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Supervised machine learning methods for geological mapping via remote sensing face limitations due to the scarcity of accurately labelled training data that can be addressed by unsupervised learning, such as dimensionality reduction and clustering. Dimensionality reduction methods have the potential to play a crucial role in improving the accuracy of geological maps. Although conventional dimensionality reduction methods may struggle with nonlinear data, unsupervised deep learning models such as autoencoders can model non-linear relationships. Stacked autoencoders feature multiple interconnected layers to capture hierarchical data representations useful for remote sensing data. This study presents an unsupervised machine learning-based framework for processing remote sensing data using stacked autoencoders for dimensionality reduction and k-means clustering for mapping geological units. We use Landsat 8, ASTER, and Sentinel-2 datasets to evaluate the framework for geological mapping of the Mutawintji region in Western New South Wales, Australia. We also compare stacked autoencoders with principal component analysis and canonical autoencoders. Our results reveal that the framework produces accurate and interpretable geological maps, efficiently discriminating rock units. We find that the accuracy of stacked autoencoders ranges from 86.6 % to 90 %, depending on the remote sensing data type, which is superior to their counterparts. We also find that the generated maps align with prior geological knowledge of the study area while providing novel insights into geological structures.

Machine Learning (ML) in low-data settings remains an underappreciated yet crucial problem. Hence, data augmentation methods to increase the sample size of datasets needed for ML are key to unlocking the transformative potential of ML in data-deprived regions and domains. Unfortunately, the limited training set constrains traditional tabular synthetic data generators in their ability to generate a large and diverse augmented dataset needed for ML tasks. To address this challenge, we introduce CLLM, which leverages the prior knowledge of Large Language Models (LLMs) for data augmentation in the low-data regime. However, not all the data generated by LLMs will improve downstream utility, as for any generative model. Consequently, we introduce a principled curation mechanism, leveraging learning dynamics, coupled with confidence and uncertainty metrics, to obtain a high-quality dataset. Empirically, on multiple real-world datasets, we demonstrate the superior performance of CLLM in the low-data regime compared to conventional generators. Additionally, we provide insights into the LLM generation and curation mechanism, shedding light on the features that enable them to output high-quality augmented datasets.

We address the problem of the best uniform approximation of a continuous function on a convex domain. The approximation is by linear combinations of a finite system of functions (not necessarily Chebyshev) under arbitrary linear constraints. By modifying the concept of alternance and of the Remez iterative procedure we present a method, which demonstrates its efficiency in numerical problems. The linear rate of convergence is proved under some favourable assumptions. A special attention is paid to systems of complex exponents, Gaussian functions, lacunar algebraic and trigonometric polynomials. Applications to signal processing, linear ODE, switching dynamical systems, and to Markov-Bernstein type inequalities are considered.

This contribution introduces a model order reduction approach for an advection-reaction problem with a parametrized reaction function. The underlying discretization uses an ultraweak formulation with an $L^2$-like trial space and an 'optimal' test space as introduced by Demkowicz et al. This ensures the stability of the discretization and in addition allows for a symmetric reformulation of the problem in terms of a dual solution which can also be interpreted as the normal equations of an adjoint least-squares problem. Classic model order reduction techniques can then be applied to the space of dual solutions which also immediately gives a reduced primal space. We show that the necessary computations do not require the reconstruction of any primal solutions and can instead be performed entirely on the space of dual solutions. We prove exponential convergence of the Kolmogorov $N$-width and show that a greedy algorithm produces quasi-optimal approximation spaces for both the primal and the dual solution space. Numerical experiments based on the benchmark problem of a catalytic filter confirm the applicability of the proposed method.

Edge detection is a fundamental task in computer vision. It has made great progress under the development of deep convolutional neural networks (DCNNs), some of which have achieved a beyond human-level performance. However, recent top-performing edge detection methods tend to generate thick and noisy edge lines. In this work, we solve this problem from two aspects: (1) the lack of prior knowledge regarding image edges, and (2) the issue of imbalanced pixel distribution. We propose a second-order derivative-based multi-scale contextual enhancement module (SDMCM) to help the model locate true edge pixels accurately by introducing the edge prior knowledge. We also construct a hybrid focal loss function (HFL) to alleviate the imbalanced distribution issue. In addition, we employ the conditionally parameterized convolution (CondConv) to develop a novel boundary refinement module (BRM), which can further refine the final output edge maps. In the end, we propose a U-shape network named LUS-Net which is based on the SDMCM and BRM for crisp edge detection. We perform extensive experiments on three standard benchmarks, and the experiment results illustrate that our method can predict crisp and clean edge maps and achieves state-of-the-art performance on the BSDS500 dataset (ODS=0.829), NYUD-V2 dataset (ODS=0.768), and BIPED dataset (ODS=0.903).

User experience on mobile devices is constrained by limited battery capacity and processing power, but 6G technology advancements are diving rapidly into mobile technical evolution. Mobile edge computing (MEC) offers a solution, offloading computationally intensive tasks to edge cloud servers, reducing battery drain compared to local processing. The upcoming integrated sensing and communication in mobile communication may improve the trajectory prediction and processing delays. This study proposes a greedy resource allocation optimization strategy for multi-user networks to minimize aggregate energy usage. Numerical results show potential improvement at 33\% for every 1000 iteration. Addressing prediction model division and velocity accuracy issues is crucial for better results. A plan for further improvement and achieving objectives is outlined for the upcoming work phase.

Agent-based models (ABM) provide an excellent framework for modeling outbreaks and interventions in epidemiology by explicitly accounting for diverse individual interactions and environments. However, these models are usually stochastic and highly parametrized, requiring precise calibration for predictive performance. When considering realistic numbers of agents and properly accounting for stochasticity, this high dimensional calibration can be computationally prohibitive. This paper presents a random forest based surrogate modeling technique to accelerate the evaluation of ABMs and demonstrates its use to calibrate an epidemiological ABM named CityCOVID via Markov chain Monte Carlo (MCMC). The technique is first outlined in the context of CityCOVID's quantities of interest, namely hospitalizations and deaths, by exploring dimensionality reduction via temporal decomposition with principal component analysis (PCA) and via sensitivity analysis. The calibration problem is then presented and samples are generated to best match COVID-19 hospitalization and death numbers in Chicago from March to June in 2020. These results are compared with previous approximate Bayesian calibration (IMABC) results and their predictive performance is analyzed showing improved performance with a reduction in computation.

This note discusses a simple modification of cross-conformal prediction inspired by recent work on e-values. The precursor of conformal prediction developed in the 1990s by Gammerman, Vapnik, and Vovk was also based on e-values and is called conformal e-prediction in this note. Replacing e-values by p-values led to conformal prediction, which has important advantages over conformal e-prediction without obvious disadvantages. The situation with cross-conformal prediction is, however, different: whereas for cross-conformal prediction validity is only an empirical fact (and can be broken with excessive randomization), this note draws the reader's attention to the obvious fact that cross-conformal e-prediction enjoys a guaranteed property of validity.

Factor models are widely used for dimension reduction in the analysis of multivariate data. This is achieved through decomposition of a p x p covariance matrix into the sum of two components. Through a latent factor representation, they can be interpreted as a diagonal matrix of idiosyncratic variances and a shared variation matrix, that is, the product of a p x k factor loadings matrix and its transpose. If k << p, this defines a parsimonious factorisation of the covariance matrix. Historically, little attention has been paid to incorporating prior information in Bayesian analyses using factor models where, at best, the prior for the factor loadings is order invariant. In this work, a class of structured priors is developed that can encode ideas of dependence structure about the shared variation matrix. The construction allows data-informed shrinkage towards sensible parametric structures while also facilitating inference over the number of factors. Using an unconstrained reparameterisation of stationary vector autoregressions, the methodology is extended to stationary dynamic factor models. For computational inference, parameter-expanded Markov chain Monte Carlo samplers are proposed, including an efficient adaptive Gibbs sampler. Two substantive applications showcase the scope of the methodology and its inferential benefits.

This paper investigates the problem of regression model generation. A model is a superposition of primitive functions. The model structure is described by a weighted colored graph. Each graph vertex corresponds to some primitive function. An edge assigns a superposition of two functions. The weight of an edge equals the probability of superposition. To generate an optimal model one has to reconstruct its structure from its graph adjacency matrix. The proposed algorithm reconstructs the~minimum spanning tree from the~weighted colored graph. This paper presents a novel solution based on the prize-collecting Steiner tree algorithm. This algorithm is compared with its alternatives.