Locked and Unlocked Chains of Planar Shapes

We extend linkage unfolding results from the well-studied case of polygonal linkages to the more general case of linkages of polygons. More precisely, we consider chains of nonoverlapping rigid planar shapes (Jordan regions) that are hinged together sequentially at rotatable joints. Our goal is to characterize the families of planar shapes that admit locked chains, where some configurations cannot be reached by continuous reconfiguration without self-intersection, and which families of planar shapes guarantee universal foldability, where every chain is guaranteed to have a connected configuration space. Previously, only obtuse triangles were known to admit locked shapes, and only line segments were known to guarantee universal foldability. We show that a surprisingly general family of planar shapes, called slender adornments, guarantees universal foldability: roughly, the distance from each edge along the path along the boundary of the slender adornment to each hinge should be monotone. In contrast, we show that isosceles triangles with any desired apex angle less than 90 degrees admit locked chains, which is precisely the threshold beyond which the inward-normal property no longer holds.Comment: 23 pages, 25 figures, Latex; full journal version with all proof details. (Fixed crash-induced bugs in the abstract.

The potential of text mining in data integration and network biology for plant research : a case study on Arabidopsis

Despite the availability of various data repositories for plant research, a wealth of information currently remains hidden within the biomolecular literature. Text mining provides the necessary means to retrieve these data through automated processing of texts. However, only recently has advanced text mining methodology been implemented with sufficient computational power to process texts at a large scale. In this study, we assess the potential of large-scale text mining for plant biology research in general and for network biology in particular using a state-of-the-art text mining system applied to all PubMed abstracts and PubMed Central full texts. We present extensive evaluation of the textual data for Arabidopsis thaliana, assessing the overall accuracy of this new resource for usage in plant network analyses. Furthermore, we combine text mining information with both protein-protein and regulatory interactions from experimental databases. Clusters of tightly connected genes are delineated from the resulting network, illustrating how such an integrative approach is essential to grasp the current knowledge available for Arabidopsis and to uncover gene information through guilt by association. All large-scale data sets, as well as the manually curated textual data, are made publicly available, hereby stimulating the application of text mining data in future plant biology studies

A discrete/rhythmic pattern generating RNN

Biological research supports the concept that advanced motion emerges from modular building blocks, which generate both rhythmical and discrete patterns. Inspired by these ideas, roboticists try to implement such building blocks using different techniques. In this paper, we show how to build such module by using a recurrent neural network (RNN) to encapsulate both discrete and rhythmical motion patterns into a single network. We evaluate the proposed system on a planar robotic manipulator. For training, we record several handwriting motions by back driving the robot manipulator. Finally, we demonstrate the ability to learn multiple motions (even discrete and rhythmic) and evaluate the pattern generation robustness in the presence of perturbations

Generating Functionals for Spin Foam Amplitudes

We construct a generating functional for the exact evalutation of a coherent representation of spin network amplitudes. This generating functional is defined for arbitrary graphs and depends only on a pair of spinors for each edge. The generating functional is a meromorphic polynomial in the spinor invariants which is determined by the cycle structure of the graph. The expansion of the spin network generating function is given in terms of a newly recognized basis of SU(2) intertwiners consisting of the monomials of the holomorphic spinor invariants. This basis is labelled by the degrees of the monomials and is thus discrete. It is also overcomplete, but contains the precise amount of data to specify points in the classical space of closed polyhedra, and is in this sense coherent. We call this new basis the discrete-coherent basis. We focus our study on the 4-valent basis, which is the first non-trivial dimension, and is also the case of interest for Quantum Gravity. We find simple relations between the new basis, the orthonormal basis, and the coherent basis. Finally we discuss the process of coarse graining moves at the level of the generating functionals and give a general prescription for arbitrary graphs. A direct relation between the polynomial of cycles in the spin network generating functional and the high temperature loop expansion of the 2d Ising model is found.Comment: PhD Thesis, 128 page