We approximate a manifold triangulation in IR using smooth implicit algebraic surface patches, which we call A-patches. Here each A-patch is a real iso-contour of a trivariate rational function de ned within a tetrahedron. The rational trivariate function provides increased degrees of freedom so that the number of surface patches needed for free-form shape modeling is signi cantly reduced compa...

Appendix Figure C-5. Route 65 hotspots identified using a binomial model (95% CI) and a three-mile moving window based on the binomial model. .

This paper is concerned with the quantum properties of the binomial model (or, the CRR-model). We show that the single-step binomial model is incomplete in the quantum setting. All risk-neutral states of the single-step binomial model in the quantum setting are characterized. Moreover, it is shown that all single-step models are incomplete in the quantum setting. Therefore, incompleteness is ba...

Over the past decade, volume graphics has been recognized as an important field of research. Most early research in volume graphics was focused on the problem of rendering of volumetric models. Only recently, volume modeling had been suggested. Volume modeling encompass the tools, data representations and algorithms that are needed to describe and manipulate the inner parts of a model, as well ...

We study the cross-sectional performance of option pricing models in which the volatility of the underlying stock is a deterministic function of the stock price and time. For each date in our sample of FTSE 100 index option prices, we fit an implied binomial tree to the panel of all European style options with different strike prices and maturities and then examine how well this model prices a ...

Many polynomial invariants are defined on graphs for encoding the combinatorial information and researching them algebraically. In this paper, we introduce the cycle polynomial and the path polynomial of directed graphs for counting cycles and paths, respectively. They satisfy recurrence relations with respect to elementary edge or vertex operations. They are related to other polynomials and ca...

Teaching Stochastic Finance on a basic level, e.g. to undergraduates or even in school is a task which is hard to fulfil with common continuous theory. It takes a lot of mathematical prerequisites, sometimes it is not even possible to introduce them since the level of education among students is too low. This is one of the main reasons for the use of discrete asset models to describe financial ...

Given a rectangular box which has been split into 24 tetrahedra, we show how to construct a C1 macroelement using polynomial pieces of degree 6.

SUMMARY When faced with proportion data that exhibit extra-binomial variation, data analysts often consider the beta-binomial distribution as an alternative model to the more common bino-mial distribution. A typical example occurs in toxicological experiments with laboratory animals, where binary observations on fetuses within a litter are often correlated with each other. In such instances, it...