We investigate the computational power of several models of dynamical systems under infinitesimal perturbations of their dynamics. We consider in our study models for discrete and continuous time dynamical systems: Turing machines, Piecewise affine maps, Linear hybrid automata and Piecewise constant derivative systems (a simple model of hybrid systems). We associate with each of these models a ...

The classical condition number is a very rough measure of the effect of perturbations on the inverse of a square matrix. First, it assumes that the perturbation is infinitesimally small. Second, it does not take into account the perturbation structure (e.g., Vandermonde). Similarly, the classical notion of the inverse of a matrix neglects the possibility of large, structured perturbations. We d...

We characterize the first-order sensitivity of approximately recovering a low-rank matrix from linear measurements, standard problem in compressed sensing. A special case covered by our analysis is approximating an incomplete matrix. This one customary approach to build recommender systems. give algorithm for computing associated condition number and demonstrate experimentally how measurements ...

This paper applies Infinitesimal Perturbation Analysis (IPA) to loss-related and workloadrelated metrics in a class of Stochastic Flow Models (SFM). It derives closed-form formulas for gradient estimators of these metrics with respect to various parameters of interest, such as buffer size, service rate and inflow rate. The IPA estimators derived are simple and fast to compute, and are further s...

This paper is concerned with the sensitivity of invariant states in linear quantum stochastic systems with respect to nonlinear perturbations. The system variables are governed by a Markovian Hudson-Parthasarathy quantum stochastic differential equation (QSDE) driven by quantum Wiener processes of external bosonic fields in the vacuum state. The quadratic system Hamiltonian and the linear syste...

In our last work, we formulate a Fourier transformation on the infinitedimensional space of functionals. Here we first calculate the Fourier transformation of infinite-dimensional Gaussian distribution exp ( −πξ ∞ −∞ α 2(t)dt ) for ξ ∈ C with Re(ξ) > 0, α ∈ L2(R), using our formulated Feynman path integral. Secondly we develop the Poisson summation formula for the space of functionals, and defi...

In this paper, we propose a new approach to nonstandard analysis without using the ultrafilters. This method is very simple in practice. Moreover, we construct explicitly the total order relation in the new field of the infinitesimal numbers. To illustrate the importance of this work, we suggest comparing  a few applications of this approach with the former methods.

Semi-solid materials undergo strain localization and shear band formation as a result of granular nature of semi-solid deformation. In the present study, to analyze the shear localization, a unified viscoplastic constitutive model was developed for the homogeneous flow. Then, a linearized analysis of the stability performed by examining the necessary condition for the perturbation growth. For t...

To determine flow curves of a material, whose plastic deformation is produced by martensitic transformation, transformation strains of a martensite plate must be characterized [1–3]. Most studies along this line adopt results obtained by the phenomenological crystallographic theory of martensitic transformation [4,5]. The theory is based on finite deformation analysis, which needs involved comp...