Geometric algorithms are often composed of a set of basic geometric predicates and constructions, also called primitives. Correctness of an algorithm is usually proved under the assumption that all primitives return the correct result. This is in sharp contrast to the naive, but common strategy of implementing such primitives with fixed-precision floating-point arithmetic. The disastrous effect...

Let a, b ∈ Q be such that exactly one of a and b is an algebraic integer, and let ft(z) := z 2 + t be a family of polynomials parametrized by t ∈ Q. We prove that the set of all t ∈ Q for which there exist m,n ≥ 0 such that f t (a) = f t (b) has bounded height. This is a special case of a more general result supporting a new bounded height conjecture in arithmetic dynamics.

Max-plus stochastic processes are counterparts of Markov diffusion processes governed by Ito sense stochastic differential equations. In this framework, expectations are linear operations with respect to max-plus arithmetic. Max-plus stochastic control problems are considered, in which a minimizing control enters the state dynamics and running cost. The minimum max-plus expected cost is equal t...

{sl let $[n]={1,dots, n}$ be colored in $k$ colors. a rainbow ap$(k)$ in $[n]$ is a $k$ term arithmetic progression whose elements have different colors. conlon, jungi'{c} and radoiv{c}i'{c} cite{conlon} prove that there exists an equinumerous 4-coloring of $[4n]$ which is rainbow ap(4) free, when $n$ is even. based on their construction, we show that such a coloring of ...

I considered the first construction in my book, Outer Billiards on Kites [S2]. The arithmetic graphs served as the main tool for understanding the dynamics of outer billiards on kites. See §2 for definitions. The second construction, which is quite general, is based on patterns of oriented lines in the Euclidean plane. See §3 for definitions. The concrete instance of the multigrid construction ...

Abstract The paper deals with a model of electricity spot prices. proposed dynamics prices is driven by mean reverting diffusion jumps having hyperexponential distribution. analytical formula for the forward contract’s price derived in crisp case. Inasmuch as parameters are considered to be evaluated imprecisely, their fuzzy counterparts introduced. With usage arithmetic, expression derived. Se...

The use of stochastic processing hardware and low precision arithmetic in atmospheric models is investigated. Stochastic processors allow hardware-induced faults in calculations, sacrificing bit-reproducibility in exchange for improvements in performance and potentially accuracy and a reduction in power consumption. A similar trade-off is achieved using low precision arithmetic, with improvemen...