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In this paper, we propose a variationally consistent technique for decreasing the maximum eigenfrequencies of structural dynamics related finite element formulations. Our approach is based on adding a symmetric positive-definite term to the mass matrix that follows from the integral of the traction jump across element boundaries. The added term is weighted by a small factor, for which we derive a suitable, and simple, element-local parameter choice. For linear problems, we show that our mass-scaling method produces no adverse effects in terms of spatial accuracy and orders of convergence. We illustrate these properties in one, two and three spatial dimension, for quadrilateral elements and triangular elements, and for up to fourth order polynomials basis functions. To extend the method to non-linear problems, we introduce a linear approximation and show that a sizeable increase in critical time-step size can be achieved while only causing minor (even beneficial) influences on the dynamic response.

An increasing number of publications present the joint application of Design of Experiments (DOE) and machine learning (ML) as a methodology to collect and analyze data on a specific industrial phenomenon. However, the literature shows that the choice of the design for data collection and model for data analysis is often driven by incidental factors, rather than by statistical or algorithmic advantages, thus there is a lack of studies which provide guidelines on what designs and ML models to jointly use for data collection and analysis. This is the first time in the literature that a paper discusses the choice of design in relation to the ML model performances. An extensive study is conducted that considers 12 experimental designs, 7 families of predictive models, 7 test functions that emulate physical processes, and 8 noise settings, both homoscedastic and heteroscedastic. The results of the research can have an immediate impact on the work of practitioners, providing guidelines for practical applications of DOE and ML.

In this paper we propose a flexible nested error regression small area model with high dimensional parameter that incorporates heterogeneity in regression coefficients and variance components. We develop a new robust small area specific estimating equations method that allows appropriate pooling of a large number of areas in estimating small area specific model parameters. We propose a parametric bootstrap and jackknife method to estimate not only the mean squared errors but also other commonly used uncertainty measures such as standard errors and coefficients of variation. We conduct both modelbased and design-based simulation experiments and real-life data analysis to evaluate the proposed methodology

Climate change in India is one of the most alarming problems faced by our community. Due to adverse and sudden changes in climate in past few years, mankind is at threat. Various impacts of climate change include extreme heat, changing rainfall patterns, droughts, groundwater, glacier melt, sea-level rise, and many more. Machine Learning can be used to analyze and predict the graph of change using previous data and thus design a model which in the future can furthermore be used to catalyze impactful work of climate change and take steps in the direction to help India fight against the upcoming climate changes. In this paper, we have analyzed 17 climate change parameters about India. We have applied linear regression, exponential regression, and polynomial regression to the parameters and evaluated the results. Using the designed model, we will predict these parameters for the years 2025,2030, 2035. These predicted values will thus help our community to prevent and take actions against the adverse and hazardous effects on mankind. We have designed and created this model which provides accurate results regarding all 17 parameters. The predicted values will therefore help India to be well equipped against climate change. This data when made available to the people of India will help create awareness among them and will help us save our country from the haphazard effects of climate change.

With the widespread use of AI systems and applications in our everyday lives, it is important to take fairness issues into consideration while designing and engineering these types of systems. Such systems can be used in many sensitive environments to make important and life-changing decisions; thus, it is crucial to ensure that the decisions do not reflect discriminatory behavior toward certain groups or populations. We have recently seen work in machine learning, natural language processing, and deep learning that addresses such challenges in different subdomains. With the commercialization of these systems, researchers are becoming aware of the biases that these applications can contain and have attempted to address them. In this survey we investigated different real-world applications that have shown biases in various ways, and we listed different sources of biases that can affect AI applications. We then created a taxonomy for fairness definitions that machine learning researchers have defined in order to avoid the existing bias in AI systems. In addition to that, we examined different domains and subdomains in AI showing what researchers have observed with regard to unfair outcomes in the state-of-the-art methods and how they have tried to address them. There are still many future directions and solutions that can be taken to mitigate the problem of bias in AI systems. We are hoping that this survey will motivate researchers to tackle these issues in the near future by observing existing work in their respective fields.

We consider a time-varying first-order autoregressive model with irregular innovations, where we assume that the coefficient function is H\"{o}lder continuous. To estimate this function, we use a quasi-maximum likelihood based approach. A precise control of this method demands a delicate analysis of extremes of certain weakly dependent processes, our main result being a concentration inequality for such quantities. Based on our analysis, upper and matching minimax lower bounds are derived, showing the optimality of our estimators. Unlike the regular case, the information theoretic complexity depends both on the smoothness and an additional shape parameter, characterizing the irregularity of the underlying distribution. The results and ideas for the proofs are very different from classical and more recent methods in connection with statistics and inference for locally stationary processes.

The learning process of deep learning methods usually updates the model's parameters in multiple iterations. Each iteration can be viewed as the first-order approximation of Taylor's series expansion. The remainder, which consists of higher-order terms, is usually ignored in the learning process for simplicity. This learning scheme empowers various multimedia based applications, such as image retrieval, recommendation system, and video search. Generally, multimedia data (e.g., images) are semantics-rich and high-dimensional, hence the remainders of approximations are possibly non-zero. In this work, we consider the remainder to be informative and study how it affects the learning process. To this end, we propose a new learning approach, namely gradient adjustment learning (GAL), to leverage the knowledge learned from the past training iterations to adjust vanilla gradients, such that the remainders are minimized and the approximations are improved. The proposed GAL is model- and optimizer-agnostic, and is easy to adapt to the standard learning framework. It is evaluated on three tasks, i.e., image classification, object detection, and regression, with state-of-the-art models and optimizers. The experiments show that the proposed GAL consistently enhances the evaluated models, whereas the ablation studies validate various aspects of the proposed GAL. The code is available at \url{//github.com/luoyan407/gradient_adjustment.git}.

Consider estimation of average treatment effects with multi-valued treatments using augmented inverse probability weighted (IPW) estimators, depending on outcome regression and propensity score models in high-dimensional settings. These regression models are often fitted by regularized likelihood-based estimation, while ignoring how the fitted functions are used in the subsequent inference about the treatment parameters. Such separate estimation can be associated with known difficulties in existing methods. We develop regularized calibrated estimation for fitting propensity score and outcome regression models, where sparsity-including penalties are employed to facilitate variable selection but the loss functions are carefully chosen such that valid confidence intervals can be obtained under possible model misspecification. Unlike in the case of binary treatments, the usual augmented IPW estimator is generalized by allowing different copies of coefficient estimators in outcome regression to ensure just-identification. For propensity score estimation, the new loss function and estimating functions are directly tied to achieving covariate balance between weighted treatment groups. We develop practical numerical algorithms for computing the regularized calibrated estimators with group Lasso by innovatively exploiting Fisher scoring, and provide rigorous high-dimensional analysis for the resulting augmented IPW estimators under suitable sparsity conditions, while tackling technical issues absent or overlooked in previous analyses. We present simulation studies and an empirical application to estimate the effects of maternal smoking on birth weights. The proposed methods are implemented in the R package mRCAL.

With the advances of data-driven machine learning research, a wide variety of prediction problems have been tackled. It has become critical to explore how machine learning and specifically deep learning methods can be exploited to analyse healthcare data. A major limitation of existing methods has been the focus on grid-like data; however, the structure of physiological recordings are often irregular and unordered which makes it difficult to conceptualise them as a matrix. As such, graph neural networks have attracted significant attention by exploiting implicit information that resides in a biological system, with interactive nodes connected by edges whose weights can be either temporal associations or anatomical junctions. In this survey, we thoroughly review the different types of graph architectures and their applications in healthcare. We provide an overview of these methods in a systematic manner, organized by their domain of application including functional connectivity, anatomical structure and electrical-based analysis. We also outline the limitations of existing techniques and discuss potential directions for future research.

Machine learning methods are powerful in distinguishing different phases of matter in an automated way and provide a new perspective on the study of physical phenomena. We train a Restricted Boltzmann Machine (RBM) on data constructed with spin configurations sampled from the Ising Hamiltonian at different values of temperature and external magnetic field using Monte Carlo methods. From the trained machine we obtain the flow of iterative reconstruction of spin state configurations to faithfully reproduce the observables of the physical system. We find that the flow of the trained RBM approaches the spin configurations of the maximal possible specific heat which resemble the near criticality region of the Ising model. In the special case of the vanishing magnetic field the trained RBM converges to the critical point of the Renormalization Group (RG) flow of the lattice model. Our results suggest an alternative explanation of how the machine identifies the physical phase transitions, by recognizing certain properties of the configuration like the maximization of the specific heat, instead of associating directly the recognition procedure with the RG flow and its fixed points. Then from the reconstructed data we deduce the critical exponent associated to the magnetization to find satisfactory agreement with the actual physical value. We assume no prior knowledge about the criticality of the system and its Hamiltonian.