Voting over economic plans

We review and provide motivation for a one-sector model of economic growth in which decisions about capital accumulation are made by a political process. If it is possible to commit for at least three periods into the future, then for any feasible consumption plan, there is a perturbation that is majority-preferred to it. Furthermore, plans that minimize the maximum vote that can be obtained against them yield a political business cycle. If it is impossible to commit, voters select the optimal consumption plan for the median voter

The Role of Aggravated Offences in Combating Hate Crime – 15 years after the CDA 1998 – Time for a change?

The racially aggravated offences created by the 1998 Act (later extended to religious aggravation) were based on a rather arbitrary selection of underlying crimes and have proved difficult to interpret and apply for a number of reasons. Moreover, the relationship between the aggravated offences and the more general duty to increase the sentence for any offence where there is racial (or religious) aggravation is problematical. This is illustrated by the common misunderstandings of the case law on the degree of mutual exclusivity between the crimes underlying the aggravated offences and the more general aggravated sentencing provisions. In the context of the question referred by the government to the Law Commission, as to whether the aggravated offences should be extended further to include a number of other grounds of aggravation, it is argued that this would be counter-productive and that their further extension would lead to even greater confusion and complexity. It is suggested that the preferable course would be to abolish the aggravated offences and to focus on a broader and better articulated sentencing provision of general application which would be all the more effective without the complications of its uncertain relationship with an anomalously selected group of aggravated offences

Optical joint correlator for real-time image tracking and retinal surgery

A method for tracking an object in a sequence of images is described. Such sequence of images may, for example, be a sequence of television frames. The object in the current frame is correlated with the object in the previous frame to obtain the relative location of the object in the two frames. An optical joint transform correlator apparatus is provided to carry out the process. Such joint transform correlator apparatus forms the basis for laser eye surgical apparatus where an image of the fundus of an eyeball is stabilized and forms the basis for the correlator apparatus to track the position of the eyeball caused by involuntary movement. With knowledge of the eyeball position, a surgical laser can be precisely pointed toward a position on the retina

Pearle's Hidden-Variable Model Revisited

Pearle (1970) gave an example of a local hidden variables model which exactly reproduced the singlet correlations of quantum theory, through the device of data-rejection: particles can fail to be detected in a way which depends on the hidden variables carried by the particles and on the measurement settings. If the experimenter computes correlations between measurement outcomes of particle pairs for which both particles are detected, he is actually looking at a subsample of particle pairs, determined by interaction involving both measurement settings and the hidden variables carried in the particles. We correct a mistake in Pearle's formulas (a normalization error) and more importantly show that the model is more simple than first appears. We illustrate with visualisations of the model and with a small simulation experiment, with code in the statistical programming language R included in the paper. Open problems are discussed.Comment: 19pp. This is now arXiv version 4 = final revision for journa

Statistics, ethics, and probiotica

A randomized clinical trial comparing an experimental new treatment to a standard therapy for a life-threatening medical condition should be stopped early on ethical grounds, in either of the following scenarios: (1) it has become overwhelmingly clear that the new treatment is better than the standard; (2) it has become overwhelmingly clear that the trial is not going to show that the new treatment is any better than the standard. The trial is continued in the third scenario: (3) there is a reasonable chance that the new treatment will finally turn out to be better than the standard, but we aren't sure yet. However, the (blinded) data monitoring committee in the "PROPATRIA" trial of an experimental probiotica treatment for patients with acute pancreatitis allowed the trial to continue at the half way interim analysis, in effect because there was still a good chance of proving that the probiotica treatment was very harmful to their patients. The committee did not know whether treatment A was the probiotica treatment or the placebo. In itself this should not have caused a problem, since it could easily have determined the appropriate decision under both scenarios. Were the decisions in the two scenarios different, then the data would have to be de-blinded, in order to determine the appropriate decision. The committee mis-read the output of SPSS, which reports the smaller of two one-sided p-values, without informing the user what it is doing. It seems that about 5 lives were sacrificed to the chance of getting a significant result that the probiotica treatment was bad for the patients in the trial

Two dimensional vernier

A two-dimensional vernier scale is disclosed utilizing a cartesian grid on one plate member with a polar grid on an overlying transparent plate member. The polar grid has multiple concentric circles at a fractional spacing of the spacing of the cartesian grid lines. By locating the center of the polar grid on a location on the cartesian grid, interpolation can be made of both the X and Y fractional relationship to the cartesian grid by noting which circles coincide with a cartesian grid line for the X and Y direction