Stepwise Function Research Articles

Conditional Model Selection in Mixed-Effects Models with cAIC4

Model selection in mixed models based on the conditional distribution is appropriate for many practical applications and has been a focus of recent statistical research. In this paper we introduce the R package cAIC4 that allows for the computation of the conditional Akaike information criterion (cAIC). Computation of the conditional AIC needs to take into account the uncertainty of the random effects variance and is therefore not straightforward. We introduce a fast and stable implementation for the calculation of the cAIC for (generalized) linear mixed models estimated with lme4 and (generalized) additive mixed models estimated with gamm4. Furthermore, cAIC4 offers a stepwise function that allows for an automated stepwise selection scheme for mixed models based on the cAIC. Examples of many possible applications are presented to illustrate the practical impact and easy handling of the package.

An EOQ model with stepwise ordering cost and the finite planning horizon under carbon cap-and-trade regulations

In this study, under the carbon cap-and-trade mechanism, the ordering cost presents a stepwise function for ordering quantity, and the optimal economic ordering quantity model aims to explore the manufacturer's total cost minimization in the finite planning horizon, in combination with the actual situation that the product will produce carbon emissions during transportation and storage. The economic order quantity (EOQ) model with stepwise ordering cost is applicable to the decision environment in which goods are utilized by sea, by rail or by air (e.g., the order cost is charged in addition to the basic fixed cost, the importer of raw materials will pay an additional freight related to delivery, such as the rent for the use of container numbers.). A heuristic algorithm is also proposed to analyze the relevant properties of the optimal solution of the model and to solve the optimal order times and quantities of the manufacturer under the constraint of carbon policy.We further compared the optimal order times with the case without carbon constraint and the order times corresponding to the manufacturer's realization of the minimum carbon emission, and obtained the conditions for the manufacturer to achieve low cost and low emission under the carbon policy.Finally, the theoretical results of the model are verified by numerical examples,and the influence of relevant parameters on the inventory strategy of manufacturers is discussed. The results show that under the carbon cap-and-trade policy, there is an optimal ordering strategy that minimizes the total cost of the manufacturer in the finite horizon. When the demand of the manufacturer is under finite horizon and the carbon policy is equal to the specific multiplier of orders, the manufacturer can achieve a win-win result of low cost and low emissions.

What are the US Spectrum Auctions for 5G Teaching Us About Auction Efficiency?

This paper seeks to assess the efficiency of the first 5G spectrum auctions held in the United States. In 2018 and 2019, the Federal Communications Commission (FCC) administered auctions 101 and 102 to assign spectrum in the 28 GHz and 24 GHz bands, respectively. Auction 101 sold spectrum on the 28 GHz band for Upper Microwave Flexible Use Service licenses and raised a total of about $700 million. Auction 102 assigned spectrum on the 24 GHz band for Upper Microwave Flexible Use Services. It raised a total of close to $2 billion. In July 2020, the FCC auctioned the 3.5 GHz band for Priority Access Licensees, raising over $4 billion. I implement an assessment of the efficiency of an auction based on its observed bidding data during the clock rounds of the auctions, while relying on revealed preference theory. Data are available at the FCC’s Auctions website. Bidding data are organised by geographical area and for each geographical area, demand point sets for each round, for each bidder. I rely on the application of the well-known Generalised Axiom of Revealed Preference or GARP, and less well-known Homothetic Axiom of Revealed Preference or HARP, to construct two indexes, Afriat Efficiency Index (AEI) and Homothetic Efficiency Index (HEI) to calculate measurements of rational bidding associated with each bidder. The US relied on an auction format, which uses demand revelation but allows the bidders to state the price at which they would demand a number of units of the same item (that is, blocks or licenses). In essence, the auction format for auctions 102 and 105 followed a multiple round format with an ascending clock not entirely driven by the auctioneer, whereby a bid is best described as a stepwise (ascending or descending) demand function revealed on the price range set by the auctioneer for the round. The difficulty in dealing with the data is that the bidding language of these auctions allows a bidder to express its demand for the items being sold in a service area by means of a stepwise function (either ascending or descending). The challenge at this stage is to suitably adapt the data to the usual data set format assumed by GARP or HARP. Using an efficiency approach, I assess each auction at two levels: assessment of efficiency through utility maximisation via AEI and an assessment of efficiency through homotheticity via HEI. Auctioneers, in particular, and spectrum authorities, in general, are concerned with the economic aspects of their spectrum assignment processes. The most important issue that pertains the results of the auction is the answer to the question, was the spectrum assigned to those bidders who can make the best use of it? Answering the question puts us on the grounds of auction efficiency. Devising methods to use the auction bidding data to answer such question has been a long-standing question. GARP and HARP are two revealed preference approaches that do not require us to adopt a parametrized utility function to represent bidder’s preferences. Those methods use the observed data and define a rigorous consistency test on the data.

Measurement of the gas flow stagnation temperature by the method of two identical thermocouples in the short-duration aerodynamic facilities

Investigations of the temperature and heat flux distributions over the external surface of flying vehicles are important for the development of hypersonic planes. For obtaining correct results, experiments are performed in short-duration high-enthalpy wind tunnels. Determination of the stagnation temperature of the flow in such facilities is a challenging task due to short start-up times and high flow temperature. In this paper a new method is proposed for determining the stagnation temperature of a gas flow in the short-duration aerodynamic wind tunnels with stepwise changes in its parameters. The method is based on using two identical thermocouples with different initial temperatures. It is shown that in the case of jump-like changes in flow parameters the instrument function of the difference of the thermocouple readings coincides with the instrument function of each thermocouple, and the instrument function itself is actually the normalized temperature difference. The instrument function obtained in the study allows temperature retrieval by the method of deconvolution. This approach is highly sensitive to random noise of experimental data; therefore, regularization methods are applied for high-frequency noise suppression. A procedure for choosing the regularization parameter for temperature reconstruction is proposed. The research novelty of the article is that the proposed method allows exact reproduction of the stepwise function and instrument function without any additional assumptions, while the measurements and dynamic calibration are performed in one experiment. Applicability of the method for obtaining the stagnation temperature in the short-duration high-enthrall wind tunnel IT-302 M ITAM SB RUS is demonstrated.

Stepwise pricing in evaluating revenue efficiency in Data Envelopment Analysis: A case study in power plants

Data envelopment analysis (DEA) technique is widely applied for performance assessment of decision making units (DMUs). The revenue efficiency (RE) evaluation is one of the controversial subject matters that can be performed through DEA context. The amount of productions and its prices are crucial factors in the RE. The classical DEA models consider the prices to be fixed and known which are not the case in real world. Also, the classical DEA models considers linear pricing in revenue assessment. However, most of real world problems deal with nonlinear prices. This paper evaluates the RE given the piecewise linear theory in non-competitive situations. In doing so, a stepwise pricing function is introduced which lets the prices to be changed in relation to the amount of the production. As an innovative idea, a more accurate mathematical modeling for the RE is proposed. We define a dynamic weights’ function in maximum revenue optimization model which no longer considers fixed prices. A case study validates our proposed model.

Phonon softening in sodium with a stepwise electron distribution

The absorption of light by a metal disturbs the electron distribution around the Fermi surface. Here, we calculate the phonon dispersion relations of free-electron-like metal, bcc sodium, with a stepwise electron distribution function by using a model potential. The step can behave as a pseudo-Fermi surface, which produces singularities at specific wave numbers in the response function. The singularity gives rise to long-range oscillations in the interatomic potential and results in phonon softening along the Γ–N direction. The effect of the smearing in the step function is also discussed.

An indirect boundary element method for analysis of 3D thermoelastic problem with cracks

In this paper, we first consider a combined boundary element method for numerical simulation of effect of temperature change on deformation due to time-varying heat conditions. The numerical simulation uses combination of an indirect boundary element method (IBEM) for temperature field and displacement discontinuity method (DDM) for displacement and stress fields. Time-varying fictitious heat source is employed in the IBEM and is approximated with a series of fictious heat sources with constant strengths that are applied incrementally at different times. Mathematically, the smooth-varying strength function of fictitious heat source is approximated with a stepwise function. The solution schemes previously developed for fictitious heat sources with constant strength are used for each increment. The combined scheme is used to compare the thermal effects caused by constant temperature and time-varying temperature on surface of a spherical cavity in an infinite body. The approximation scheme is verified with analytical solution when the temperature on the spherical cavity surface varies linearly with time. Then thermal fields around a conceptual thermal energy storage tank is simulated. Finally, the effects of temperature change in cracks connected to a vertical borehole on the propagation pattern of the cracks are investigated with the numerical scheme. It is found that cold temperature on the crack surfaces could help to reduce curvature of crack surfaces when multiple cracks are used, compared with fluid flow driven growth.

Numerical and experimental analysis of Cu–Fe functionally graded beam subjected to tensile loading

Functionally graded materials are new types of composites with heterogeneous microstructure in which some particular physical and mechanical properties change continuously in the thickness direction. In this research, a five-layer copper–iron functionally graded material was fabricated by changing the composition of the layers in a stepwise function between copper and iron using powder metallurgy method. The effect of fabrication process on the microstructure and tensile strength of functionally graded beam was investigated by using two types of presses: uniaxial press and cold iso-static press. Microscopic studies demonstrated appropriate connections between the layers and particles. To achieve ultimate tensile strength and strain, functionally graded copper–iron specimens were tested in tensile loading. The stress–strain graphs obtained from the test showed enhancement in tensile strength of copper and iron functionally graded beam compared to pure copper and iron beams. Finally, a model of this functionally graded material was analysed in ABAQUS finite element code, and the results were verified by experimental tests. Therefore, the present finite element model would be useful to investigate tensile behaviour of functionally graded materials.

Space-time symmetry of brownian motors controlled by a dichotomous process

Studying the symmetry of different systems allows one to formulate a variety of conclusions regarding their properties without knowing the detailed information about a particular system. The models of Brownian motors (ratchets) relate the spatial-temporal dependence of the potential energy of Brownian particles and the resulting ratchet effect. In this article, we use the symmetry description of ratchet systems to study the mechanisms of the influence of the spatial and (or) temporal asymmetry of a nanosystem on the average velocity of Brownian motors of the two main types - with fluctuating periodic potential energy and fluctuating force (the so-called pulsating and forced (or tilted) ratchets). We consider the overdamped motion of a Brownian particle in an unbiased force field, which is described by a periodic stepwise coordinate function, that undergoes dichotomous changes with time. The use of symmetry transformations and symmetry properties of Brownian motors made it possible to obtain compact analytical representations of the average velocity of pulsating and forced ratchets as a function of the parameters of the spatial and temporal asymmetries of the force fields. The fundamental difference between the dependences of the average velocity of the Brownian motors of these two types on the asymmetry parameters is revealed. For the pulsating Brownian motors, the directed motion of nanoparticles is absent in a spatially symmetric system regardless of the presence of temporal asymmetry; the motion appears in the presence of spatial asymmetry, and it is possible to obtain the motor stopping points by tuning the temporal asymmetry parameter of the control process. For the forced Brownian motors, it is the temporal asymmetry that permits the ratchet effect in spatially symmetric systems. For this reason, stopping points as a result of competition of spatial and temporal asymmetries are easier to realize precisely for the motors with fluctuating forces (forced ratchets). The results presented in this article were obtained by analyzing only general symmetry properties, without involving hidden symmetries of ratchet systems, therefore the results are also valid for inertial dynamics.

Vertex ordering with optimal number of adjacent predecessors

In this paper, we study the complexity of the selection of a graph discretization order with a stepwise linear cost function. Finding such vertex ordering has been proved to be an essential step to solve discretizable distance geometry problems (DDGPs). DDGPs constitute a class of graph realization problems where the vertices can be ordered in such a way that the search space of possible positions becomes discrete, usually represented by a binary tree. In particular, it is useful to find discretization orders that minimize an indicator of the size of the search tree. Our stepwise linear cost function generalizes this situation and allows to discriminate the vertices into three categories depending on the number of adjacent predecessors of each vertex in the order and on two parameters K and U. We provide a complete study of NP-completeness for fixed values of K and U. Our main result is that the problem is NP-complete in general for all values of K and U such that U ≥ K + 1 and U ≥ 2. A consequence of this result is that the minimization of vertices with exactly K adjacent predecessors in a discretization order is also NP-complete.

Assessing Dysglycemia Risk Among Younger Adults: A Validation of the Canadian Diabetes Risk Questionnaire

ObjectivesThe Canadian prevalence and incidence of diabetes has increased by the greatest extent in young adulthood. The original Canadian Diabetes Risk Questionnaire (CANRISK) was created to assess dysglycemia risk among adults ≥40 years of age, but it has not been validated among younger adults. Furthermore, it is unclear whether a young adult-specific risk score would better identify dysglycemia in this age group. MethodsAnalyses were done on participants who completed the self-administered CANRISK and underwent anthropometric and blood glucose measurements, were 18 to 39 years of age, were not pregnant and had no previous diabetes diagnosis. A risk model was generated from a lenient stepwise function fit with predictors identified through univariate analyses. Risk scores were produced from adjusted odds ratios. Model performance was internally validated using bootstrap methods and compared with the original CANRISK prognostic tool. ResultsOf the 3,334 participants included in the study, 194 (5.8%) and 51 (1.5%) were living with prediabetes or undiagnosed diabetes, respectively. The model displayed an area under the curve of 73.0%, adjusted to 72.9% after bootstrapping; however, using the original CANRISK model resulted in similar results (area under the curve, 71.4%). Sensitivity and specificity of the new and original models were also comparable (78.8% vs 77.1% and 54.0% vs 55.0%, respectively). ConclusionsThe original CANRISK score performed well among young adults, even when compared with a young adult-specific model. We suggest that the cut point be lowered for young adults and the tool be permitted for use in this age group.

Experimental study on preparation of coaxial drug-loaded tissue-engineered bone scaffold by 3D printing technology.

In order to combine the drug with the tissue-engineered bone scaffold and make the drugs on the scaffolds stable to achieve sustained-release stepwise function, a new method for preparing coaxial drug-loaded tissue engineering bone scaffolds using coaxial three-dimensional printing technology is proposed, in which inner layer material can carry drugs and the outer material can adjust the drug sustained-release rate. The coupling mechanism of both shape control and property control in the process of coaxial three-dimensional printing micro-structural unit is presented. Design-Expert software is introduced for experimental design. The influences of extrusion speed, filling speed, and delamination height on the forming quality are analyzed, and a coaxial gradient composite scaffold model with controllable micro-structure is established. The macro-structure, mechanical properties, in vitro degradation rate, and drug release rate of the scaffolds were analyzed. The experimental results show that the proposed forming technology and process parameter optimization can effectively improve the forming quality of the coaxial scaffold. At the same time, this design of the coaxial structure can effectively slow down the degradation rate of the scaffold and enables stable and long-time drug release. Furthermore, the presented method provides a new technical approach for the further implementation of implantable drug delivery systems for the effective treatment of bone tuberculosis.

Phase Correlation Decomposition: The Impact of Illumination Variation for Robust Subpixel Remotely Sensed Image Matching

Illumination variation is one of the major problems in multitemporal earth observation (EO) image matching. Despite much research has been focused on illumination invariant image matching, subpixel image matching under large illumination variation without prior knowledge is still a challenge. This paper proposes a phase correlation decomposition (PCD) theory model in order to analyze the joint effects of zenith and azimuth angles of the lighting source. A novel stepwise least-squares fitting-based PC (SLSF-PC) is proposed to accurately calculate the subpixel image shift by a stepwise function in the frequency domain. Our mathematical investigation is validated by image alignment and stereo dense matching experiments using simulated terrain shading images representing four different landscapes and a multi-illumination remotely sensed image data set containing eight different scenes under seasonal and daily illumination variation. Image matching experiments demonstrate the superior performance of the proposed SLSF-PC compared to the state-of-the-art image matching algorithms, such as speeded up robust features (SURF), mutual information (MI), and normalized cross correlation (NCC). Even under great illumination angle change, the proposed SLSF-PC is able to achieve 0.1 subpixel matching accuracy on average while other methods fail to find the correspondence.

Insulin-Related Lipohypertrophy in Hemodialyzed Diabetic People: a Multicenter Observational Study and a Methodological Approach.

IntroductionEnd-stage renal disease (ESRD) is associated with increased cardiovascular mortality (CVM) and diabetes mellitus (DM), which in many cases is treated with insulin. Skin lipohypertrophy (LH) very often occurs in insulin-treated (IT) patients as a consequence of inadequate injection technique and is one of the most prominent contributors to hypoglycemia (HYPO), glycemic variability (GV), and poor metabolic control (PMC).MethodThe aim of our multicenter observational study was to assess LH prevalence at self-injection sites and any possible factors predicting high LH/HYPO rates and GV in 296 dialyzed ITDM patients characterized by 64 ± 7 years of age, 7 ± 2 years disease duration, 2.6 ± 2.2 years dialysis duration, preferred pen utilization (80%), and basal-bolus regimen (87.4%) with self-injections (62.6%) largely surpassing caregiver-assisted ones (16.9%), and a mix of the two injection methods (20.5%).ResultsLH was detected in 57% of patients. Univariate analysis followed by backwards stepwise multivariate logistic regression function showed increased odds for developing LH in patients characterized by needle reuse, smaller injection areas, missed injection site rotation, higher HbA1c levels, and more prominent rates of HYPO and GV.ConclusionThis was the first time such observation was made. It is now time for further studies aimed at providing evidence also in ESRD ITDM patients for the cause–effect relationship among wrong injection behavior, LH, and poor metabolic control and for the long-term preventative role of suitable educational countermeasures.Electronic supplementary materialThe online version of this article (10.1007/s13300-019-0650-2) contains supplementary material, which is available to authorized users.

213-LB: Developing a Prognostic Model to Assess Dysglycemia Risk in Canadians Aged 18-39

In Canada, the prevalence of diabetes has seen the greatest relative increase in young adulthood, where the disorder is severely pathological compared to later-onset. Still, few prognostic models have been developed to screen young adults for dysglycemia risk and boost early identification and intervention. We sought to establish predictors of dysglycemia risk among young Canadian adults (aged 18-39) and evaluate their utility in identifying high-risk individuals. The Canadian Diabetes Risk Questionnaire (CANRISK) study collected questionnaire, anthropometric, and oral glucose tolerance test (OGTT) data from a large, multiethnic convenience sample of Canadians over two phases. Young adults with diagnosed diabetes, missing OGTT data, or pregnant were excluded. Potential factors that modestly predicted (p<0.20) dysglycemia status (FPG≥6.1mmol/L or 2h-PG≥7.8mmol/L) were entered into a lenient stepwise function, producing a young adult-specific model; risk scores were developed from adjusted odds ratios. Discriminatory ability was assessed by optimism-corrected area under the curve (AUC) via bootstrapping and goodness-of-fit by Hosmer-Lemeshow (H-L) test and calibration plot. More than half of the 3334 participants were female (62.4%), non-white (79.2%), less than 25kg/m2 (50.7%), and reported a family history of diabetes (55.4%); based on OGTT results, 7.3% were dysglycemic. The young adult-specific model displayed an adjusted AUC of 72.9%, and reasonable goodness-of-fit (H-L p=0.49). Model performance was similar when run sex-specifically (males: unadjusted AUC of 72.1%, H-L p=0.67; females: 73.6%, p=0.67). Employing a cut-point of 22, the tool displayed high sensitivity (78.8%) but low specificity (54.0%). Only 3% of those identified as low risk by the tool were misclassified. This young adult-specific risk score shows promise to identify high-risk individuals in a multiethnic Canadian sample. Additional studies are needed to assess its generalizability to new datasets. Disclosure S.A. Srugo: None. Y. Jiang: None. H.I. Morrison: None. M.M. deGroh: None.

Improving the Restorability of Bulk Power Systems With the Implementation of a WF-BESS System

This paper proposes a restorability improvement strategy to accelerate system restoration through the implementation of a wind farm-battery energy storage system (WF-BESS) system. The concept of restorability is introduced and a restorability improvement model (RIM) is proposed and formulated as a mixed integer linear programming problem. To simulate the cylinder temperature drop during outages, the cranking time of a unit is modeled as a stepwise function of its startup time in the RIM. The WF might fail to meet its scheduled generation outputs optimized by the RIM due to the intermittency of wind. To tackle this problem, a linearized control strategy for the BESS (CSBESS) is proposed to minimize the difference between the scheduled wind power outputs and the combined power of the WF-BESS system. An iterative method is employed to efficiently solve the RIM and CSBESS by introducing optimality cuts. An actual power system case is employed to illustrate the effective performance of the proposed approach.

Reactive explorers to unravel network topology

A procedure is developed and tested to recover the distribution of connectivity of an a priori unknown network, by sampling the dynamics of an ensemble made of reactive walkers. The relative weight between reaction and relocation is gauged by a scalar control parameter, which can be adjusted at will. Different equilibria are attained by the system, following the externally imposed modulation, and reflecting the interplay between reaction and diffusion terms. The information gathered on the observation node is used to predict the stationary density as displayed by the system, via a direct implementation of the celebrated Heterogeneous Mean Field (HMF) approximation. This knowledge translates into a linear problem which can be solved to return the entries of the sought distribution. A variant of the model is then considered which consists in assuming a localized source where the reactive constituents are injected, at a rate that can be adjusted as a stepwise function of time. The linear problem obtained when operating in this setting allows one to recover a fair estimate of the underlying system size. Numerical experiments are carried so as to challenge the predictive ability of the theory.

Evaluation of flow dependent external costs in freight logistics networks

AbstractIn this paper we face a distribution problem arising in a freight logistics context. More precisely, we are involved with the containerized flow originating from maritime terminals and going to inland destinations using the road transportation network. The goal is the minimization of the total shipping costs, given by the travelled distance, vehicles and external cost components. In particular, we consider accidental and polluting costs as external negative costs. Note that the proposed externality costs depend on the amount of flow through the selected arcs in the route and their capacity; therefore, a novel stepwise function is proposed and analyzed. A deep analysis is performed for evaluating the impact of environmental externalities on the choice of the route in terms of costs and distances depending on the density of the traffic. Results of an extensive computational experimentation performed with randomly generated instances of different size and capacity values of the arcs are reported. A real case instance related to the logistics network connecting the main ports of the Liguria County (Italy) to the main inland destinations is finally proposed and analyzed.

Combining data from TCGA and GEO databases and reverse transcription quantitative PCR validation to identify gene prognostic markers in lung cancer.

BackgroundThe aim of this study was to predict and explore the possible mechanism and clinical value of genetic markers in the development of lung cancer with a combined database to screen the prognostic genes of lung cancer.Materials and methodsCommon differential genes in two gene expression chips (GSE3268 and GSE10072 datasets) were investigated by collecting and calculating from Gene Expression Omnibus and The Cancer Genome Atlas databases using R language. Five markers of gene composition (ribonucleotide reductase regulatory subunit M2 [RRM2], trophoblast glycoprotein [TPBG], transmembrane protease serine 4[TMPRFF4], chloride intracellular channel 3 [CLIC3], and WNT inhibitory factor-1 [WIF1]) were found by the stepwise Cox regression function when we further screened combinations of gene models, which were more meaningful for prognosis. By analyzing the correlation between gene markers and clinicopathological parameters of lung cancer and its effect on prognosis, the TPBG gene was selected to analyze differential expression, its possible pathways and functions were predicted using gene set enrichment analysis (GSEA), and its protein interaction network was constructed using the Search Tool for the Retrieval of Interacting Genes/Proteins (STRING) database; then, quantitative PCR and the Oncomine database were used to verify the expression differences of TPBG in lung cancer cells and tissues.ResultsThe expression levels of five genetic markers were correlated with survival prognosis, and the total survival time of the patients with high expression of the genetic markers was shorter than those with low expression (P<0.001). GSEA showed that these high-expression samples enriched the gene sets of cell adhesion, cytokine receptor interaction pathway, extracellular matrix receptor pathway, adhesion pathway, skeleton protein regulation, cancer pathway and TGF-β pathway.ConclusionThe high expression of five gene constituent markers is a poor prognostic factor in lung cancer and may serve as an effective biomarker for predicting metastasis and prognosis of patients with lung cancer.

Higher-order temporal scheme for ground heat exchanger analytical models

Several models have been proposed in the literature to simulate and design earth heat exchangers, mostly used in the context of ground-source heat pump systems. Some models were based on numerical approaches and other on analytical solutions. The analytic models are mostly based on a convolution of response factors, with a stepwise function assuming a constant heat load during each time step. In this work, Duhamel’s theorem is used to derive the analytical expression of the infinite line source, the infinite cylindrical source and the finite line source, and to obtain analytical expressions integrating high-order temporal schemes allowing the load to vary linearly between successive time steps. It is shown that when the load varies with time, and long-time steps are required, a high-order temporal scheme can be advantageous. The proposed method can be applied to the models where the temporal superposition of pulses was used previously.