t-1$, but also on the memory of…
We analyse large deviations of time-averaged quantities in stochastic processes with long-range memory, where the dynamics at time t depends itself on the value q_t of the time-averaged quantity. First we consider the elephant random walk…
We investigate the win-lose relations between strategies of iterated prisoner's dilemma games by using a directed network concept to display the replicator dynamics results. In the giant strongly-connected component of the win/lose network,…
The utility of learning a dynamics/world model of the environment in reinforcement learning has been shown in a many ways. When using neural networks, however, these models suffer catastrophic forgetting when learned in a lifelong or…
Memory effects in the dynamics of open systems have been the subject of significant interest in the last decades. The methods involved in quantifying this effect, however, are often difficult to compute and may lack analytical insight. With…
Structural results impose sufficient conditions on the model parameters of a Markov decision process (MDP) so that the optimal policy is an increasing function of the underlying state. The classical assumptions for MDP structural results…
The Mike-Farmer (MF) model was constructed empirically based on the continuous double auction mechanism in an order-driven market, which can successfully reproduce the cubic law of returns and the diffusive behavior of stock prices at the…
We present an extended version of the recently proposed "LLOB" model for the dynamics of latent liquidity in financial markets. By allowing for finite cancellation and deposition rates within a continuous reaction-diffusion setup, we…
According to the long-memory principle appears in fractional-order dynamical systems, analysis of these systems is commonly more complicated than those described by nonlinear ordinary differential equations. Another difficulty is due to the…
We study the generalized dynamic factor model in a long-memory setting. Unlike most recent work, which assumes a finite-dimensional factor space and short memory, our framework allows the factor space to be infinite-dimensional and the…
We discuss several models in order to shed light on the origin of power-law distributions and power-law correlations in financial time series. From an empirical point of view, the exponents describing the tails of the price increments…
In this paper, we propose a new framework for the design of incentives aimed at promoting innovation diffusion in social influence networks. In particular, our framework relies on an extension of the Friedkin and Johnsen opinion dynamics…
Inductive biases influence the behavior and performance of sequential models. In this work, we study an underexplored inductive bias in sequential modeling: continuity in time. We ask a simple question: do models motivated by…
We explore the nonlinear dynamics of a macroeconomic model with resource constraints. The dynamics is derived from a production function that considers capital and a generalized form of energy as inputs. Energy, the new variable, is…
Submodular functions are discrete functions that model laws of diminishing returns and enjoy numerous algorithmic applications. They have been used in many areas, including combinatorial optimization, machine learning, and economics. In…
Dynamic input-output models are standard tools for understanding inter-industry dependencies and how economies respond to shocks like disasters and pandemics. However, traditional approaches often assume fixed prices, limiting their ability…