Haphazard Intentional Sampling in Survey and Allocation Studies on COVID-19 Prevalence and Vaccine Efficacy

Haphazard intentional sampling is a method developed by our research group for two main purposes: (i) sampling design, where the interest is to select small samples that accurately represent the general population regarding a set of covariates of interest; or (ii) experimental design, where the interest is to assemble treatment groups that are similar to each other regarding a set of covariates of interest. Rerandomization is a similar method proposed by K. Morgan and D. Rubin. Both methods intentionally select good samples but, in slightly different ways, also introduce some noise in the selection procedure aiming to obtain a decoupling effect that avoids systematic bias or other confounding effects. This paper compares the performance of the aforementioned methods and the standard randomization method in two benchmark problems concerning SARS-CoV-2 prevalence and vaccine efficacy. Numerical simulation studies show that haphazard intentional sampling can either reduce operating costs in up to 80% to achieve the same estimation errors yielded by the standard randomization method or, the other way around, reduce estimation errors in up to 80% using the same sample sizes.     

Theory of reality

Bell's theorem is used to guide the formulation of a unified theory of reality that incorporates the basic principles of relativistic quantum theory.Work supported by U. S. Energy Research and Development Administration.     

On twisted reality conditions

Letters in Mathematical Physics - We study the twisted reality condition of Brzeziński et al. (Math Phys Anal Geom 19(3):11, 2016), for spectral triples, in particular with respect to the...     

Heisenberg picture and reality

The idea is discussed according to which, in the Heisenberg picture, the operators correspond to the dynamic properties while the density matrix corresponds to our knowledge. A simple, soluble model is made use of in order to determine in what way this idea needs to be refined and what it then tells us about the relationship of reality and physics.     

Weak-measurement elements of reality

A brief review of the attempts to define elements of reality in the framework of quantum theory is presented. It is noted that most definitions of elements of reality have in common the feature to be a definite outcome of some measurement. Elements of reality are extended to pre- and post- selected systems and to measurements which fulfill certain criteria of weakness of the coupling. Some features of the newly introduced concepts are discussed.This research was supported in part by grant 614/65 of the Basic Research Foundation (administered by the Israel Academy of Sciences and Humanities.     

No return to classical reality

At a fundamental level, the classical picture of the world is dead, and has been dead now for almost a century. Pinning down exactly which quantum phenomena are responsible for this has proved to be a tricky and controversial question, but a lot of progress has been made in the past few decades. We now have a range of precise statements showing that whatever the ultimate laws of nature are, they cannot be classical. In this article, we review results on the fundamental phenomena of quantum theory that cannot be understood in classical terms. We proceed by first granting quite a broad notion of classicality, describe a range of quantum phenomena (such as randomness, discreteness, the indistinguishability of states, measurement-uncertainty, measurement-disturbance, complementarity, non-commutativity, interference, the no-cloning theorem and the collapse of the wave-packet) that do fall under its liberal scope, and then finally describe some aspects of quantum physics that can never admit a classical understanding – the intrinsically quantum mechanical aspects of nature. The most famous of these is Bell’s theorem, but we also review two more recent results in this area. Firstly, Hardy’s theorem shows that even a finite-dimensional quantum system must contain an infinite amount of information, and secondly, the Pusey–Barrett–Rudolph theorem shows that the wave function must be an objective property of an individual quantum system. Besides being of foundational interest, results of this sort now find surprising practical applications in areas such as quantum information science and the simulation of quantum systems.     

Leibniz rules and reality conditions

An analysis is made of reality conditions within the context of non-commutative geometry. We show that if a covariant derivative satisfies a given left Leibniz rule then a right Leibniz rule fixes the reality condition for the covariant derivative itself. We show also that the map which determines the right Leibniz rule must satisfy the braid equation if the extension of the covariant derivative to tensor products is to satisfy the reality condition. Received: 6 June 2000 / Published online: 9 August 2000     

Protective measurement and quantum reality

It is shown that from the expectation values of obervables, which can be measured for a single system using protective measurements, the linear structure, inner product, and observables in the Hilbert space can be reconstructed. A universal method of measuring the wave function of a single particle using its gravitational field is given. Protective measurement is generalized to the measurement of a degenerate state and to many particle systems. The question of whether the wave function is real is examined, and an argument of Einstein in favor of the ensemble interpretation of quantum theory is refuted.     

In search of quantum reality

Announcement

In search of quantum reality     

Quantum structures in macroscopic reality

We show that it is possible to construct macroscopic entities that entail a quantum logical structure. We do this by means of the introduction of a simple macroscopic entity and study its structure in terms of lattices and graphs, and show that the lattice is non-Boolean.     

Laws, symmetries and reality

It is argued that quantum mechanics follows naturally from the assumptions that there are no fundamental causal laws but only probabilities for physical processes that are constrained by symmetries, and reality is relational in the sense that an object is real only in relation to another object that it is interacting with. The first assumption makes it natural to include in the action for a gauge theory all terms that are allowed by the symmetries, enabling cancellation of infinities, with only the terms in the standard model observable at the energies at which we presently do our experiments. In this approach, it is also natural to have an infinite number of fundamental interactions.     

Cryobiology, wildlife conservation and reality

Conservation is about protecting and nurturing species so that they can survive, not only now but also into the future. Ideally this means protecting genetically diverse populations and not simply breeding a few individuals. In principle, cryobiology offers the means to help maintain genetic diversity by storing genetically important germplasm that could reinvigorate populations in the future. Unfortunately the technical problems associated with this ideal goal still provide a major barrier to the practical use of cryopreservation technology. Sometimes these are technical problems with the cryobiology, but lack of basic biological information about unusual species, coupled with difficulties in obtaining such information, means that progress will be possible with only a few species that are subject to intensive scrutiny. The opportunities nevertheless exist for cryobiologists and reproductive biologists to make useful and global contributions to species conservation. I argue here that there are often two mutually suspicious groups of biologists, who do not interact or even understand each others goals. If conservation biologists and biotechnologists were more prepared to join forces and share their expertise, there would be much improved prospects for achieving lasting success in the conservation of a small, but well targeted, number of threatened species.     

Recursive definition for elements of reality

Elements of reality are defined as in the work of Einstein, Podolsky, and Rosen. It is further assumed that the sum or product of twocommuting elements of reality also is an element of reality. An algebra contradiction ensues.Dedicated to Sir Karl Popper, on the occasion of his 90th birthday.     

Influences,histories, and reality

It is stressed that any theory of which it is claimed that it is compatible both with standard realism and with the experimental data is subject to severe constraints. One is that it must either incorporate superluminal influences or negate the free will of the experimentalist. The other one is that, in it. it is only at the price of accepting backward causality that a measurement can he interpreted as revealing the value the measured quantity had, just before, rather than just after, the measurement look place.Dedicated to Professor Max Jammer on the occasion of his 80th birthday.