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Stability is a fundamental concept that refers to a system's ability to return close to its original state after disturbances. The minimal conditions for stability when system parameters vary in time, though common in physics, have been…
Multi-model ensembles provide a pragmatic approach to the representation of model uncertainty in climate prediction. However, such representations are inherently ad hoc, and, as shown, probability distributions of climate variables based on…
In this technical note, we study the mean square stability-based analysis of stochastic continuous-time linear networked systems. The stochastic uncertainty is assumed to enter multiplicatively in system dynamics through input and output…
This paper introduces a method for predicting the likely behaviors of continuous nonlinear systems in equilibrium in which the input values can vary. The method uses a parameterized equation model and a lower bound on the input joint…
A causal input-output system may be described by a function space for inputs, a function space for outputs, and a causal operator mapping the input space into the output space. A particular representation of the state of such a system at…
Linear dynamical systems are canonical models for learning-based control of plants with uncertain dynamics. The setting consists of a stochastic differential equation that captures the state evolution of the plant understudy, while the true…
The relative stability of three-dimensional icosahedral quasicrystals in multi-component systems has been investigated based on a coupled-mode Swift-Hohenberg model with two-length-scales. A recently developed projection method, which…
Hamiltonian systems with long-range interactions give rise to long lived out of equilibrium macroscopic states, so-called quasi-stationary states. We show here that, in a suitably generalized form, this result remains valid for many such…
Nearly all nontrivial real-world systems are nonlinear dynamical systems. Chaos describes certain nonlinear dynamical systems that have a very sensitive dependence on initial conditions. Chaotic systems are always deterministic and may be…
We introduce a stability criterion for quantum statistical ensembles describing macroscopic systems. An ensemble is called "stable" when a small number of local measurements cannot significantly modify the probability distribution of the…
The analysis of the time evolution of unstable states which are linear superposition of other, observable, states can, in principle, be carried out in two distinct, non-equivalent ways. One of the methods, usually employed for the neutral…
Stoichiometric constraints play a role in the dynamics of natural populations, but are not explicitly considered in most mathematical models. Recent theoretical works suggest that these constraints can have a significant impact and should…
In statistical mechanics, measuring the number of available states and their probabilities, and thus the system's entropy, enables the prediction of the macroscopic properties of a physical system at equilibrium. This predictive capacity…
A probabilistic framework is proposed for the optimization of efficient switched control strategies for physical systems dominated by stochastic excitation. In this framework, the equation for the state trajectory is replaced with an…
Species or population that proliferate faster than others become dominant in numbers. Catalysis allows catalytic sets within a molecular reaction network to dominate the non catalytic parts of the network by processing most of the available…
This paper provides a semiparametric model of estimating states of the volatility defined as the squared diffusion coefficient of a stochastic differential equation. Without assuming any functional form of the volatility function, we…
The quasistatic approximation is a useful but questionable simplification for analyzing step instabilities during the growth/evaporation of vicinal surfaces. Using this approximation, we characterized in Part I of this work the effect on…
The work analyzes the stability of the quantum eigenstates when they are submitted to fluctuations by using the stochastic generalization of the Madelung quantum hydrodynamic approach. In the limit of sufficiently slow kinetics, the quantum…
Truly stable metastable states are an artifact of the mean-field approximation or the zero temperature limit. If such appealing concepts in glass theory as configurational entropy are to have a meaning beyond these approximations, one needs…
In this work we analyze and bound the effect of modeling errors on the stabilization of pure states or subspaces for quantum stochastic evolutions. Different approaches are used for open-loop and feedback control protocols. For both, we…