Estimating the grid of time-points for the piecewise exponential model

One of the greatest challenges related to the use of piecewise exponential models (PEMs) is to find an adequate grid of time-points needed in its construction. In general, the number of intervals in such a grid and the position of their endpoints are ad-hoc choices. We extend previous works by introducing a full Bayesian approach for the piecewise exponential model in which the grid of time-points (and, consequently, the endpoints and the number of intervals) is random. We estimate the failure rates using the proposed procedure and compare the results with the non-parametric piecewise exponential estimates. Estimates for the survival function using the most probable partition are compared with the Kaplan-Meier estimators (KMEs). A sensitivity analysis for the proposed model is provided considering different prior specifications for the failure rates and for the grid. We also evaluate the effect of different percentage of censoring observations in the estimates. An application to a real data set is also provided. We notice that the posteriors are strongly influenced by prior specifications, mainly for the failure rates parameters. Thus, the priors must be fairly built, say, really disclosing the expert prior opinion.     

Head Canting in Paintings: An Historical Study

Head canting, a lateral shift of the head toward the shoulder axis, was examined in 1498 figures in the complete works of 11 painters from the XIV to the XX century: Martini, van Eyck Hubert and Jan, Holbein, Carracci, Velazquez, Rembrandt, Degas, Cèzanne, Klimt, and Modigliani. All figures (up to 9 in any one painting) that were not in complete profile and that were not depicted bowing or shifting their bodies were selected for analysis. Our analysis found a higher frequency (49%) of head canting in paintings than previously reported in naturalistic settings. Head canting was significantly higher in female figures than male figures. If a figure's head was facing laterally, head canting was more likely to be to the contralateral side. Head canting was lower in older figures than in children, youths, and adults. The highest level of head canting was seen in religious and mythological figures. Head canting was lower in figures of artists and professionals and virtually absent in depictions of nobles. Figures in pose were depicted with less head canting than those in natural settings. Head canting was lower in figures gazing toward the observer. Single-figure portraits head canted less than subjects in multiple-figure paintings. Author analysis revealed that head canting was pronounced in painters of religious subjects and in modern painters, whereas its degree was reduced in official portrait painters. These results are discussed in terms of dominance theory.     

An Optimization‐Based Framework for the Identification of Vulnerabilities in Electric Power Grids Exposed to Natural Hazards

This article proposes a novel mathematical optimization framework for the identification of the vulnerabilities of electric power infrastructure systems (which is a paramount example of critical infrastructure) due to natural hazards. In this framework, the potential impacts of a specific natural hazard on an infrastructure are first evaluated in terms of failure and recovery probabilities of system components. Then, these are fed into a bi‐level attacker–defender interdiction model to determine the critical components whose failures lead to the largest system functionality loss. The proposed framework bridges the gap between the difficulties of accurately predicting the hazard information in classical probability‐based analyses and the over conservatism of the pure attacker–defender interdiction models. Mathematically, the proposed model configures a bi‐level max‐min mixed integer linear programming (MILP) that is challenging to solve. For its solution, the problem is casted into an equivalent one‐level MILP that can be solved by efficient global solvers. The approach is applied to a case study concerning the vulnerability identification of the georeferenced RTS24 test system under simulated wind storms. The numerical results demonstrate the effectiveness of the proposed framework for identifying critical locations under multiple hazard events and, thus, for providing a useful tool to help decisionmakers in making more‐informed prehazard preparation decisions.     

Assessing the Performance of a Classification‐Based Vulnerability Analysis Model

In this article, a classification model based on the majority rule sorting (MR‐Sort) method is employed to evaluate the vulnerability of safety‐critical systems with respect to malevolent intentional acts. The model is built on the basis of a (limited‐size) set of data representing (a priori known) vulnerability classification examples. The empirical construction of the classification model introduces a source of uncertainty into the vulnerability analysis process: a quantitative assessment of the performance of the classification model (in terms of accuracy and confidence in the assignments) is thus in order. Three different app oaches are here considered to this aim: (i) a model–retrieval‐based approach, (ii) the bootstrap method, and (iii) the leave‐one‐out cross‐validation technique. The analyses are presented with reference to an exemplificative case study involving the vulnerability assessment of nuclear power plants.     

Optimization of Cascade‐Resilient Electrical Infrastructures and its Validation by Power Flow Modeling

Large‐scale outages on real‐world critical infrastructures, although infrequent, are increasingly disastrous to our society. In this article, we are primarily concerned with power transmission networks and we consider the problem of allocation of generation to distributors by rewiring links under the objectives of maximizing network resilience to cascading failure and minimizing investment costs. The combinatorial multiobjective optimization is carried out by a nondominated sorting binary differential evolution (NSBDE) algorithm. For each generators–distributors connection pattern considered in the NSBDE search, a computationally cheap, topological model of failure cascading in a complex network (named the Motter‐Lai [ML] model) is used to simulate and quantify network resilience to cascading failures initiated by targeted attacks. The results on the 400 kV French power transmission network case study show that the proposed method allows us to identify optimal patterns of generators–distributors connection that improve cascading resilience at an acceptable cost. To verify the realistic character of the results obtained by the NSBDE with the embedded ML topological model, a more realistic but also more computationally expensive model of cascading failures is adopted, based on optimal power flow (namely, the ORNL‐Pserc‐Alaska) model). The consistent results between the two models provide impetus for the use of topological, complex network theory models for analysis and optimization of large infrastructures against cascading failure with the advantages of simplicity, scalability, and low computational cost.     

Stock Exchange Markets in Hong Kong: Structure and Main Problems

With reference to a previous analysis of the characteristics and morphology of the stock markets of Mainland China (Shanghai and Shenzhen), the study aims at completing the overview of the main Asian stock exchanges (excluding Japan), by examining the Hong Kong stock exchange. After a review of the main literature, the paper considers the historical-legislative process that has defined the current organizational-functional structure of the market. The analysis also shows the main statistical data of the market (number of listed companies, trading volume, performance of the main indices, etc.). For every considered phenomenon, the study suggests plausible explanations. The paper also provides further considerations about the main issues of the market, through a comparison with the stock exchanges of Mainland China.     

Italian Social Enterprises at the Crossroads: Their Role in the Evolution of the Welfare State

This paper investigates the relationship between the emergence of social enterprises (SEs) and the historical development of the Italian welfare state. Our research offers a comprehensive overview of the internal and external influences that shaped the constitutive relations between the welfare state and SEs. A qualitative methodology based on semi-structured interviews and focus groups has been adopted. This study suggests that two interconnected dynamics—the emergence of new social needs being answered by private organisations and the increased prominence of third sector actors during the privatisation of the welfare state—shaped the co-evolution of the welfare state and SEs in Italy. The study also suggests that the emergence and evolution of Social Enterprises in the years leading up to 2001 was mainly a bottom-up phenomena stemming from the actions of citizens setting up private organisations (often cooperatives) to answer to social problems created by new social needs and the structural reform of the welfare state. After 2001 especially with the new law on SEs in 2016, the evolution of SEs seems to have been increasingly influenced by the surrounding ecosystem of actors and supranational policy discourses rather than SEs themselves.     

Tests for noninferiority trials with binomial endpoints: A guide to modern and quasi‐exact methods for biomedical researchers

Applied statisticians and pharmaceutical researchers are frequently involved in the design and analysis of clinical trials where at least one of the outcomes is binary. Treatments are judged by the probability of a positive binary response. A typical example is the noninferiority trial, where it is tested whether a new experimental treatment is practically not inferior to an active comparator with a prespecified margin δ. Except for the special case of δ = 0, no exact conditional test is available although approximate conditional methods (also called second‐order methods) can be applied. However, in some situations, the approximation can be poor and the logical argument for approximate conditioning is not compelling. The alternative is to consider an unconditional approach. Standard methods like the pooled z‐test are already unconditional although approximate. In this article, we review and illustrate unconditional methods with a heavy emphasis on modern methods that can deliver exact, or near exact, results. For noninferiority trials based on either rate difference or rate ratio, our recommendation is to use the so‐called E‐procedure, based on either the score or likelihood ratio statistic. This test is effectively exact, computationally efficient, and respects monotonicity constraints in practice. We support our assertions with a numerical study, and we illustrate the concepts developed in theory with a clinical example in pulmonary oncology; R code to conduct all these analyses is available from the authors.