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In this paper, we consider a two-stage stochastic weekly operating room planning problem with an exponential number of scenarios. The objective function is to minimize the sum of the fixed opening cost of operating rooms and the expected overtime costs that are computed in the second stage. We propose a state-variable model to formulate the two-stage stochastic operating room planning problem and prove its validity. The main advantage of the proposed state-variable model is that it has a pseudo-polynomial number of variables and constraints that are significantly fewer than the number of variables and constraints in an equivalent scenario-based stochastic programming model. We improve the quality of the proposed model by developing an enhanced model that includes remarkably fewer variables and constraints. We also strengthen the model by developing several valid inequalities, including worst-case scenario and symmetry-breaking cuts. We carried out extensive computational experiments to evaluate the performance of the proposed model. The computational results show that the proposed model is capable of finding optimal solutions of instances with 50 surgeries and 1.55E+40 scenarios that is a significant improvement over the state-of-the-art models. The results revealed that the model finds feasible solutions with an average optimality gap of 0.78% for instances with 80 surgeries and 1.48E+64 scenarios.

The concept of essential biodiversity variables (EBVs) was proposed in 2013 to improve harmonization of biodiversity data into meaningful metrics. EBVs were conceived as a small set of variables which collectively capture biodiversity change at multiple spatial scales and within time intervals that are of scientific and management interest. Despite the apparent simplicity of the concept, a plethora of variables that describes not only biodiversity but also any environmental features have been proposed as potential EBV (i.e. candidate EBV). The proliferation of candidates reflects a lack of clarity on what may constitute a variable that is essential to track biodiversity change, which hampers the operationalization of EBVs and therefore needs to be urgently addressed. Here, we propose that an EBV should be defined as a biological state variable in three key dimensions (time, space, and biological organization) that is critical to accurately document biodiversity change.

The understanding of unsaturated soil mechanics principles is of interest to a wide spectrum of geotechnical problems associated with soils above water table and compacted soils. This paper describes the stress state variables and constitutive equations based on the unsaturated soil mechanics principles. In addition, the basic concepts for characterization of unsaturated soils and measurements of matric suction (or negative pore-water pressures) are also explained. The application of unsaturated soil mechanics theories is illustrated through the use of capillary barrier system for minimizing rain infiltration into residual soil slopes.

The phase rule of Gibbs is one of the basic equations in phase equilibria. Although it has been with us for 150 years, discussions, interpretations and extensions have been published. Here, the following new content is provided: (i). the choice of independent components is discussed, and the component rule is introduced, (ii). independent state variables are divided into compositional and non-compositional ones, (iii). the generalized phase rule is derived replacing number two in the original phase rule by the number of independent non-compositional state variables introduced above, (iv). the degree of freedom is decreased by the number of compositional constraints in special points (azeotrope and congruent melting) of phase diagrams, (v). a rule is derived connecting the maximum number of coexisting phases with the dimensions of the phase diagram, (vi). examples show how to apply the phase rule to unary, binary and ternary phase diagrams and their sections, (vii). the same is extended with the discussion of calculable and not calculable phase fractions, (viii). it is shown that the current definition of the degree of freedom is not sufficient in the number of cases, (ix). the current definition of the degree of freedom is extended, (x). the application of the generalized phase rule is demonstrated when other non-compositional state variables are applied for nano-phase diagrams, and/or for phase diagrams under the influence of electric potential difference, external magnetic field, mechanical strain or the gravitational field.

The global reliability analysis of complex engineering structures considering the correlations between basic random variables remains a challenge, especially for nonlinear correlation problems. In this work, to take into account the influence of nonlinear correlation between random variables, an enhanced high-order moment method is proposed for structural global reliability analysis. Firstly, the traditional Nataf transformation is reviewed, and the generalized Nataf transformation is presented by introducing the Copula theory. Secondly, the corresponding performance functions of global reliability problems are described uniformly by the state variable description method, and the GL 2 -discrepancy point set is developed for the high-order moments estimation and sensitivity analysis of the state variable. Thirdly, the global reliability of the structures is accurately determined by using the improved maximum entropy method (IMEM). Finally, two examples, including one static and one dynamic, are investigated to demonstrate the accuracy and efficiency of the proposed method and the influence of nonlinear correlation between random variables on the global reliability of the structures, in which the results obtained from the proposed method are compared with Monte Carlo simulation (MCS) method. The results of the examples show the nonlinear correlation between random variables has a significant impact on the global reliability of structures, and the proposed method has fairly high accuracy and efficiency for structural high-order moments estimation and global reliability analysis.

Evolutionary fitness is determined by how an organism allocates energy, or other limited resources, to reproduction during its lifetime. For iteroparous organisms, two alternative patterns of lifetime reproductive allocation are terminal investment and reproductive restraint. Terminal investment maximizes an individual’s current reproductive output by allocating all available resources to current reproduction at the cost of future reproduction. In contrast, the reproductive restraint strategy allocates the individual’s resources toward future survival and reproductive events. We used dynamic state variable modeling to investigate the conditions under which the burying beetle, Nicrophorus orbicollis, would balance between reproductive restraint and terminal investment over their lifetime. Our model provides a formal extension, specific to burying beetle biology, of the dynamic terminal investment threshold conceptual model. For young females, we show that delayed reproduction and reproductive restraint are the optimal tactic for all individuals except for those in the highest condition. However, as age increases, terminal investment becomes the optimal tactic over an increasingly broader range of individual conditions. Surprisingly, manipulation of a variety of factors, such as survival rate, resource availability, and metabolic costs, causes only minor changes in the general pattern observed. We suggest that in burying beetles, and other similar organisms, age plays a dominant role in determining the pattern of reproductive allocation over a lifetime. Individual energetic condition is important in changing the boundaries between alternative reproductive strategies, but it does not change the overall pattern of dominance of delayed reproduction or reproductive restraint at early ages and dominance of terminal investment with increasing age.Significance statementIn this model of the dynamic terminal investment threshold, age is the dominant determinant of reproductive allocation over a lifetime. Differences in survival rate, resource availability, and metabolic costs result in only slight adjustments to the optimal reproductive allocation strategy. Our model predicts the coexistence of multiple reproductive strategies and suggests that patterns of reproductive allocation identified for burying beetles may be broadly applicable across diverse taxa (e.g., insect parasitoids, altricial birds) that share similar life history characteristics and constraints with burying beetles. Furthermore, even in species that exhibit dramatically different life histories from burying beetles (e.g., long-lived, indeterminate growth, absence of reproductive senescence) this approach of dynamic state variable modeling shows potential for characterizing and comparing lifetime reproductive allocation patterns.

We present a corrosion internal state variable (ISV) damage model based upon the integrated computational materials engineering (ICME) hierarchical multiscale paradigm. Structure–property experiments for magnesium alloys were used where the only inputs were the volume fractions of each element of the periodic table. This macroscale ISV corrosion model finds its basis in Horstemeyer’s mechanical damage model, which includes three separate ISVs for damage nucleation, growth, and coalescence, as well as Walton’s inclusion of corrosion, which introduces five new ISVs for pit nucleation, growth, and coalescence, along with general corrosion and intergranular corrosion. While Walton’s corrosion ISVs are phenomenological in nature, herein we develop a multiscale physical basis for the corrosion ISVs. The parameters for the macroscale corrosion ISVs were garnered from the mesoscale Butler–Volmer equations. Pure magnesium with differing amounts of aluminum were used in corrosion tests to exemplify the different pitting, general corrosion, and intergranular corrosion rates, and the macroscale ISV model was calibrated with said data, in which the only inputs to the model are the volume percentages of the elements magnesium and aluminum. Although magnesium alloys were used to motivate and calibrate the model, the model is abstract enough to possibly capture other material systems as well.

Based on the “21.7” Henan extreme rainstorm case, this study investigates the influence of updating model state variables in the GSI-EnKF (Gridpoint Statistical Interpolation–ensemble Kalman filter) system with the Thompson microphysics scheme. Six sensitivity experiments are conducted to assess the impact of updating different model state variables on the EnKF analysis and subsequent forecast. The experiments include the Z_ALL experiment (updating all variables), the Z_NoEnv experiment (excluding dynamical and thermodynamical variables), the Z_NoNr experiment (excluding rainwater number concentration), and three additional experiments that examine the removal of updating horizontal wind (U, V), vertical wind (W), and perturbation potential temperature (T), which are marked as Z_NoUV, Z_NoW, and Z_NoT. The results indicate that updating different model state variables leads to various effects on dynamical, thermodynamical, and hydrometeor fields. Specifically, excluding the update of vertical wind or perturbation potential temperature has little effect on the rainwater mixing ratio, whereas excluding the update of the rainwater number concentration causes a significant increase in the rainwater mixing ratio, particularly in the northern region of Zhengzhou. Not updating horizontal wind or environmental variables shifts the rainwater mixing ratio northward, deviating from the observed rainfall center. The analysis of near-surface divergence and vertical wind also reveals that not updating certain variables could result in weaker or less detailed wind structures. Although radar reflectivity, which is mainly influenced by the mixing ratios of hydrometeors, shows consistent spatial distribution across experiments, their intensity varies, with the Z_ALL experiment showing the most accurate prediction. The 4 h deterministic forecasts based on the ensemble mean analysis demonstrate that updating all variables provides the best improvement in predicting the “21.7” Henan extreme rainstorm. These results emphasize the importance of updating all relevant model variables for improving predictions of extreme rainstorms.

An active vibration-isolation system (AVIS) utilizes a geophone sensor, a type of velocity sensor, to control microvibration. The structure of the sensor is modeled by mass, damper, and spring. The mathematical model of the geophone sensor is a second-order model with a resonant frequency. However, at low-band frequencies, the response characteristic is nonlinear and phase delay occurs. Compared with the ideal velocity signals of the system, the velocity signals measured from the geophone sensor were distorted in low-band frequencies. Consequently, this measurement issue in feedback control loops can affect the stability and performance of the AVIS. This paper proposes design rules for a state-variable filter (SVF) that can compensate for the nonlinearity of the geophone sensors in low-band frequencies and evaluates vibration attenuation performance of the AVIS by applying the proposed SVF. To evaluate the effectiveness of the filter in compensating for the nonlinear response of the geophone sensor, we compared Bode plots generated through simulation and experimental results obtained using a dynamic signal analyzer. The experimental results demonstrated that the proposed SVF effectively reduces the resonance peak of the geophone sensor and expands the frequency bands that maintain a constant magnitude in range of 0.8–10 Hz. By applying the geophone sensor with SVF to AVIS, the microvibration attenuation improved to − 18.4 dB near 4.5 Hz.

Estimating crop coefficients and evapotranspiration (ET) accurately is crucial for optimizing irrigation. Remote sensing techniques using green canopy cover, leaf area index (LAI), and normalized difference vegetation index (NDVI) have been applied to estimate basal crop coefficients (Kcb) and ET for different crops. However, analysis of the potential of these techniques to improve water management in irrigated potato (Solanum tuberosum L.) is still lacking. This study aimed to assess the modified nonlinear relationship between LAI, Kcb and NDVI in estimating crop coefficients (Kc) and ET of potato. Moreover, Kc and ET were derived from the measured fraction of green canopy cover (FGCC) and the FAO-56 approach. ET estimated from the FAO-56, FGCC and NDVI approaches were compared with the ET simulated using the LINTUL-Potato model. The results showed that the Kc values based on FGCC and NDVI were on average 0.16 lower than values based on FAO-56 Kc during the mid-season growing stage. ET estimated from FAO-56, FGCC and NDVI compared well with ET calculated by the LINTUL-Potato model, with RMSE values of 0.83, 0.79, and 0.78 mm day−1 , respectively. These results indicate that dynamic crop coefficients and potato ET can be estimated from canopy cover and NDVI. The outcomes of this study will assist potato growers in determining crop water requirements using real-time ETo, canopy state variables and NDVI data from satellite images.