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This paper aims to develop a semi-formal design space for Human-AI interactions, by building a set of interaction primitives which specify the communication between users and AI systems during their interaction. We show how these primitives can be combined into a set of interaction patterns which can provide an abstract specification for exchanging messages between humans and AI/ML models to carry out purposeful interactions. The motivation behind this is twofold: firstly, to provide a compact generalisation of existing practices, that highlights the similarities and differences between systems in terms of their interaction behaviours; and secondly, to support the creation of new systems, in particular by opening the space of possibilities for interactions with models. We present a short literature review on frameworks, guidelines and taxonomies related to the design and implementation of HAI interactions, including human-in-the-loop, explainable AI, as well as hybrid intelligence and collaborative learning approaches. From the literature review, we define a vocabulary for describing information exchanges in terms of providing and requesting particular model-specific data types. Based on this vocabulary, a message passing model for interactions between humans and models is presented, which we demonstrate can account for existing systems and approaches. Finally, we build this into design patterns as mid-level constructs that capture common interactional structures. We discuss how this approach can be used towards a design space for Human-AI interactions that creates new possibilities for designs as well as keeping track of implementation issues and concerns.

In this work, we provide a simulation algorithm to simulate from a (multivariate) characteristic function, which is only accessible in a black-box format. We construct a generative neural network, whose loss function exploits a specific representation of the Maximum-Mean-Discrepancy metric to directly incorporate the targeted characteristic function. The construction is universal in the sense that it is independent of the dimension and that it does not require any assumptions on the given characteristic function. Furthermore, finite sample guarantees on the approximation quality in terms of the Maximum-Mean Discrepancy metric are derived. The method is illustrated in a short simulation study.

Modelling of systems where the full system information is unknown is an oft encountered problem for various engineering and industrial applications, as it's either impossible to consider all the complex physics involved or simpler models are considered to keep within the limits of the available resources. Recent advances in greybox modelling like the deep hidden physics models address this space by combining data and physics. However, for most real-life applications, model generalizability is a key issue, as retraining a model for every small change in system inputs and parameters or modification in domain configuration can render the model economically unviable. In this work we present a novel enhancement to the idea of hidden physics models which can generalize for changes in system inputs, parameters and domains. We also show that this approach holds promise in system discovery as well and helps learn the hidden physics for the changed system inputs, parameters and domain configuration.

This article aims to study efficient/trace optimal designs for crossover trials, with multiple response recorded from each subject in each time period. A multivariate fixed effect model is proposed with direct and carryover effects corresponding to the multiple responses and the error dispersion matrix allowing for correlations to exist between and within responses. Two correlation structures, namely the proportional and the generalized markov covariances are studied. The corresponding information matrices for direct effects under the two covariances are used to determine efficient designs. Efficiency of orthogonal array designs of Type $I$ and strength $2$ is investigated for the two covariance forms. To motivate the multivariate crossover designs, a gene expression data in a $3 \times 3$ framework is utilized.

Within Bayesian nonparametrics, dependent Dirichlet process mixture models provide a highly flexible approach for conducting inference about the conditional density function. However, several formulations of this class make either rather restrictive modelling assumptions or involve intricate algorithms for posterior inference, thus preventing their widespread use. In response to these challenges, we present a flexible, versatile, and computationally tractable model for density regression based on a single-weights dependent Dirichlet process mixture of normal distributions model for univariate continuous responses. We assume an additive structure for the mean of each mixture component and incorporate the effects of continuous covariates through smooth nonlinear functions. The key components of our modelling approach are penalised B-splines and their bivariate tensor product extension. Our proposed method also seamlessly accommodates parametric effects of categorical covariates, linear effects of continuous covariates, interactions between categorical and/or continuous covariates, varying coefficient terms, and random effects, which is why we refer our model as a Dirichlet process mixture of normal structured additive regression models. A noteworthy feature of our method is its efficiency in posterior simulation through Gibbs sampling, as closed-form full conditional distributions for all model parameters are available. Results from a simulation study demonstrate that our approach successfully recovers true conditional densities and other regression functionals in various challenging scenarios. Applications to a toxicology, disease diagnosis, and agricultural study are provided and further underpin the broad applicability of our modelling framework. An R package, \texttt{DDPstar}, implementing the proposed method is publicly available at \url{//bitbucket.org/mxrodriguez/ddpstar}.

In the present paper, we propose a block variant of the extended Hessenberg process for computing approximations of matrix functions and other problems producing large-scale matrices. Applications to the computation of a matrix function such as f(A)V, where A is an nxn large sparse matrix, V is an nxp block with p<<n, and f is a function are presented. Solving shifted linear systems with multiple right hand sides are also given. Computing approximations of these matrix problems appear in many scientific and engineering applications. Different numerical experiments are provided to show the effectiveness of the proposed method for these problems.

In a topology optimization setting, design-dependent fluidic pressure loads pose several challenges as their direction, magnitude, and location alter with topology evolution. This paper offers a compact 100-line MATLAB code, TOPress, for topology optimization of structures subjected to fluidic pressure loads using the method of moving asymptotes. The code is intended for pedagogical purposes and aims to ease the beginners' and students' learning toward topology optimization with design-dependent fluidic pressure loads. TOPress is developed per the approach first reported in Kumar et al. (Struct Multidisc Optim 61(4):1637-1655, 2020). The Darcy law, in conjunction with the drainage term, is used to model the applied pressure load. The consistent nodal loads are determined from the obtained pressure field. The employed approach facilitates inexpensive computation of the load sensitivities using the adjoint-variable method. Compliance minimization subject to volume constraint optimization problems are solved. The success and efficacy of the code are demonstrated by solving benchmark numerical examples involving pressure loads, wherein the importance of load sensitivities is also demonstrated. TOPress contains six main parts, is described in detail, and is extended to solve different problems. Steps to include a projection filter are provided to achieve loadbearing designs close to~0-1. The code is provided in Appendix~B and can also be downloaded along with its extensions from \url{//github.com/PrabhatIn/TOPress}.

The proximal gradient method is a generic technique introduced to tackle the non-smoothness in optimization problems, wherein the objective function is expressed as the sum of a differentiable convex part and a non-differentiable regularization term. Such problems with tensor format are of interest in many fields of applied mathematics such as image and video processing. Our goal in this paper is to address the solution of such problems with a more general form of the regularization term. An adapted iterative proximal gradient method is introduced for this purpose. Due to the slowness of the proposed algorithm, we use new tensor extrapolation methods to enhance its convergence. Numerical experiments on color image deblurring are conducted to illustrate the efficiency of our approach.

Spatial areal models encounter the well-known and challenging problem of spatial confounding. This issue makes it arduous to distinguish between the impacts of observed covariates and spatial random effects. Despite previous research and various proposed methods to tackle this problem, finding a definitive solution remains elusive. In this paper, we propose a simplified version of the spatial+ approach that involves dividing the covariate into two components. One component captures large-scale spatial dependence, while the other accounts for short-scale dependence. This approach eliminates the need to separately fit spatial models for the covariates. We apply this method to analyse two forms of crimes against women, namely rapes and dowry deaths, in Uttar Pradesh, India, exploring their relationship with socio-demographic covariates. To evaluate the performance of the new approach, we conduct extensive simulation studies under different spatial confounding scenarios. The results demonstrate that the proposed method provides reliable estimates of fixed effects and posterior correlations between different responses.

This paper proposes several approaches as baselines to compute a shared active subspace for multivariate vector-valued functions. The goal is to minimize the deviation between the function evaluations on the original space and those on the reconstructed one. This is done either by manipulating the gradients or the symmetric positive (semi-)definite (SPD) matrices computed from the gradients of each component function so as to get a single structure common to all component functions. These approaches can be applied to any data irrespective of the underlying distribution unlike the existing vector-valued approach that is constrained to a normal distribution. We test the effectiveness of these methods on five optimization problems. The experiments show that, in general, the SPD-level methods are superior to the gradient-level ones, and are close to the vector-valued approach in the case of a normal distribution. Interestingly, in most cases it suffices to take the sum of the SPD matrices to identify the best shared active subspace.