Structural Assumptions Research Articles

Estimation of separable direct and indirect effects in a continuous-time illness-death model.

In this article we study the effect of a baseline exposure on a terminal time-to-event outcome either directly or mediated by the illness state of a continuous-time illness-death process with baseline covariates. We propose a definition of the corresponding direct and indirect effects using the concept of separable (interventionist) effects (Robins and Richardson in Causality and psychopathology: finding the determinants of disorders and their cures, Oxford University Press, 2011; Robins et al. in arXiv:2008.06019 , 2021; Stensrud et al. in J Am Stat Assoc 117:175-183, 2022). Our proposal generalizes Martinussen and Stensrud (Biometrics 79:127-139, 2023) who consider similar causal estimands for disentangling the causal treatment effects on the event of interest and competing events in the standard continuous-time competing risk model. Unlike natural direct and indirect effects (Robins and Greenland in Epidemiology 3:143-155, 1992; Pearl in Proceedings of the seventeenth conference on uncertainty in artificial intelligence, Morgan Kaufmann, 2001) which are usually defined through manipulations of the mediator independently of the exposure (so-called cross-world interventions), separable direct and indirect effects are defined through interventions on different components of the exposure that exert their effects through distinct causal mechanisms. This approach allows us to define meaningful mediation targets even though the mediating event is truncated by the terminal event. We present the conditions for identifiability, which include some arguably restrictive structural assumptions on the treatment mechanism, and discuss when such assumptions are valid. The identifying functionals are used to construct plug-in estimators for the separable direct and indirect effects. We also present multiply robust and asymptotically efficient estimators based on the efficient influence functions. We verify the theoretical properties of the estimators in a simulation study, and we demonstrate the use of the estimators using data from a Danish registry study.

How does the effect of external financing on profitability differ across tiers? Evidence from the automotive supply chain

Due to the importance of automotive industry for the Czech Republic (in a broader sense for European countries) and due to the unprecedented development of both national and European economies caused by the COVID-19 outbreak, also having implications on the financial sector, we aim to explore the main determinants of operating performance within the automotive supply chain. This study is based on the data sample composed of complete individual financial statements (audited if available) of firms conducting their business in the Czech Republic from 2011 to 2018 and belonging to the automotive supply chain. This supply chain is defined as (sub) deliveries of the Czech automotive industry represented mainly by companies classified under NACE 22, 27, 25, 24. The hypothesis claiming that the investment and leverage-based variables are the important drivers of operating profitability was only partly confirmed (valid predominantly for Tier 3), which shows that the supply chain organization also plays a crucial role as well as (valid for Tier 1). Also, we have shown (illustrated) that the assumption of different capital structures among tiers is valid. The average overall indebtedness of Tier 3 is higher by approximately 50% (altogether, the short- and long-term leverage are higher by 40% and 62% respectively) than Tier 1 firms. The need for relatively high capital expenditures (applicable to Tier 1) and working capital investments (applicable to Tier 3) is partly facilitated by external funds reflected in the indebtedness, which is associated with the costs reducing overall low profits from these investments. The leverageprofitability relationship seems to be nonlinear for long-term debts contrary to short-term debts where the linear relationship prevails.

Gradient method with AFEM for parameter-estimation

We consider the adaptive finite element discretization of parameter estimation problems for nonlinear elliptic partial differential equations. The idea is to use a gradient method on the finite-dimensional parameter space for the minimization of the least-squares residual. Since the gradient involves solution of partial differential equations, it is not accesable, and is replaced by an approximation obtained by finite elements. This results into a perturbed gradient method. We use an (a posteriori) error estimator to control the accuracy of the gradient approximation and propose an algorithm, which links the estimator to the progress of the iteration. We show convergence of the algorithm under typical structural assumptions.

A null model for the distribution of fitness effects of mutations

The distribution of fitness effects (DFE) of new mutations is key to our understanding of many evolutionary processes. Theoreticians have developed several models to help understand the patterns seen in empirical DFEs. Many such models reproduce the broad patterns seen in empirical DFEs but these models often rely on structural assumptions that cannot be tested empirically. Here, we investigate how much of the underlying "microscopic" biological processes involved in the mapping of new mutations to fitness can be inferred from "macroscopic" observations of the DFE. We develop a null model by generating random genotype-to-fitness maps and show that the null DFE is that with the largest possible information entropy. We further show that, subject to one simple constraint, this null DFE is a Gompertz distribution. Finally, we illustrate how the predictions of this null DFE match empirically measured DFEs from several datasets, as well as DFEs simulated from Fisher's geometric model. This suggests that a match between models and empirical data is often not a very strong indication of the mechanisms underlying the mapping of mutation to fitness.

An efficient derivation of spatial Green's function of open-radiating rectangular cavity using CGF-CI technique

ABSTRACT A new technique for efficient calculation of spatial Green's function of open-radiating rectangular cavity is presented. The method is based on separability assumption of the original structure and characteristic Green's function method. Using complex image (CI) technique in spectral domain and well-known Weyl's identity, a closed-form relation for spatial Green's function can be derived. To obtain more accurate closed-form Green's function, before applying CI, discrete spectrum contribution part of the derived relation is modified by replacing more accurate reflection coefficients of surface wave modes from walls of the open-radiating cavity. Verification of the derivations of the proposed method is shown for dielectric loaded metallic box which is a separable structure. Method of moment + multilevel fast multipole method solution and also exact numerical integration approach for open-radiating rectangular cavity are considered to search the accuracy as well as speed of the proposed method. It is shown that the main advantage of the proposed method lies in its speed as well as its simple implementation while the accuracy is preserved.

Overcoming the Long Horizon Barrier for Sample-Efficient Reinforcement Learning with Latent Low-Rank Structure

The practicality of reinforcement learning algorithms has been limited due to poor scaling with respect to the problem size, as the sample complexity of learning an ε-optimal policy is Ω(|S||A|H/ ε2) over worst case instances of an MDP with state space S, action space A, and horizon H. We consider a class of MDPs for which the associated optimal Q* function is low rank, where the latent features are unknown. While one would hope to achieve linear sample complexity in |S| and |A| due to the low rank structure, we show that without imposing further assumptions beyond low rank of Q*, if one is constrained to estimate the Q function using only observations from a subset of entries, there is a worst case instance in which one must incur a sample complexity exponential in the horizon H to learn a near optimal policy. We subsequently show that under stronger low rank structural assumptions, given access to a generative model, Low Rank Monte Carlo Policy Iteration (LR-MCPI) and Low Rank Empirical Value Iteration (LR-EVI) achieve the desired sample complexity of Õ((|S|+|A|)poly (d,H)/ε2) for a rank d setting, which is minimax optimal with respect to the scaling of |S|, |A|, and ε. In contrast to literature on linear and low-rank MDPs, we do not require a known feature mapping, our algorithm is computationally simple, and our results hold for long time horizons. Our results provide insights on the minimal low-rank structural assumptions required on the MDP with respect to the transition kernel versus the optimal action-value function.

Sharp Hessian estimates for fully nonlinear elliptic equations under relaxed convexity assumptions, oblique boundary conditions and applications

We derive global W2,p estimates (with n≤p<∞) for viscosity solutions to fully nonlinear elliptic equations under relaxed structural assumptions on the governing operator that are weaker than convexity and oblique boundary conditions as follows:{F(D2u,Du,u,x)=f(x)inΩβ(x)⋅Du(x)+γ(x)u(x)=g(x)on∂Ω, for f∈Lp(Ω) and under appropriate assumptions on the data β,γ, g and Ω⊂Rn. Our approach makes use of geometric tangential methods, which consist of importing “fine regularity estimates” from a limiting profile, i.e., the Recession operator, associated with the original second-order one via compactness and stability procedures. As a result, we pay special attention to the borderline scenario, i.e., f∈BMOp⊋L∞. In such a setting, we prove that solutions enjoy BMOp type estimates for their second derivatives. Finally, as another application of our findings, we obtain Hessian estimates to obstacle-type problems under oblique boundary conditions and no convexity assumptions, which may have their own mathematical interest. A density result for a suitable class of viscosity solutions will also be addressed.

Property improvement of thermosetting natural rubber asphalt binder by mineral oil

To achieve environmental sustainability, a new type of thermosetting binder, namely thermosetting natural rubber asphalt binder (TNRA), was prepared using natural rubber. However, TNRA has some limitations such as poor compatibility, high initial viscosity, and insufficient flexibility, which require improvement. Mineral oil, a clean additive derived from petroleum fractionation products, has great potential for solving these problems associated with TNRA. This study aims to investigate the effect of mineral oil on TNRA compatibility, as well as its impact on workability, thermal stability, and mechanical properties. Experimental results demonstrate that mineral oil can enhance the compatibility of natural rubber-modified asphalt (NRMA), with aromatic oil playing a more significant role. Improving compatibility leads to improved flexibility of the cured NRMA (that is, TNRA). Furthermore, by balancing the effects of mineral oil on these properties, it is suggested that the ideal dosages of mineral oil are 1.5 times those of natural rubber latex. Finally, the mechanism of improving TNRA properties by mineral oil is explained from the perspective of asphalt colloid structure. The assumption of asphalt heterogeneous equilibrium colloidal structure provided in this study has been confirmed by experiments, and it is feasible to improve the compatibility of other polymer-modified asphalts by selecting light substances, such as mineral oil.

On the rate of convergence of a deep recurrent neural network estimate in a regression problem with dependent data

A regression problem with dependent data is considered. Regularity assumptions on the dependency of the data are introduced, and it is shown that under suitable structural assumptions on the regression function a deep recurrent neural network estimate is able to circumvent the curse of dimensionality.

Overcoming the Long Horizon Barrier for Sample-Efficient Reinforcement Learning with Latent Low-Rank Structure

Reinforcement learning (RL) methods have been increasingly popular in sequential decision making tasks due to its empirical success. However, large state and action spaces in real-world problems modeled as a Markov decision processes (MDPs) limit the use of RL algorithms. Given a finite-horizon MDP with state space S, action space A, and horizon H, one needs Ω |S|A|H3/ε2 samples given a generative model to learn an optimal policy [3], which can be impractical when S and A are large. The above tabular RL framework does not capture the fact that many realworld systems in fact have additional structure that if exploited should improve computational and statistical efficiency. Moreover, [1] empirically verifies that optimal and near-optimal action-value functions (both viewed as |S|-by- |A| matrices) of classical stochastic control tasks have low rank. Thus, the critical question is what are the minimal low rank structural assumptions that allow for computationally and statistically efficient learning.

Breathers and rogue waves for semilinear curl-curl wave equations

We consider localized solutions of variants of the semilinear curl-curl wave equation s(x) partial _t^2 U +nabla times nabla times U + q(x) U pm V(x) vert U vert ^{p-1} U = 0 for (x,t)in {mathbb {R}}^3times {mathbb {R}} and arbitrary p>1. Depending on the coefficients s, q, V we can prove the existence of three types of localized solutions: time-periodic solutions decaying to 0 at spatial infinity, time-periodic solutions tending to a nontrivial profile at spatial infinity (both types are called breathers), and rogue waves which converge to 0 both at spatial and temporal infinity. Our solutions are weak solutions and take the form of gradient fields. Thus they belong to the kernel of the curl-operator so that due to the structural assumptions on the coefficients the semilinear wave equation is reduced to an ODE. Since the space dependence in the ODE is just a parametric dependence we can analyze the ODE by phase plane techniques and thus establish the existence of the localized waves described above. Noteworthy side effects of our analysis are the existence of compact support breathers and the fact that one localized wave solution U(x, t) already generates a full continuum of phase-shifted solutions U(x,t+b(x)) where the continuous function b:{mathbb {R}}^3rightarrow {mathbb {R}} belongs to a suitable admissible family.

Global small solutions of MHD boundary layer equations in Gevrey function space*

In this paper, we obtain global small solutions and decay estimates for the two-dimensional MHD boundary layer in Gevrey space without any structural assumptions, generalizing the results of [20] in analytic space. The proof method is mainly inspired by [14] and [26], using new auxiliary functions and finer structural analysis to overcome the difficulty of the loss of derivatives and then we obtain the global well-posedness of the MHD boundary layer in the Gevrey 32 space.

“Another (hard) day moving in the city”: Development and validation of the MCSS, a multimodal commuting stress scale

Although most of the literature on stress-related factors uniformly points out several negative health, performance, and safety issues as potential outcomes attributable to a prolonged exposition to stressful situations, the applications of these assumptions to the field of urban mobility (and more specifically to commuting) remain considerably scarce. Indeed, while commuters worldwide usually face daily situations such as traffic jams, dearth of transport choices, crowded public transport services, long trips, and road conflicts, there are only a few studies that have methodologically addressed the issue of commuting stress (CS). AimThis paper aims to present in detail the development and validation of the Multimodal Commuting Stress Scale (MCSS), a self-report tool for assessing commuting stress-related factors among urban commuters of different modalities. MethodsThis cross-sectional study retrieved data from a nationwide sample of 1,429 commuters (aged between 18 and 78; average 34.42 years) from all 17 Spanish regions. Data were analyzed through Structural Equation Model-based competitive Confirmatory Factor Analyses, thus testing the psychometric performance of the scale under different structural assumptions, as well as its reliability, consistency, and validity insights. ResultsThe outcomes of this study suggest that the developed MCSS has a clear four-dimensional structure, an optimal set of factor loadings, fair goodness-of-fit indexes, and satisfactory internal consistency and reliability. Additionally, validity analyses show that commuting stress factors measured through the MCSS have coherent associations with both physical/mental health indexes and trip-related factors, while it also discriminates commuting stress scores by sex, age, and commuting modality. ConclusionAll in sum, the findings of this study endorse the suitability of the Multimodal Commuting Stress Scale for measuring stress-related factors affecting urban commuters, as well as to make comparisons among different groups of them.

Gevrey Well-posedness of the MHD boundary layer system with temperature

We study the MHD boundary layer system with temperature and establish the existence and uniqueness of the solutions in Gevrey function space with Gevrey index σ∈(1,32] without any structural assumption. Our proof is based on a new type of cancellation mechanism in this system to overcome the difficulty caused by the loss of derivatives.

Generation of Helical States - Breaking of Symmetries, Curie's Principle, and Excited States.

Herein, we deeply detail for the very first time mathematical concepts behind the generation of helical molecular orbitals (MOs) for linear chains of atoms. We first give a definition of helical MOs and we provide an index measuring how far a given helical states is from a perfect helical distribution. Structural properties of helical distribution for twisted -cumulene and cumulene version of Möbius systems are given. We then give some simple structural assumptions as well as symmetry requirements ensuring the existence of helical MOs. Considering molecules which do not admit helical MOs, we provide a first way to induce helical states by the breaking of symmetries. We also explore an alternative way using excited conformations of given molecules as well as different electronic multiplicities.

A numerical study of lightning-induced NOx and formation of NOy observed at the summit of Mt. Fuji using an explicit bulk lightning and photochemistry model

This study coupled a meteorological model with explicit bulk lightning and chemical transport models to investigate the impacts of lightning-induced nitrogen oxides (LNOx) on nitrogen monoxide (NO), nitrogen dioxide (NO2), and total reactive nitrogen oxide (NOy) measured on August 22, 2017, at the top of Mt. Fuji, Japan. Our simulation results indicated that the LNOx emitted around Wakasa Bay in the windward area of Mt. Fuji largely contributed to the NOy content measured at the top of Mt. Fuji. Furthermore, sensitivity experiments regarding the height of LNOx emissions indicated that the NOy content measured atop Mt. Fuji originated from LNOx emitted below 6 km. Our simulation assumed that a two-mode vertical distribution of LNOx emissions was more consistent with measured NOy at Mt. Fuji than a single-mode structure assumption in this case. A comparison of simulated NOx (= NO + NO2) and measured NOx at Mt. Fuji indicated that the reaction rates of the NO and NO2 cycles were well reproduced in our model; however, the ratio of NOz (NOy species other than NOx) to NOy estimated by the model were lower than the observed value, implying that the model either underestimated the reaction rate of LNOx or overestimated the wet removal of lightning-induced NOz. Finally, our results also suggest that the simultaneous observation of NOy and NOx is important for understanding LNOx emissions, subsequent atmospheric chemical reactions, and removal processes, as well as validating chemical transport models.

Sparse clusterability: testing for cluster structure in high dimensions

BackgroundCluster analysis is utilized frequently in scientific theory and applications to separate data into groups. A key assumption in many clustering algorithms is that the data was generated from a population consisting of multiple distinct clusters. Clusterability testing allows users to question the inherent assumption of latent cluster structure, a theoretical requirement for meaningful results in cluster analysis.ResultsThis paper proposes methods for clusterability testing designed for high-dimensional data by utilizing sparse principal component analysis. Type I error and power of the clusterability tests are evaluated using simulated data with different types of cluster structure in high dimensions. Empirical performance of the new methods is evaluated and compared with prior methods on gene expression, microarray, and shotgun proteomics data. Our methods had reasonably low Type I error and maintained power for many datasets with a variety of structures and dimensions. Cluster structure was not detectable in other datasets with spatially close clusters.ConclusionThis is the first analysis of clusterability testing on both simulated and real-world high-dimensional data.

Modeling the dependence of capillary sorptivity on initial water content for cement-based materials in view of water sensitivity

As a broadly used transport property indicating the durability of cement-based materials (CBMs), capillary sorptivity strongly depends on initial water content. Based on the underlying assumption of static pore structure in classical unsaturated flow theory, several models have been proposed to quantify the dependence of unsaturated sorptivity on initial water content, but all fail to capture the measured unsaturated sorptivity of CBMs. Considering water sensitivity of C-S-H gels (swell upon wetting and contract upon drying), a new model for unsaturated sorptivity is theoretically developed according to the inherent relationships among sorptivity, hydraulic diffusivity and permeability, and then successfully validated with reported experimental data of various CBMs. It is found relative sorptivity is dominated by the shape parameter representing tortuosity of pore structure, which is crucial in describing unsaturated mass transport. When measuring sorptivity, special attention should be paid to the drying preconditioning of tested specimens with certain uniform water content.

Development and validation of a higher-order thinking skills assessment scale for pre-service teachers

Higher-order thinking skills (HOTS) are highly required to be possessed by prospective teachers in the 21st century but there are limited studies on the development of appropriate measurement tools for this HOTS. Therefore, this study was conducted to develop a HOTS quantitative assessment instrument for pre-service teachers by collecting data from a sample of 701 pre-service teachers in China. The EFA (n = 310) confirmed a "4-dimensional, 14-factor" assessment structure which includes four main dimensions:critical thinking, problem-solving, teamwork, and practical innovation skills. Moreover, the correlated and hierarchical models run by CFA (n = 392) were consistent with the measurement theory structural assumptions, and the scale was observed to have ideal values of internal consistency reliability, convergent validity, and discriminant validity. The findings suggest that the PT-HOTS Test Scale is reliable and valid to measure the level of HOTS possessed by preservice teachers.

Perfectly matched sets in graphs: Parameterized and exact computation

In an undirected graph G=(V,E), we say that (A,B) is a pair of perfectly matched sets if A and B are disjoint subsets of V and every vertex in A (resp. B) has exactly one neighbor in B (resp. A). The size of a pair of perfectly matched sets (A,B) is |A|=|B|. The PERFECTLY MATCHED SETS problem is to decide whether a given graph G has a pair of perfectly matched sets of size k. We show that PMS is W[1]-hard when parameterized by solution size k even when restricted to split graphs and bipartite graphs. We observe that PMS is FPT when parameterized by clique-width, and give FPT algorithms with respect to the parameters distance to cluster, distance to co-cluster and treewidth. Complementing FPT results, we show that PMS does not admit a polynomial kernel when parameterized by vertex cover number unless NP⊆coNP/poly. We also provide an exact exponential algorithm running in time O⁎(1.966n). Finally, considering graphs with structural assumptions, we show that PMS remains NP-hard on planar graphs.