Parameter estimation has been studied quite extensively in standard mixture models.

NNS problem and should be used for the original data.

A sensor has the ability to probe its surroundings. However, uncertainties in its exact location can significantly compromise its sensing performance. The radius of robust feasibility defines the maximum range within which robust feasibility is ensured. This work introduces a novel approach integrating it with the directional sensor networks to enhance coverage using a distributed greedy algorithm. In particular, we provide an exact formula for the radius of robust feasibility of sensors in a directional sensor network. The proposed model strategically orients the sensors in regions with high coverage potential, accounting for robustness in the face of uncertainty. We analyze the algorithm's adaptability in dynamic environments, demonstrating its ability to enhance efficiency and robustness. Experimental results validate its efficacy in maximizing coverage and optimizing sensor orientations, highlighting its practical advantages for real-world scenarios.

In this paper, we propose a combinatorial framework for the semi-discrete OT, which can be viewed as an extension of the combinatorial framework for the discrete OT but requires several new ideas.

Parameter estimation has been studied quite extensively in standard mixture models.

See proof of Proposition 3 below for the form of the Jacobian. Theorem 4.7] and so is the product p Equation ( 50) is an element-wise division. The main preprocessing we did was to (i) remove the "label" attribute from each data set, and (ii) Descriptions for all data set are below. All data have been completely anonymized. The original task was to predict whether an applicant would be recommended for acceptance by hierarchical decision model, which has been removed during preprocessing.

Figure S1(a) shows a noisy circle-torus model (cf. To show the result, it is enough to use Theorem 2 with properly chosen (fake) centers on the above dataset. The code is provided as a ZIP file as part of the supplementary material. True clusters are distinguished by their color. We have the following extension of Proposition 3. Proposition S1.