Qualitative reasoning about physical systems has become one of the most active and productive areas in AI in recent years. While there are many different kinds of qualitative reasoning, the central role is played by qualitative simulation: prediction of the possible behaviors consistent with incomplete knowledge of the structure of physical system. In the retrospective on my 1984 paper, “Common...

Usually mathematicians use Hodgkin-Huxley model or FitzHug-Nagumo model to simulate action potentials of skeletal muscle fibers. These models are electrically excitable, but skeletal muscle fibers are stimulated chemically. To investigate skeletal muscle fibers we use a model with six ordinary differential equations. This dynamical system is sensitive to initial value of some variables so it is...

In most cases authors are permitted to post their version of the article (e.g. in Word or Tex form) to their personal website or institutional repository. Authors requiring further information regarding Elsevier's archiving and manuscript policies are encouraged to visit: a b s t r a c t In this paper we deal with the qualitative behavior of the solutions of the following difference equation x ...

This paper deals with the qualitative properties of an n-dimensional autonomous system of differential equations, modeling the general ratio-dependent predator-prey interaction.

Mathematical models in continuous or discrete time are widely used to simplify real-world systems in order to understand their mechanisms for a particular purpose. Consequently, a welldefined model should be able to carry out some predictions and be fitted to observational data in a variety of time measurements (seconds, hours, days, weeks, months, or years). Therefore, the time scales approach...

(λk(u), rk(u) being the k-th eigenvalue and a corresponding eigenvector of A(u)) is either the whole space or consists of a finite number of smooth, N−1dimensional, connected, manifolds that are transversal to the characteristic vector field rk. Relying on an adapted wave tracing method, we obtain the same tipe of error estimates valid for hyperbolic systems satisfying the classical assumptions...

This paper discusses the restriction of qualitative models of physical systems in order to ensure more specific behavior. Restriction is performed by adding constraints : (i) directly on exogenous parameters, and (ii) on non exogenous or dependent param eters . The former are termed primary restrictions, and the latter are called derived restrictions . We show the connection between primary and...

The purpose of this qualitative study was to understand influential factors associated with decisions to obtain breast or cervical cancer screening by diverse Latinas after attending a community-based educational program. Forty-five interviews were conducted in Arkansas, New York City and Buffalo, New York. Thematic data analyses were conducted to understand influential factors following from t...

TRANSCEND, a system for monitoring and diagnosis of abrupt faults in complex dynamic systems, relies on system models to predict dynamic behavior in response to abrupt faults. The use of qualitative predictions of this transient behavior mitigates complexity issues and convergence problems that exist in numerical diagnosis approaches. In this framework, it is important to model the system under...

Building models of the physical world from examples is an important challenge for qualitative reasoning systems. We describe a system that can learn intuitive models of physical behaviors from a corpus of multimodal, multi-state stimuli, consisting of sketches and text. The system extracts and temporally encodes exemplars from the stimuli and uses analogical generalization to abstract prototypi...