Topological Data Analysis (TDA) is a new branch of statistics devoted to the study ‘shape’ data. As TDA's tools are typically defined in complex spaces, kernel methods often used perform inferential task by implicitly mapping topological summaries, most noticeably Persistence Diagram (PD), vector spaces. For positive definite kernels on PDs, however, embeddings do not fully retain metric struct...

BACKGROUND The shells of molluscs survive well in many sedimentary contexts and yield information about the diet of prehistoric humans. They also yield evidence of symbolic behaviours through their use as beads for body adornments. Researchers often analyse the location of perforations in shells to make judgements about their use as symbolic objects (e.g., beads), the assumption being that hole...

In this paper we propose a framework for supervised and semi-supervised learning based on reformulating the learning problem as a regularized Fredholm integral equation. Our approach fits naturally into the kernel framework and can be interpreted as constructing new data-dependent kernels, which we call Fredholm kernels. We proceed to discuss the “noise assumption” for semi-supervised learning ...

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microwave assisted fluidized bed drying is a novel drying technique which reduces drying time and yields higher quality products. in this study the effect of this method on color changes of whole and cut hazelnut kernels was investigated. the parameters of color and resulting total color change, chroma, hue angle and browning index were also calculated during drying in three temperatures (40, 5...

The main purpose of the research is to study composition walnut shells. Walnut kernels are widely used in food industry, but, at same time, shell obtained stage cleaning usually disposed by burning. Given multi-ton volume fruit processing, output production waste also significant. When processing even one ton walnuts, an unused product remains – a weighing over 550 kg, which requires removal an...

The high efficiency of monocoque cylindrical shells in carrying axial loads is curtailed by their extreme sensitivity to imperfections. For practical applications, this issue has been alleviated by introducing closely stiffened shells which, however, require expensive manufacturing. Here we present an alternative approach that provides a fundamentally different solution. We design symmetry-brea...