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Arnau Mir

Publications and source records attributed to Arnau Mir.

15 recordsLinked to original sources
arXiv2026

Diagnosis Support of Sickle Cell Anemia by Classifying Red Blood Cell Shape in Peripheral Blood Images

Red blood cell (RBC) deformation is the consequence of several diseases, including sickle cell anemia, which causes recurring episodes of pain and severe pronounced anemia. Monitoring patients with these diseases involves the observation of peripheral blood samples under a microscope, a time-consuming procedure. Moreover, a specialist is required to perform this technique, and owing to the subjective nature of the observation of isolated RBCs, the error rate is high. In this paper, we propose an automated method for differentially enumerating RBCs that uses peripheral blood smear image analysis. In this method, the objects of interest in the image are segmented using a Chan-Vese active contour model. An analysis is then performed to classify the RBCs, also called erythrocytes, as normal or elongated or having other deformations, using the basic shape analysis descriptors: circular shape factor (CSF) and elliptical shape factor (ESF). To analyze cells that become partially occluded in a cluster during sample preparation, an elliptical adjustment is performed to allow the analysis of erythrocytes with discoidal and elongated shapes. The images of patient blood samples used in the study were acquired by a clinical laboratory specialist in the Special Hematology Department of the ``Dr. Juan Bruno Zayas'' General Hospital in Santiago de Cuba. A comparison of the results obtained by the proposed method in our experiments with those obtained by some state-of-the-art methods showed that the proposed method is superior for the diagnosis of sickle cell anemia. This superiority is achieved for evidenced by the obtained F-measure value (0.97 for normal cells and 0.95 for elongated ones) and several overall multiclass performance measures. The results achieved by the proposed method are suitable for the purpose of clinical treatment and diagnostic support of sickle cell anemia.

cs.CV↗
arXiv2025

An Efficient Computational Framework for Discrete Fuzzy Numbers Based on Total Orders

Discrete fuzzy numbers, and in particular those defined over a finite chain $L_n = \{0, \ldots, n\}$, have been effectively employed to represent linguistic information within the framework of fuzzy systems. Research on total (admissible) orderings of such types of fuzzy subsets, and specifically those belonging to the set $\mathcal{D}_1^{L_n\rightarrow Y_m}$ consisting of discrete fuzzy numbers $A$ whose support is a closed subinterval of the finite chain $L_n = \{0, 1, \ldots, n\}$ and whose membership values $A(x)$, for $x \in L_n$, belong to the set $Y_m = \{ 0 = y_1 < y_2 < \cdots < y_{m-1} < y_m = 1 \}$, has facilitated the development of new methods for constructing logical connectives, based on a bijective function, called $\textit{pos function}$, that determines the position of each $A \in \mathcal{D}_1^{L_n\rightarrow Y_m}$. For this reason, in this work we revisit the problem by introducing algorithms that exploit the combinatorial structure of total (admissible) orders to compute the $\textit{pos}$ function and its inverse with exactness. The proposed approach achieves a complexity of $\mathcal{O}(n^{2} m \log n)$, which is quadratic in the size of the underlying chain ($n$) and linear in the number of membership levels ($m$). The key point is that the dominant factor is $m$, ensuring scalability with respect to the granularity of membership values. The results demonstrate that this formulation substantially reduces computational cost and enables the efficient implementation of algebraic operations -- such as aggregation and implication -- on the set of discrete fuzzy numbers.

cs.LO↗
arXiv2021

Explicit solution of divide-and-conquer dividing by a half recurrences with polynomial independent term

Divide-and-conquer dividing by a half recurrences, of the form $x_n =a\cdot x_{\left\lceil{n}/{2}\right\rceil}+a\cdot x_{\left\lfloor{n}/{2}\right\rfloor}+p(n)$, $n\geq 2$, appear in many areas of applied mathematics, from the analysis of algorithms to the optimization of phylogenetic balance indices. The Master Theorems that solve these equations do not provide the solution's explicit expression, only its big-$Θ$ order of growth. In this paper we give an explicit expression (in terms of the binary decomposition of $n$) for the solution $x_n$ of a recurrence of this form, with given initial condition $x_1$, when the independent term $p(n)$ is a polynomial in $\lceil{n}/{2}\rceil$ and $\lfloor{n}/{2}\rfloor$.

cs.DM↗
arXiv2020

Squaring within the Colless index yields a better balance index

The Colless index for bifurcating phylogenetic trees, introduced by Colless (1982), is defined as the sum, over all internal nodes $v$ of the tree, of the absolute value of the difference of the sizes of the clades defined by the children of $v$. It is one of the most popular phylogenetic balance indices, because, in addition to measuring the balance of a tree in a very simple and intuitive way, it turns out to be one of the most powerful and discriminating phylogenetic shape indices. But it has some drawbacks. On the one hand, although its minimum value is reached at the so-called maximally balanced trees, it is almost always reached also at trees that are not maximally balanced. On the other hand, its definition as a sum of absolute values of differences makes it difficult to study analytically its distribution under probabilistic models of bifurcating phylogenetic trees. In this paper we show that if we replace in its definition the absolute values of the differences of clade sizes by the squares of these differences, all these drawbacks are overcome and the resulting index is still more powerful and discriminating than the original Colless index.

q-bio.PE↗
arXiv2019

A balance index for phylogenetic trees based on rooted quartets

We define a new balance index for rooted phylogenetic trees based on the symmetry of the evolutive history of every set of 4 leaves. This index makes sense for multifurcating trees and it can be computed in time linear in the number of leaves. We determine its maximum and minimum values for arbitrary and bifurcating trees, and we provide exact formulas for its expected value and variance on bifurcating trees under Ford's $α$-model and Aldous' $β$-model and on arbitrary trees under the $α$-$γ$-model.

q-bio.PE↗
arXiv2018

Sound Colless-like balance indices for multifurcating trees

The Colless index is one of the most popular and natural balance indices for bifurcating phylogenetic trees, but it makes no sense for multifurcating trees. In this paper we propose a family of Colless-like balance indices $\mathfrak{C}_{D,f}$, which depend on a dissimilarity $D$ and a function $f:\mathbb{N}\to \mathbb{R}_{\geq 0}$, that generalize the Colless index to multifurcating phylogenetic trees. We provide two functions $f$ such that the most balanced phylogenetic trees according to the corresponding indices $\mathfrak{C}_{D,f}$ are exactly the fully symmetric ones. Next, for each one of these two functions $f$ and for three popular dissimilarities $D$ (the variance, the standard deviation, and the mean deviation from the median), we determine the range of values of $\mathfrak{C}_{D,f}$ on the sets of phylogenetic trees with a given number $n$ of leaves. We end the paper by assessing the performance of one of these indices on TreeBASE and using it to show that the trees in this database do not seem to follow either the uniform model for multifurcating trees or the $α$-$γ$-model, for any values of $α$ and $γ$.

q-bio.PE↗
arXiv2013

The expected value of the squared euclidean cophenetic metric under the Yule and the uniform models

The cophenetic metrics $d_{φ,p}$, for $p\in {0}\cup[1,\infty[$, are a recent addition to the kit of available distances for the comparison of phylogenetic trees. Based on a fifty years old idea of Sokal and Rohlf, these metrics compare phylogenetic trees on a same set of taxa by encoding them by means of their vectors of cophenetic values of pairs of taxa and depths of single taxa, and then computing the $L^p$ norm of the difference of the corresponding vectors. In this paper we compute the expected value of the square of $d_{φ,2}$ on the space of fully resolved rooted phylogenetic trees with $n$ leaves, under the Yule and the uniform probability distributions.

q-bio.PE↗
arXiv2013

Cophenetic metrics for phylogenetic trees, after Sokal and Rohlf

Phylogenetic tree comparison metrics are an important tool in the study of evolution, and hence the definition of such metrics is an interesting problem in phylogenetics. In a paper in Taxon fifty years ago, Sokal and Rohlf proposed to measure quantitatively the difference between a pair of phylogenetic trees by first encoding them by means of their half-matrices of cophenetic values, and then comparing these matrices. This idea has been used several times since then to define dissimilarity measures between phylogenetic trees but, to our knowledge, no proper metric on weighted phylogenetic trees with nested taxa based on this idea has been formally defined and studied yet. Actually, the cophenetic values of pairs of different taxa alone are not enough to single out phylogenetic trees with weighted arcs or nested taxa. In this paper we define a family of cophenetic metrics that compare phylogenetic trees on a same set of taxa by encoding them by means of their vectors of cophenetic values of pairs of taxa and depths of single taxa, and then computing the $L^p$ norm of the difference of the corresponding vectors. Then, we study, either analytically or numerically, some of their basic properties: neighbors, diameter, distribution, and their rank correlation with each other and with other metrics.

q-bio.PE↗
arXiv2012

Exact formulas for the variance of several balance indices under the Yule model

One of the main applications of balance indices is in tests of null models of evolutionary processes. The knowledge of an exact formula for a statistic of a balance index, holding for any number n of leaves, is necessary in order to use this statistic in tests of this kind involving trees of any size. In this paper we obtain exact formulas for the variance under the Yule model of the Sackin index, the Colless index and the total cophenetic index of binary rooted phylogenetic trees with n leaves. We also obtain the covariance of the Sackin and the total cophenetic index.

q-bio.PE↗
arXiv2012

The expected value under the Yule model of the squared path-difference distance

The path-difference metric is one of the oldest and most popular distances for the comparison of phylogenetic trees, but its statistical properties are still quite unknown. In this paper we compute the expected value under the Yule model of evolution of its square on the space of fully resolved rooted phylogenetic trees with n leaves. This complements previous work by Steel-Penny and Mir-Rosselló, who computed this mean value for fully resolved unrooted and rooted phylogenetic trees, respectively, under the uniform distribution.

q-bio.PE↗
arXiv2012

A new balance index for phylogenetic trees

Several indices that measure the degree of balance of a rooted phylogenetic tree have been proposed so far in the literature. In this work we define and study a new index of this kind, which we call the total cophenetic index: the sum, over all pairs of different leaves, of the depth of their least common ancestor. This index makes sense for arbitrary trees, can be computed in linear time and it has a larger range of values and a greater resolution power than other indices like Colless' or Sackin's. We compute its maximum and minimum values for arbitrary and binary trees, as well as exact formulas for its expected value for binary trees under the Yule and the uniform models of evolution. As a byproduct of this study, we obtain an exact formula for the expected value of the Sackin index under the uniform model, a result that seems to be new in the literature.

q-bio.PE↗
arXiv2009

The mean value of the squared path-difference distance for rooted phylogenetic trees

The path-difference metric is one of the oldest distances for the comparison of fully resolved phylogenetic trees, but its statistical properties are still quite unknown. In this paper we compute the mean value of the square of the path-difference metric between two fully resolved rooted phylogenetic trees with $n$ leaves, under the uniform distribution. This complements previous work by Steel and Penny, who computed this mean value for fully resolved unrooted phylogenetic trees.

q-bio.PE↗