Watch the clock-engineering biological systems to be on time.
ABSTRACT Inspired by natural time-keeping devices controlling the circadian clock, managing information processing in the brain and coordinating physiological activities on a daily (feeding and sleeping) or seasonal timescale (reproductive activity or hibernation), synthetic biologists have successfully assembled functional synthetic clocks from cataloged genetic components with standardized activities and arranging them in transcription circuits containing positive and negative feedback loops with integrated time-delay dynamics. While the positive feedback loop drives the clock like the (balance) spring in a mechanical watch the negative time-delay circuit represents the pulse generator defining a minimal time unit and precision of the clock like the pendulum fallback or the movement of the balance wheel in a classical mechanic watch. This basic design principle enabled the construction of a variety of synthetic oscillators whose design details are concisely covered in this review.
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ABSTRACT: "Symmetry is a complexity-reducing concept [...]; seek it every-where." - Alan J. Perlis Many natural and man-made objects exhibit significant symmetries or contain repeated substructures. This paper presents a new algorithm that processes geometric models and efficiently discovers and extracts a compact representation of their Euclidean symmetries. These symmetries can be partial, approximate, or both. The method is based on matching simple local shape signatures in pairs and using these matches to accumulate evidence for symmetries in an appropriate transformation space. A clustering stage extracts potential significant symmetries of the object, followed by a verification step. Based on a statistical sampling analysis, we provide theoretical guarantees on the success rate of our algorithm. The extracted symmetry graph representation captures important high-level information about the structure of a geometric model which in turn enables a large set of further processing operations, including shape compression, segmentation, consistent editing, symmetrization, indexing for retrieval, etc. Copyright © 2006 by the Association for Computing Machinery, Inc.
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ABSTRACT: We present an algorithm to approximate the 3D Minkowski sum of polyhedral objects. Our algorithm decomposes the polyhedral objects into convex pieces, generates pairwise convex Minkowski sums, and computes their union. We approximate the union by generating a voxel grid, computing signed distance on the grid points, and performing isosurface extraction from the distance field. The accuracy of the algorithm is mainly governed by the resolution of the underlying volumetric grid. Insufficient resolution can result in unwanted handles or disconnected components in the approximation. We use an adaptive subdivision algorithm that overcomes these problems by generating a volumetric grid at an appropriate resolution. We guarantee that our approximation has the same topology as the exact Minkowski sum. We also provide a two-sided Hausdorff distance bound on the approximation. Our algorithm is relatively simple to implement and works well on complex models. We have used it for exact 3D translation motion planning, offset computation, mathematical morphological operations, and bounded-error penetration depth estimation.Graphical Models. 01/2006;
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ABSTRACT: Computer programs that simulate the deformations of geometric shapes have played a key role in the increasing popularity of software tools for artistic animation. Previously published techniques for specifying and animating deformations are either limited in their domain or ill-suited for interactive editing and visualization, because the effects of alterations performed by the animator on the model's parameters may not always be anticipated, and because realtime animation may only be produced by visualizing precomputed sequences of 3D frames obtained by a slow process and require vast amounts of storage. To support an interactive environment for animation design, we have developed a new, simple, and efficient animation primitive: a Parameterized Interpolating Polyhedron (PIP). PIPs are easily specified and edited by providing their initial and final shapes, which may be any polyhedra, and need not have corresponding boundary elements, nor be convex. PIPs may be efficiently animated on standard graphic hardware because a PIP is a smoothly varying family of polyhedra bounded by faces that evolve with time. The faces have constant orientations and vertices that each move on a straight line between a vertex of the initial shape and a vertex of the final one. The cost of recalculating the time dependent information of a PIP is small in comparison to the display cost. We provide simple and efficient algorithms, based on Minkowski sum operations, for computing PIPs. When both the initial and final shapes are convex, the resulting faces are the true boundary of the deforming object, otherwise subsets of the resulting faces may lie inside the object. In both cases, correct images are automatically generated using standard depth-buffer hardware. The tools we have developed are convenient for interactively designing animation sequences that show the metamorphosis of 3D shapes. They may also be used to simulate the geometric effect of a variety of manufacturing operations, and for interactively selecting the optimal compromise between two or more shapes. They have been integrated in the LAMBADA design and inspection environment for animated assemblies, where deformations and rigid-body motions may be easily combined and synchronized using a hierarchical representation.Computers & Graphics. 01/1992;