Ángela Torres

Use of fuzzy clustering technique and matrices to classify amino acids and its impact to Chou's pseudo amino acid composition.

In this paper we present a study of classification of the 20 amino acids via a fuzzy clustering technique. In order to calculate distances among the various elements we employ two different distance functions: the Minkowski distance function and the NTV metric. In the clustering procedure we take into account several physical properties of the amino acids. We examine the effect of the number and nature of properties taken into account to the clustering procedure as a function of the degree of similarity and the distance function used. It turns out that one should use the properties that determine in the more important way the behavior of the amino acids and that the use of the appropriate metric can help in defining the separation into groups.

Fuzzy logic in medicine and bioinformatics.

The purpose of this paper is to present a general view of the current applications of fuzzy logic in medicine and bioinformatics. We particularly review the medical literature using fuzzy logic. We then recall the geometrical interpretation of fuzzy sets as points in a fuzzy hypercube and present two concrete illustrations in medicine (drug addictions) and in bioinformatics (comparison of genomes).

Analysis of an SIR epidemic model with pulse vaccination and distributed time delay.

Pulse vaccination, the repeated application of vaccine over a defined age range, is gaining prominence as an effective strategy for the elimination of infectious diseases. An SIR epidemic model with pulse vaccination and distributed time delay is proposed in this paper. Using the discrete dynamical system determined by the stroboscopic map, we obtain the exact infection-free periodic solution of the impulsive epidemic system and prove that the infection-free periodic solution is globally attractive if the vaccination rate is larger enough. Moreover, we show that the disease is uniformly persistent if the vaccination rate is less than some critical value. The permanence of the model is investigated analytically. Our results indicate that a large pulse vaccination rate is sufficient for the eradication of the disease.

Midpoints for fuzzy sets and their application in medicine

Using Koskos hypercube, we identify a fuzzy set with a point in a unit hypercube. A non-fuzzy or crisp subset of a set is a vertex of the hypercube. We introduce some new ideas: the definition of the fuzzy segment joining two given fuzzy subsets of a set, the set of midpoints between those two fuzzy subsets, and the set of equidistant points from given points. We present some basic properties and relations between these concepts and provide a complete description of fuzzy segments and midpoints. In the majority of cases, there is no unique midpoint; one has an infinite set of possibilities to choose from. This situation is totally different from classical Euclidean geometry where, for two given points, there is a unique midpoint. We use the obtained results to study two sets of medical data and present two applications in medicine: the fuzzy degree of two concurrent food and drug addictions, and a fuzzy representation of concomitant causal mechanisms of stroke.

The fuzzy polynucleotide space: basic properties

MOTIVATION Any triplet codon may be regarded as a 12-dimensional fuzzy code. Sufficient information about a particular sequence may not be available in certain situations. The investigator will be confronted with imprecise sequences, yet want to make comparisons of sequences. Fuzzy polynucleotides can be compared by using geometrical interpretation of fuzzy sets as points in a hypercube. RESULTS We introduce the space of fuzzy polynucleotides and a means of measuring dissimilitudes between them. We establish mathematical principles to measure dissimilarities between fuzzy polynucleotides and present several examples in this metric space. We calculate the frequencies of the nucleotides at the three base sites of a codon in the coding sequences of Escherichia coli K-12 and Mycobacterium tuberculosis H37Rv, and consider them as points in that fuzzy space. We compute the distance between the genomes of E.coli and M.tuberculosis.

Comparison of relaxation training with a cognitive-behavioural intervention for indicated prevention of depression in university students: A randomized controlled trial

Although cognitive-behavioural programmes for preventing depression have produced promising findings, their administration requires extensive training. Relaxation techniques are more straightforward psychological strategies, but they have not been investigated in the prevention of depression. This trial aimed to compare the results of relaxation training (RT) with that of a cognitive-behavioural programme (CBT) for prevention of depression in university students with elevated depressive symptoms. The 133 participants (mean age 23.3 years, 82% women) were randomly assigned to CBT or RT. Both programmes were administered to groups of 5 or 6 participants in eight weekly 90-min sessions. Participants were evaluated by independent raters before, immediately after, and 3 and 6 months after taking part in the programmes. By itself, intervention type had no significant effect on either depression or anxiety scores. The scores were lower at the follow-up time points with respect to pre-intervention scores. Effect size was greatest between pre- and immediately post-intervention scores for CBT, d = 1.32, 95% CI [1.00, 1.64], and between pre- and 6-month post-intervention scores for RT, d = 0.75, 95% CI [0.47, 1.03]. Anxiety symptoms were significantly improved by both interventions at 3-month follow-up, and by CBT at 6-month follow-up also. In the medium term (3-6 months), relaxation training produced similar reductions in depressive and anxiety symptoms as a more complex cognitive-behavioural programme.

Biomathematical modeling and analysis of blood flow in an intracranial aneurysm.

Abstract The basic hypothesis of this study is that the intracranial aneurysm may enlarge and rupture due to dynamic instabilities of the blood flow and pressure inside the aneurysm. The specific question we attempted to answer is: which parameter(s) of aneurysmal geometry can serve as a reliable predictor(s) for aneurysmal rupture? We consider an idealized cylindrical aneurysm of the human common carotid artery and develop a mathematical model of blood flow through a normal artery and aneurysm connected in series. The mathematical model is nonlinear. It comprises nonlinear rheological properties of the normal artery and aneurysmal materials, and the inertial and resistance properties of the blood flow. The model equations were solved numerically and analyzed by methods of nonlinear dynamics. The critical aneurysmal diameter (CAD) is defined as a boundary point between the stable and unstable states of the model equations. The results confirm that a limit point of flow stability can occur only for a certain difference between aneurysmal and artery radii which are pre-disposed from a difference in their material properties. It was shown that CAD is dependent on both aneurysmal length and age of patient. Finally, the results suggest that the ratio between aneurysmal and normal artery diameters is a more reliable predictor of the aneurysmal rupture than the diameter alone. We conclude that an aneurysm diameter twice that of the normal artery could be dangerous.

A nonlinear biomathematical model for the study of intracranial aneurysms

The formation and rupture of aneurysms is a significant medical problem, but is not clearly understood. Most intracranial aneurysm are located in the circle of Willis. We consider a nonlinear mathematical model that simulates the blood flow inside the aneurysm, one of the relevant factors in the evolution of an aneurysm. Different techniques from nonlinear analysis are used in order to obtain, from the model, several consequences that would help to understand some medical aspects of aneurysms of the circle of Willis.

A Metric Space to Study Differences between Polynucleotides

Kosko [12] introduced a geometrical interpretation of fuzzy sets as points in a hypercube. Indeed, for a given set X = { ~1, . . . , x,}, a fuzzy subset is just a mapping p : x + 1 = [O, 11, Research partially supported by Ministerio de Ciencia y Tecnologia (Spain) and FEDER, Project BFM2001-3884.

A study of entropy/clarity of genetic sequences using metric spaces and fuzzy sets.

The study of genetic sequences is of great importance in biology and medicine. Sequence analysis and taxonomy are two major fields of application of bioinformatics. In the present paper we extend the notion of entropy and clarity to the use of different metrics and apply them in the case of the Fuzzy Polynuclotide Space (FPS). Applications of these notions on selected polynucleotides and complete genomes both in the I(12×k) space, but also using their representation in FPS are presented. Our results show that the values of fuzzy entropy/clarity are indicative of the degree of complexity necessary for the description of the polynucleotides in the FPS, although in the latter case the interpretation is slightly different than in the case of the I(12×k) hypercube. Fuzzy entropy/clarity along with the use of appropriate metrics can contribute to sequence analysis and taxonomy.