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Chaos arises in many complex dynamical systems, from weather to power grids, but is difficult to accurately model using data-driven emulators, including neural operator architectures. For chaotic systems, the inherent sensitivity to initial…
A principal curve serves as a powerful tool for uncovering underlying structures of data through 1-dimensional smooth and continuous representations. On the basis of optimal transport theories, this paper introduces a novel principal curve…
This paper is motivated by the fact that many systems need to be maintained continually while the underlying costs change over time. The challenge is to continually maintain near-optimal solutions to the underlying optimization problems,…
We study approximation in the unit interval by rational numbers whose numerators are selected randomly with certain probabilities. Previous work showed that an analogue of Khintchine's Theorem holds in a similar random model and raised the…
Our main contribution in this article is the achievement of the turnpike property in its integral and exponential forms for parameter-dependent systems with averaged observations in the cost functional. Namely, under suitable assumptions…
In this paper we investigate a dynamic pricing model for constant demand elasticity where customers have a probability distribution on the number of items they order. This is a generalization from standard models which restrict customers to…
Mathematical models of the real world are simplified representations of complex systems. A caveat to using mathematical models is that predicted causal effects and conditional independences may not be robust under model extensions, limiting…
The problem of nonparametric inference on a monotone function has been extensively studied in many particular cases. Estimators considered have often been of so-called Grenander type, being representable as the left derivative of the…
We consider a continuous-review inventory system in which the setup cost of each order is a general function of the order quantity and the demand process is modeled as a Brownian motion with a positive drift. Assuming the holding and…
We compare, for the static potential and at short distances, perturbation theory with the results of lattice simulations. We show that a renormalon-dominance picture explains why in the literature sometimes agreement, and another…
We examine synchronization of identical chaotic systems coupled in a drive/response manner. A rigorous criterion is presented which, if satisfied, guarantees that synchronization to the driving trajectory is linearly stable to…
In Part II of this paper, we concentrate our analysis on the price dynamical model with the moving average rules developed in Part I of this paper. By decomposing the excessive demand function, we reveal that it is the interplay between…
Whether there is similarity between two physical processes in the movement of objects and the complexity of behavior is an essential problem in science. How to seek similarity through the adoption of quantitative and qualitative research…
In an $L_\infty$-framework, we present a few extension theorems for linear operators. We focus the attention on majorant preserving and sandwich preserving types of extensions. These results are then applied to the study of price systems…
Collocated adaptive control of underactuated systems is still a main concern for the control community, all the more so because the collocated dynamics is no longer linear with respect to the constant base parameters. This work extends and…
Probabilistic automata constitute a versatile and elegant model for concurrent probabilistic systems. They are equipped with a compositional theory supporting abstraction, enabled by weak probabilistic bisimulation serving as the reference…
The average cost optimality is known to be a challenging problem for partially observable stochastic control, with few results available beyond the finite state, action, and measurement setup, for which somewhat restrictive conditions are…
We present stability conditions for deterministic time-varying nonlinear discrete-time systems whose inputs aim to minimize an infinite-horizon time-dependent cost. Global asymptotic and exponential stability properties for general…
In this paper, we present a robust adaptive model predictive control (MPC) scheme for linear systems subject to parametric uncertainty and additive disturbances. The proposed approach provides a computationally efficient formulation with…
Continuous-time Markov chains are frequently used as stochastic models for chemical reaction networks, especially in the growing field of systems biology. A fundamental problem for these Stochastic Chemical Reaction Networks (SCRNs) is to…