Breaking of ensemble equivalence in networks

It is generally believed that, in the thermodynamic limit, the microcanonical description as a function of energy coincides with the canonical description as a function of temperature. However, various examples of systems for which the microcanonical and canonical ensembles are not equivalent have been identified. A complete theory of this intriguing phenomenon is still missing. Here we show that ensemble nonequivalence can manifest itself also in random graphs with topological constraints. We find that, while graphs with a given number of links are ensemble-equivalent, graphs with a given degree sequence are not. This result holds irrespective of whether the energy is nonadditive (as in unipartite graphs) or additive (as in bipartite graphs). In contrast with previous expectations, our results show that: (1) physically, nonequivalence can be induced by an extensive number of local constraints, and not necessarily by long-range interactions or nonadditivity; (2) mathematically, nonquivalence is determined by a different large-deviation behaviour of microcanonical and canonical probabilities for a single microstate, and not necessarily for almost all microstates. The latter criterion, which is entirely local, is not restricted to networks and holds in general.Comment: Final version accepted for publication on Physical Review Letter

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Minimum entropy production principle from a dynamical fluctuation law

The minimum entropy production principle provides an approximative variational characterization of close-to-equilibrium stationary states, both for macroscopic systems and for stochastic models. Analyzing the fluctuations of the empirical distribution of occupation times for a class of Markov processes, we identify the entropy production as the large deviation rate function, up to leading order when expanding around a detailed balance dynamics. In that way, the minimum entropy production principle is recognized as a consequence of the structure of dynamical fluctuations, and its approximate character gets an explanation. We also discuss the subtlety emerging when applying the principle to systems whose degrees of freedom change sign under kinematical time-reversal.Comment: 17 page

Fewer but better: Proportionate size of the group affects evaluation of transgressive leaders

A group may be badly affected if its leader transgresses important rules. Nonetheless, an emerging body of evidence suggests that in intergroup contexts, group members apply a double standard when judging ingroup leaders – They respond less punitively to transgressions by their leader than by non-leaders. In this article, two experiments investigated how proportionate ingroup size affects reactions to transgressive ingroup leaders. We demonstrate that ingroup leaders from larger, but not smaller, groups benefit from the double standard. The experiments testing the effects of two different types of transgressions (nepotistic favouritism and corruption, respectively) show that transgressive leaders from larger groups are evaluated more positively than both comparable non-leaders and leaders from smaller groups. In contrast, transgressive leaders from smaller groups are evaluated similarly to comparable transgressive non-leaders. Experiment 2 investigated a potential explanation for this phenomenon. Faced with a transgressive leader, members of a smaller group report greater embarrassment than do members of larger groups in relation to the leaders’ actions. Implications of these findings and directions for future research are discussed

Cumulative measure of correlation for multipartite quantum states

The present article proposes a measure of correlation for multiqubit mixed states. The measure is de?ned recursively, accumulating the correlation of the subspaces, making it simple to calculate without the use of regression. Unlike usual measures, the proposed measure is continuous additive and re?ects the dimensionality of the state space, allowing to compare states with di?erent dimensions. Examples show that the measure can signal critical points (CPs) in the analysis of Quantum Phase Transitions (QPTs) in Heisenberg models

Anthropometrics and ageing : impact of weight status on health

Background: Weight status is one of the factors that influence healthy ageing. It is often assessed with anthropometric measures such as body mass index (BMI) and waist circumference (WC), which indicate underweight or excess fat. Both are associated with adverse health outcomes in adults. The first paper of this thesis investigates whether this association is consistent over calendar time, to check for possible influences of improved healthcare procedures over time. In old age, this association is unclear. Using several anthropometric measures, the subsequent five papers examine the impact of weight status and development of weight status on coronary heart disease (CHD), mortality, and quality of life (QoL) among the elderly and during ageing. Methods: A meta-regression analysis of 31 international cohort studies (n=389,212) was used to estimate the multivariable adjusted relative risk (RR) of CHD for an increased BMI and whether the RR was different between calendar periods (i.e. studies that started before 1985 and studies that started after 1985) taking account of the age of the population. Associations of BMI and changes in eight anthropometric measures with all-cause and cause-specific mortality in old age were studied by means of multivariable Cox regression analyses using data from the Survey in Europe on Nutrition and the Elderly: a concerted action study including 70–77-year-olds (n=1,061–1,970). Moreover, the association of WC with all-cause and cause-specific mortality was studied by means of a meta-analysis of 29 international cohort studies including 65–74-year-olds (n=58,609). For an ageing population, we used the Doetinchem Cohort Study including 20–70-year-olds (n=3,408–4,135) and three to four repeated measures of weight and height over a period of 10 to 15 years. In this study population, we used a multivariable regression analysis to examine the association of changes in weight and long-term BMI patterns with QoL (measured by the SF-36 questionnaire). Results: After simultaneous inclusion of calendar period and age of the population in the model, the meta-regression analysis showed no difference in the RR of CHD in the association with a high BMI between calendar periods. However, a 10-year increment in population age lowered the 1.28 [95%confidence interval (CI): 1.22–1.34] RR of CHD for a five-BMI-unit increment by 29% (95%CI: -55 to -5). Among the elderly, BMI was associated with all-cause mortality, cardiovascular disease (CVD) mortality, and mortality due to causes other than CVD, cancer, and respiratory diseases (p2and above 30 kg/m2were the thresholds at which risks of cause-specific mortality were increased by 10%. WC was associated with all-cause, CVD, cancer, and respiratory disease mortality (p2) as the reference, we observed the highest all-cause and CVD mortality risk of approximately 2.0 for underweight (2; in combination with a small WC), and abdominal obesity within healthy ranges of BMI. Changes in BMI and WC were not associated with all-cause and CVD mortality, except for a decrease in WC ≥3.1 cm in the association with all-cause mortality (1.52, 95%CI: 1.01–2.31). Similarly, a decrease in weight ≥3.2 kg was associated with a 1.48 (95%CI: 0.99–2.20) increased all-cause mortality risk. Moreover, both a decrease and an increase in mid-upper arm circumference (MUAC) were associated with all-cause mortality and CVD mortality. A decrease of ≥1.6 cm and 0.6–1.6 cm in MUAC was associated with a 1.81 (95%CI: 1.17–2.79) and a 1.66 (95%CI: 1.10–2.49) all-cause mortality risk. An increase of ≥1.3 cm in MUAC was associated with a 1.52 (95%CI: 1.00–2.31) all-cause mortality risk and a 1.94 (95%CI: 1.00–3.75) CVD mortality risk. In an ageing population, we found that weight gain, especially weight gain of >6 kg, resulted in a decline in QoL. Weight loss (>2 kg) did not result in large changes in QoL. However, both weight gain and weight loss were adversely associated with changes in QoL as compared to a stable weight (changes ≤2 kg). From examination of long-term BMI patterns, the lowest QoL was observed for the ‘persistent obesity (≥30 kg/ m2)’ pattern. The BMI patterns, ‘persistent obesity’, ‘developing overweight (25.0–29.9 kg/m2’, ‘developing obesity’, and ‘switching between BMI categories’ scored 1.8–11.6 points (p2)’ pattern. The BMI pattern ‘persistent overweight’ generally did not differ from the ‘persistent healthy weight’ pattern. These findings were consistent among age groups. Conclusions: Although the risk of CHD in the association with BMI attenuated with increasing age, we found associations of BMI and WC with all-cause and cause-specific mortality among the elderly. These anthropometric measures can be used as single predictors of mortality for the elderly, but higher cut-off points for BMI and WC to indicate underweight and excess fat should be considered. Moreover, a combination of these two anthropometric measures can be recommended, as that would provide more information of the body composition than one anthropometric alone. With regard to assessing changes in body composition, MUAC might be recommended for the elderly. Furthermore, a stable weight is best for health maintenance among all ages, provided this stable weight does not fall within the extreme values of weight, i.e. too light or too heavy. In all, our results underscore the value of anthropometric measures in the management of weight and the importance of the maintenance of a stable weight during ageing.</p

Order of Grover's search algorithm with both total and local depolarizing channel error

Noise is an inherent part of quantum computation. Although there exists a fault-tolerant approach to quantum computing, this requires many computational resources. Hence, it is important to analyze how noise affects well-known algorithms. In this paper the effect of noise in Grover?s search algorithm is studied. The noise is modeled as both total depolarizing channel (TDCh), and local depolarizing channel (LDCh) in every qubit. An analysis of the order has been made analytically for the TDCh, and an approximation has been done for the LDCh