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This paper mainly focuses on a resource leveling variant of a two-processor scheduling problem. The latter problem is to schedule a set of dependent UET jobs on two identical processors with minimum makespan. It is known to be polynomial-time solvable. In the variant we consider, the resource constraint on processors is relaxed and the objective is no longer to minimize makespan. Instead, a deadline is imposed on the makespan and the objective is to minimize the total resource use exceeding a threshold resource level of two. This resource leveling criterion is known as the total overload cost. Sophisticated matching arguments allow us to provide a polynomial algorithm computing the optimal solution as a function of the makespan deadline. It extends a solving method from the literature for the two-processor scheduling problem. Moreover, the complexity of related resource leveling problems sharing the same objective is studied. These results lead to polynomial or pseudo-polynomial algorithms or NP-hardness proofs, allowing for an interesting comparison with classical machine scheduling problems.

The Spatial AutoRegressive model (SAR) is commonly used in studies involving spatial and network data to estimate the spatial or network peer influence and the effects of covariates on the response, taking into account the spatial or network dependence. While the model can be efficiently estimated with a Quasi maximum likelihood approach (QMLE), the detrimental effect of covariate measurement error on the QMLE and how to remedy it is currently unknown. If covariates are measured with error, then the QMLE may not have the $\sqrt{n}$ convergence and may even be inconsistent even when a node is influenced by only a limited number of other nodes or spatial units. We develop a measurement error-corrected ML estimator (ME-QMLE) for the parameters of the SAR model when covariates are measured with error. The ME-QMLE possesses statistical consistency and asymptotic normality properties. We consider two types of applications. The first is when the true covariate cannot be measured directly, and a proxy is observed instead. The second one involves including latent homophily factors estimated with error from the network for estimating peer influence. Our numerical results verify the bias correction property of the estimator and the accuracy of the standard error estimates in finite samples. We illustrate the method on a real dataset related to county-level death rates from the COVID-19 pandemic.

Molecular and genomic technological advancements have greatly enhanced our understanding of biological processes by allowing us to quantify key biological variables such as gene expression, protein levels, and microbiome compositions. These breakthroughs have enabled us to achieve increasingly higher levels of resolution in our measurements, exemplified by our ability to comprehensively profile biological information at the single-cell level. However, the analysis of such data faces several critical challenges: limited number of individuals, non-normality, potential dropouts, outliers, and repeated measurements from the same individual. In this article, we propose a novel method, which we call U-statistic based latent variable (ULV). Our proposed method takes advantage of the robustness of rank-based statistics and exploits the statistical efficiency of parametric methods for small sample sizes. It is a computationally feasible framework that addresses all the issues mentioned above simultaneously. An additional advantage of ULV is its flexibility in modeling various types of single-cell data, including both RNA and protein abundance. The usefulness of our method is demonstrated in two studies: a single-cell proteomics study of acute myelogenous leukemia (AML) and a single-cell RNA study of COVID-19 symptoms. In the AML study, ULV successfully identified differentially expressed proteins that would have been missed by the pseudobulk version of the Wilcoxon rank-sum test. In the COVID-19 study, ULV identified genes associated with covariates such as age and gender, and genes that would be missed without adjusting for covariates. The differentially expressed genes identified by our method are less biased toward genes with high expression levels. Furthermore, ULV identified additional gene pathways likely contributing to the mechanisms of COVID-19 severity.

The adoption of cloud computing is steadily increasing in designing and implementing software systems, thus it becomes imperative to consider the sustainability implications of these processes. While there has already been some academic research on this topic, there is a lack of perspective from practitioners. To bridge this gap, we utilize software repository mining techniques to examine 192 discussions among practitioners on the Software Engineering forum of the StackExchange platform, aiming to build an annotated dataset containing cloud architectural discussions and to understand the current discussion on sustainability in cloud architecture. To identify these discussions, we first put together a list of terms indicating sustainability as the topic. Our initial findings indicate practitioners mainly focus on design aspects (analysis, synthesis, and implementation) while avoiding complex activities like evaluation and maintenance. Technical sustainability is emphasized, while the economic dimension has the most discussions exclusively focused on it. This contrasts with previous academic literature, which highlighted environmental sustainability.

Federated Learning (FL) enables local devices to collaboratively learn a shared predictive model by only periodically sharing model parameters with a central aggregator. However, FL can be disadvantaged by statistical heterogeneity produced by the diversity in each local devices data distribution, which creates different levels of Independent and Identically Distributed (IID) data. Furthermore, this can be more complex when optimising different combinations of FL parameters and choosing optimal aggregation. In this paper, we present an empirical analysis of different FL training parameters and aggregators over various levels of statistical heterogeneity on three datasets. We propose a systematic data partition strategy to simulate different levels of statistical heterogeneity and a metric to measure the level of IID. Additionally, we empirically identify the best FL model and key parameters for datasets of different characteristics. On the basis of these, we present recommended guidelines for FL parameters and aggregators to optimise model performance under different levels of IID and with different datasets

Neural networks that can capture key principles underlying brain computation offer exciting new opportunities for developing artificial intelligence and brain-like computing algorithms. Such networks remain biologically plausible while leveraging localized forms of synaptic learning rules and modular network architecture found in the neocortex. Compared to backprop-driven deep learning approches, they provide more suitable models for deploying on neuromorphic hardware and have greater potential for scalability on large-scale computing clusters. The development of such brain-like neural networks depends on having a learning procedure that can build effective internal representations from data. In this work, we introduce and evaluate a brain-like neural network model capable of unsupervised representation learning. It builds on the Bayesian Confidence Propagation Neural Network (BCPNN), which has earlier been implemented as abstract as well as biophyscially detailed recurrent attractor neural networks explaining various cortical associative memory phenomena. Here we developed a feedforward BCPNN model to perform representation learning by incorporating a range of brain-like attributes derived from neocortical circuits such as cortical columns, divisive normalization, Hebbian synaptic plasticity, structural plasticity, sparse activity, and sparse patchy connectivity. The model was tested on a diverse set of popular machine learning benchmarks: grayscale images (MNIST, Fashion-MNIST), RGB natural images (SVHN, CIFAR-10), QSAR (MUV, HIV), and malware detection (EMBER). The performance of the model when using a linear classifier to predict the class labels fared competitively with conventional multi-layer perceptrons and other state-of-the-art brain-like neural networks.

Bayesian neural networks (BNN) promise to combine the predictive performance of neural networks with principled uncertainty modeling important for safety-critical systems and decision making. However, posterior uncertainty estimates depend on the choice of prior, and finding informative priors in weight-space has proven difficult. This has motivated variational inference (VI) methods that pose priors directly on the function generated by the BNN rather than on weights. In this paper, we address a fundamental issue with such function-space VI approaches pointed out by Burt et al. (2020), who showed that the objective function (ELBO) is negative infinite for most priors of interest. Our solution builds on generalized VI (Knoblauch et al., 2019) with the regularized KL divergence (Quang, 2019) and is, to the best of our knowledge, the first well-defined variational objective for function-space inference in BNNs with Gaussian process (GP) priors. Experiments show that our method incorporates the properties specified by the GP prior on synthetic and small real-world data sets, and provides competitive uncertainty estimates for regression, classification and out-of-distribution detection compared to BNN baselines with both function and weight-space priors.

Training spiking neural networks to approximate complex functions is essential for studying information processing in the brain and neuromorphic computing. Yet, the binary nature of spikes constitutes a challenge for direct gradient-based training. To sidestep this problem, surrogate gradients have proven empirically successful, but their theoretical foundation remains elusive. Here, we investigate the relation of surrogate gradients to two theoretically well-founded approaches. On the one hand, we consider smoothed probabilistic models, which, due to lack of support for automatic differentiation, are impractical for training deep spiking neural networks, yet provide gradients equivalent to surrogate gradients in single neurons. On the other hand, we examine stochastic automatic differentiation, which is compatible with discrete randomness but has never been applied to spiking neural network training. We find that the latter provides the missing theoretical basis for surrogate gradients in stochastic spiking neural networks. We further show that surrogate gradients in deterministic networks correspond to a particular asymptotic case and numerically confirm the effectiveness of surrogate gradients in stochastic multi-layer spiking neural networks. Finally, we illustrate that surrogate gradients are not conservative fields and, thus, not gradients of a surrogate loss. Our work provides the missing theoretical foundation for surrogate gradients and an analytically well-founded solution for end-to-end training of stochastic spiking neural networks.

Graph representation learning for hypergraphs can be used to extract patterns among higher-order interactions that are critically important in many real world problems. Current approaches designed for hypergraphs, however, are unable to handle different types of hypergraphs and are typically not generic for various learning tasks. Indeed, models that can predict variable-sized heterogeneous hyperedges have not been available. Here we develop a new self-attention based graph neural network called Hyper-SAGNN applicable to homogeneous and heterogeneous hypergraphs with variable hyperedge sizes. We perform extensive evaluations on multiple datasets, including four benchmark network datasets and two single-cell Hi-C datasets in genomics. We demonstrate that Hyper-SAGNN significantly outperforms the state-of-the-art methods on traditional tasks while also achieving great performance on a new task called outsider identification. Hyper-SAGNN will be useful for graph representation learning to uncover complex higher-order interactions in different applications.