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The giant single-celled slime mould Physarum polycephalum has inspired rapid develop- ments in unconventional computing substrates since the start of this century. This is primarily due to its simple component parts and the distributed…
Computing a polygon defining a set of planar points is a classical problem of modern computational geometry. In laboratory experiments we demonstrate that a concave hull, a connected alpha-shape without holes, of a finite planar set is…
We propose a novel method to determine the dissimilarity between subjects for functional data clustering. Spline smoothing or interpolation is common to deal with data of such type. Instead of estimating the best-representing curve for each…
The smoothing spline is one of the most popular curve-fitting methods, partly because of empirical evidence supporting its effectiveness and partly because of its elegant mathematical formulation. However, there are two obstacles that…
B-spline models are a powerful way to represent scientific data sets with a functional approximation. However, these models can suffer from spurious oscillations when the data to be approximated are not uniformly distributed. Model…
We propose a new material viscoelastic model and mathematical solution to simulate relaxation modulus and viscoelastic response. The model formula of relaxation modulus is extended from sigmoidal function considering nonlinear strain…
Traditional problems in computational geometry involve aspects that are both discrete and continuous. One such example is nearest-neighbor searching, where the input is discrete, but the result depends on distances, which vary continuously.…
B-spline models are a powerful way to represent scientific data sets with a functional approximation. However, these models can suffer from spurious oscillations when the data to be approximated are not uniformly distributed. Model…
The giant single-celled slime mould Physarum polycephalum exhibits complex morphological adaptation and amoeboid movement as it forages for food and may be seen as a minimal example of complex robotic behaviour. Swarm computation has…
The novel Locally Refined B-spline (LR B-spline) surface format is suited for representing terrain and seabed data in a compact way. It provides an alternative to the well know raster and triangulated surface representations. An LR B-spline…
Normal multi-scale transform [4] is a nonlinear multi-scale transform for representing geometric objects that has been recently investigated [1, 7, 10]. The restrictive role of the exact order of polynomial reproduction $P_e$ of the…
I describe a new method for smoothing a one-dimensional curve in Euclidian space with an arbitrary number of dimensions. The basic idea is borrowed from renormalization group theory which previously was applied to biological macromolecules.…
Slime mould \emph{Physarum polycephalum} is a large single cell capable for distributed sensing, concurrent information processing, parallel computation and decentralised actuation. The ease of culturing and experimenting with Physarum…
The plasmodium of the slime mould Physarum polycephalum has recently received significant attention for its value as a highly malleable amorphous computing substrate. In laboratory-based experiments, micro- and nanoscale artificial circuit…
Reconstruction of geometry based on different input modes, such as images or point clouds, has been instrumental in the development of computer aided design and computer graphics. Optimal implementations of these applications have…
Materials used in real clothing exhibit remarkable complexity and spatial variation due to common processes such as stitching, hemming, dyeing, printing, padding, and bonding. Simulating these materials, for instance using finite element…
The growing prevalence of nonsmooth optimization problems in machine learning has spurred significant interest in generalized smoothness assumptions. Among these, the (L0, L1)-smoothness assumption has emerged as one of the most prominent.…
The slime mould Physarum polycephalum is known to construct proto- plasmic transport networks which approximate proximity graphs by forag- ing for nutrients during its plasmodial life cycle stage. In these networks, nodes are represented by…
We present two results on slime mold computations. In wet-lab experiments (Nature'00) by Nakagaki et al. the slime mold Physarum polycephalum demonstrated its ability to solve shortest path problems. Biologists proposed a mathematical…
Given a data set (t_i, y_i), i=1,..., n with the t_i in [0,1] non-parametric regression is concerned with the problem of specifying a suitable function f_n:[0,1] -> R such that the data can be reasonably approximated by the points (t_i,…