Structural Assumptions Research Articles

Statistical inference for principal components of spiked covariance matrices

In this paper, we study the asymptotic behavior of the extreme eigenvalues and eigenvectors of the high-dimensional spiked sample covariance matrices, in the supercritical case when a reliable detection of spikes is possible. In particular, we derive the joint distribution of the extreme eigenvalues and the generalized components of the associated eigenvectors, that is, the projections of the eigenvectors onto arbitrary given direction, assuming that the dimension and sample size are comparably large. In general, the joint distribution is given in terms of linear combinations of finitely many Gaussian and Chi-square variables, with parameters depending on the projection direction and the spikes. Our assumption on the spikes is fully general. First, the strengths of spikes are only required to be slightly above the critical threshold and no upper bound on the strengths is needed. Second, multiple spikes, that is, spikes with the same strength, are allowed. Third, no structural assumption is imposed on the spikes. Thanks to the general setting, we can then apply the results to various high dimensional statistical hypothesis testing problems involving both the eigenvalues and eigenvectors. Specifically, we propose accurate and powerful statistics to conduct hypothesis testing on the principal components. These statistics are data-dependent and adaptive to the underlying true spikes. Numerical simulations also confirm the accuracy and powerfulness of our proposed statistics and illustrate significantly better performance compared to the existing methods in the literature. In particular, our methods are accurate and powerful even when either the spikes are small or the dimension is large.

Multivariate ranks and quantiles using optimal transport: Consistency, rates and nonparametric testing

In this paper, we study multivariate ranks and quantiles, defined using the theory of optimal transport, and build on the work of Chernozhukov et al. (Ann. Statist. 45 (2017) 223–256) and Hallin et al. (Ann. Statist. 49 (2021) 1139–1165). We study the characterization, computation and properties of the multivariate rank and quantile functions and their empirical counterparts. We derive the uniform consistency of these empirical estimates to their population versions, under certain assumptions. In fact, we prove a Glivenko–Cantelli type theorem that shows the asymptotic stability of the empirical rank map in any direction. Under mild structural assumptions, we provide global and local rates of convergence of the empirical quantile and rank maps. We also provide a sub-Gaussian tail bound for the global L2-loss of the empirical quantile function. Further, we propose tuning parameter-free multivariate nonparametric tests—a two-sample test and a test for mutual independence—based on our notion of multivariate quantiles/ranks. Asymptotic consistency of these tests are shown and the rates of convergence of the associated test statistics are derived, both under the null and alternative hypotheses.

Seismic displacement ratios for soil-pile-structure systems allowed to uplift

In this paper, the soil-pile-structure interaction effects on seismic displacement demands are investigated using various dimensionless parameters. The code prescribed procedures for estimating seismic displacement demands are built upon fixed-base structure assumption and neglect the effect of foundation uplift. Tensile index, the ratio of the summation of the tensile strength of all piles to the weight of the structure, is introduced as a novel dimensionless ratio for the seismic assessments. The seismic behavior of the structures with a small tensile index is close to the structures with uplift-allowed shallow foundations. Structures with a large tensile index behave like tied foundation structures. The tensile index paves the path to cover the interaction effects from the soil-structure to soil-pile-structure interaction. The considered simplified structure in this study is a single degree of freedom model with a rigid foundation mounted on a group of piles simulated using the Winkler springs. The piles are simulated using nonlinear uniaxial springs with asymmetrical behavior under tensile and compressive forces. The accuracy of the model is verified by calculating the displacement ratios for four cases; The first three cases representing high tensile index (tied foundation), are verified with the code results, and Case 4, which represents low tensile index (uplift-allowed foundation), is compared to the literature. More than 150,000 nonlinear response history dynamic analyses are conducted for several dimensionless parameters and 20 ground motion records with various intensities and for each analysis, the displacement of the structure, linear and nonlinear hinge plastic rotation, and the foundation rotation and uplift are collected. The results, including elastic and inelastic displacement ratios, are finally compared with those of ASCE41 for shallow fixed-base foundations. It is concluded that for the cases with no pile slippage, the code prediction is accurate enough. However, in cases with high soil-pile-structure interaction effects and low tensile index, the displacement ratios are up to twice the code predictions. • Tensile index is developed to assess the soil-pile-structure interaction effects. • Simplified uplift-allowed SDOF model with piles simulated using Winkler springs. • Elastic and inelastic displacement ratios are compared with the code predictions. • Foundation uplift, tensile index and aspect and periodic ratios are investigated.

Structure of turbulence in temporal planar jets

A detailed analysis of the structure of turbulence in a temporal planar turbulent jet is reported. Instantaneous snapshots of the flow and three-dimensional spatial correlation functions are considered. It is found that the flow is characterized by large-scale spanwise vortices whose motion is felt in the entire flow field. Superimposed to this large-scale motion, a hierarchy of turbulent structures is present. The most coherent ones take the form of quasi-streamwise vortices and high and low streamwise velocity streaks. The topology of these interacting structures is analyzed by quantitatively addressing their shape and size in the different flow regions. Such information is recognized to be relevant for a structural description of the otherwise disorganized motion in turbulent free-shear flows and can be used for the assessment of models based on coherent structure assumptions. Finally, the resulting scenario provides a phenomenological description of the elementary processes at the basis of turbulence in free-shear flows.

Essential Regression: A generalizable framework for inferring causal latent factors from multi-omic datasets

SummaryHigh-dimensional cellular and molecular profiling of biological samples highlights the need for analytical approaches that can integrate multi-omic datasets to generate prioritized causal inferences. Current methods are limited by high dimensionality of the combined datasets, the differences in their data distributions, and their integration to infer causal relationships. Here, we present Essential Regression (ER), a novel latent-factor-regression-based interpretable machine-learning approach that addresses these problems by identifying latent factors and their likely cause-effect relationships with system-wide outcomes/properties of interest. ER can integrate many multi-omic datasets without structural or distributional assumptions regarding the data. It outperforms a range of state-of-the-art methods in terms of prediction. ER can be coupled with probabilistic graphical modeling, thereby strengthening the causal inferences. The utility of ER is demonstrated using multi-omic system immunology datasets to generate and validate novel cellular and molecular inferences in a wide range of contexts including immunosenescence and immune dysregulation.

Effect of gas compressibility on fluid field of air‐cooled turbo‐generator

The effect of gas compressibility on the fluid flow characteristics of a 350 MW air-cooled turbo-generator is investigated in this paper. Two gas models taking gas compressibility and incompressibility into account are established for numerical calculation. Then, a one-fourth physical model based on the practical ventilation structure and basic assumption is built to analyse the flow velocity and flow rate using the finite volume method (FVM). The FVM-predicted flow rate and flow velocity of cooling medium in the air cavity, stator and rotor of the generator show the distribution characteristics of flow rate and velocity in the generator is affected by the gas compressibility model selection. The comparison of FVM-predicted flow rate and experimental value shows that the FVM-predicted results using the gas compressibility model is more accurate when comparing to those using the incompressible model. Therefore, the gas compressibility model is an appealing approach to analyse the flow fluid characteristics of the air-cooled turbo-generator.

Understanding Dynamics of Nonlinear Representation Learning and Its Application.

Representations of the world environment play a crucial role in artificial intelligence. It is often inefficient to conduct reasoning and inference directly in the space of raw sensory representations, such as pixel values of images. Representation learning allows us to automatically discover suitable representations from raw sensory data. For example, given raw sensory data, a deep neural network learns nonlinear representations at its hidden layers, which are subsequently used for classification (or regression) at its output layer. This happens implicitly during training through minimizing a supervised or unsupervised loss. In this letter, we study the dynamics of such implicit nonlinear representation learning. We identify a pair of a new assumption and a novel condition, called the on-model structure assumption and the data architecture alignment condition. Under the on-model structure assumption, the data architecture alignment condition is shown to be sufficient for the global convergence and necessary for global optimality. Moreover, our theory explains how and when increasing network size does and does not improve the training behaviors in the practical regime. Our results provide practical guidance for designing a model structure; for example, the on-model structure assumption can be used as a justification for using a particular model structure instead of others. As an application, we then derive a new training framework, which satisfies the data architecture alignment condition without assuming it by automatically modifying any given training algorithm dependent on data and architecture. Given a standard training algorithm, the framework running its modified version is empirically shown to maintain competitive (practical) test performances while providing global convergence guarantees for deep residual neural networks with convolutions, skip connections, and batch normalization with standard benchmark data sets, including MNIST, CIFAR-10, CIFAR-100, Semeion, KMNIST, and SVHN.

Development and implementation of multi-agent systems for demand response aggregators in an industrial context

Demand Response (DR) mechanisms are an important pillar in the transition to a bigger share of renewable energy in the power grid. To utilize DR, industrial companies can offer load flexibility at DR markets by cooperating with DR aggregators. Numerous studies promote the use of multi-agent systems (MAS) in this domain, however there is a lack of actual implementations and real world adaption. The literature has identified several reasons for this. These include research that often focuses on a high level of abstraction, the assumption of homogeneous structures for the use of agents, and insufficient tools and solutions for industrial deployment. To help DR aggregators use MAS in their existing virtual power plants, this paper presents a MAS that enables a step-by-step switch to agent technology and enables them to implement the solutions developed by the research community to improve the management of their systems. The proposed technical implementation on standard industrial equipment and the required interfaces to flexibility provider and DR aggregator are derived from the German DR market requirements. A simulation of the MAS implemented on a laboratory setup via the Java Agent DEvelopment Framework will be presented. This should provide a foundation for the transition to real world adaption in the future, which will then be discussed to show the benefits and drawbacks of this solution.

Prestressed ultra-high performance concrete (UHPC) beams for reusable structural systems: design and testing

With the aim to reduce the environmental footprint of buildings, this paper presents an original structural system concept for two-way slabs in residential and office buildings. The proposed system extends the best practice in terms of modularity, versatility, demountability, reusability, and durability. A finite set of elements can be used to form the main load-bearing system of multiple successively constructed buildings having different and unpredicted layouts and static systems. Ultra-High Performance Concrete (UHPC) was identified as one of the most promising materials for this application because of its high strength, extreme durability and the opportunities it opens for shape optimization and material consumption reduction. In the first part of this contribution, the main features of the new structural system and preliminary design assumptions for UHPC modules are briefly outlined. Then, the authors present and discuss the results of an experimental campaign on prestressed UHPC beams that were tested in bending and shear, under service and ultimate load conditions. Beams with transversal openings in the web were also tested to assess the influence of these openings on the cracking behavior and shear strength of the beams. Experimental results provide useful information for the subsequent modeling of the structural system. Thanks to the presence of fibers, transversal openings in the web only have a limited influence on the response of the beams, thus allowing horizontal technical shafts to pass through the structural thickness of the slab.

Time-smoothing for parabolic variational problems in metric measure spaces

In 2013, Masson and Siljander determined a method to prove that the minimal p-weak upper gradient $$g_{f_\varepsilon }$$ for the time mollification $$f_\varepsilon $$ , $$\varepsilon >0$$ , of a parabolic Newton–Sobolev function $$f\in L^p_\mathrm {loc}(0,\tau ;N^{1,p}_\mathrm {loc}(\Omega ))$$ , with $$\tau >0$$ and $$\Omega $$ open domain in a doubling metric measure space $$(\mathbb {X},d,\mu )$$ supporting a weak (1, p)-Poincaré inequality, $$p\in (1,\infty )$$ , is such that $$g_{f-f_\varepsilon }\rightarrow 0$$ as $$\varepsilon \rightarrow 0$$ in $$L^p_\mathrm {loc}(\Omega _\tau )$$ , $$\Omega _\tau $$ being the parabolic cylinder $$\Omega _\tau :=\Omega \times (0,\tau )$$ . Their approach involved the use of Cheeger’s differential structure, and therefore exhibited some limitations; here, we shall see that the definition and the formal properties of the parabolic Sobolev spaces themselves allow to find a more direct method to show such convergence, which relies on p-weak upper gradients only and which is valid regardless of structural assumptions on the ambient space, also in the limiting case when $$p=1$$ .

Study on instability discriminating condition and permeability variation of triangle articulated structure in highly inclined goaf

The huge, inclined goaf formed by the mining of steeply inclined and extra thick coal seams has the characteristics of occupying a large space and being subject to complex breaking behavior of its overlying rock structure, especially the rock block structure characteristics of the interface area between the goaf and the lower working face which is difficult to be characterized, leading to a hidden danger when mining the lower working face. In response to the aforementioned problems, the following conclusions are drawing as follows: (1) with the aid of the contradiction method, the critical condition governing instability of the triangular articulated structure was obtained to explain the correctness of the assumption of the triangular hinged structure; (2) three-point truss structure was composed of key layer blocks; (3) in the stabilization stage of the triangular hinged structure, the fracture network area was extracted, and the centerline intensive equivalent method of a single fracture segment was adopted to directly measure the equivalent length. Meanwhile, the value of equivalent average width with the equivalent length of a single crack was calculated by integral operation and equivalent figure calculation; (4) the mathematical expressions of permeability which was positively exponential function related to the ratio of equivalent average width to equivalent length were derived. Furthermore, the vectorized solution of seepage rate was carried out respectively for the goaf area and the extracted network area by using COMSOL software. The distribution of the strong seepage area of CBM and the ratio of equivalent average width to equivalent length is found to be consistent to a large extent, which provides theoretical support for subsequent CBM management.

An Adaptive Surrogate-Assisted Endmember Extraction Framework Based on Intelligent Optimization Algorithms for Hyperspectral Remote Sensing Images

As the foremost step of spectral unmixing, endmember extraction has been one of the most challenging techniques in the spectral unmixing processing due to the mixing of pixels and the complexity of hyperspectral remote sensing images. The existing geometrial-based endmember extraction algorithms have achieved the ideal results, but most of these algorithms perform poorly when they do not meet the assumption of simplex structure. Recently, many intelligent optimization algorithms have been employed to solve the problem of endmember extraction. Although they achieved the better performance than the geometrial-based algorithms in different complex scenarios, they also suffer from the time-consuming problem. In order to alleviate the above problems, balance the two key indicators of accuracy and running time, an adaptive surrogate-assisted endmember extraction (ASAEE) framework based on intelligent optimization algorithms is proposed for hyperspectral remote sensing images in this paper. In the proposed framework, the surrogate-assisted model is established to reduce the expensive time cost of the intelligent algorithms by fitting the fully constrained evaluation value with the low-cost estimated value. In more detail, three commonly used intelligent algorithms, namely genetic algorithm, particle swarm optimization algorithm and differential evolution algorithm, are specifically designed into the ASAEE framework to verify the effectiveness and robustness. In addition, an adaptive weight surrogate-assisted model selection strategy is proposed, which can automatically adjust the weights of different surrogate models according to the characteristics of different intelligent algorithms. Experimental results on three data sets (including two simulated data sets and one real data set) show the effectiveness and the excellent performance of the proposed ASAEE framework.

On the use of sulphur as a tracer for abundances in galaxies

Abstract 2+We present a methodology for the use of sulphur as global metallicity tracer in galaxies, allowing performing a complete abundance analysis using only the red-to-near-infrared spectral region. We have applied it to a compilation of high-quality data split into two samples: H ii regions (DHR) in spiral and irregular galaxies, and dwarf galaxies dominated by a strong starburst (H ii Gal). Sulphur abundances have been derived by direct methods under the assumption of an ionization structure composed of two zones: an intermediate-ionization one where S++ is originated, and a low-ionization one where S+ is formed. Ionization correction factors (ICF) have been calculated from the Ar/Ar3+ ratio and are shown to correlate with the hardness of the radiation field. Only about 10 per cent of the objects show S3+ contributions to the total abundance larger than 30 per cent. A good correlation exists between sulphur abundance and ionizing temperature with low-metallicity objects being ionized by hotter stars. No correlation is found between ionization parameter and total S/H abundance. Most of the H ii Gal objects show S/O ratios below the solar value and a trend for increasing S/O ratios with increasing sulphur abundances, while DHR objects show S/O ratios larger than solar and a tendency for lower S/O ratios for higher metallicities. Finally, we present a calibration of the sulphur abundance through the S23 parameter that remains single valued up to sulphur abundances well beyond the solar value. S23 is independent of the ionization parameter and only weakly dependent on ionizing temperature.

Comparison of kriging and least-squares collocation – Revisited

Abstract The well-known to physical geodesists method of least-squares collocation and the geostatistical method of kriging probably known to the broader audience are compared. Both methods are rooted in Wiener–Kolmogorov’s (W–K) prediction theory; but, since necessity is the mother of invention, the W–K foundations have been extended to satisfy the needs of particular applications. The paper presents a link or rather an equivalence of the two methods as far as their basic forms are considered (specialization to geodetic boundary-value problems, covariance propagation between functionals and nonlinear geostatistical methods are excluded from this comparison). Only scalar random fields (univariate case) and the assumption of a second-order structure of a random function are considered. Due to the equivalence of their basic formulas, both techniques share the same advantages and disadvantages. The paper also shows the difference as to the predicted values and prediction variances in case of exact and filtered (noise reduction) prediction models. This theoretical comparison of the methods has practical implications because of readily available geostatistical software that, in local as well as global applications, can be used for predictive problems occurring in geodesy and surveying.

Multiscale scattering in nonlinear Kerr-type media

We propose a multiscale approach for a nonlinear Helmholtz problem with possible oscillations in the Kerr coefficient, the refractive index, and the diffusion coefficient. The method does not rely on structural assumptions on the coefficients and combines the multiscale technique known as Localized Orthogonal Decomposition with an adaptive iterative approximation of the nonlinearity. We rigorously analyze the method in terms of well-posedness and convergence properties based on suitable assumptions on the initial data and the discretization parameters. Numerical examples illustrate the theoretical error estimates and underline the practicability of the approach.

Full waveform inversion using Random Mixing

Most deterministic full waveform inversion (FWI) approaches require an initial model, which serves as a starting point for the inversion. Determining such an initial model, however, is not straight forward. In this paper, a geostatistical inversion approach called Random Mixing (RM) for FWI is presented. Instead of an initial model, RM requires the assumption of a spatial dependence structure and a univariate marginal distribution. RM uses linear combinations of spatial random fields to constrain the velocity field during inversion. As it is realization-based, RM allows quantification of estimation uncertainty in terms of estimation variance. The presented algorithm uses the finite element method to discretize the seismic forward model and Message Passing Interface is used to parallelize the algorithm. Two synthetic examples are presented to demonstrate the applicability of RM for FWI.

Hölder continuity for vectorial local minimizers of variational integrals

This note deals with vectorial local minimizers of some integral functionals related to nonlinear elasticity theory. Under some structural assumptions, we derive that each component of the local minimizers lies in the De Giorgi class, thus the minimizers are locally Hölder continuous. We emphasize that no convexity is assumed. On the other hand, a special dependence on minors, taken from the Jacobian matrix, plays an important role in the proof.

CANONICAL THRESHOLDING FOR NON-SPARSE HIGH-DIMENSIONAL LINEAR REGRESSION.

We consider a high-dimensional linear regression problem. Unlike many papers on the topic, we do not require sparsity of the regression coefficients; instead, our main structural assumption is a decay of eigenvalues of the covariance matrix of the data. We propose a new family of estimators, called the canonical thresholding estimators, which pick largest regression coefficients in the canonical form. The estimators admit an explicit form and can be linked to LASSO and Principal Component Regression (PCR). A theoretical analysis for both fixed design and random design settings is provided. Obtained bounds on the mean squared error and the prediction error of a specific estimator from the family allow to clearly state sufficient conditions on the decay of eigenvalues to ensure convergence. In addition, we promote the use of the relative errors, strongly linked with the out-of-sample R 2. The study of these relative errors leads to a new concept of joint effective dimension, which incorporates the covariance of the data and the regression coefficients simultaneously, and describes the complexity of a linear regression problem. Some minimax lower bounds are established to showcase the optimality of our procedure. Numerical simulations confirm good performance of the proposed estimators compared to the previously developed methods.

Estimating latent, dynamic processes of breast cancer tumour growth and distant metastatic spread from mammography screening data.

We propose a framework for jointly modelling tumour size at diagnosis and time to distant metastatic spread, from diagnosis, based on latent dynamic sub-models of growth of the primary tumour and of distant metastatic detection. The framework also includes a sub-model for screening sensitivity as a function of latent tumour size. Our approach connects post-diagnosis events to the natural history of cancer and, once refined, may prove useful for evaluating new interventions, such as personalised screening regimes. We evaluate our model-fitting procedure using Monte Carlo simulation, showing that the estimation algorithm can retrieve the correct model parameters, that key patterns in the data can be captured by the model even with misspecification of some structural assumptions, and that, still, with enough data it should be possible to detect strong misspecifications. Furthermore, we fit our model to observational data from an extension of a case-control study of post-menopausal breast cancer in Sweden, providing model-based estimates of the probability of being free from detected distant metastasis as a function of tumour size, mode of detection (of the primary tumour), and screening history. For women with screen-detected cancer and two previous negative screens, the probabilities of being free from detected distant metastases 5 years after detection and removal of the primary tumour are 0.97, 0.89 and 0.59 for tumours of diameter 5, 15 and 35 mm, respectively. We also study the probability of having latent/dormant metastases at detection of the primary tumour, estimating that 33% of patients in our study had such metastases.

Dual-Polarized FDD Massive MIMO: A Comprehensive Framework

We propose a comprehensive scheme for realizing a massive multiple-input multiple-output (MIMO) system with dual-polarized antennas in frequency division duplexing (FDD) mode. Dual-polarized arrays are commonly employed due to the favorable property that, in principle, they can double the number of channel spatial degrees of freedom with a less-than-proportional increase in array size. However, processing a dual-polarized massive MIMO channel is demanding due to the high channel dimension and the lack of Uplink-Downlink (UL-DL) channel reciprocity in FDD mode. In particular, the difficulty arises in common channel training and DL precoding in a multi-user setup. To address this, we develop a unified framework consisting of three steps: (1) covariance estimation to efficiently estimate the UL covariance from noisy UL pilots; (2) a UL-DL covariance transformation method that obtains the DL covariance from the estimated UL covariance, eliminating the need for DL channel covariance training via pilot transmission; <xref ref-type="disp-formula" rid="deqn3a-deqn3b" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">(3)</xref> a joint multi-user DL channel training method, which enables the BS to estimate <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">effective DL channels</i> given any protocol-specific pilot dimension and to use them for interference-free DL beamforming and data transmission. Through extensive simulations, we show that our scheme is applicable to a variety of communication scenarios in terms of the number of antennas, UL and DL pilot dimensions, and angular scattering properties. Unlike the common trend in the literature, we do <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">not</i> make strong structural assumptions about the wireless channel (such as angular sparsity), ensuring a general treatment of the problem.