Generating a Quadratic Forms from a Given Genus

Given a non-empty genus in $n$ dimensions with determinant $d$, we give a randomized algorithm that outputs a quadratic form from this genus. The time complexity of the algorithm is poly$(n,\log d)$; assuming Generalized Riemann Hypothesis (GRH).Comment: arXiv admin note: text overlap with arXiv:1409.619

Renormalization-Group Treatment of the Random Resistor Network in 6−ε Dimensions

We consider a hypercubic lattice in which neighboring points are connected by resistances which assume independently the random values σ\u3e−1 and σ\u3c−1 with respective probabilities p and 1−p. For σ\u3c=0 the lattice is viewed as consisting of irreducible nodes connected by chains of path length L. This geometrical length is distinct from the characteristic length Lr which sets a scale of resistance in the random network or Lm which sets a scale of effective exchange in a dilute magnet. Near the percolation concentration pc one sets L~|p−pc|−ζ, Lr~|p−pc|−ζr and Lm~|p−pc|−ζm. Stephen and Grest (SG) have already shown that ζm=1+o(ε2) for spatial dimensionality d=6−ε. Here we show in a way similar to SG that ζr=1+o(ε2). Thus it is possible that ζm=ζr=1 for a continuous range of d below 6. However, increasing evidence suggests that this equality does not hold for d\u3c4, and in particular a calculation in 1+ε dimensions analogous to that of SG for ζm does not seem possible

Measurement issues of on-Silicon de- embedding test structures in the Sub-THz range

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Renormalization-Group Approach to Percolation Problems

The relation between the s-state Ashkin-Teller-Potts (ATP) model and the percolation problem given by Fortuin and Kasteleyn is used to formulate a renormalization-group treatment of the percolation problem. Both an ε expansion near 6 spatial dimensions and cluster approximations for the recursion relations of a triangular lattice are used. Series results for the ATP model are adapted to the percolation problem

On wafer small signal characterization beyond 100 GHz for compact model assessment

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