We describe an implementation of Shor’s quantum algorithm to factor n-bit integers using only 2n+2 qubits. In contrast to previous space-optimized implementations, ours features a purely Toffoli based modular multiplication circuit. The circuit depth and the overall gate count are in O(n3) and O(n3 logn), respectively. We thus achieve the same space and time costs as Takahashi et al. [1], while...

We study closures of GL+2 (R)-orbits on the total space ΩMg of the Hodge bundle over the moduli space of curves under the assumption that they are algebraic manifolds. We show that, in the generic stratum, such manifolds are the whole stratum, the hyperelliptic locus or parameterize curves whose Jacobian has additional endomorphisms. This follows from a cohomological description of the tangent ...

This paper demonstrates the advantages of using a hybrid reinforcement–modular neural network architecture for non-linear control. Specifically, the method of ACTION-CRITIC reinforcement learning, modular neural networks, competitive learning and stochastic updating are combined. This provides an architecture able to both support temporal difference learning and probabilistic partitioning of th...

The elliptic norm curve Qn in space S„_i admits a group G2ni of collineations, and in fact there is a single infinity of such curves which admit the same group. A particular Qn of the family is distinguished by a value of the parameter t , itself an elliptic modular function defined by the modular group congruent to identity (mod. n). In the group G2n2, there are certain involutory collineation...

Teichmiiller theory for super Riemann surfaces is rigorously developed using the supermanifold theory" of Rogers. In the case of trivial topology in the soul directions, relevant for superstring applications, the following results are proven. The super Teichmiiller space is a complex super-orbifold whose body is the ordinary Teichmiiller space of the associated Riemann surfaces with spin struct...

We present and discuss the implications of recent results by several researchers on computational issues in supervisory control of discrete event systems. The first issue discussed is the boundary between decidability and undecidability in centralized and decentralized control problems for systems modeled by finite-state automata and subject to regular language specifications. The second issue ...