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Compact locally maximal hyperbolic sets are studied via geometrically defined functional spaces that take advantage of the smoothness of the map in a neighborhood of the hyperbolic set. This provides a self-contained theory that not only…
We suggest a spatially local feedback mechanism for stabilizing periodic orbits in spatially extended systems. Our method, which is based on a comparison between present and past states of the system, does not require the external…
We give a pedagogical introduction to the generalized uncertainty principle (GUP), by showing how it naturally emerges when the action of gravity is taken into account in measurement processes. We review some physical predictions of the…
Mechanistic dynamic models of biochemical networks such as Ordinary Differential Equations (ODEs) contain unknown parameters like the reaction rate constants and the initial concentrations of the compounds. The large number of parameters as…
The eccentricity of a planet's orbit and the inclination of its orbital plane encode important information about its formation and history. However, exoplanets detected via direct-imaging are often only observed over a very small fraction…
Orbital debris is a pressing problem which presents a danger to global space operations and a barrier to continued development of the space economy and space infrastructure. As research continues regarding orbital debris, there is a need…
Using a suite of self-gravitating, collisionless N-body models, we systematically explore a parameter space relevant to the onset and behavior of the radial orbit instability (ROI), whose strength is measured by the systemic axis ratios of…
In dynamical systems of few degrees of freedom, periodic solutions consist the backbone of the phase space and the determination and computation of their stability is crucial for understanding the global dynamics. In this paper we study the…
Location estimation is a fundamental sensing task in robotic applications, where the world is uncertain, and sensors and effectors are noisy. Most systems make various assumptions about the dependencies between state variables, and…
Observability of state variables and parameters of a dynamical system from an observed time series is analyzed and quantified by means of the Jacobian matrix of the delay coordinates map. For each state variable and each parameter to be…
Environmental sensors provide crucial data for understanding our surroundings. For example, air quality maps based on sensor readings help users make decisions to mitigate the effects of pollution on their health. Standard maps show…
In this paper, we investigate a discrete inverse problem of determining three unknowns, i.e. initial displacement, initial velocity and random source term, in a fully discrete approximation of one-dimensional stochastic hyperbolic equation.…
We discuss some issues arising in the evaluation of confidence intervals in the presence of nuisance parameters (systematic uncertainties) by means of direct Neyman construction in multi-dimensional space. While this kind of procedure…
We consider constrained partial differential equations of hyperbolic type with a small parameter $\varepsilon>0$, which turn parabolic in the limit case, i.e., for $\varepsilon=0$. The well-posedness of the resulting systems is discussed…
We present an online and data-driven uncertainty quantification method to enable the development of safe human-robot collaboration applications. Safety and risk assessment of systems are strongly correlated with the accuracy of…
Robotic systems often use predictive uncertainty to decide whether to act autonomously or defer to a fallback policy. In threshold-gated autonomy, uncertainty matters mainly through its ability to rank likely errors. Standard metrics such…
We prove for the $N$-body problem the existence of hyperbolic motions for any prescribed limit shape and any given initial configuration of the bodies. The energy level $h>0$ of the motion can also be chosen arbitrarily. Our approach is…
In orthodox quantum theory, decoherence is presumed to be caused by observation. In this paper, the idea of replacing observation, as the cause of decoherence, with rules derived from the dynamics of the system is addressed. Such rules…
The orbital symmetry of the superconducting order parameter in UPt_3 is identified by evaluating the directionally dependent thermalconductivity and ultrasound attenuation in the clean limit and compared with the existing data for both…
For $n\geq 3$ and $\Gamma$ a cocompact lattice acting on the hyperbolic space $\mathbb{H}^n$, we investigate the average behaviour of the error term in the circle problem. First, we explore the local average of the error term over compact…