
On the weight and density bounds of polynomial threshold functions
In this report, we show that all nvariable Boolean function can be repr...
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Bipartite Perfect Matching as a Real Polynomial
We obtain a description of the Bipartite Perfect Matching decision probl...
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Drawing planar graphs with few segments on a polynomial grid
The visual complexity of a plane graph drawing is defined to be the numb...
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Periodic Fourier representation of boolean functions
In this work, we consider a new type of Fourierlike representation of b...
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On the complexity of optimally modifying graphs representing spatial correlation in areal unit count data
Lee and Meeks recently demonstrated that improved inference for areal un...
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VTrails: Inferring Vessels with Geodesic Connectivity Trees
The analysis of vessel morphology and connectivity has an impact on a nu...
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How many Fourier coefficients are needed?
We are looking at families of functions or measures on the torus (in dim...
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Representing polynomial of CONNECTIVITY
We show that the coefficients of the representing polynomial of any monotone Boolean function are the values of a Moebius function of an atomistic lattice related to this function. Using this we determine the representing polynomial of any Boolean function corresponding to a direct acyclic graph connectivity problem. Only monomials corresponding to unions of paths have nonzero coefficients which are (1)^D where D is an easily computable function of the graph corresponding to the monomial (it is the number of plane regions in the case of planar graphs). We estimate the number of monomials with nonzero coefficients for the twodimensional grid connectivity problem as being between Ω(1.641^2n^2) and O(1.654^2n^2).
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