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Purpose Eating disorder (ED) symptoms are common psychopathological manifestations, with significant impacts on quality of life, particularly among female adolescents. Despite the high mortality rates of full-blown EDs (5–20%), the mechanisms underlying vulnerability remain poorly understood. Traditional approaches primarily examine probabilistic sufficient factors (i.e., regression coefficients); however, these models fail to accurately predict ED symptoms onset in non-clinical populations. This study shifts focus to necessary conditions—factors whose absence precludes the development of the outcome—using necessary condition analysis (NCA), a novel methodological approach. Methods We examined whether lower self-esteem is a necessary condition for restriction-oriented cognitions ( Drive for Thinness ), dissatisfaction about one's body ( Body Dissatisfaction ), and dysregulated eating behaviors ( Bulimia ) in female adolescents ( N  = 84; mean age = 15.74 ± 1.30 years) after 12 months. Results Results preliminarily indicated that lower self-esteem emerged as a necessary condition for restriction-oriented cognitions ( d  = 0.25,  p  < 0.003) and for dissatisfaction with the body ( d  = 0.22,  p  < 0.003). However, it was not a necessary condition for dysregulated eating behavior. Conclusions These findings highlight the potential of NCA to refining theoretical models and clinical interventions by distinguishing necessary conditions from sufficient factors. The study underscores the importance of integrating necessity logic into ED research, offering insights for targeted prevention and personalized care. Level of evidence : Level III: Evidence obtained from well-designed cohort or case–control analytic studies.

Main problem of detonation theory, self-sustained regimes finding, is solved for liquid aerosols. Combustion modelling is performed at two scale levels, where the irreversible processes such as aerosol atomization, daughter droplets' evaporation and chemical energy release kinetics are represented at the lower scale. Instability of flow in conjugated boundary layers at drop surface is adopted as mechanism of aerosol atomization. Vapour mixing with oxidizer forms combustible moles, whose chemical induction times are calculated individually, so that the moles are stack-ordered. At the upper scale, equations of overall motion of two-velocity, two-temperature, five-component reacting medium are composed. Two key aspects of the main problem are considered: (i) detonation wave structure in stationary zone is calculated and analysed and (ii) self-sustained regime velocities are determined. The first reveals the existence of two mixture burning modes: explosive kinetic and smooth diffusive, which are separated by conclusive micro-explosion. The second shows the existence of only two front velocity values in aerosol system, at which the interphase processes provide fulfilment of Zeldovich's necessary condition. Explanation is found for incomplete burnout regime: it stands on specific balance between the rate ratio of physical-to-chemical processes, which is reached at such front velocity, when sonic state is attained exactly after the conclusive micro-explosion.

A statistical functional, such as the mean or the median, is called elicitable if there is a scoring function or loss function such that the correct forecast of the functional is the unique minimizer of the expected score. Such scoring functions are called strictly consistent for the functional. The elicitability of a functional opens the possibility to compare competing forecasts and to rank them in terms of their realized scores. In this paper, we explore the notion of elicitability for multi-dimensional functionals and give both necessary and sufficient conditions for strictly consistent scoring functions. We cover the case of functionals with elicitable components, but we also show that one-dimensional functionals that are not elicitable can be a component of a higher order elicitable functional. In the case of the variance, this is a known result. However, an important result of this paper is that spectral risk measures with a spectral measure with finite support are jointly elicitable if one adds the \"correct\" quantiles. A direct consequence of applied interest is that the pair (Value at Risk, Expected Shortfall) is jointly elicitable under mild conditions that are usually fulfilled in risk management applications.

PurposeThis research introduces the combined use of partial least squares–structural equation modeling (PLS-SEM) and necessary condition analysis (NCA) that enables researchers to explore and validate hypotheses following a sufficiency logic, as well as hypotheses drawing on a necessity logic. The authors’ objective is to encourage the practice of combining PLS-SEM and NCA as complementary views of causality and data analysis.Design/methodology/approachThe authors present guidelines describing how to combine PLS-SEM and NCA. These relate to the specification of the research objective and the theoretical background, the preparation and evaluation of the data set, running the analyses, the evaluation of measurements, the evaluation of the (structural) model and relationships and the interpretation of findings. In addition, the authors present an empirical illustration in the field of technology acceptance.FindingsThe use of PLS-SEM and NCA enables researchers to identify the must-have factors required for an outcome in accordance with the necessity logic. At the same time, this approach shows the should-have factors following the additive sufficiency logic. The combination of both logics enables researchers to support their theoretical considerations and offers new avenues to test theoretical alternatives for established models.Originality/valueThe authors provide insights into the logic, assessment, challenges and benefits of NCA for researchers familiar with PLS-SEM. This novel approach enables researchers to substantiate and improve their theories and helps practitioners disclose the must-have and should-have factors relevant to their decision-making.

We study mechanism design in dynamic quasilinear environments where private information arrives over time and decisions are made over multiple periods. We make three contributions. First, we provide a necessary condition for incentive compatibility that takes the form of an envelope formula for the derivative of an agent's equilibrium expected payoff with respect to his current type. It combines the familiar marginal effect of types on payoffs with novel marginal effects of the current type on future ones that are captured by \"impulse response functions.\" The formula yields an expression for dynamic virtual surplus that is instrumental to the design of optimal mechanisms and to the study of distortions under such mechanisms. Second, we characterize the transfers that satisfy the envelope formula and establish a sense in which they are pinned down by the allocation rule (\"revenue equivalence\"). Third, we characterize perfect Bayesian equilibrium-implementable allocation rules in Markov environments, which yields tractable sufficient conditions that facilitate novel applications. We illustrate the results by applying them to the design of optimal mechanisms for the sale of experience goods (\"bandit auctions\").

Necessary condition analysis (NCA) is an increasingly used or suggested method in many business and management disciplines including, for example, entrepreneurship, human resource management, international business, marketing, operations, public and nonprofit management, strategic management, and tourism. In the light of this development, our work delivers a review of the topics analyzed with NCA or in which NCA is proposed as a method. The review highlights the tremendous possibilities of using NCA, which hopefully encourages other researchers to try the method. To support researchers in future NCA studies, this article also provides detailed guidelines about how to best use NCA. These cover eight topics: theoretical justification, meaningful data, scatter plot, ceiling line, effect size, statistical test, bottleneck analysis, and further descriptions of NCA.

The sole purpose of the enhanced standard analysis (ESA) is to prevent so-called untenable assumptions in Qualitative Comparative Analysis (QCA). One source of such assumptions can be statements of necessity. QCA realists, the majority of QCA researchers, have elaborated a set of criteria for meaningful claims of necessity: empirical consistency, empirical relevance, and conceptual meaningfulness. I show that once Thiem’s (2017) data mining approach to detecting supersets is constrained by adhering to those standards, no CONSOL effect of Schneider and Wagemann’s ESA exists. QCA idealists, challenging most of QCA realists’ conventions, argue that separate searches for necessary conditions are futile because the most parsimonious solution formula reveals the minimally necessary disjunction of minimally sufficient conjunctions. Engaging with this perspective, I address several unresolved empirical and theoretical issues that seem to prevent the QCA idealist position from becoming mainstream.

A multiobjective optimization problem (MOP) with inequality and equality constraints is considered where the objective and inequality constraint functions are locally Lipschitz and equality constraint functions are differentiable. Burachik and Rizvi [J. Optim. Theory Appl. 155, 477-491 (2012)] gave Guignard and generalized Abadie regularity conditions for a differentiable programming problem and derived Karush-Kuhn-Tucker (KKT) type necessary optimality conditions. In this paper, we have defined the nonsmooth versions of Guignard and generalized Abadie regularity conditions given by Burachik and Rizvi and obtained KKT necessary optimality conditions for efficient and weak efficient solutions of (MOP). Further several constraint qualifications sufficient for the above newly defined constraint qualifications are introduced for (MOP) with no equality constraints. Relationships between them are presented and examples are constructed to support the results.

Although reconsolidation opens up new avenues to erase excessive fear memory, subtle boundary conditions put constraints on retrieval-induced plasticity. Reconsolidation may only take place when memory reactivation involves an experience that engages new learning (prediction error). Thus far, it has not been possible to determine the optimal degree of novelty required for destabilizing the memory. The occurrence of prediction error could only be inferred from the observation of a reconsolidation process itself. Here, we provide a noninvasive index of memory destabilization that is independent from the occurrence of reconsolidation. Using this index, we show in humans that prediction error is (i) a necessary condition for reconsolidation of associative fear memory and (ii) determined by the interaction between original learning and retrieval. Insight into the process of memory updating is crucial for understanding the optimal and boundary conditions on reconsolidation and provides a clear guide for the development of reconsolidation-based treatments.

In this paper, new concepts of monotonicity, namely (Φ,ρ)-monotonicity, (Φ,ρ) -pseudo-monotonicity and (Φ,ρ)-quasi-monotonicityare introduced for functions defined in Banach spaces. Series of necessary conditions are also given that relate (Φ,ρ)-invexity and generalized (Φ,ρ)-invexity of the function with (Φ,ρ)-monotonicity and generalized (Φ,ρ)-monotonicity of its gradient. 2010Mathematics Subject Classification: 90C26, 90C30. Key words and phrases: (Φ,ρ)-Monotonicity, (Φ,ρ)-Pseudo-monotonicity, (Φ,ρ)-Quasi-monotonicity, (Φ,ρ)-Invexity, (Φ,ρ)-Pseudo-invexity, (Φ,ρ)-Quasi-invexity.