A Topological Approach to Scaling in Financial Data

Autor: de Carufel, Jean, Brooks, Martin, Stieber, Michael, Britton, Paul

There is a large body of work, built on tools developed in mathematics and physics, demonstrating that financial market prices exhibit self-similarity at different scales. In this paper, we explore the use of analytical topology to characterize finan

Externí odkaz: http://arxiv.org/abs/1710.08860

Persistence Lenses: Segmentation, Simplification, Vectorization, Scale Space and Fractal Analysis of Images

Autor: Brooks, Martin

A persistence lens is a hierarchy of disjoint upper and lower level sets of a continuous luminance image's Reeb graph. The boundary components of a persistence lens's interior components are Jordan curves that serve as a hierarchical segmentation of

Externí odkaz: http://arxiv.org/abs/1604.07361

Varilets: Additive Decomposition, Topological Total Variation, and Filtering of Scalar Fields

Autor: Brooks, Martin

Continuous interpolation of real-valued data is characterized by piecewise monotone functions on a compact metric space. Topological total variation of piecewise monotone function f:X->R is a homeomorphism-invariant generalization of 1D total variati

Externí odkaz: http://arxiv.org/abs/1503.04867

An Optimal Linear Time Algorithm for Quasi-Monotonic Segmentation

Autor: Lemire, Daniel, Brooks, Martin, Yan, Yuhong

Publikováno v: Daniel Lemire, Martin Brooks and Yuhong Yan, An Optimal Linear Time Algorithm for Quasi-Monotonic Segmentation. International Journal of Computer Mathematics 86 (7), 2009.

Monotonicity is a simple yet significant qualitative characteristic. We consider the problem of segmenting a sequence in up to K segments. We want segments to be as monotonic as possible and to alternate signs. We propose a quality metric for this pr

Externí odkaz: http://arxiv.org/abs/0709.1166

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