in this paper, we show how certain metabelian groups can be found within polynomial evaluation groupoids. we show that every finite abelian group can beobtained as a polynomial evaluation groupoid.

It is well a known and fundamental result that the Jones polynomial can be expressed as Potts and vertex partition functions of signed plane graphs. Here we consider constructions of the Jones polynomial as state models of unsigned graphs and show that the Jones polynomial of any link can be expressed as a vertex model of an unsigned embedded graph. In the process of deriving this result, we sh...

Posynomial models are widely used in various engineering design endeavors, such as circuits, aerospace and structural design, mainly due to the fact that design problems cast in terms of posynomial objectives and constraints can be solved efficiently by means of a convex optimization technique known as geometric programming (GP). However, while quite a vast literature exists on GP-based design,...

This paper is aimed at investigating background subtraction based on second-order polynomial models. Recently, preliminary results suggested that quadratic models hold the potential to yield superior performance in handling common disturbance factors, such as noise, sudden illumination changes and variations of camera parameters, with respect to state-of-the-art background subtraction methods. ...

Nonlinear state-space modelling is a very powerful black-box approach. However powerful, the resulting models tend to be complex, described by large number of parameters. In many cases interpretability preferred over complexity, making too complex unfit or undesired. this work, complexity such reduced retrieving more structured, parsimonious model from data, without exploiting physical knowledg...

This paper shows a complete upward collapse in the Polynomial Hierarchy (PH) if for ZPP, two queries to a SAT oracle is equivalent to one query. That is, ZPP = ZPP =⇒ ZPP = PH. These ZPP machines are required to succeed with probability at least 1/2+ 1/p(n) on inputs of length n for some polynomial p(n). This result builds upon recent work by Tripathi [16] who showed a collapse of PH to S2 . Th...

The approach of subset selection in polynomial regression model building assumes that the chosen fixed full set of predefined basis functions contains a subset that is sufficient to describe the target relation sufficiently well. However, in most cases the necessary set of basis functions is not known and needs to be guessed – a potentially non-trivial (and long) trial and error process. In our...

Model-based Diagnosis allows the identification of the parts which fail in a system. The models are based on the knowledge of the system to diagnose, and they can be represented by constraints associated to the components. The variables including in these constraints can be observable or non-observable, depending on the situation of sensors. In order to obtain the minimal diagnosis in a system,...

IN THIS PAPER I construct a state model for the (original) Jones polynomial [5]. (In [6] a state model was constructed for the Conway polynomial.) As we shall see, this model for the Jones polynomial arises as a normalization of a regular isotopy invariant of unoriented knots and links, called here the bracket polynomial, and denoted 〈K〉 for a link projectionK . The concept of regular isotopy w...

We develop standard models for commuting tuples of bounded linear operators on a Hilbert space under certain polynomial positivity conditions, generalizing the work of V. Müller and F.-H. Vasilescu in [6], [14]. As a consequence of the model, we prove a von Neumann-type inequality for such tuples. Up to similarity, we obtain the existence of in a certain sense “unitary” dilations.