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Multiplicative degree-Kirchhoff index is a very interesting topological index. In this article, we compute analytical expression for the expected value of the Multiplicative degree-Kirchhoff index in a random polygonal. Based on the result above, we also get the Multiplicative degree-Kirchhoff index of all polygonal chains with extremal values and average values.

Two famous topological indices, the Gutman index and Schultz index, are studied in this article. We mainly calculate the exact analytical formulae for the expected values of the Gutman index and Schultz index of a random regular polygonal chain with n regular polygons. Moreover, we determine the average values and the extremal values of the indices in regard to the set of all these regular polygonal chains.

Respiratory syncytial virus (RSV) imposes a substantial burden on pediatric hospital capacity in Europe. Promising prophylactic interventions against RSV including monoclonal antibodies (mAb) and maternal immunizations (MI) are close to licensure. Therefore, we aimed to evaluate the cost-effectiveness of potential mAb and MI interventions against RSV in infants, for six European countries. We used a static cohort model to compare costs and health effects of four intervention programs to no program and to each other: year-round MI, year-round mAb, seasonal mAb (October to April), and seasonal mAb plus a catch-up program in October. Input parameters were obtained from national registries and literature. Influential input parameters were identified with the expected value of partial perfect information and extensive scenario analyses (including the impact of interventions on wheezing and asthma). From the health care payer perspective, and at a price of €50 per dose (mAb and MI), seasonal mAb plus catch-up was cost-saving in Scotland, and cost-effective for willingness-to-pay (WTP) values ≥€20,000 (England, Finland) or €30,000 (Denmark) per quality adjusted life-year (QALY) gained for all scenarios considered, except when using ICD-10 based hospitalization data. For the Netherlands, seasonal mAb was preferred (WTP value: €30,000-€90,000) for most scenarios. For Veneto region (Italy), either seasonal mAb with or without catch-up or MI was preferred, depending on the scenario and WTP value. From a full societal perspective (including leisure time lost), the seasonal mAb plus catch-up program was cost-saving for all countries except the Netherlands. The choice between a MI or mAb program depends on the level and duration of protection, price, availability, and feasibility of such programs, which should be based on the latest available evidence. Future research should focus on measuring accurately age-specific RSV-attributable hospitalizations in very young children.

Many salamander populations are declining, and methods to determine how best to allocate limited resources to slow or reverse these declines could support land managers in their decision‐making processes. Multiple types of uncertainty may delay management decisions, including when (1) knowledge of a species' ecology is incomplete, (2) climate change effects on environmental covariates are uncertain, and (3) the efficacy of management alternatives is unknown. For management decisions, a value‐of‐information analysis can identify which uncertainties are critical to reduce in order to identify an optimal strategy from a set of possible management actions. If the same management action is optimal across the full range of uncertainties, then resources for research can be redirected toward active management. Using value‐of‐information analyses, we examine the effect of uncertainty on identifying optimal management to maximize the future expected occupancy of Plethodon shenandoah, a Federally Endangered high‐elevation endemic salamander that is threatened by climate change. Out of 11 management actions proposed by National Park Service managers, those that increase environmental moisture are expected to maximize occupancy, and we find that the selection of this action is robust to all the identified uncertainties. We show that, even in systems with multiple sources of large uncertainty, value of information analyses discriminate among investments in species management.

The explicit consideration of uncertainty is essential in addressing most planning and operation issues encountered in the management of complex systems. Unfortunately, the resulting stochastic programming formulations, integer ones in particular, are generally hard to solve when applied to realistically-sized instances. A common approach is to consider the simpler deterministic version of the formulation, even if it is well known that the solution quality could be arbitrarily bad. In this paper, we aim to identify meaningful information, which can be extracted from the solution of the deterministic problem, in order to reduce the size of the stochastic one. Focusing on two-stage formulations, we show how and under which conditions the reduced costs associated to the variables in the deterministic formulation can be used as an indicator for excluding/retaining decision variables in the stochastic model. We introduce a new measure, the Loss of Reduced Costs-based Variable Fixing (LRCVF), computed as the difference between the optimal values of the stochastic problem and its reduced version obtained by fixing a certain number of variables. We relate the LRCVF with existing measures and show how to select the set of variables to fix. We then illustrate the interest of the proposed LRCVF and related heuristic procedure, in terms of computational time reduction and accuracy in finding the optimal solution, by applying them to a wide range of problems from the literature.

A network game assigns a level of collectively generated wealth to every network that can form on a given set of players. A variable network game combines a network game with a network formation probability distribution, describing certain restrictions on network formation. Expected levels of collectively generated wealth and expected individual payoffs can be formulated in this setting. We investigate properties of the resulting expected wealth levels as well as the expected variants of well-established network game values as allocation rules that assign to every variable network game a payoff to the players in a variable network game. We establish two axiomatizations of the Expected Myerson Value, originally formulated and proven on the class of communication situations, based on the well-established component balance, equal bargaining power and balanced contributions properties. Furthermore, we extend an established axiomatization of the Position Value based on the balanced link contribution property to the Expected Position Value.

The role of values in climate-related decision-making is a prominent theme of climate communication research. The present study examines whether forest professionals are more driven by values than scientists are, and if this results in value polarization. A questionnaire was designed to elicit and assess the values assigned to expected effects of climate change by forest professionals and scientists working on forests and climate change in Europe. The countries involved covered a north-to-south and west-to-east gradient across Europe, representing a wide range of bio-climatic conditions and a mix of economic–social–political structures. We show that European forest professionals and scientists do not exhibit polarized expectations about the values of specific impacts of climate change on forests in their countries. In fact, few differences between forest professionals and scientists were found. However, there are interesting differences in the expected values of forest professionals with regard to climate change impacts across European countries. In Northern European countries, the aggregated values of the expected effects are more neutral than they are in Southern Europe, where they are more negative. Expectations about impacts on timber production, economic returns, and regulatory ecosystem services are mostly negative, while expectations about biodiversity and energy production are mostly positive.

Why do we sometimes opt for actions or items that we do not value the most? Under current neurocomputational theories, such preference reversals are typically interpreted in terms of errors that arise from the unreliable signaling of value to brain decision systems. But, an alternative explanation is that people may change their mind because they are reassessing the value of alternative options while pondering the decision. So, why do we carefully ponder some decisions, but not others? In this work, we derive a computational model of the metacognitive control of decisions or MCD. In brief, we assume that fast and automatic processes first provide initial (and largely uncertain) representations of options' values, yielding prior estimates of decision difficulty. These uncertain value representations are then refined by deploying cognitive (e.g., attentional, mnesic) resources, the allocation of which is controlled by an effort-confidence tradeoff. Importantly, the anticipated benefit of allocating resources varies in a decision-by-decision manner according to the prior estimate of decision difficulty. The ensuing MCD model predicts response time, subjective feeling of effort, choice confidence, changes of mind, as well as choice-induced preference change and certainty gain. We test these predictions in a systematic manner, using a dedicated behavioral paradigm. Our results provide a quantitative link between mental effort, choice confidence, and preference reversals, which could inform interpretations of related neuroimaging findings.

This study is aimed at analysing the requirements for compressive strength values of rocks used in the universally understood construction industry as stone materials. The compressive strength value obtained in laboratory tests may prove significantly different from the actual compressive strength of a given rock, depending on its application. According to PN-EN 1342:2013, lower expected value must be declared for paving block stone, normalised value for wall components, as per PN-EN 1996-1-1:2023 and PN-EN 771-6:2015, while with respect to stone for hydrotechnical works – structural integrity acc. to PN-EN 13383-1:2003. Despite testing samples in the same manner, e.g. acc. to PN-EN 1926:2007, all these parameters differ with the declared value and, in many cases, significantly differ from the most frequently used average compressive strength value. The analysis involved the results of compressive strength tests performed as per PN-EN 1926:2007, for samples of sandstone, granite, and limestone. The tests were performed for the aforementioned rocks in the air-dry condition, after saturation, and after the frost resistance test. On average, for all rock types, the lower expected value vs. average value was lower: in the air-dry condition by 25%, after saturation by 29%, and after frost resistance test by 37%. Furthermore, in most analysed cases, lower expected value did not exceed minimum compressive strength value. Normalised value in the air-dry condition was by approximately 15% lower than the average value, while after saturation totalled from 10% to 25%, depending on rock type.

In this paper, we propose two new optimal reinsurance models in which both premium budget constraints and the reinsurer’s risk limits are taken into account. To be precise, we assume that the reinsurance premium has an upper bound, and that the admissible ceded loss functions have a pre-specified upper limit. Moreover, we assume that the reinsurance premium principle is calculated by the expected value premium principle. Under the optimality criteria of minimizing the value at risk and conditional value at risk of the insurer’s total risk exposure, we derive the explicit optimal reinsurance treaties, which are layer reinsurance treaties. A new approach is developed to construct the optimal reinsurance treaties. Comparisons with existing studies are also made. Finally, we provide a numerical study based on real data and an example to illustrate the proposed models and results. Our work provides a novel generalization of several known achievements in the literature.