Characterization of wastewater methane emission sources with computer vision and remote sensing

Methane emissions are responsible for at least one-third of the total anthropogenic climate forcing and current estimations expect a significant increase in these emissions in the next decade. Consequently, methane offers a unique opportunity to mitigate climate change while addressing energy supply problems. From the five primary methane sources, residual water treatment provided 7% of the emissions in 2010. This ratio will undoubtedly increase with global population growth. Therefore, locating sources of methane emissions is a crucial step in characterizing the current distribution of GHG better. Nevertheless, there is a lack of comprehensive global and uniform databases to bind those emissions to concrete sources and there is no automatic method to accurately locate sparse human infrastructures such as wastewater treatment plants (WWTPs). WWTP detection is an open problem posing many obstacles due to the lack of freely accessible high-resolution imagery, and the variety of real-world morphologies and sizes. In this work, we tackle this state-of-the-art complex problem and go one step forward by trying to infer capacity using one end-to-end Deep Learning architecture and multi-modal remote sensing data. This goal has a groundbreaking potential impact, as it could help estimate mapped methane emissions for improving emission inventories and future scenarios prediction. We will address the problem as a combination of two parallel inference exercises by proposing a novel network to combine multimodal data based on the hypothesis that the location and the capacity can be inferred based on characteristics such as the plant situation, size, morphology, and proximity to water bodies or population centers. We explore technical documentation and literature to develop these hypotheses and validate their soundness with data analysis. To validate the architecture and the hypotheses, we develop a model and a dataset in parallel with a series of ablation tests. The process is facilitated by an automatic pipeline, also developed in this work, to create datasets and validate models leveraging those datasets. We test the best-obtained model at scale on a mosaic composed of satellite imagery covering the region of Catalonia. The goal is to find plants not previously labeled but present in wastewater treatment plant (WWTP) databases and to compare the distribution and magnitude of the inferred capacity with the ground truth. Results show that we can achieve state-of-the-art results by locating more than half of the labeled plants with the same precision ratio and by only using orthophotos from multispectral imagery. Moreover, we demonstrate that additional data sources related to water basins and population are valuable resources that the model can exploit to infer WWTP capacity. During the process, we also demonstrate the benefit of using negative instances to train our model and the impact of using an appropriate loss function such as Dice's loss

On Gruenhage spaces, separating σ-isolated families, and their relatives

We prove that, given a topological space X, the following conditions are equivalent. (α) X is a Gruenhage space. (β) X has a countable cover by sets of small local diameter (property SLD) by F∩G sets. (γ) X has a separating σ-isolated family M⊂F∩G. (δ) X has a one-to-one continuous map into a metric space which has a σ-isolated base of F∩G sets. Besides, we provide an example which shows Fragmentability ⇏ property SLD ⇏ the space to be Gruenhage.This work has been partially supported by the Generalitat Valenciana project GV/2014/072 and Universidad de Alicante project GRE11-08

On dentability and cones with a large dual

In this paper we provide some equivalences on dentability in normed spaces. Among others we prove: the origin is a denting point of a pointed cone C if and only if it is a point of continuity for such a cone and C∗ − C∗ = X∗; x is a denting point of a convex set A if and only if x is a point of continuity and a weakly strongly extreme point of A. We also analize how our results help us to shed some light on several open problems in the literature.M. A. Melguizo Padial has been supported by project MTM2017-86182-P (AEI/FEDER, UE). Fernando García-Castaño has been partially supported by MINECO and FEDER (MTM2014-54182), by Fundación Séneca—Región de Murcia (19275/PI/14), and by MTM2017-86182-P (AEI/FEDER, UE)

A natural extension of the classical envelope theorem in vector differential programming

The aim of this paper is to extend the classical envelope theorem from scalar to vector differential programming. The obtained result allows us to measure the quantitative behaviour of a certain set of optimal values (not necessarily a singleton) characterized to become minimum when the objective function is composed with a positive function, according to changes of any of the parameters which appear in the constraints. We show that the sensitivity of the program depends on a Lagrange multiplier and its sensitivity.This work has been partially supported by the Generalitat Valenciana project GV/2014/072 and Universidad de Alicante project GRE11-08

A set-valued Lagrange theorem based on a process for convex vector programming

In this paper, we present a new set-valued Lagrange multiplier theorem for constrained convex set-valued optimization problems. We introduce the novel concept of Lagrange process. This concept is a natural extension of the classical concept of Lagrange multiplier where the conventional notion of linear continuous operator is replaced by the concept of closed convex process, its set-valued analogue. The behaviour of this new Lagrange multiplier based on a process is shown to be particularly appropriate for some types of proper minimal points and, in general, when it has a bounded base.The authors have been supported by project MTM2017-86182-P (AEI, Spain and ERDF/FEDER, EU). The author Fernando García-Castaño has also been supported by MINECO and FEDER (MTM2014-54182)

Existence and Density Theorems of Henig Global Proper Efficient Points in Non-Convex Vector Optimization Problems

In this work, we provide some novel results that establish both the existence of Henig global proper efficient points and their density in the efficient set for vector optimization problems in arbitrary normed spaces. Our results do not require the assumption of convexity, and in certain cases, can be applied to unbounded sets. However, it is important to note that a weak compactness condition on the set (or on a section of it) and a separation property between the order cone and its conical neighborhoods remains necessary. The weak compactness condition ensures that certain convergence properties hold. The separation property enables the interpolation of a family of Bishop-Phelps cones between the order cone and each of its conic neighborhoods. This interpolation, combined with the proper handling of two distinct types of conic neighborhoods, plays a crucial role in the proofs of our results, which include as a particular case other results that have already been established under more restrictive conditions

Sensitivity Analysis in Convex Optimization through the Circatangent Derivative

The main goal of this paper is to analyse the sensitivity of a vector convex optimization problem according to variations in the right-hand side. We measure the quantitative behavior of a certain set of Pareto optimal points characterized to become minimum when the objective function is composed with a positive function. Its behavior is analysed quantitatively using the circatangent derivative for set-valued maps. Particularly, it is shown that the sensitivity is closely related to a Lagrange multiplier solution of a dual program.Research partially supported by the University of Alicante, project GRE11-08

Sublinear scalarizations for proper and approximate proper efficient points in nonconvex vector optimization

We show that under a separation property, a Q-minimal point in a normed space is the minimum of a given sublinear function. This fact provides sufficient conditions, via scalarization, for nine types of proper efficient points; establishing a characterization in the particular case of Benson proper efficient points. We also obtain necessary and sufficient conditions in terms of scalarization for approximate Benson and Henig proper efficient points. The separation property we handle is a variation of another known property and our scalarization results do not require convexity or boundedness assumptions.Open Access funding provided thanks to the CRUE-CSIC agreement with Springer Nature. Fernando García-Castaño and Miguel Ángel Melguizo-Padial acknowledge the financial support from the Spanish Ministry of Science, Innovation and Universities (MCIN/AEI) under grant PID2021-122126NB-C32, co-funded by the European Regional Development Fund (ERDF) under the slogan “A way of making Europe”

La Medicina de Familia ante la ley sobre la ayuda médica para morir: responsabilidad y garantías.

The approval of the euthanasia law represents a challenge for medicine and culminates a process of civic maturation of society in the face of death. There are challenges that the application of the law will have to meet. Seeking an objective and irreversible medical solution to subjective suffering - where there may be conditioning social determinants - implies a serious risk of inequity that requires policies that establish a pre-decisional guaranteeing framework. Euthanasia should be an exception thanks to the existence of strong clinical, informational and relational safeguards that can only be guaranteed in the context of a solvent primary care that accompanies people throughout their lives. In this primarist and community context, euthanasia can be the last resort of a professional committed to not abandoning a patient with severe and irreversible suffering who requests it