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Several concepts on the measure of observability, reachability, and robustness are defined and illustrated for both linear and nonlinear control systems. Defined by using computational dynamic optimization, these concepts are applicable to…
The ideas behind the concept of algebraic ("integration-by-parts") algorithms for multiloop calculations are reviewed. For any topology and mass pattern, a finite iterative algebraic procedure is proved to exist which transforms the…
With the rise of computers, simulation models have emerged beside the more traditional statistical and mathematical models as a third pillar for ecological analysis. Broadly speaking, a simulation model is an algorithm, typically…
To develop robust manipulation policies, quantifying robustness is essential. Evaluating robustness in general manipulation, nonetheless, poses significant challenges due to complex hybrid dynamics, combinatorial explosion of possible…
Traditionally, numerical algorithms are seen as isolated pieces of code confined to an {\em in silico} existence. However, this perspective is not appropriate for many modern computational approaches in control, learning, or optimization,…
Computer experiments with both quantitative and qualitative (QQ) inputs are commonly used in science and engineering applications. Constructing desirable emulators for such computer experiments remains a challenging problem. In this…
Image processing has always been a topic of significant importance to society. Recently, this field has gained considerable prominence due to the development of intelligent systems. In this work, we present a new method of image processing…
The study of controlled hybrid systems requires practical tools for approximation and comparison of system behaviors. Existing approaches to these problems impose undue restrictions on the system's continuous and discrete dynamics.…
The simulation of large nonlinear dynamical systems, including systems generated by discretization of hyperbolic partial differential equations, can be computationally demanding. Such systems are important in both fluid and kinetic…
Hamiltonian systems of ordinary and partial differential equations are fundamental mathematical models spanning virtually all physical scales. A critical property for the robustness and stability of computational methods in such systems is…
The study of biological systems witnessed a pervasive cross-fertilization between experimental investigation and computational methods. This gave rise to the development of new methodologies, able to tackle the complexity of biological…
Optimization problems in engineering and applied mathematics are typically solved in an iterative fashion, by systematically adjusting the variables of interest until an adequate solution is found. The iterative algorithms that govern these…
A new approach is developed to integrate numerically the equations of motion for systems of interacting rigid polyatomic molecules. With the aid of a leapfrog framework, we directly involve principal angular velocities into the integration,…
It is known that statistical model selection as well as identification of dynamical equations from available data are both very challenging tasks. Physical systems behave according to their underlying dynamical equations which, in turn, can…
We propose an algorithm to actively estimate the parameters of a linear dynamical system. Given complete control over the system's input, our algorithm adaptively chooses the inputs to accelerate estimation. We show a finite time bound…
The exact computation of orbits of discrete dynamical systems on the interval is considered. Therefore, a multiple-precision floating point approach based on error analysis is chosen and a general algorithm is presented. The correctness of…
We present a new efficient algortithm for construction of linear latent structure (LLS) models. This algorithm reduces a problem of estimation of model parameters to a sequence of problems of linear algebra, which assures a low…
Rigid bodies, plastic impact, persistent contact, Coulomb friction, and massless limbs are ubiquitous simplifications introduced to reduce the complexity of mechanics models despite the obvious physical inaccuracies that each incurs…
By any account, the 1998 proof of the Kepler conjecture is complex. The thesis underlying this article is that the proof is complex because it is highly under-automated. Throughout that proof, manual procedures are used where automated ones…
We harness the power of Bayesian emulation techniques, designed to aid the analysis of complex computer models, to examine the structure of complex Bayesian analyses themselves. These techniques facilitate robust Bayesian analyses and/or…