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Symmetry-breaking instabilities play an important role in understanding the mechanisms underlying the diversity of patterns observed in nature, such as in Turing's reaction--diffusion theory, which connects cellular signalling and transport…
Under non-exponential discounting, we develop a dynamic theory for stopping problems in continuous time. Our framework covers discount functions that induce decreasing impatience. Due to the inherent time inconsistency, we look for…
In many real world chaotic systems, the interest is typically in determining when the system will behave in an extreme manner. Flooding and drought, extreme heatwaves, large earthquakes, and large drops in the stock market are examples of…
This paper provides new summation inequalities in both single and double forms to be used in stability analysis of discrete-time systems with time-varying delays. The potential capability of the newly derived inequalities is demonstrated by…
This article proposes a non-autonomous mathematical model with delay for confrontation between two countries, and examines the stability of its equilibrium state. Our criteria for stability take into account the influence of the factor of…
Human travelling behaviours are markedly regular, to a large extent, predictable, and mostly driven by biological necessities (\eg sleeping, eating) and social constructs (\eg school schedules, synchronisation of labour). Not surprisingly,…
Atmospheric modeling has recently experienced a surge with the advent of deep learning. Most of these models, however, predict concentrations of pollutants following a data-driven approach in which the physical laws that govern their…
The use of available disturbance predictions within a nominal model predictive control formulation is studied. The main challenge that arises is the loss of recursive feasibility and stability guarantees when a persistent disturbance is…
In this paper, we consider a dynamic equilibrium transportation problem. There is a fixed number of cars moving from origin to destination areas. Preferences for arrival times are expressed as a cost of arriving before or after the…
A method to quantify robust performance for situations where structured parameter variations and initial state errors rather than extraneous disturbances are the main performance limiting factors is presented. The approach is based on the…
Time-dependent driving holds the promise of realizing dynamical phenomenon absent in static systems. Here, we introduce a correlated random driving protocol to realize a spatiotemporal order that cannot be achieved even by periodic driving,…
Recent research reveals that machine learning (ML) models are highly sensitive to minor changes in their training procedure, such as the inclusion or exclusion of a single data point, leading to conflicting predictions on individual data…
In this work we revisit the existence, stability and dynamics of unstable traveling solitary waves in the context of lattice dynamical systems. We consider a nonlinear lattice of an $\alpha$-Fermi-Pasta-Ulam type with the additional feature…
This paper presents a novel approach to distinguish the impact of duration-dependent forces and adverse selection on the exit rate from unemployment by leveraging variation in the length of layoff notices. I formulate a Mixed Hazard model…
We consider the influence of disorder on the non-equilibrium steady state of a minimal model for intracellular transport. In this model particles move unidirectionally according to the \emph{totally asymmetric exclusion process} (TASEP) and…
A discrete delay is included to model the time between the capture of the prey and its conversion to viable biomass in the simplest classical Gause type predator-prey model that has equilibrium dynamics without delay. As the delay increases…
Early-exiting neural networks enable adaptive inference by allowing inputs to exit at intermediate classifiers, reducing computation for easy samples while maintaining high accuracy. In practice, exits can be trained sequentially by…
Instantaneous dynamic equilibrium (IDE) is a standard game-theoretic concept in dynamic traffic assignment in which individual flow particles myopically select en route currently shortest paths towards their destination. We analyze IDE…
Using theory and experiments, this paper shows that the difficulty of making tradeoffs offers a parsimonious explanation for a wide range of behavioral phenomena. We develop a model of imprecise comparisons applicable to multiattribute,…
Multistability is a phenomenon prevalent in many natural systems. In climate, for example, it allows the possibility of irreversible consequences on planetary scale as a result of climate change. Indeed, a climate ``tipping element'' is a…