A comparison of one-sided variables acceptance sampling methods when measurements are subject to error

One-sided variables acceptance sampling plans such as the one presented in Schilling1 assume that a quality characteristic of interest, X, has a normal distribution and that measurements are exact. However, when measurements contain error and standard plans are used, the probability of accepting a lot for a fixed population proportion nonconforming varies widely depending on the population and measurement error parameter values. In this dissertation we consider methods for variables acceptance sampling in the presence of measurement error and evaluate their performance under lower bound constraints on the population variance;In the late 1950\u27s, David, Fay and Walsh2 suggested a one-sided variables acceptance sampling method (David) for problems where the measurement error variance is known. A competitor to this plan (MLE) is one based on plugging maximum likelihood estimates for the parameters of the population into the normal cumulative distribution function and determining lot disposal based the on estimated proportion nonconforming. With great improvements in the speed of computers, other more computationally intensive plans can be compared with the earlier methods. This dissertation develops two other variables acceptance sampling plans (LRT1 and LRT2) where the accept/reject decision is based on the value of a likelihood ratio statistic;For a fixed sample size, each of the four plans is developed to guarantee a maximum producer\u27s risk no larger than a pre-specified upper bound under the restriction that the ratio of population to measurement error variance is bounded below. The best plan gives the smallest maximum consumer\u27s risk;The major findings are that the LRT2 method generally yields smaller maximum consumer risks than the other three methods. (In some special cases, the David method yields smaller values.) This result is true across a variety of different combinations of plan parameters;Additionally, variations on the David and MLE methods are developed and compared for the situation where the measurement error variance is unknown, but can be estimated. Plans are developed for two different approaches to estimating the error variance. It is not clear which method is more useful because neither method out-performs the other in all situations. ftn1Schilling, Edward G. (1982) Acceptance Sampling in Quality Control, Marcel Dekker, Inc., New York. 2David, H. T., E. A. Fay and J. E. Walsh. (1959) Acceptance Inspection by Variables when Measurements are Subject to Error. Annals of the Institute of Statistical Mathematics, 10: 107-129

Adequacy of the Dicke model in cavity QED: a counter-"no-go" statement

The long-standing debate whether the phase transition in the Dicke model can be realized with dipoles in electromagnetic fields is yet an unsettled one. The well-known statement often referred to as the "no-go theorem", asserts that the so-called A-square term, just in the vicinity of the critical point, becomes relevant enough to prevent the system from undergoing a phase transition. At variance with this common belief, in this paper we prove that the Dicke model does give a consistent description of the interaction of light field with the internal excitation of atoms, but in the dipole gauge of quantum electrodynamics. The phase transition cannot be excluded by principle and a spontaneous transverse-electric mean field may appear. We point out that the single-mode approximation is crucial: the proper treatment has to be based on cavity QED, wherefore we present a systematic derivation of the dipole gauge inside a perfect Fabry-P\'erot cavity from first principles. Besides the impact on the debate around the Dicke phase transition, such a cleanup of the theoretical ground of cavity QED is important because currently there are many emerging experimental approaches to reach strong or even ultrastrong coupling between dipoles and photons, which demand a correct treatment of the Dicke model parameters

Chemotactile social recognition in the blue-ringed octopus, Hapalochlaena maculosa

Social recognition is the ability of individuals in a species to differentiate among conspecifics based on their identity or biologically meaningful demographic. Despite evidence that they have sophisticated brains, complex behavioural repertoires, and acute sensory processing, surprisingly little is known about mechanisms aiding social recognition in cephalopods. This class's unique chemotactile sense by the ventral arm surfaces gathers considerable information used in predator-prey interactions. Does it also help mediate social interactions? This study utilised 366 h of focal animal observations to assess the likelihood of Hapalochlaena maculosa, a nocturnal species, to retreat after physically contacting conspecifics based on their sex, familiarity and mating history. Females retreated from both sexes equally, while males were more likely to retreat after contacting female conspecifics. Most conspicuously, males were significantly more likely to retreat after contacting females with which they had already mated. These findings provide the first evidence for chemotactile sex discrimination and mate recognition within cephalopods, and supplement previous observations that male H. maculosa do not appear to detect the sex of conspecifics from a distance. The decision to retreat from or stay with an individual based on their sex or mating history, only after physical contact, emphasises the importance of chemotactile behaviour in octopus sensory ecology and behaviour. Furthermore, male octopuses have limited spermatophore production, and the use of chemotactile social recognition observed here may highlight the importance of reproduction, specifically sperm allocation and avoidance of sexual cannibalism, on the evolution of sensory ecology and cognition within this lineage

Jamming, relaxation, and memory in a structureless glass former

Real structural glasses form through various out-of-equilibrium processes, including temperature quenches, rapid compression, shear, and aging. Each of these processes should be formally understandable within the recently formulated dynamical mean-field theory of glasses, but many of the numerical tools needed to solve the relevant equations for sufficiently long timescales do not yet exist. Numerical simulations of structureless (and therefore mean-field-like) model glass formers can nevertheless aid searching for and understanding such solutions, thanks to their ability to disentangle structural from dimensional effects. We here study the infinite-range Mari-Kurchan model under simple non-equilibrium processes and compare the results with those from the random Lorentz gas [J. Phys. A: Math. Theor. 55 334001, (2022)], which are both mean-field-like and become formally equivalent in the limit of infinite spatial dimensions. Of particular interest are jamming from crunching and under instantaneous temperature quenches. The study allows for an algorithmic understanding of the jamming density and of its approach to the infinite-dimensional limit. The results provide important insight into the eventual solution of the dynamical mean-field theory, including onsets and anomalous relaxation, as well as into the various algorithmic schemes for jamming.Comment: 13 pages, 6 figure

Local stability of spheres via the convex hull and the radical Voronoi diagram

Jamming is an emergent phenomenon wherein the local stability of individual particles percolates to form a globally rigid structure. However, the onset of rigidity does not imply that every particle becomes rigid, and indeed some remain locally unstable. These particles, if they become unmoored from their neighbors, are called \textit{rattlers}, and their identification is critical to understanding the rigid backbone of a packing, as these particles cannot bear stress. The accurate identification of rattlers, however, can be a time-consuming process, and the currently accepted method lacks a simple geometric interpretation. In this manuscript, we propose two simpler classifications of rattlers based on the convex hull of contacting neighbors and the maximum inscribed sphere of the radical Voronoi cell, each of which provides geometric insight into the source of their instability. Furthermore, the convex hull formulation can be generalized to explore stability in hyperstatic soft sphere packings, spring networks, non-spherical packings, and mean-field non-central-force potentials.Comment: 9 pages, 9 figure

Tactical tentacles: new insights on the processes of sexual selection among the Cephalopoda

The cephalopods (Mollusca: Cephalopoda) are an exceptional class among the invertebrates, characterised by the advanced development of their conditional learning abilities, long-term memories, capacity for rapid colour change and extremely adaptable hydrostatic skeletons. These traits enable cephalopods to occupy diverse marine ecological niches, become successful predators, employ sophisticated predator avoidance behaviours and have complex intraspecific interactions. Where studied, observations of cephalopod mating systems have revealed detailed insights to the life histories and behavioural ecologies of these animals. The reproductive biology of cephalopods is typified by high levels of both male and female promiscuity, alternative mating tactics, long-term sperm storage prior to spawning, and the capacity for intricate visual displays and/or use of a distinct sensory ecology. This review summarises the current understanding of cephalopod reproductive biology, and where investigated, how both pre-copulatory behaviours and post-copulatory fertilisation patterns can influence the processes of sexual selection. Overall, it is concluded that sperm competition and possibly cryptic female choice are likely to be critical determinants of which individuals' alleles get transferred to subsequent generations in cephalopod mating systems. Additionally, it is emphasised that the optimisation of offspring quality and/or fertilisation bias to genetically compatible males are necessary drivers for the proliferation of polyandry observed among cephalopods, and potential methods for testing these hypotheses are proposed within the conclusion of this review. Further gaps within the current knowledge of how sexual selection operates in this group are also highlighted, in the hopes of prompting new directions for research of the distinctive mating systems in this unique lineage