Multidimensional Domain Research Articles

Nonparametric tests for semiparametric regression models

Semiparametric regression models have received considerable attention over the last decades, because of their flexibility and their good finite sample performances. Here we propose an innovative nonparametric test for the linear part of the models, based on random sign-flipping of an appropriate transformation of the residuals, that exploits a spectral decomposition of the residualizing matrix associated with the nonparametric part of the model. The test can be applied to a vast class of extensively used semiparametric regression models with roughness penalties, with nonparametric components defined over one-dimensional, as well as over multi-dimensional domains, including, for instance, models based on univariate or multivariate splines. We prove the good asymptotic properties of the proposed test. Moreover, by means of extensive simulation studies, we show the superiority of the proposed test with respect to current parametric alternatives, demonstrating its excellent control of the Type I error, accompanied by a good power, even in challenging data scenarios, where instead current parametric alternatives fail.

Differential-difference systems in the analysis of weak solvability of initial-boundary value problems with a spatial variable in a network-like domain

In the work, the approach and the corresponding methods, which make it possible to construct a priori estimates of weak solutions of a differential-difference system with a spatial variable varying in a multidimensional network-like domain are indicated. Such estimates in spaces of summable functions are used to find solvability conditions for boundary value problems of various types for differential-difference systems. In addition, a priori estimates are used to justify the application of the method of discretization with respect to the time variable (semi-discretization) to the analysis of the weak solvability of initial-boundary value problems and the subsequent construction of approximations of weak solutions. The rationale for the approach used is the fact that in a fairly wide class applied analysis of the problems of transporting continuous media networks-like carriers, the representation of mathematical models of the process using the formalisms of differential-difference systems is the only tool for effectively solving these problems. For example, the reduction of a differential system (initial-boundary value problem) to the corresponding differential-difference system makes it possible not only to significantly simplify the analysis of problems of optimal control of a differential system (since this analysis reduces to studying the problem of optimal control of a system of elliptic equations), but also, using classical methods of control theory for elliptic systems, algorithmize the original problem. The reduction used often facilitates establishing the conditions for the existence and uniqueness of optimal control of a differential system. These problems also include a fairly large range of studies of non-stationary network-like hydrodynamic processes and flow phenomena. As an illustration of the approach used and the results obtained, the analysis of the solvability of the linearized Navier–Stokes system is given and the ways of studying the nonlinear Navier–Stokes system are indicated.

Barcoding, linear and nonlinear analysis of full-day leg movements in infants with typical development and infants at risk of developmental disabilities: Cross-sectional study.

Traditional methods do not capture the multidimensional domains and dynamic nature of infant behavioral patterns. We aim to compare full-day, in-home leg movement data between infants with typical development (TD) and infants at risk of developmental disabilities (AR) using barcoding and nonlinear analysis. Eleven infants with TD (2-10 months) and nine infants AR (adjusted age: 2-14 months) wore a sensor on each ankle for 7 days. We calculated the standard deviation for linear variability and sample entropy (SampEn) of leg acceleration and angular velocity for nonlinear variability. Movements were also categorized into 16 barcoding states, and we calculated the SampEn and proportions of the barcoding. All variables were compared between the two groups using independent-samples t-test or Mann-Whitney U test. The AR group had larger linear variability compared to the TD group. SampEn was lower in the AR group compared to TD group for both acceleration and angular velocity. Two barcoding states' proportions were significantly different between the two groups. The results showed that nonlinear analysis and barcoding could be used to identify the difference of dynamic multidimensional movement patterns between infants AR and infants with TD. This information may help early diagnosis of developmental disabilities in the future.

Cauchy–Dirichlet Problem to Semilinear Multi-Term Fractional Differential Equations

In this paper, we analyze the well-posedness of the Cauchy–Dirichlet problem to an integro-differential equation on a multidimensional domain Ω⊂Rn in the unknown u=u(x,t), Dtν0(ϱ0u)−Dtν1(ϱ1u)−L1u−∫0tK(t−s)L2u(x,s)ds=f(x,t)+g(u),0<ν1<ν0<1, where Dtνi are the Caputo fractional derivatives, ϱi=ϱi(x,t) with ϱ0≥μ0>0, and Li are uniform elliptic operators with time-dependent smooth coefficients. The principal feature of this equation is related to the integro-differential operator Dtν0(ϱ0u)−Dtν1(ϱ1u), which (under certain assumption on the coefficients) can be rewritten in the form of a generalized fractional derivative with a non-positive kernel. A particular case of this equation describes oxygen delivery through capillaries to tissue. First, under proper requirements on the given data in the linear model and certain relations between ν0 and ν1, we derive a priori estimates of a solution in Sobolev–Slobodeckii spaces that gives rise to providing the Hölder regularity of the solution. Exploiting these estimates and constructing appropriate approximate solutions, we prove the global strong solvability to the corresponding linear initial-boundary value problem. Finally, obtaining a priori estimates in the fractional Hölder classes and assuming additional conditions on the coefficients ϱ0 and ϱ1 and the nonlinearity g(u), the global one-valued classical solvability to the nonlinear model is claimed with the continuation argument method.

On a limiting system of the triangular SKT competition model with large cross-diffusion and random-diffusion

This paper mainly focus on the limiting system which arises from the study of SKT competition model when both the cross-diffusion rate and the random-diffusion rate tend to infinity. For multi-dimensional domains, the existence of positive steady states bifurcating from a double eigenvalue can be proved by applying the bifurcation argument with some special transformation when the birth rate of one species is near some critical value. Further by virtue of the spectral perturbation argument based on the Lyapunov–Schmidt decomposition method, we prove the spectral instability of such nontrivial positive steady states for the limiting system.

TERFDA: Tensor Embedding RF Domain Adaptation for varying noise interference

Radio frequency machine learning (RFML) can be loosely termed as a field that machine learning (ML) and deep learning (DL) techniques to applications related to wireless communications. However, traditional RFML basically assume that the data of training set and test set are independent and identically distributed and only a large number of labeled data can train a classification model which can effectively classify test set data. In other words, without enough training samples, it is impossible to learn an automatic modulation classifier that performs well in varying noise interference environment. Feature-based transfer learning minimizes the distribution difference between historical modulated signal data and new data by learning similarity-maximizing feature spaces. Therefore, in this paper, Dynamic Distribution Adaptation (DDA) is adopted to address the above challenges. We propose a Tensor Embedding RF Domain Adaptation (TERFDA) approach, which learns the latent subspace of the tensors formed by the time–frequency maps of the signals, so that use the multi-dimensional domain information of the signals to jointly learn the shared feature subspace of the source domain and the target domain, then perform DDA in the shared subspace. The experimental results show that under the modulated signal data, compared with the state-of-the-art DA algorithm, TERFDA has less requirements on the number of samples and categories, and has superior performance for confrontation the varying noise interference between source domain and target domain.

Multidimensional Domain Knowledge Framework for Poet Profiling

Authorship profiling is a subtask of authorship identification. This task can be regarded as an analysis of personal writing styles, which has been widely investigated. However, no previous studies have attempted to analyze the authorship of classical Chinese poetry. First, we provide an approach to evaluate the popularity of poets, and we also establish a public corpus containing the top 20 most popular poets in the Tang Dynasty for authorship profiling. Then, a novel poetry authorship profiling framework named multidimensional domain knowledge poet profiling (M-DKPP) is proposed, combining the knowledge of authorship attribution and the text’s stylistic features with domain knowledge described by experts in traditional poetry studies. A case study for Li Bai is used to prove the validity and applicability of our framework. Finally, the performance of M-DKPP framework is evaluated with four poem datasets. On all datasets, the proposed framework outperforms several baseline approaches for authorship attribution.

Machine learning and micromechanics as allies to establish composition-property correlations in cement pastes

Composition-property correlations are fundamental to understand cement-based materials behavior and optimize their formulation. Modelling based on fundamental material component constitutes a reliable tool to establish these correlations with the advantage of better exploring formulation space when compared with the often adopted experimental trial-and-error approaches. In this context, Machine Learning (ML) and Micromechanics-Based (MB) methods have been concurrently used for property prediction from material composition. Here, we show that these techniques can be allies for establishing composition-property correlations. We focus on predictions of Ordinary Portland Cement pastes elastic properties, but the outlined strategy can be extended to other cement systems. Various microstructures representations are considered in MB estimates, including multiscale representations and representations with ellipsoidal inclusions. In contrast, ML predictions do not need any a priori assumption on material microstructure. Predictions using ML and MB yield similar accuracy when compared against test datasets (but ML performed much better regarding the error estimated in training datasets). Working as allies, ML can be deployed to evaluate the (lack of) knowledge over the multi-dimensional parametric domains, and micromechanics provides a theoretical background for property data curation and is a tool to make up for missing data in databases.

The Impact of Academic, Sociodemographic, and Program Growth Factors on Admission Offers to U.S. Graduate Education Programs in Communication Sciences and Disorders: National Trends in 2016-2020 Cycles.

The purpose of this study was to investigate the impact of academic factors and sociodemographic factors on offers of admission to graduate education programs in communication sciences and disorders (speech-language pathology and audiology) in the United States. A retrospective analysis of extant data from undergraduate students applying to graduate education programs through the Communication Sciences and Disorders Centralized Application Service (CSDCAS) was conducted. Descriptive, parametric, nonparametric, and multivariate hierarchical logistic modeling analyses were applied to data from 38,625 unique applicants across four consecutive application cycles from 2016 to 2020 to assess relationships between admission offers, and academic and sociodemographic factors. The academic factors included Graduate Record Examination (GRE) and grade point average (GPA; cumulative undergraduate GPA and cumulative communication sciences and disorders [CSD] GPA), and sociodemographic factors included race/ethnicity, age, disadvantaged socioeconomic status, first-generation status, and multilinguistic status. The rate of receiving an offer of admission continuously increased from 59.4% in the 2016-2017 cycle to 75.4% in the 2019-2020 cycle (p < .001). The significant predictors for admission offers across all four application cycles were GPA, GRE, and applicant age. While the odds ratios of GRE and age were relatively stable, the odds ratios of GPA had a decreasing trend. Bivariate analyses showed that students who were non-White, older, socioeconomically disadvantaged, first-generation, and nonmultilingual were significantly less likely to receive offers of admission than their counterparts, but the relationships between those sociodemographic factors, except for age, and admission offers diminished when all factors were considered in the logistic regression analyses. Academic and sociodemographic factors significantly affected the likelihood of obtaining at least one offer of admission to a graduate program in CSD at different levels. While the effect sizes were variable, these findings provide evidence-based guidance for admission committees seeking to improve the inclusiveness of admission processes and the realization of greater diversity across multidimensional domains (e.g., race/ethnicity, socioeconomic status, age).

Echo-state-network-based iterative learning control of distributed systems

The paper proposes an effective modeling and control procedure for the distributed-parameter systems using the echo-state network. The main idea is to reconstruct the spatiotemporal dynamics defined in a given multi-dimensional domain. In the investigated problem positions of both sensors and actuators are fixed allowing to delegate the complex system dynamics to echo-state network. Imposing a proper partitioning of the spatial domain, a specific topology of a neural network is used to form a reservoir capable to follow not only temporal but also spatial dynamics of the system. Based on available historical data, neural network model is initially trained and then used to derive the control law in the framework of iterative learning control. The echo-state network can be retrained after a particular control iterate in order to reduce model uncertainty and to fit it to the current operating conditions as much as possible. The performance of the proposed approach is tested and evaluated on the example of the squared clamped plate control.

Effect of the COVID-19 Pandemic on the Self-Perceived Change of Caregivers' Burden in Providing Care for People With Dementia.

Objectives: To explore how the COVID-19 pandemic affects caregiver (CG) burden, the quality of care provided to people with dementia (PwD) and their perceived changes between before and during the pandemic. Methods: A cross-sectional study surveyed primary CGs about burden and self-perceived change in multidimensional domains and compared these before and during the pandemic. Results: About 135 primary CGs of PwD were enrolled at Siriraj Hospital's Geriatric Clinic in Thailand and assessed using various online platforms. About 13.8% of CGs had a "mild to moderate" burden. The NPI-Q score and level of functional capacity of the PwD declined during the COVID-19 pandemic (p-value .001 and .001, respectively). The CG-associated factors that related to a higher CG burden were younger age (mean age of 54.2 years old), female (76.3%), and high educational level (80.7%). Conflict between CG and PwD was associated with an increase in CG burden (p-value .004; 95% CI [1.19, 6.12]). Regarding the COVID-19-related factors, there was no association between CG burden and the PwD's characteristics or COVID-19-related concerns. Conclusions: The COVID-19 pandemic was associated with a higher CG burden. Identifying the related factors in an unusual situation may help reduce the CG burden and improve the care of PwD.

Optimal function-on-scalar regression over complex domains

In this work we consider the problem of estimating function-on-scalar regression models when the functions are observed over multi-dimensional or manifold domains and with potentially multivariate output. We establish the minimax rates of convergence and present an estimator based on reproducing kernel Hilbert spaces that achieves the minimax rate. To better interpret the derived rates, we extend well-known links between RKHS and Sobolev spaces to the case where the domain is a compact Riemannian manifold. This is accomplished using an interesting connection to Weyl’s Law from partial differential equations. We conclude with a numerical study and an application to 3D facial imaging.

The Cauchy problem for matrix factorization of the Helmholtz equation in a multidimensional unbounded domain

In the present paper, a Carleman matrix is constructed and, on the basis of this matrix, an approximate solution of the Cauchy problem in a multidimensional unbounded domain is found in an explicit form.

Exposing and understanding synergistic effects in co-pyrolysis of biomass and plastic waste via machine learning

During co-pyrolysis of biomass with plastic waste, bio-oil yields (BOY) could be either induced or reduced significantly via synergistic effects (SE). However, investigating/ interpreting the SE and BOY in multidimensional domains is complicated and limited. This work applied XGBoost machine-learning and Shapley additive explanation (SHAP) to develop interpretable/ explainable models for predicting BOY and SE from co-pyrolysis of biomass and plastic waste using 26 input features. Imbalanced training datasets were improved by synthetic minority over-sampling technique. The prediction accuracy of XGBoost models was nearly 0.90 R2 for BOY while greater than 0.85 R2 for SE. By SHAP, individual impact and interaction of input features on the XGBoost models can be achieved. Although reaction temperature and biomass-to-plastic ratio were the top two important features, overall contributions of feedstock characteristics were more than 60 % in the system of co-pyrolysis. The finding provides a better understanding of co-pyrolysis and a way of further improvements.

Gaussian Orthogonal Latent Factor Processes for Large Incomplete Matrices of Correlated Data

We introduce Gaussian orthogonal latent factor processes for modeling and predicting large correlated data. To handle the computational challenge, we first decompose the likelihood function of the Gaussian random field with a multi-dimensional input domain into a product of densities at the orthogonal components with lower-dimensional inputs. The continuous-time Kalman filter is implemented to compute the likelihood function efficiently without making approximations. We also show that the posterior distribution of the factor processes is independent, as a consequence of prior independence of factor processes and orthogonal factor loading matrix. For studies with large sample sizes, we propose a flexible way to model the mean, and we derive the marginal posterior distribution to solve identifiability issues in sampling these parameters. Both simulated and real data applications confirm the outstanding performance of this method.

Extension of an exponential discretization scheme to multidimensional convection–diffusion problems

ENATE (Enhanced Numerical Approximation of a Transport Equation) is a high-order exponential scheme for convection–diffusion problems, such as those that govern the transport of fluid properties in a flow field. The scheme was intended to be employed in fluid-related transport equations, although it can be used for any inhomogeneous second-order ordinary differential equation. The value of a variable ϕ at a generic point is related to those of adjacent nodes via an algebraic equation. Thus, a three-point stencil is associated to each node. The coefficients of this equation contain integrals of some fluid and flow parameters. One important property is that the scheme allows to obtain a machine-accurate solution of an inhomogeneous transport equation if these integrals can be obtained analytically. As the scheme is essentially one-dimensional, getting the machine-accurate solution of multidimensional problems is not guaranteed even in cases where ENATE integrals are analytic along each coordinate. In this regard the paper presents a simple way of getting solutions in multidimensional problems while still using the one-dimensional formulation. Moreover, if the problem is such that the solution is machine-accurate in the one-dimensional problem along coordinate lines, it will also be for the multidimensional domain. Two different methods of evaluating those terms that come out of the discretization will be explained and compared in various cases.

CovNet: Covariance Networks for Functional Data on Multidimensional Domains

AbstractCovariance estimation is ubiquitous in functional data analysis. Yet, the case of functional observations over multidimensional domains introduces computational and statistical challenges, rendering the standard methods effectively inapplicable. To address this problem, we introduce Covariance Networks (CovNet) as a modelling and estimation tool. The CovNet model is universal—it can be used to approximate any covariance up to desired precision. Moreover, the model can be fitted efficiently to the data and its neural network architecture allows us to employ modern computational tools in the implementation. The CovNet model also admits a closed-form eigendecomposition, which can be computed efficiently, without constructing the covariance itself. This facilitates easy storage and subsequent manipulation of a covariance in the context of the CovNet. We establish consistency of the proposed estimator and derive its rate of convergence. The usefulness of the proposed method is demonstrated via an extensive simulation study and an application to resting state functional magnetic resonance imaging data.

On-grid compressive sampling for spherical field measurements in acoustics.

We derive a compressive sampling method for acoustic field reconstruction using field measurements on a pre-defined spherical grid that has theoretically guaranteed relations between signal sparsity, measurement number, and reconstruction accuracy. This method can be used to reconstruct band limited spherical harmonic or Wigner D-function series (spherical harmonic series are a special case) with sparse coefficients. Contrasting typical compressive sampling methods for Wigner D-function series that use arbitrary random measurements, the new method samples randomly on an equiangular grid, a practical and commonly used sampling pattern. Using its periodic extension, we transform the reconstruction of a Wigner D-function series into a multi-dimensional Fourier domain reconstruction problem. We establish that this transformation has a bounded effect on sparsity level and provide numerical studies of this effect. We also compare the reconstruction performance of the new approach to classical Nyquist sampling and existing compressive sampling methods. In our tests, the new compressive sampling approach performs comparably to other guaranteed compressive sampling approaches and needs a fraction of the measurements dictated by the Nyquist sampling theorem. Moreover, using one-third of the measurements or less, the new compressive sampling method can provide over 20 dB better de-noising capability than oversampling with classical Fourier theory.

Low Dose and Non-Targeted Radiation Effects in Environmental Protection and Medicine-A New Model Focusing on Electromagnetic Signaling.

The role of signalling in initiating and perpetuating effects triggered by deposition of ionising radiation energy in parts of a system is very clear. Less clear are the very early steps involved in converting energy to chemical and biological effects in non-targeted parts of the system. The paper aims to present a new model, which could aid our understanding of the role of low dose effects in determining ultimate disease outcomes. We propose a key role for electromagnetic signals resulting from physico-chemical processes such as excitation decay, and acoustic waves. These lead to the initiation of damage response pathways such as elevation of reactive oxygen species and membrane associated changes in key ion channels. Critically, these signalling pathways allow coordination of responses across system levels. For example, depending on how these perturbations are transduced, adverse or beneficial outcomes may predominate. We suggest that by appreciating the importance of signalling and communication between multiple levels of organisation, a unified theory could emerge. This would allow the development of models incorporating time, space and system level to position data in appropriate areas of a multidimensional domain. We propose the use of the term “infosome” to capture the nature of radiation-induced communication systems which include physical as well as chemical signals. We have named our model “the variable response model” or “VRM” which allows for multiple outcomes following exposure to low doses or to signals from low dose irradiated cells, tissues or organisms. We suggest that the use of both dose and infosome in radiation protection might open up new conceptual avenues that could allow intrinsic uncertainty to be embraced within a holistic protection framework.

The structure of (local) ordinal Bayesian incentive compatible random rules

We explore the structure of locally ordinal Bayesian incentive compatible (LOBIC) random Bayesian rules (RBRs). We show that under lower contour monotonicity, for almost all prior profiles (with full Lebesgue measure), a LOBIC RBR is locally dominant strategy incentive compatible (LDSIC). We further show that for almost all prior profiles, a unanimous and LOBIC RBR on the unrestricted domain is random dictatorial, and thereby extend the result in Gibbard (Econometrica 45:665–681, 1977) for Bayesian rules. Next, we provide a sufficient condition on a domain so that for almost all prior profiles, unanimous RBRs on it are tops-only. Finally, we provide a wide range of applications of our results on single-peaked (on arbitrary graphs), hybrid, multiple single-peaked, single-dipped, single-crossing, multi-dimensional separable domains, and domains under partitioning. Since OBIC implies LOBIC by definition, all our results hold for OBIC RBRs.