Consider a general polynomial system S in x1, . . . , xn of degree q and its corresponding vector of monomials of degree less than or equal to q. The system can be written as M0 · [xq1, xq−1 1 x2, . . . , xn, x1, . . . , xn, 1] = [0, 0, . . . , 0, 0, . . . , 0, 0] (1) in terms of its coefficient matrix M0. Here and hereafter, [...] T means the transposition. Further, [ξ1, ξ2, . . . , ξn] is one...

Numeric data such as statistics and from sensors are increasingly published on the Web and – if brought together for comparisons and calculations – can answer important questions in science, industry, and politics. For instance, natural scientists compare rainfall values from sensors with hydrological estimations documented in a semantic wiki; financial analysts evaluate companies based on comp...

The objective is to solve the college physics problem of a block sliding down movable smooth wedge without friction anywhere using spatial-numeric perspective. drawing method used sum normal force and weight find acceleration. results are equivalent algebra within accuracy. result geometric construction with regular uncertainly was shown for case any horizontal applied force. For given force, a...

17 In this article, we present a method for determining whether a model is at least locally identifiable and in the case of non-identifiable models whether any of the parameters are individually at least locally identifiable. This method combines symbolic and numeric methods to create an algorithm that is extremely accurate compared to other numeric methods and computationally inexpensive. A se...

This paper proposes a new connectionist approach to numeric law discovery; i.e., neural networks (law-candidates) are trained by using a newly invented second-order learning algorithm based on a quasi-Newton method, called BPQ, and the MDL criterion selects the most suitable from law-candidates. The main advantage of our method over previous work of symbolic or connectionist approach is that it...