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We examine the effects of memory and different updating paradigms in a game-theoretic model of competitive learning, where agents are influenced in their choice of strategy by both the choices made by, and the consequent success rates of,…
We consider the modification of the Cahn-Hilliard equation when a time delay process through a memory function is taken into account. We then study the process of spinodal decomposition in fast phase transitions associated with a conserved…
The limit order book (LOB) depicts the fine-grained demand and supply relationship for financial assets and is widely used in market microstructure studies. Nevertheless, the availability and high cost of LOB data restrict its wider…
Fractional-order dynamical systems are used to describe processes that exhibit long-term memory with power-law dependence. Notable examples include complex neurophysiological signals such as electroencephalogram (EEG) and blood-oxygen-level…
While the long-ranged correlation of market orders and their impact on prices has been relatively well studied in the literature, the corresponding studies of limit orders and cancellations are scarce. We provide here an empirical study of…
In this article, we delve into the applications and extensions of the queue-reactive model for the simulation of limit order books. Our approach emphasizes the importance of order sizes, in conjunction with their type and arrival rate, by…
We consider a dynamic pricing problem where customer response to the current price is impacted by the customer price expectation, aka reference price. We study a simple and novel reference price mechanism where reference price is the…
Keeping a memory of evolving stimuli is ubiquitous in biology, an example of which is immune memory for evolving pathogens. However, learning and memory storage for dynamic patterns still pose challenges in machine learning. Here, we…
Recent empirical studies have demonstrated long-memory in the signs of orders to buy or sell in financial markets [2, 19]. We show how this can be caused by delays in market clearing. Under the common practice of order splitting, large…
Stemming on the idea that a key objective in reinforcement learning is to invert a target distribution of effects, end-effect drives are proposed as an effective way to implement goal-directed motor learning, in the absence of an explicit…
We develop a physics-informed neural network (PINN) framework for parameter estimation in fractional-order SEIRD epidemic models. By embedding the Caputo fractional derivative into the network residuals via the L1 discretization scheme, our…
In this paper, we consider an infinite horizon, continuous-review, stochastic inventory system in which cumulative customers' demand is price-dependent and is modeled as a Brownian motion. Excess demand is backlogged. The revenue is earned…
We report an innovative model for predicting entanglement distribution between end parties of a quantum network using our in-house simulation algorithm. Our implementation is based on stochastic methods that are built upon a unique global…
We present a simple dynamic equilibrium model for an online exchange where both buyers and sellers arrive according to a exogenously defined stochastic process. The structure of this exchange is motivated by the limit order book mechanism…
We consider the evolution of correlation functions in a non-Markov version of the contact model in the continuum. The memory effects are introduced by assuming the fractional evolution equation for the statistical dynamics. This leads to a…
Episodic control enables sample efficiency in reinforcement learning by recalling past experiences from an episodic memory. We propose a new model-based episodic memory of trajectories addressing current limitations of episodic control. Our…
The paper presents two representative classes of Impulsive Fractional Differential Equations defined with generalized Caputo\'s derivative, with fixed lower limit and changing lower limit, respectively. Memory principle is studied and…
Discrete dynamics arise naturally in systems with broken temporal translation symmetry and are typically described by first-order recurrence relations representing classical or quantum Markov chains. When memory effects induced by hidden…
Inspired by the cognitive science theory of the explicit human memory systems, we have modeled an agent with short-term, episodic, and semantic memory systems, each of which is modeled with a knowledge graph. To evaluate this system and…
In this study, we show that the discharge voltage pattern of a fractional-order supercapacitor from the same initial steady-state voltage into a constant resistor is dependent on the past charging voltage profile. The charging voltage was…