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The level set function is initialised in the image using the object detector and can come directly from the level set shape-filtering stage of the object detector in the form of a single shape, or the binary image at the output of the filtering stage in the form of a set of shapes.
(c) The single-qubit gate v i = R ( θ i + θ a ) u R ( θ i + θ r ) is applied to a register qubit j by two applications of L with an ancilla initialised in the state | i 〉, i = 0, 1.
We may implement an entangling two-qubit gate between register qubits j and k using an ancilla initialised in the state | 0 〉 by interacting the ancilla sequentially with qubits j and k before completing the gate with a second interaction with the j qubit.
Hence we may implement an entangling gate which is locally equivalent to CZ between pairs of register qubits using only K gates and ancillas initialised in the computational basis.1 The circuit diagram for this two-qubit gate on the register is given in Figure 2.
(b) The two-qubit entangling gate N k j is implemented on the register qubits j and k via the sequence of Eq. (13) with an ancilla initialised in the state | 0 〉, where the form of N k j is given in Eq. (14).
All of the connection weights were randomly initialised in the range (−1, +1).
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The VAPAH algorithm was initialised in parallel using the Raijin Fujitsu Primenergy HPC located at the National Computing Infrastructure (NCI) at the Australian National University (ANU).
For this simulation, 2 / 3 of the sample paths were initialised in a run and the remainder in a resting state so that the system was again encouraged to relax quickly.
For the above simulations, half the sample paths are initialised in a run and half are initialised in a rest.
The SPH particles are initialised in a homogeneous sphere constructed from a face-centred cubic lattice, and the radial positions of the particles are then adjusted so as to match the density profile from the evolution code.5 The internal energies of the particles are then assigned from the temperature (and mean molecular weight) distribution from the stellar evolution code.
All data were obtained from the Soft Tissue Sarcoma Register of the BG University Hospital Bochum, which was initialised in 1991.
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