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We present an algorithm for generating all polynomial invariants of P-solvable loops with assignments and nested conditionals. We prove termination of our algorithm. The proof relies on showing that the dimensions of the prime ideals from the minimal decom ...
Springer-Verlag New York, Ms Ingrid Cunningham, 175 Fifth Ave, New York, Ny 10010 Usa2010
We investigate numerical simulations and visualizations of the problem of tying a knot in a piece of rope. The goal is to use the least possible rope of a fixed, prescribed radius to tie a particular knot, e.g. a trefoil, a figure eight, and so on. The rop ...
We describe the new software package Aligator for automatically inferring polynomial loop invariants, The package combines algorithms from symbolic summation and polynomial algebra with computational logic, and is applicable to the rich class of P-solvable ...
Springer-Verlag New York, Ms Ingrid Cunningham, 175 Fifth Ave, New York, Ny 10010 Usa2008
Enforcing a specific symmetry group on a curve, knotted or not, is not trivial using standard interpolations such as polygons or splines. For a prescribed symmetry group we present a symmetrization process based on a Fourier description of a knot. The pres ...
How about fastening a knot? not with ropes... but with timber panels. Timber Fabric
Structures (TFS) originate from such an inspiration. An architectural reinterpretation
of fabric techniques (mainly braiding) using building scale timber panels to design ...
We demonstrate Optical-Resolution Photoacoustic Microscopy (OR-PAM), where the optical field is focused and scanned using Digital Phase Conjugation through a multimode fiber. The focus is scanned across the field of view using digital means, and the acoust ...
This thesis concerns optimal packing problems of tubes, or thick curves, where thickness is defined as follows. Three points on a closed space curve define a circle. Taking the infimum over all radii of pairwise-distinct point triples defines the thickness ...
This paper discusses practical implementation of a generic camera model for a wide variety of common cameras equipped with catadioptric, fish-eye, short- or long focal length lenses. A unified approach of deriving approximate model parameters followed by a ...
We present a method for generating polynomial invariants for a subfamily of imperative loops operating on numbers, called the P-solvable loops. The method uses algorithmic combinatorics and algebraic techniques. The approach is shown to be complete for som ...
Springer-Verlag New York, Ms Ingrid Cunningham, 175 Fifth Ave, New York, Ny 10010 Usa2008
The main subject of the present thesis is the experimental study of the scaling properties of DNA knots of different complexities by tapping mode atomic force microscopy (AFM) in air. Homo- or heterogeneous mixture of DNA knot types were deposited onto mic ...
