Mathematical indices for the influence of risk factors on the lethality of a disease.

We develop a theoretical model to measure the relative relevance of different pathologies of the lethality of a disease in society. This approach allows a ranking of diseases to be determined, which can assist in establishing priorities for vaccination campaigns or prevention strategies. Among all possible measurements, we identify three families of rules that satisfy a combination of relevant properties: neutrality, irrelevance, and one of three composition concepts. One of these families includes, for instance, the Shapley value of the associated cooperative game. The other two families also include simple and intuitive indices. As an illustration, we measure the relative relevance of several pathologies in lethality due to COVID-19.

Benchmarking Analysis of the Accuracy of Classification Methods Related to Entropy.

In the machine learning literature we can find numerous methods to solve classification problems. We propose two new performance measures to analyze such methods. These measures are defined by using the concept of proportional reduction of classification error with respect to three benchmark classifiers, the random and two intuitive classifiers which are based on how a non-expert person could realize classification simply by applying a frequentist approach. We show that these three simple methods are closely related to different aspects of the entropy of the dataset. Therefore, these measures account somewhat for entropy in the dataset when evaluating the performance of classifiers. This allows us to measure the improvement in the classification results compared to simple methods, and at the same time how entropy affects classification capacity. To illustrate how these new performance measures can be used to analyze classifiers taking into account the entropy of the dataset, we carry out an intensive experiment in which we use the well-known J48 algorithm, and a UCI repository dataset on which we have previously selected a subset of the most relevant attributes. Then we carry out an extensive experiment in which we consider four heuristic classifiers, and 11 datasets.

On the Difficulty of Budget Allocation in Claims Problems with Indivisible Items and Prices.

In this paper we study the class of claims problems where the amount to be divided is perfectly divisible and claims are made on indivisible units of several items. Each item has a price, and the available amount falls short to be able to cover all the claims at the given prices. We propose several properties that may be of interest in this particular framework. These properties represent the common principles of fairness, efficiency, and non-manipulability by merging or splitting. Efficiency is our focal principle, which is formalized by means of two axioms: non-wastefulness and Pareto efficiency. We show that some combinations of the properties we consider are compatible, others are not.

Whole organ, venation and epidermal cell morphological variations are correlated in the leaves of Arabidopsis mutants.

Despite the large number of genes known to affect leaf shape or size, we still have a relatively poor understanding of how leaf morphology is established. For example, little is known about how cell division and cell expansion are controlled and coordinated within a growing leaf to eventually develop into a laminar organ of a definite size. To obtain a global perspective of the cellular basis of variations in leaf morphology at the organ, tissue and cell levels, we studied a collection of 111 non-allelic mutants with abnormally shaped and/or sized leaves, which broadly represent the mutational variations in Arabidopsis thaliana leaf morphology not associated with lethality. We used image-processing techniques on these mutants to quantify morphological parameters running the gamut from the palisade mesophyll and epidermal cells to the venation, whole leaf and rosette levels. We found positive correlations between epidermal cell size and leaf area, which is consistent with long-standing Avery's hypothesis that the epidermis drives leaf growth. In addition, venation parameters were positively correlated with leaf area, suggesting that leaf growth and vein patterning share some genetic controls. Positional cloning of the genes affected by the studied mutations will eventually establish functional links between genotypes, molecular functions, cellular parameters and leaf phenotypes.