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Spekkens' toy model is a non-contextual hidden variable model with an epistemic restriction, a constraint on what an observer can know about reality. The aim of the model, developed for continuous and discrete prime degrees of freedom, is to advocate the epistemic view of quantum theory, where quantum states are states of incomplete knowledge about a deeper underlying reality. Many aspects of quantum mechanics and protocols from quantum information can be reproduced in the model. In spite of its significance, a number of aspects of Spekkens' model remained incomplete. Formal rules for the update of states after measurement had not been written down, and the theory had only been constructed for prime-dimensional and infinite dimensional systems. In this work, we remedy this, by deriving measurement update rules and extending the framework to derive models in all dimensions, both prime and non-prime. Stabiliser quantum mechanics (SQM) is a sub-theory of quantum mechanics with restricted states, transformations and measurements. First derived for the purpose of constructing error correcting codes, it now plays a role in many areas of quantum information theory. Previously, it had been shown that Spekkens' model was operationally equivalent to SQM in the case of odd prime dimensions. Here, exploiting known results on Wigner functions, we extend this to show that Spekkens' model is equivalent to SQM in all odd dimensions, prime and non-prime. This equivalence provides new technical tools for the study of technically difficult compound-dimensional SQM.

Dynamic models have long been a common tool to support management of ecological and economic systems and played a prominent role in the early days of resilience research. Model applications have largely focused on policy assessment, the development of optimal management strategies, or analysis of system stability. However, modeling can serve many other purposes such as understanding system responses that emerge from complex interactions of system components, supporting participatory processes, and analyzing consequences of human behavioral complexity. The diversity of purposes, types, and applications of models offers great potential for social-ecological systems (SESs) research, but has created much confusion because modeling approaches originate from different disciplines, are based on different assumptions, focus on different levels of analysis, and use different analytical methods. This diversity makes it difficult to identify which approach is most suitable for addressing a specific question. Here, our aims are: (1) to introduce the most common types of dynamic models used in SESs research and related fields, and (2) to align these models with SESs research aims to support the selection and communication of the most suitable approach for a given study. To this end, we organize modeling approaches into a reference scheme called “modelling for social-ecological systems research” (ModSES) along two dimensions: the degree of realism and the degree of knowledge integration. These two dimensions capture key challenges of SESs research related to the need to account for context dependence and the intertwined nature of SESs as systems of humans embedded in nature across multiple scales, as well as to acknowledge different problem framings, understandings, interests, and values. We highlight the need to be aware of the potentials, limitations, and conceptual backgrounds underlying the different approaches. Critical engagement with modeling for different aims of SESs research can contribute to developing integrative understanding and action toward enhanced resilience and sustainability.

The description of unitary evolution using non-Hermitian but ‘hermitizable’ Hamiltonians H is feasible via an ad hoc metric Θ = Θ(H) and a (non-unique) amendment 〈ψ₁|ψ₂⟩ → 〈ψ₁|Θ|ψ₂⟩ of the inner product in Hilbert space. Via a proper fine-tuning of Θ(H) this opens the possibility of reaching the boundaries of stability (i.e. exceptional points) in many quantum systems sampled here by the fairly realistic Bose–Hubbard (BH) and discrete anharmonic oscillator (AO) models. In such a setting, it is conjectured that the EP singularity can play the role of a quantum phase-transition interface between different dynamical regimes. Three alternative ‘AO ↔ BH’ implementations of such an EP-mediated dynamical transmutation scenario are proposed and shown, at an arbitrary finite Hilbert-space dimension N, exact and non-numerical.

We investigate the dynamics of two quantum mechanical oscillator system–bath toy models obtained by truncating to zero spatial dimensions linearized gravity coupled to a massive scalar field and scalar quantum electrodynamics (QED). The scalar-gravity toy model maps onto the phase damped oscillator, while the scalar QED toy model approximately maps onto an oscillator system subject to two-photon damping. The toy models provide potentially useful insights into solving for open system quantum dynamics relevant to the full scalar QED and weak gravitational field systems, in particular operational probes of the decoherence for initial scalar field system superposition states.

Before interacting with the magnetosphere, an interplanetary shock travels through the magnetosheath where its speed and shape are modified. Previous studies have reported widely different answers to the question of the speed of an interplanetary shock in the magnetosheath. Observational studies generally answer this question “macroscopically”, by measuring the time delay between detections of the interplanetary shock at two or more locations and inferring its average speed. In this letter, we instead propose a local predictive model for the velocity and show that paradoxical results from previous authors arise naturally from their use of different detection methods. Our model can be used to predict the propagation of an interplanetary shock in the magnetosheath with a simple laptop, yet provides results which are in broad agreement with much heavier magnetohydrodynamics and hybrid particle‐in‐cell simulations.

Online chatter is important because it is spontaneous, passionate, information rich, granular, and live. Thus, it can forewarn and be diagnostic about potential problems with automobile models, known as nameplates. The authors define \"perverse halo\" (or negative spillover) as the phenomenon whereby negative chatter about one nameplate increases negative chatter for another nameplate. The authors test the existence of such a perverse halo for 48 nameplates from four different brands during a series of automobile recalls. The analysis is by individual and panel vector autoregressive models. The study finds that perverse halo is extensive. It occurs for nameplates within the same brand across segments and across brands within segments. It is strongest between brands of the same country. Perverse halo is asymmetric, being stronger from a dominant brand to a less dominant brand than vice versa. Apology advertising about recalls has harmful effects on both the recalled brand and its rivals. Furthermore, these halo effects affect downstream performance metrics such as sales and stock market performance. Online chatter amplifies the negative effect of recalls on downstream sales by about 4.5 times.

Thus far, we know much more about the significant outcomes of perceived ethical leadership than we do about its antecedents. In this study, we focus on multiple types of ethical role models as antecedents of perceived ethical leadership. According to social learning theory, role models facilitate the acquisition of moral and other types of behavior. Yet, we do not know whether having had ethical role models influences follower perceptions of one's ethical leadership and, if so, what kinds of role models are important. We conducted a field study, surveying supervisors and their subordinates to examine the relationship between three types of ethical role models and ethical leadership: the leader's childhood role models, career mentors, and top managers. We found that having had an ethical role model during the leader's career was positively related to subordinate-rated ethical leadership. As expected, this effect was moderated by leader age, such that the relationship between career mentoring and ethical leadership was stronger for older leaders. Leader age also moderated the relationship between childhood models and ethical leadership ratings, such that having had childhood ethical role models was more strongly and positively related to ethical leadership for younger leaders. We found no effect for top management ethical role models. Implications for research and practice are discussed.

The authors used child fixed effects models to estimate the effects of parental divorce and death on a variety of outcomes using 2 large national data sets: (a) the Early Childhood Longitudinal Study, Kindergarten Cohort (kindergarten through the 5th grade) and (b) the National Educational Longitudinal Study (8th grade to the senior year of high school). In both data sets, divorce and death were associated with multiple negative outcomes among children. Although evidence for a causal effect of divorce on children was reasonably strong, effect sizes were small in magnitude. A second analysis revealed a substantial degree of variability in children's outcomes following parental divorce, with some children declining, others improving, and most not changing at all. The estimated effects of divorce appeared to be strongest among children with the highest propensity to experience parental divorce.

Previous research on the association between parenthood and life satisfaction has shown that parents of minor children are not more satisfied with their lives than childless people. This study addressed the question of why children do not enhance their parents' life satisfaction. A major objective of this study was to determine whether and to what extent the costs of raising children act as suppressors of life satisfaction. The empirical analysis applied fixed-effects models and used data from the German Socio-Economic Panel (1994–2010, N = 16,021). The 3 primary findings of this study were that (a) parenthood by itself has substantial and enduring positive effects on life satisfaction; (b) these positive effects are offset by financial and time costs of parenthood; and (c) the impact of these costs varies considerably with family factors, such as the age and number of children, marital status, and the parents' employment arrangements.

Children often \"overimitate,\" comprehensively copying others' actions despite manifest perceptual cues to their causal ineffectuality. The inflexibility of this behavior renders its adaptive significance difficult to apprehend. This study explored the boundaries of overimitation in 3- to 6-year-old children of three distinct cultures: Westernized, urban Australians (N = 64 in Experiment 1; N = 19 in Experiment 2) and remote communities of South African Bushmen (N = 64) and Australian Aborigines (N = 19). Children overimitated at high frequency in all communities and generalized what they had learned about techniques and object affordances from one object to another. Overimitation thus provides a powerful means of acquiring and flexibly deploying cultural knowledge. The potency of such social learning was also documented compared to opportunities for exploration and practice.