Additive Decomposition Research Articles

Computational investigation into the effect of constitutive formulations for flow modeling of high elasticity

• Three constitutive formulations of the Leonov model are numerically investigated. • It is verified that keeping positive-definiteness of the conformation tensor is crucial for computational evolution while appropriate interpolation of exponentially convecting domain is essential for accuracy. • Swirling asymmetric corner vortices are described in 3D contraction flow modeling. For the purpose of defeating the high Deborah (or Weissenberg) number problems in viscoelastic flow modeling, the matrix-logarithmic formulation of the constitutive equations has been suggested and proven probably the most effective. This transformation of the conformation tensor endows proper resolution of the boundary layer with exponential convection as well as conservation of its positive definiteness. Herein we make an attempt to evaluate numerical consequences of these two features independently for the Leonov viscoelastic model mainly in the contraction flow. To this end, we from the viewpoint of computational stability and accuracy investigate three formulations written with variables such as the original conformation tensor c (c form), its matrix-logarithm (h form) and additive decomposition (b form). 2D planar 4:1 contraction flow in the limit of vanishing inertia in addition to its 1D toy problem is considered in the framework of finite element method. The h and b forms are designed to preserve the positive definiteness of c , and furthermore the h form grants efficient interpolation of exponentially convecting variables. The 1D analogy expresses the characteristics qualitatively equivalent to the original problem in a simpler fashion. The c form modeling of 2D flow exhibits typical nonevolutionary behavior when the Deborah number ( De ) exceeds a certain limit, and this degradation gets worse with finer mesh. While the h and b forms have always been computationally stable with proper description of steady behavior or elastic instability otherwise, the h form manifests faster mesh convergence. As a complementary study, the h form calculation of full 3D flow along an axisymmetric contraction channel has been performed, which also attests well-posedness without upper bound in De . Its steady result is corroborated with the one under axisymmetric flow approximation. Loss of convergence in the axisymmetric flow regime at high De is verified to result from the occurrence of 3D instability, which is then well portrayed in 3D modeling. In this instability, swirling of asymmetric structure for the corner vortices about the geometrical symmetry axis plausibly mimics experimental observation. Consequently, maintaining the positive definiteness in terms of h or b form is crucial for numerically stable evolution, and the h form interpolation delineating appropriately the exponential convection assures the fastest mesh convergence, hence enhancing the accuracy.

Impact of programming on primary mathematics learning

The aim of this study is to investigate whether a programming activity might serve as a learning vehicle for mathematics acquisition in grades four and five. For this purpose, the effects of a programming activity, an essential component of computational thinking, were evaluated on learning outcomes of three mathematical notions: Euclidean division (N = 1,880), additive decomposition (N = 1,763) and fractions (N = 644). Classes were randomly assigned to the programming (with Scratch) and control conditions. Multilevel analyses indicate negative effects (effect size range −0.16 to −0.21) of the programming condition for the three mathematical notions. A potential explanation of these results is the difficulties in the transfer of learning from programming to mathematics.

Three dimensional modeling and numerical analysis of hydrogen effects on the thermomechanical response of Nickel–Titanium orthodontic applications

This paper deals with effects of the hydrogen presence on the thermo-mechanical behavior of NiTi shape memory alloys (SMAs), widely considered for manufacturing orthodontic archwires. A three dimensional phenomenological model is formulated, based on thermodynamics of irreversible processes. It takes into account the experimentally observed effects on the main physical mechanisms (martensitic transformation and reorientation of martensite). The assumption of an additive decomposition between a reversible lattice and a trapped hydrogen concentrations is adopted. The complete problem including chemical, thermal and mechanical balanced equations and their weak form are solved by the finite element method. A 3D hexahedral continuum finite element with five degrees of freedom per node (displacements, temperature and total hydrogen concentration) is developed. Its implementation is carried out in the Abaqus finite element software. Numerical results are presented and compared to experimental ones which show the significant effects of the hydrogen presence in NiTi SMA.

Pediatric burden and seasonality of human metapneumovirus over 5 years in Managua, Nicaragua.

Human metapneumovirus (hMPV) is an important cause of pediatric respiratory infection. We leveraged the Nicaraguan Pediatric Influenza Cohort Study (NPICS) to assess the burden and seasonality of symptomatic hMPV infection in children. NPICS is an ongoing prospective study of children in Managua, Nicaragua. We assessed children for hMPV infection via real-time reverse-transcription polymerase chain reaction (RT-PCR). We used classical additive decomposition analysis to assess the temporal trends, and generalized growth models (GGMs) were used to estimate effective reproduction numbers. From 2011 to 2016, there were 564 hMPV symptomatic infections, yielding an incidence rate of 5.74 cases per 100 person-years (95% CI 5.3, 6.2). Children experienced 3509 acute lower respiratory infections (ALRIs), of which 160 (4.6%) were associated with hMPV infection. Children under the age of one had 55% of all symptomatic hMPV infections (62/112) develop into hMPV-associated ALRIs and were five times as likely as children over one to have an hMPV-associated ALRI (rate ratio 5.5 95% CI 4.1, 7.4 p < 0.001). Additionally, symptomatic reinfection with hMPV was common. In total, 87 (15%) of all observed symptomatic infections were detected reinfections. The seasonality of symptomatic hMPV outbreaks varied considerably. From 2011 to 2016, four epidemic periods were observed, following a biennial seasonal pattern. The mean ascending phase of the epidemic periods were 7.7weeks, with an overall mean estimated reproductive number of 1.2 (95% CI 1.1, 1.4). Symptomatic hMPV infection was associated with substantial burden among children in the first year of life. Timing and frequency of symptomatic hMPV incidence followed biennial patterns.

Ranks with Respect to a Projective Variety and a Cost-Function

Let X⊂Pr be an integral and non-degenerate variety. A “cost-function” (for the Zariski topology, the semialgebraic one, or the Euclidean one) is a semicontinuous function w:=[1,+∞)∪+∞ such that w(a)=1 for a non-empty open subset of X. For any q∈Pr, the rank rX,w(q) of q with respect to (X,w) is the minimum of all ∑a∈Sw(a), where S is a finite subset of X spanning q. We have rX,w(q)<+∞ for all q. We discuss this definition and classify extremal cases of pairs (X,q). We give upper bounds for all rX,w(q) (twice the generic rank) not depending on w. This notion is the generalization of the case in which the cost-function w is the constant function 1. In this case, the rank is a well-studied notion that covers the tensor rank of tensors of arbitrary formats (PARAFAC or CP decomposition) and the additive decomposition of forms. We also adapt to cost-functions the rank 1 decomposition of real tensors in which we allow pairs of complex conjugate rank 1 tensors.

Seasonality of Primary Small Bowel Volvulus and Its Variations Based on Sex and Place of Residence, North Western Ethiopia.

BackgroundPrimary small bowel volvulus is a common surgical emergency in some parts of the globe. Its seasonal nature has not been widely researched. The main objective of this study was to assess its underlying patterns among different gender and geographical location.Materials and methodsA hospital-based retrospective cross-sectional study was conducted from November 2020 to February 2021 at two comprehensive specialized hospitals in North West Ethiopia. The monthly count of primary small bowel volvulus was analyzed for patterns using Minitab 18. Graphical techniques such as run sequence plots, multiple box plots, and correlogram were used. Additive decomposition was also done. The degree of seasonal variation was measured in terms of seasonal indices generated for each month. A chi-square goodness-of-fit test at p < 0.05 was applied to determine statistical significance.ResultsA total of 235 patients were found to have surgically confirmed diagnosis of primary small bowel volvulus over six years. Most were males (77.4%) and from rural residence (73.2%). The mean age in years was 40.5 (±16.7). Overall, 179 (76.2%) of the total cases, 148 (81.3%) of males, and 138 (80.2%) of rural cases were admitted during June through November.ConclusionSeasonal variation was found to be a feature of primary small bowel volvulus. Knowing its seasonal nature helps raise the threshold of suspicion among health care providers to pass timely clinical decisions particularly in resource-limited setups.

Efficiency evaluation of a two-stage production process with feedback: an improved DEA model

This study explores the additive decomposition method in which the overall efficiency is a weighted average of the two stage efficiencies in a feedback system. In the additive decomposition method, the weight is often expressed as the proportion of total resources devoted to each stage, reflecting the relative importance of the stage. When this approach of determining weights is used in the additive two-stage data envelopment analysis (DEA) model with feedback, we find that the weight of the first stage is never less than that of the second stage, indicating that the first stage is favored, which causes a biased efficiency evaluation. Additionally, the weight of the first stage decreases when its efficiency increases, which does not conform to the belief that to maximize the overall efficiencies, a larger weight should be assigned to the stage with higher efficiency. In this study, we build an improved feedback two-stage DEA model with constant weights and develop a heuristic method to solve it. An empirical dataset covering the high-tech industry of 30 regions in mainland China in 2019 is studied to illustrate the applicability and superiority of our improved model.

Fragmentation-Based Decomposition of a Metalloenzyme-Substrate Interaction: A Case Study for a Lytic Polysaccharide Monooxygenase.

We present a novel decomposition scheme for electronic interaction energies based on the flexible formulation of fragmentation schemes through fragment combination ranges (FCRs; J. Chem. Phys., 2021, 155, 164105). We devise a clear additive decomposition with contribution of nondisjoint fragments and correction terms for overlapping fragments and apply this scheme to the metalloenzyme-substrate complex of a lytic polysaccharide monooxygenase (LPMO) with an oligosaccharide. By this, we further illustrate the straightforward adaptability of the FCR-based schemes to novel systems. Our calculations suggest that the description of the electronic structure is a larger error source than the fragmentation scheme. In particular, we find a large impact of the basis set size on the interaction energies. Still, the introduction of three-body interaction terms in the fragmentation setup improves the agreement to the supermolecular reference. Yet, the qualitative results for the decomposition scheme with two-body terms only largely agree within the investigated electronic-structure approaches and basis sets, which are B97-3c, DFT (TPSS and B3LYP), and MP2 methods. The overlap contributions are found to be small, allowing analysis of the interaction energy into individual amino acid residues: We find a particularly strong interaction between the substrate and the LPMO copper active site.

Thermo-mechanically coupled constitutive equations for soft elastomers with arbitrary initial states

It is a long-standing challenge to predict the thermo-mechanically coupled behaviors of initially stressed soft elastomers since most of the existing theories ignore the influences of thermoelastic deformation histories. The constitutive equations may be completely different even for the same initial stresses, if the latter is originated from isothermal and adiabatic deformations, respectively. In this paper, we establish a general framework for deriving constitutive equations for soft elastomers with arbitrary initial states. Instead of using the virtual stress-free configuration, we define the natural state by imposing the stress-free condition and the natural temperature condition. The derivations are based on a new proposed intrinsic embedding method of initial states, in which an additive decomposition of material strains is employed and the material coordinates can be properly defined. Once the natural-state-based free energy density and internal constraint are specified, the required constitutive equations can be accordingly obtained. We then derive the explicit formulations of the Cauchy stress and the entropy by linearization. On this basis, the embedding of initial states in Saint Venant–Kirchhoff, Blatz–Ko, Mooney–Rivlin, Neo-Hookean, Gent, and exponential form elastomers are detailed discussed. The influences brought by the initial stresses, the initial temperature, and the internal constraint on the elastic coefficients are analyzed separately. The new proposed constitutive equations show quantitative agreement with the classical theories under isothermal circumstances and fill a theoretical blank in this field under non-isothermal circumstances. Our approaches significantly improve the current constitutive theory of soft materials and may shed some light on the theoretical modeling of multi-field coupling problems.

Additive decomposition of the curvature tensor of a reducible tensorial connection

Additive decomposition of the curvature tensor of a reducible tensorial connection

The regression approach to the estimation and additive decomposition of the Foster-Greer-Thorbecke poverty measures

ABSTRACT We propose a new regression-based approach to the estimation and additive decomposition of the Foster-Greer-Thorbecke (FGT) poverty measures. Unlike the original additive decomposition for which subgroup population shares are used as weights, the new additive decomposition uses subgroup poor population shares as weights. Our simulation results reveal low biases of the regression-based estimators of the FGT poverty measures even for moderate sample sizes.

A Survey on High-dimensional Gaussian Process Modeling with Application to Bayesian Optimization

Bayesian Optimization (BO), the application of Bayesian function approximation to finding optima of expensive functions, has exploded in popularity in recent years. In particular, much attention has been paid to improving its efficiency on problems with many parameters to optimize. This attention has trickled down to the workhorse of high-dimensional BO, high-dimensional Gaussian process regression, which is also of independent interest. The great flexibility that the Gaussian process prior implies is a boon when modeling complicated, low-dimensional surfaces but simply says too little when dimension grows too large. A variety of structural model assumptions have been tested to tame high dimensions, from variable selection and additive decomposition to low-dimensional embeddings and beyond. Most of these approaches in turn require modifications of the acquisition function optimization strategy as well. Here, we review the defining structural model assumptions and discuss the benefits and drawbacks of these approaches in practice.

Subsampling bootstrap in network DEA

Data Envelopment Analysis (DEA), provides an empirical estimation of the production frontier, based on an observed sample of decision making units (DMUs). Except for the single input-single output case, the asymptotic distribution of the DEA estimator can only be approximated through bootstrapping approaches. Therefore, bootstrapping techniques have been widely applied in the DEA literature to make statistical inference for the cases when the production process has a single-stage structure. However, in many cases, the transformation of inputs into outputs has an inner structure that needs to be considered. This paper examines the applicability of the subsampling bootstrap procedure in the approximation of the asymptotic distribution of the DEA estimator when the production process has a network structure, and in the presence of undesirable factors. Evidence on the performance of subsampling bootstrap is obtained through Monte Carlo experiments for the case of two-stage series structures, where overall and stage efficiency estimates are calculated using the additive decomposition approach. Results indicate great sensitivity both to the sample and subsample size, as well as to the data generating process. Subsampling methodology is then applied to construct confidence interval estimates for the overall and stage efficiency scores of railways in 22 European countries, where the railway transport process is decomposed into two stages and the railway noise pollution problem is considered as an undesirable output.

Adsorption and decomposition of ZDDP on lightweight metallic substrates: Ab initio and experimental insights

Lightweight alloys substitute steel in a wide range of industrial applications. It is still unclear whether the lubricant additives currently employed to reduce friction of sliding metallic parts are also efficient on non-ferrous substrates. In particular, the functionality of zinc dialkyldithiophosphates (ZDDPs) in contact with Al- and Mg-containing alloys still needs to be understood. In this work, we describe the properties of ZDDP at Al(111), Al(001), Al(331), Mg(0001) and Mg17Al12 surfaces and interfaces. Our calculations indicate that molecular fragments originated from ZDDP chemisorb more strongly on the intermetallic phase Mg17Al12 with respect to aluminum and magnesium, due to the higher surface energy of the mixed substrate. Ab initio molecular dynamics simulations show that the kinetics of the additive decomposition is significantly different on Al and the mixed phase. These results are supported by atomic force microscopy sliding tests, which revealed that the tribofilm formation is observed only on the latter substrate. This work suggests that the tribological performance of lightweight alloys can be enhanced by increasing the additive-surface chemical interactions.

Stabilized formulation for phase‐field fracture in nearly incompressible hyperelasticity

AbstractThis work presents a stabilized formulation for phase‐field fracture of hyperelastic materials near the limit of incompressibility. At this limit, traditional mixed displacement and pressure formulations must satisfy the inf‐sup condition for solution stability. The mixed formulation coupled with the damage field can lead to an inhibition of crack opening as volumetric changes are severely penalized effectively creating a pressure‐bubble. To overcome this bottleneck, we utilize a mixed formulation with a perturbed Lagrangian formulation which enforces the incompressibility constraint in the undamaged material and reduces the pressure effect in the damaged material. A mesh‐dependent stabilization technique based on the residuals of the Euler–Lagrange equations multiplied with a differential operator acting on the weight space is used, allowing for linear interpolation of all field variables of the elastic subproblem. This formulation was validated with three examples at finite deformations: a plane‐stress pure‐shear test, a two‐dimensional geometry in plane‐stress, and a three‐dimensional notched sample. In the last example, we incorporate a hybrid formulation with an additive strain energy decomposition to account for different behaviors in tension and compression. The results show close agreement with analytical solutions for crack tip opening displacements and performs well at the limit of incompressibility.

LocalGLMnet: interpretable deep learning for tabular data

ABSTRACT Deep learning models have gained great popularity in statistical modeling because they lead to very competitive regression models, often outperforming classical statistical models such as generalized linear models. The disadvantage of deep learning models is that their solutions are difficult to interpret and explain, and variable selection is not easily possible because deep learning models solve feature engineering and variable selection internally in a nontransparent way. Inspired by the appealing structure of generalized linear models, we propose a new network architecture that shares similar features as generalized linear models but provides superior predictive power benefiting from the art of representation learning. This new architecture allows for variable selection of tabular data and for interpretation of the calibrated deep learning model, in fact, our approach provides an additive decomposition that can be related to other model interpretability techniques.

How does stakeholder engagement through environmental, social, and governance affect eco‐efficiency and profitability efficiency? Zooming into Apple Inc.'s counterparts

AbstractAs global ecological degradation intensifies, a trade‐off has arisen between environmental protection and production efficiency to achieve sustainable development for the environment, society, and the company itself. However, the potential reverse causality relationship between environmental, social, and governance (ESG) and corporate efficiency may lead to confusion. This study estimates the eco‐efficiency of Apple Incorporated's value‐chain counterparts in the first stage and creates values and profitability in the second stage of efficiency evaluation. Results obtained from the (i) directional distance function in the two‐stage data envelopment analysis (DEA), (ii) additive efficiency decomposition two‐stage network DEA model, and (iii) network slacks‐based measure model are consistent. That is, Apple counterparts manage more efficient eco‐efficiency than profitability efficiency, implying that eco‐efficiency is their competitive advantage. We thus also run a regression analysis to examine how the ESG ratings of Apple counterparts explain their eco‐efficiency and profitability efficiency. Although the overall ESG rating positively explains the efficiencies, we found that the individual governance rating shows no statistically significant effect. The regression results provide insight for practitioners on the importance of investing in the three aspects of a firm's collective conscientiousness for societal and environmental governance. This paper integrates companies' eco‐efficiency and profitability efficiency to resolve the conflict between environmental issues and production efficiency. It also analyzes in depth the effects of ESG and its three individual factors on eco‐, profitability, and average efficiencies. The diversity of research methods also provides new ideas for future research related to firm efficiency.

Role of Age and Education as the Determinant of Income Inequality in Poland: Decomposition of the Mean Logarithmic Deviation.

Measures of inequality can be used to illustrate inequality between and within groups, but the choice of the appropriate measure can have different implications. This study focused on the Mean Logarithmic Deviation, the measure proposed by Theil and based on the techniques of statistical information theory. The MLD was selected because of its attractive properties: fulfillment of the principle of monotonicity and the possibility of additive decomposition. The following study objectives were formulated: (1) to assess the degree of inequality in the population and in the distinguished subgroups, (2) to determine the extent to which education and age influence the level of inequality, and (3) to ascertain what factors contribute to changes in the level of inequality in Poland. The study confirmed an association between the level of education and the average income of the groups distinguished on this basis. The education level of the household head remains an important determinant of household income inequality in Poland, despite the decline in the “educational bonus”. The study also found that differences in the age of the household head had a smaller effect on income inequality than the level of education. However, it can be concluded that the higher share of older people may contribute to an increase in income inequality between groups, as the income from pension in Poland is more homogeneous than the income from work in younger groups. Moreover, the current paper seeks to situate Theil’s approach in the context of scholarly writings since 1967.

Effect of moisture on the nonlinear viscoelastic fracture behavior of polymer nanocompsites: a finite deformation phase-field model

The mechanisms underlying damage in high-performance polymer nanocomposites are remarkably affected by hygrothermal conditions. In this study, we develop a phase-field formulation to investigate the influence of hygrothermal conditions on the nonlinear viscoelastic fracture behavior of epoxy resins and their nanocomposites at finite deformation. For this, the Helmholtz free energy, capturing the effect of temperature and moisture and nanoparticle contents, is defined based on an additive decomposition of the energy into an equilibrium, a non-equilibrium, and a volumetric contribution with different definitions under tensile and compressive loading. The coupled displacement phase-field problem is solved using a quasi-Newton monolithic algorithm and a staggered solution scheme. Numerical examples show that the monolithic algorithm is more efficient. Simulations are performed to investigate the effect of temperature, deformation rate, and moisture content on the force–displacement response of boehmite nanoparticle/epoxy samples in benchmark numerical problems. Comparing numerical predictions and experimental data for compact-tension tests shows good agreement at different nanoparticle contents. Also, the model’s capability to predict fracture patterns is evaluated using simulations of single-edge notched nanocomposite plates under tensile and shear loading.

The set of forms with bounded strength is not closed

The strength of a homogeneous polynomial (or form) is the smallest length of an additive decomposition expressing it whose summands are reducible forms. Using polynomial functors, we show that the set of forms with bounded strength is not always Zariski-closed. More specifically, if the ground field is algebraically closed, we prove that the set of quartics with strength $\leq3$ is not Zariski-closed for a large number of variables.