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

American Millennials: An Ideological Overview

In an attempt to further understand the inner workings and beliefs held by the majority of my own generation located in the geographic scope of the United States of America, this report will be a conduction of research to further examine the overall beliefs and ideologies of the generation in the United States that older generations, such as Generation X and Baby Boomers, stereotypically view as “the problem” with the country’s political landscape. This report will seek to explain the reasoning behind the ideologies and beliefs of millennials, those Americans born between 1980 and 2000 (probe.org), and what particular world events, if any, result in the beliefs in question. It is fair to say that millennials are at a conflicting turning point politically in the United States, with heated political topics including the Trump Administration and Gun Control, a presentation of political confliction is prevalent in the United States, especially with younger voters. This report will thoroughly cover a prediction of findings, a comprehensive presentation of the findings in question, world events that affect the findings, overall voting trends of millennials, comparison of the findings to the predictions, and a concluding statement

Byttedyr levering, byttedyr håndtering og døgnrytme ved to fjellvåk (Buteo lagopus) reir avslørt ved bruk av videoovervåking

Two Rough-legged buzzard (Buteo lagopus) nests, were video monitored during the nestling period in 2017 in Norway. One nest was in Surnadal in Møre and Romsdal county and the other, Goppollvatnet in Innlandet county. This was to gain knowledge on the prey delivered, circadian rhythm at the nests regarding parent delivery and precise time the day and the ability of unassisted feeding as a function of nestling age. Data were collected using video recordings that were activated by sensors when movement was detected at the nest. Videoclips were reviewed on a large screen to identify all deliveries from the surveillance period. The circadian rhythm revealed that prey was delivered during daytime. The diel pattern of delivery differed between the nests, with one distinct delivery peak for Surnadal at 12.30-15.00 hours and two peaks at Goppollvatnet at 08.00-09.00 and 16.00-17.45 hours. At Goppollvatnet 349 prey items were delivered and at Surnadal 159. The most frequent prey delivered at both nests were Microtus voles with 28.3 % at Surnadal and 39.8 % at Goppollvatnet. Lemmings made up 29.8 % of the prey items at Goppollvatnet and none at Surnadal. Birds made up 33.8 % of the delivered estimated prey mass at Surnadal and 4.8 % at Goppollvatnet. The parent delivering pattern as a function of nestling age differed between the two nests. The single nestling in Surnadal started feeding unassisted at a younger age than the two nestlings at Goppollvatnet. This might be due to the female food allocation to increase the survival rate for siblings. Both prey type and nestling age affected the probability of female feeding at Surnadal but only prey type at Goppollvatnet. At Goppollvatnet the probability of feeding unassisted was larger for Microtus voles compared to Norwegian lemmings (Lemmus lemmus) which might explain the difference between the nests in the ability of nestlings feeding unassisted. The probability of swallowing a prey whole was affected by the prey mass at both nests. Whether prey was a shrew, or a vole has affected the probability of swallowing whole at both nests. In the future it might be an idea to set up two cameras from opposite angles to optimize the recordings. This would help getting better images when a nestling might be shielding the prey from one angle. At the same time, the sensibility on the sensors might be adjusted a bit down to avoid unnecessary recordings.M-N