Schrödinger's Cat Meets Occam's Razor.

We discuss V.P. Belavkin's approach to the Schrödinger cat problem and show its close relation to ideas based on superselection and interaction with the environment developed by N.P. Landsman. The purpose of the paper is to explain these ideas in the most simple possible context, namely: discrete time and separable Hilbert spaces, in order to make them accessible to those coming from the philosophy of science and not too happy with idiosyncratic notation and terminology and sophisticated mathematical tools. Conventional elementary mathematical descriptions of quantum mechanics take "measurement" to be a primitive concept. Paradoxes arise when we choose to consider smaller or larger systems as measurement devices in their own right, by making different and apparently arbitrary choices of location of the "Heisenberg cut". Various quantum interpretations have different resolutions of the paradox. In Belavkin's approach, the classical world around us does really exist, and it evolves stochastically and dynamically in time according to probability laws following from successive applications of the Born law. It is a collapse theory. The quantum/classical distinction is determined by the arrow of time. The underlying unitary evolution of the wave-function of the universe enables the designation of a collection of beables which grows as time evolves, and which therefore can be assigned random, classical trajectories. In a slogan: the past is particles, the future is a wave. We, living in the now, are located on the cutting edge between past and future.

Gull's Theorem Revisited.

In 2016, Steve Gull has outlined has outlined a proof of Bell's theorem using Fourier theory. Gull's philosophy is that Bell's theorem (or perhaps a key lemma in its proof) can be seen as a no-go theorem for a project in distributed computing with classical, not quantum, computers. We present his argument, correcting misprints and filling gaps. In his argument, there were two completely separated computers in the network. We need three in order to fill all the gaps in his proof: a third computer supplies a stream of random numbers to the two computers representing the two measurement stations in Bell's work. One could also imagine that computer replaced by a cloned, virtual computer, generating the same pseudo-random numbers within each of Alice and Bob's computers. Either way, we need an assumption of the presence of shared i.i.d. randomness in the form of a synchronised sequence of realisations of i.i.d. hidden variables underlying the otherwise deterministic physics of the sequence of trials. Gull's proof then just needs a third step: rewriting an expectation as the expectation of a conditional expectation given the hidden variables.

A Nonparametric Bayesian Approach to the Rare Type Match Problem.

The "rare type match problem" is the situation in which, in a criminal case, the suspect's DNA profile, matching the DNA profile of the crime stain, is not in the database of reference. Ideally, the evaluation of this observed match in the light of the two competing hypotheses (the crime stain has been left by the suspect or by another person) should be based on the calculation of the likelihood ratio and depends on the population proportions of the DNA profiles that are unknown. We propose a Bayesian nonparametric method that uses a two-parameter Poisson Dirichlet distribution as a prior over the ranked population proportions and discards the information about the names of the different DNA profiles. This model is validated using data coming from European Y-STR DNA profiles, and the calculation of the likelihood ratio becomes quite simple thanks to an Empirical Bayes approach for which we provided a motivation.

A comment on the PCAST report: Skip the "match"/"non-match" stage.

This letter comments on the report "Forensic science in criminal courts: Ensuring scientific validity of feature-comparison methods" recently released by the President's Council of Advisors on Science and Technology (PCAST). The report advocates a procedure for evaluation of forensic evidence that is a two-stage procedure in which the first stage is "match"/"non-match" and the second stage is empirical assessment of sensitivity (correct acceptance) and false alarm (false acceptance) rates. Almost always, quantitative data from feature-comparison methods are continuously-valued and have within-source variability. We explain why a two-stage procedure is not appropriate for this type of data, and recommend use of statistical procedures which are appropriate.

A proof of Bell's inequality in quantum mechanics using causal interactions.

We give a simple proof of Bell's inequality in quantum mechanics using theory from causal interaction, which, in conjunction with experiments, demonstrates that the local hidden variables assumption is false. The proof sheds light on relationships between the notion of causal interaction and interference between treatments.

Development and antitumor activity of a BCL-2 targeted single-stranded DNA oligonucleotide.

PNT100 is a 24-base, chemically unmodified DNA oligonucleotide sequence that is complementary to a region upstream of the BCL-2 gene. Exposure of tumor cells to PNT100 results in suppression of proliferation and cell death by a process called DNA interference. PNT2258 is PNT100 that is encapsulated in protective amphoteric liposomes developed to efficiently encapsulate the PNT100 oligonucleotide, provide enhanced serum stability, optimized pharmacokinetic properties and antitumor activity of the nanoparticle both in vivo and in vitro. PNT2258 demonstrates broad antitumor activity against BCL-2-driven WSU-DLCL2 lymphoma, highly resistant A375 melanoma, PC-3 prostate, and Daudi-Burkitt's lymphoma xenografts. The sequence specificity of PNT100 was demonstrated against three control sequences (scrambled, mismatched, and reverse complement) all encapsulated in a lipid formulation with identical particle characteristics, and control sequences did not demonstrate antiproliferative activity in vivo or in vitro. PNT2258 is currently undergoing clinical testing to evaluate safety and antitumor activity in patients with recurrent or refractory non-Hodgkin's lymphoma and additional studies are planned.

Product-limit estimators of the gap time distribution of a renewal process under different sampling patterns.

Nonparametric estimation of the gap time distribution in a simple renewal process may be considered a problem in survival analysis under particular sampling frames corresponding to how the renewal process is observed. This note describes several such situations where simple product limit estimators, though inefficient, may still be useful.

Maximal violation of the Collins-Gisin-Linden-Massar-Popescu inequality for infinite dimensional states.

We present a much simplified version of the Collins-Gisin-Linden-Massar-Popescu inequality for the 2x2xd Bell scenario. Numerical maximization of the violation of this inequality over all states and measurements suggests that the optimal state is far from maximally entangled, while the best measurements are the same as conjectured best measurements for the maximally entangled state. For very large values of d the inequality seems to reach its minimal value given by the probability constraints. This gives numerical evidence for a tight quantum Bell inequality (or generalized Csirelson inequality) for the 2x2xinfinity scenario.