Bayesian Forecast Combination for VAR Models

We consider forecast combination and, indirectly, model selection for VAR models when there is uncertainty about which variables to include in the model in addition to the forecast variables. The key dierence from traditional Bayesian variable selection is that we also allow for uncertainty regarding which endogenous variables to include in the model. That is, all models include the forecast variables, but may otherwise have diering sets of endogenous variables. This is a dicult problem to tackle with a traditional Bayesian approach. Our solution is to focus on the forecasting performance for the variables of interest and we construct model weights from the predictive likelihood of the forecast variables. The procedure is evaluated in a small simulation study and found to perform competitively in applications to real world data.Bayesian model averaging; Predictive likelihood; GDP forecasts

Maximum observable correlation for a bipartite quantum system

The maximum observable correlation between the two components of a bipartite quantum system is a property of the joint density operator, and is achieved by making particular measurements on the respective components. For pure states it corresponds to making measurements diagonal in a corresponding Schmidt basis. More generally, it is shown that the maximum correlation may be characterised in terms of a `correlation basis' for the joint density operator, which defines the corresponding (nondegenerate) optimal measurements. The maximum coincidence rate for spin measurements on two-qubit systems is determined to be (1+s)/2, where s is the spectral norm of the spin correlation matrix, and upper bounds are obtained for n-valued measurements on general bipartite systems. It is shown that the maximum coincidence rate is never greater than the computable cross norm measure of entanglement, and a much tighter upper bound is conjectured. Connections with optimal state discrimination and entanglement bounds are briefly discussed.Comment: Revtex, no figure

Finding the Kraus decomposition from a master equation and vice versa

For any master equation which is local in time, whether Markovian, non-Markovian, of Lindblad form or not, a general procedure is reviewed for constructing the corresponding linear map from the initial state to the state at time t, including its Kraus-type representations. Formally, this is equivalent to solving the master equation. For an N-dimensional Hilbert space it requires (i) solving a first order N^2 x N^2 matrix time evolution (to obtain the completely positive map), and (ii) diagonalising a related N^2 x N^2 matrix (to obtain a Kraus-type representation). Conversely, for a given time-dependent linear map, a necessary and sufficient condition is given for the existence of a corresponding master equation, where the (not necessarily unique) form of this equation is explicitly determined. It is shown that a `best possible' master equation may always be defined, for approximating the evolution in the case that no exact master equation exists. Examples involving qubits are given.Comment: 16 pages, no figures. Appeared in special issue for conference QEP-16, Manchester 4-7 Sep 200

A 185-215-GHz Subharmonic Resistive Graphene FET Integrated Mixer on Silicon

A 200-GHz integrated resistive subharmonic mixer based on a single chemical vapor deposition graphene field-effect transistor (G-FET) is demonstrated experimentally. This device has a gate length of 0.5 μm and a gate width of 2x40 μm. The G-FET channel is patterned into an array of bow-tie-shaped nanoconstrictions, resulting in the device impedance levels of ~50 Ω and the ON-OFF ratios of ≥4. The integrated mixer circuit is implemented in coplanar waveguide technology and realized on a 100-μm-thick highly resistive silicon substrate. The mixer conversion loss is measured to be 29 ± 2 dB across the 185-210-GHz band with 12.5-11.5 dBm of local oscillator (LO) pump power and >15-dB LO-RF isolation. The estimated 3-dB IF bandwidth is 15 GHz

Asymptotically simple solutions of the vacuum Einstein equations in even dimensions

We show that a set of conformally invariant equations derived from the Fefferman-Graham tensor can be used to construct global solutions of the vacuum Einstein equations, in all even dimensions. This gives, in particular, a new, simple proof of Friedrich's result on the future hyperboloidal stability of Minkowski space-time, and extends its validity to even dimensions.Comment: 25p