Recent work by Wan and McLean has shown that all quantum measurements may be reduced to local position measurements. Using an array of particle detectors as the measuring apparatus we show how a model employing superselection rules and unitary evolution leads to a single detector triggering in each act of measurement. We also present an explicit model of particle detection as a unitary ionization process producing a single ion in the detector, subsequent amplification of which to the visible can be (...) described adequately in classical terms. (shrink)

Traditionally, there has been a clear distinction between classical systems and quantum systems, particularly in the mathematical theories used to describe them. In our recent work on macroscopic quantum systems, this distinction has become blurred, making a unified mathematical formulation desirable, so as to show up both the similarities and the fundamental differences between quantum and classical systems. This paper serves this purpose, with explicit formulations and a number of examples in the form of superconducting circuit systems. We introduce three (...) classes of physical systems with finite degrees of freedom: classical, standard quantum, and mixed quantum, and present a unified Hilbert space treatment of all three types of system. We consider the classical/quantum divide and the relationship between standard quantum and mixed quantum systems, illustrating the latter with a derivation of a superselection rule in superconducting systems. (shrink)

We investigate the complexity of isomorphisms of computable structures on cones in the Turing degrees. We show that, on a cone, every structure has a strong degree of categoricity, and that degree of categoricity is${\rm{\Delta }}_\alpha ^0 $-complete for someα. To prove this, we extend Montalbán’sη-system framework to deal with limit ordinals in a more general way. We also show that, for any fixed computable structure, there is an ordinalαand a cone in the Turing degrees such that the exact complexity (...) of computing an isomorphism between the given structure and another copy${\cal B}$in the cone is a c.e. degree in${\rm{\Delta }}_\alpha ^0\left$. In each of our theorems the cone in question is clearly described in the beginning of the proof, so it is easy to see how the theorems can be viewed as general theorems with certain effectiveness conditions. (shrink)

At Moore’s time, the main-stream ethical theory is the doctrine that pleasure alone is good as an end as held by the hedonistic utilitarianism. Moore, however, asserts that good, not composed of any parts, is a simple notion and indefinable, and naturalistic ethical theories, in particular hedonistic utilitarianism, interpret intrinsic good as a property of a single natural object---pleasure, which is also the sole end of life, thus violates naturalistic fallacy. Moore seems to believe that there exist things other than (...) pleasure that are also intrinsically good and has searched for them. But Moore has not clearly stated what these things are, nor has he given any justification for why they are intrinsically good. This paper discusses Moore’s arguments and difficulties of utilitarianism. With the subjectivistic utilitarian theory of value, Unified Utilitarian Theory (UTT) discards the classification of value into intrinsic and instrumental and proves to be exempt of all theexisting difficulties with utilitarianism related to pleasure, including naturalistic fallacy, vagueness of pleasure and sole end of life, double counting, etc. (shrink)

The $\Omega $ numbers—the halting probabilities of universal prefix-free machines—are known to be exactly the Martin-Löf random left-c.e. reals. We show that one cannot uniformly produce, from a Martin-Löf random left-c.e. real $\alpha $, a universal prefix-free machine U whose halting probability is $\alpha $. We also answer a question of Barmpalias and Lewis-Pye by showing that given a left-c.e. real $\alpha $, one cannot uniformly produce a left-c.e. real $\beta $ such that $\alpha - \beta $ is neither left-c.e. (...) nor right-c.e. (shrink)

In a recent article JRS , 68 f. Nicholas Horsfall sought to demonstrate that Corythus, which Virgil makes the original home of Dardanus , should be identified with Tarquinii, some 50 miles north-west of Rome, on the coast of Etruria, rather than with Cortona, roughly twice as far away, to the north, and inland. In doing so he expressed surprise that the Virgilian evidence should have been completely ignored by previous writers on the subject : and, using the Aeneid as (...) the main source on which his own argument was based, he supported his conclusion with a careful examination of several other aspects of the problem. (shrink)

In a recent article JRS, 68 f. Nicholas Horsfall sought to demonstrate that Corythus, which Virgil makes the original home of Dardanus, should be identified with Tarquinii, some 50 miles north-west of Rome, on the coast of Etruria, rather than with Cortona, roughly twice as far away, to the north, and inland. In doing so he expressed surprise that the Virgilian evidence should have been completely ignored by previous writers on the subject : and, using the Aeneid as the main (...) source on which his own argument was based, he supported his conclusion with a careful examination of several other aspects of the problem. (shrink)

The objective of this study is to evaluate auditors’ perceived responsibility for fraud detection. Auditors play a critical role in managing fraud risk within organizations. Although professional standards and guidance prescribe responsibility in the area, little is known about auditors’ sense of responsibility for fraud detection, the factors affecting perceived responsibility, and how responsibility affects auditor performance. We use the triangle model of responsibility as a theoretical basis for examining responsibility and the effects of accountability, fraud type, and auditor type (...) on auditors’ perceived fraud detection responsibility. We also test how perceived responsibility affects auditor brainstorming performance given the importance of brainstorming in audits. A sample of 878 auditors participated in an experiment with accountability pressure and fraud type manipulated randomly between subjects. As predicted, accountable auditors report higher detection responsibility than anonymous auditors. We also find a significant fraud type × auditor type interaction with external auditors perceiving the most detection responsibility for financial statement fraud, while internal auditors report similar detection responsibility for all fraud types. Analysis of the triangle model’s formative links reveals that professional obligation and personal control are significantly related to responsibility, while task clarity is not. Finally, the results indicate that perceived responsibility positively affects the number of detection procedures brainstormed and partially mediates the significant accountability–brainstorming relation. (shrink)

There is a Turing computable embedding $\Phi $ of directed graphs $\mathcal {A}$ in undirected graphs. Moreover, there is a fixed tuple of formulas that give a uniform effective interpretation; i.e., for all directed graphs $\mathcal {A}$, these formulas interpret $\mathcal {A}$ in $\Phi $. It follows that $\mathcal {A}$ is Medvedev reducible to $\Phi $ uniformly; i.e., $\mathcal {A}\leq _s\Phi $ with a fixed Turing operator that serves for all $\mathcal {A}$. We observe that there is a graph G (...) that is not Medvedev reducible to any linear ordering. Hence, G is not effectively interpreted in any linear ordering. Similarly, there is a graph that is not interpreted in any linear ordering using computable $\Sigma _2$ formulas. Any graph can be interpreted in a linear ordering using computable $\Sigma _3$ formulas. Friedman and Stanley [4] gave a Turing computable embedding L of directed graphs in linear orderings. We show that there is no fixed tuple of $L_{\omega _1\omega }$ -formulas that, for all G, interpret the input graph G in the output linear ordering $L$. Harrison-Trainor and Montalbán [7] have also shown this, by a quite different proof. (shrink)

§ 1. The dates for Peisistratus’ reigns and exiles in the Athenaion Politeia, as given in the papyrus, which is the sole authority for the text, are as follows.

Ductin is the highest conserved membrane protein yet found in eukaryotes. It is multifunctional, being the subunit c or proteolipid component of the vacuolar H+‐ATPase and at the same time the protein component of a form of gap junction in metazoan animals. Analysis of its structure shows it to be a tandem repeat of two 8‐kDa domains derived from the subunit c of the F0 proton pore from the F1F0 ATPase. Each domain contains two transmembrane α‐helices, which together may form (...) a four‐helix bundle. In both the V‐ATPase and gap junction channel, ductin is probably arranged as a hexamer of subunits forming a central channel of gap junction‐like proportions. The two functions appear to be seggregated by ductin having two orientations in the bilayer. Ductin is also the major component of the mediatophore, a protein complex which may aid in the release of neurotransmitters across the pre‐synaptic membrane. It is also a target for a class of poorly understood viral polypeptides. These polypeptides are small and highly hydrophobic and some have oncogenic activity. Ductin thus appears to be at the crossroads of a number of biological processes. (shrink)

The encounter between Socrates and Thrasymachus in Republic I is notoriously baffling. Most of what is said seems straightforward, and the issues at stake are ones of common concern, but the argument remains elusive. The purpose of this paper is to investigate the nature and grounds of this elusiveness, and to show that some of it can be dispelled by a sufficiently free-ranging exegesis that bears in mind the general character of Plato’s writing.