Sistemes lineals: una aproximació a algun dels seus conceptes i problemes rellevants

L'objectiu que m'he proposat al preparar aquesta exposicióha estat el de mostrar. per una banda, com alguns delsproblemes bàsics de la teoria de Sistemes Dinàmics Linealstenen una resposta senzilla en termes de l' Álgebra lineal i,d'altra, com alguns problemes importants d'aquesta teorias'entronquen amb conceptes i tècniques bàsiques de la geometriai la topologia

Modelos dinámicos en finanzas

El problema de la modelización dinámica enfinanzas tiene mucho que ver con el tipo deproblema que se pretende estudiar. Es preciso teneren cuenta el subyacente así como las magnitudesque se pretende estimar para elegir el modeloadecuado.-

Periodic orbits of integrable birational maps on the plane: blending dynamics and algebraic geometry, the Lyness' case

Contingut del Pòster presentat al congrés New Trends in Dynamical Systems

Using MILP to plan holidays and working hours under an annualised hours agreement

Annualising work hours (AH) is a means of achievement flexibility in the use of human resources to face the seasonal nature of demand. In Corominas et al. (1) two MILP models are used to solve the problem of planning staff working hours with annual horizon. The costs due to overtime and to the employment of temporary workers are minimised, and the distribution of working time over the course of the year for each worker and the distribution of working time provided by temporary workers are regularised.In the aforementioned paper, the following is assumed: (i) the holiday weeks are fixed a priori and (ii) the workers are from different categories who are able to perform specific type of task have se same efficiency; moreover, the values of the binary variables (and others) in the second model are fixed to those in the first model (thus, in the second model these will intervene as constants and not as variables, resulting in an LP model).In the present paper, these assumptions are relaxed and a more general problem is solved. The computational experiment leads to the conclusion that MILP is a technique suited to dealing with the problem.

Reconstruction of networks from their betweenness centrality

In this paper we study the reconstruction of a network topology from the values of its betweenness centrality, a measure of the influence of each of its nodes in the dissemination of information over the network. We consider a simple metaheuristic, simulated annealing, as the combinatorial optimization method to generate the network from the values of the betweenness centrality. We compare the performance of this technique when reconstructing different categories of networks –random, regular, small-world, scale-free and clustered–. We show that the method allows an exact reconstruction of small networks and leads to good topological approximations in the case of networks with larger orders. The method can be used to generate a quasi-optimal topology fora communication network from a list with the values of the maximum allowable traffic for each node.

Phylogeography and population genetics of north European Atlantic salmon (Salmo salar L.)

Although abundant in the number of individuals, the Atlantic salmon may be considered as a threatened species in many areas of its native distribution range. Human activities such as building of power plant dams, offshore overfishing, pollution, clearing of riverbeds for timber floating and badly designed stocking regimes have diminished the distribution of Atlantic salmon. As a result of this, many of the historical populations both in Europe and northern America have gone extinct or are severely depressed. In fact, only 1% of Atlantic salmon existing today are of natural origin, the rest being farmed salmon. All of this has lead to a vast amount of research and many restoration programmes aiming to bring Atlantic salmon back to rivers from where it has vanished. However, many of the restoration programmes conducted thus far have been unsuccessful due to inadequate scientific research or lack of its implementation, highlighting the fact that more research is needed to fully understand the biology of this complex species. The White and Barents Seas in northwest Russia are among the last regions in Europe where Atlantic salmon populations are still stable, thus forming an important source of biodiversity for the entire European region. Salmon stocks from this area are also of immense economic and social importance for the local people in the form of fishing tourism. The main aim of this thesis was to elucidate the post-glacial history and population genetic structure of north European and particularly northwest Russian Atlantic salmon, both of which are aspects of great importance for the management and conservation of the species. Throughout the whole thesis, these populations were studied by utilizing microsatellites as the main molecular tool. One of the most important discoveries of the thesis was the division of Atlantic salmon from the White and Barents Seas into four separate clusters, which has not been observed in previous studies employing nuclear markers although is supported by mtDNA studies. Populations from the western Barents Sea clustered together with the northeast Atlantic populations into a clearly distinguishable group while populations from the White Sea and eastern Barents Sea were separated into three additional groups. This has important conservation implications as this thesis clearly indicates that conservation of populations from all of the observed clusters is warranted in order to conserve as much of the genetic diversity as possible in this area. The thesis also demonstrates how differences in population life histories within a species, migratory behaviour in this case, and in their phylogeographic origin affect the genetic characteristics of populations, namely diversity and divergence levels. The anadromous populations from the Atlantic Ocean, White Sea and Barents Sea possessed higher levels of genetic diversity than the anadromous populations form the Baltic Sea basin. Among the non-anadromous populations the result was the opposite: the Baltic freshwater populations were more variable. This emphasises the importance of taking the life history of a population into consideration when developing conservation strategies: due to the limited possibilities for new genetic diversity to be generated via gene flow, it is expected that freshwater Atlantic salmon populations would be more vulnerable to extinction following a population crash and thus deserve a high conservation status. In the last chapter of this thesis immune relevant marker loci were developed and screened for signatures of natural selection along with loci linked to genes with other functions or no function at all. Also, a novel landscape genomics method, which combines environmental information with molecular data, was employed to investigate whether immune relevant markers displayed significant correlations to various environmental variables more frequently than other loci. Indications of stronger selection pressure among immune-relevant loci compared to non-immune relevant EST-linked loci was found but further studies are needed to evaluate whether it is a common phenomenon in Atlantic salmon.

Past, present and future - assessing changes in aquatic environments using subfossil diatoms

The deterioration of surface waters is one of the most important issues in the environmental management of the European Union. Thus, the EU Water Framework Directive 2000/60/EC (WFD) requires “good ecological and chemical status” of surface waters by 2015 allowing only a slight departure from ecological reference conditions characterized by the biological communities typical for the conditions of minimal anthropogenic impact. The WFD requires the determination of ecological reference conditions and the present ecological status of surface waters. To meet this legislative demand, sedimentary diatom assemblages were used in these studies with various methods 1) to assess natural and human activity induced environmental changes, 2) to characterize background conditions 3) to evaluate the present ecological status and 4) to predict the future of the water bodies in the light of palaeolimnological data. As the WFD refers to all surface waters, both coastal and inland sites were included. Two long and two short sediment cores from the Archipelago Sea in the northern Baltic Sea were examined for their siliceous microfossils in order to assess (1) the Holocene palaeoenvironmental history and (2) the recent eutrophication of the area. The diatom record was divided into local diatom assemblage zones (LDAZ, long cores) and diatom assemblage zones (DAZ, short cores). Locally weighted weighted averaging regression and calibration (LWWA) was applied for the quantitative reconstruction of past TN concentrations (short cores). An age model for the long cores was constructed by using independent palaeomagnetic and AMS-14C methods. The short cores were dated using radiometric (210Pb, 226Ra and 137Cs) methods. The long cores date back to the early history of the Archipelago Sea, which was freshwater – no salinity increase referable to the brackish phase of the Yoldia Sea is recognized. The nutrient status of the lacustrine phase was slightly higher in the Archipelago Sea than in the Baltic Proper. Initial brackish-water influence is observed at 8 150 ±80 cal. BP (LDAZ4), but fully brackish conditions were established at 7 700 ±80 cal. BP (LDAZ5). The diatom assemblages indicate increasing salinity, warming climate and possible eutrophic conditions during the lacustrine to brackish-water transition. The decreasing abundance of Pseudosolenia calcar-avis (Schultze) Sundström and the increasing abundance of the ice-cover indicator species Pauliella taeniata (Grunow) Round and Basson indicate decreasing salinity and climatic cooling after ca. 5 000 cal. BP. Signs of eutrophication are visible in the most recent diatom assemblage zones of both short cores. Diatom-inferred total nitrogen (DI-TN) reconstructions partially fail to trace the actual measured total nitrogen concentrations especially from the late 1980s to the mid 1990s. This is most likely due to the dominating diatom species Pauliella taeniata, Thalassiosira levanderi Van Goor and Fragilariopsis cylindrus (Grunow) W. Krieger being more influenced by factors such as the length of the ice-season rather than nutrient concentrations. It is concluded that the diatom assemblages of the study sites are principally governed by climate fluctuations, with a slight influence of eutrophication visible in the most recent sediments. There are indications that global warming, with reduced ice cover, could impact the spring blooming diatom species composition in the Archipelago Sea. In addition, increased sediment accumulation in the early 90s coincides with the short ice-seasons suggesting that warming climate with decreasing ice-cover may increase sedimentation in the study area. The diverse diatom assemblages dominated by benthic species (54 %) in DAZ1 in the Käldö Fjärd core can be taken as background diatom assemblages for the Archipelago Sea. Since then turbidity has increased and the diatom assemblages have been dominated by planktonic diatoms from around the mid 1800s onwards. The reconstructed reference conditions for the total nitrogen concentrations fluctuate around 400 μg l-1. Altogether two short sediment cores and eight short cores for top-bottom analysis were retrieved from Lake Orijärvi and Lake Määrjärvi to assess the impact of the acid mine drainage (AMD) derived metals from the Orijärvi mine tailings on the diatom communities of the lakes. The Cu (Pb, Zn) mine of Orijärvi (1757 – 1956) was the first one in Finland where flotation techniques (1911 – 1955) were used to enrich ore and large quantities of tailings were produced. The AMD derived metal impact to the lakes was found to be among the heaviest thus far recorded in Finland. Concentrations of Cu, Pb and Zn in Lake Orijärvi sediments are two to three orders of magnitude higher than background values. The metal inputs have affected Lake Orijärvi and Lake Määrjärvi diatom communities at the community levels through shifts in dominant taxa (both lakes) and at the individual level through alteration in frustule morphology (Lake Orijärvi). At present, lake water still has elevated heavy metal levels, indicating that the impact from the tailings area continues to affect both lakes. Lake Orijärvi diatom assemblages are completely dominated by benthic species and are lacking planktonic diatoms. In Lake Määrjärvi the proportion of benthic and tychoplanktonic diatoms has increased and the planktonic taxa have decreased in abundance. Achnanthidium minutissimum Kützing and Brachysira vitrea (Grun.) R. Ross in Hartley were the most tolerant species to increased metal concentrations. Planktonic diatoms are more sensitive to metal contamination than benthic taxa, especially species in the genus Cyclotella (Kützing) Brébisson. The ecological reference conditions assessed in this study for Lake Orijärvi and Lake Määrjärvi comprise diverse planktonic and benthic communitites typical of circumneutral oligotrophic lakes, where the planktonic diatoms belonging to genera Cyclotella , Aulacoseira Thwaites, Tabellaria Ehrenberg and Asterionella Hassall dominate in relative abundances up to ca. 70%. The benthic communities are more diverse than the planktonic consisting of diatoms belonging to the genera Achnanthes Bory, Fragilaria Lyngbye and Navicula St. Vincent. This study clearly demonstrates that palaeolimnological methods, especially diatom analysis, provide a powerful tool for the EU Water Frame Work Directive for defining reference conditions, natural variability and current status of surface waters. The top/bottom approach is a very useful tool in larger-scale studies needed for management purposes. This “before and after” type of sediment sampling method can provide a very time and cost effective assessment of ecological reference conditions of surface waters.

Soldiering and the making of Finnish manhood : conscription and masculinity in interwar Finland, 1918–1939

Military conscription and peacetime military service were the subjects of heated political, social and cultural controversies during the early years of national independence in Finland. Both the critics and the supporters of the existing military system described it as strongly formative of young men’s physical and moral development into adult men and male citizens. The conflicts over conscription prompted the contemporaries to express their notions about what Finnish men were like, at their best and at their worst, and what should and could be done about it. This thesis studies military conscription as an arena for the “making of manhood” in peacetime Finnish society, 1918–1939. It examines a range of public images of conscripted soldiering, asking how soldiering was depicted and given gendered meanings in parliamentary debates, war hero myths, texts concerned with the military and civic education of conscripts, as well as in works of fiction and reminiscences about military training as a personal experience. Studying conscription with a focus on masculinity, the thesis explores the different cultural images of manliness, soldiering and male citizenship on offer in Finnish society. It investigates how political parties, officers, educators, journalists, writers and “ordinary” conscripts used and developed, embraced or rejected these notions, according to their political purposes or personal needs. The period between the two world wars can be described as a fast-forward into military modernity in Finland. In the process, European middle class gender ideologies clashed with Finnish agrarian masculinities. Nationalistic agendas for the militarisation of Finnish manhood stumbled against intense class conflicts and ideological resistance. Military propaganda used images of military heroism, civic virtue and individual success to persuade the conscripts into ways of thinking and acting that were shaped by bourgeois mentality, nationalistic ideology and religious morality. These images are further analysed as expressive of the personal experiences and emotions of their middle-aged, male authors. The efforts of these military educators were, however, actively resisted on many fronts, ranging from rural working class masculinities among the conscripted young men to ideological critiques of the standing army system in parliament. In narratives about military training, masculinity was depicted as both strengthened and contradicted by the harsh and even brutal practices of interwar Finnish military training. The study represents a combination of new military history and the historical study of men and masculinities. It approaches masculinity as a contested and highly political form of social and cultural knowledge that is actively and selectively used by historic actors. Instead of trying to identify a dominant or “hegemonic” form of masculinity within a pre-determined theoretical structure, this study examines how the meanings ascribed to manhood varied according to class, age, political ideology and social situation. The interwar period in Finland can be understood as a period of contest between different notions of militarised masculinity, yet to judge by the materials studied, there was no clear winning party in that contest. A gradual movement from an atmosphere of conflict surrounding conscription towards political and cultural compromises can be discerned, yet this convergence was incomplete and many division lines remained.

Carnap and Kuhn on linguistic frameworks and scientific revolutions

Several recent works in history and philosophy of science have re-evaluated the alleged opposition between the theses put forth by logical empiricists such as Carnap and the so-called "post-positivists", such as Kuhn. Although the latter came to be viewed as having seriously challenged the logical positivist views of science, recent authors (e.g., Friedman, Reisch, Earman, Irzik and Grünberg) maintain that some of the most notable theses of the Kuhnian view of science have striking similarities with some aspects of Carnap's philosophy. Against that reading, Oliveira and Psillos argue that within Carnap's philosophy there is no place for the Kuhnian theses of incommensurability, holism, and theory-ladenness of observations. This paper presents each of those readings and argues that Carnap and Kuhn have non-opposing views on holism, incommensurability, the theory-ladenness of observations, and scientific revolutions. We note at the very end - without dwelling on the point, however - that they come apart on other matters, such as their views on metaphysics and on the context of discovery/justification distinction.

Structural aspects and floristic similarity among tropical dry forest fragments with different management histories in northern Minas Gerais, Brazil

In order to produce useful knowledge to the initiatives of protection and management of forest fragments, more specifically for tropical dry forests which suffer with frequent anthropic activities, and due to the lack of specific studies, this article aimed describe the structure and the floristic similarity among three areas of dry forest with different management histories. The study was developed in Capitão Enéas municipality, Northern Minas Gerais, Brazil, where three fragments were evaluated, being one in regeneration for 30 years, another submitted to occasional fire and the third with selective cut in small scale. The sampling was developed through the point quarter method considering all the alive phanerophyte individuals with circumference at breast height (CBH) > 15 cm. In the three fragments, 512 individuals, distributed in 60 species, 47 genera, and 23 families were sampled. The most representative families were Fabaceae (26), Anacardiaceae (4), Bignoniaceae (3) and Combretaceae (3). However, fourteen families were represented by only one species. Only eight species were common to all fragments - Myracrodruon urundeuva standed out with 26.9% of all sampled individuals - while a great number of species were exclusive of each fragment. The floristic and structural differences between the fragments are possibly related to the history and intensity of management in each area besides the topography variations and the presence or absence of limestone outcrops. These results show the importance of each fragment, indicating that the loss of anyone would cause negative impacts on the regional flora and consequently to the associated biodiversity.

St. Petersburg Court Chant and the Tradition of Eastern Slavic Church Singing

The present study examines the repertory of liturgical chant known as St. Petersburg Court Chant which emerged within the Imperial Court of St. Petersburg, Russia, and appeared in print in a number of revisions during the course of the 19th century, eventually to spread throughout the Russian Empire and even abroad. The study seeks answers to questions on the essence and composition of Court Chant, its history and liturgical background, and most importantly, its musical relationship to other repertories of Eastern Slavic chant. The research questions emerge from previous literary accounts of Court Chant (summarized in the Introduction), which have tended to be inaccurate and generally not based on critical research. The study is divided into eight main chapters. Chapter 1 provides a survey of the history of Eastern Slavic chant and the Imperial Court Chapel of St. Petersburg until 1917, with special emphasis on the history of singing traditional chant in polyphony, the status of the Court Chapel as a government authority, and its endeavours in publishing church music. Chapter 2 deals with the liturgical background of Eastern chant, the chant genres, and main repertories of Eastern Slavic chant. Chapter 3 concentrates on chant sources: it introduces the musical notations utilised, after which a typology of chant books is presented. The discussion continues with a survey of the sources of Court Chant and their content, the specimens selected for closer analysis, the comparative materials from other repertories, and ends with a commentary on some chant sources that have been excluded. The comparative sources include a specimen from around the beginning of the 12th century, a few manuscripts from the 17th century, and printed and manuscript chant books from the early 18th to early 20th century, covering the geographical area that delimits to the western Ukraine, Astrakhan, Nizhny Novgorod, and the Solovetsky Monastery. Chapter 4 presents the approach and methods used in the subsequent analytical comparisons. After a survey of the pitch organization of Eastern Slavic chant, the customary harmonization strategy of traditional chant polyphony is examined, according to which a method for meaningful analysis of the harmony is proposed. The method is based on the observation that the harmonic framework of chant polyphony derives from the standard pitch collection of monodic chant known as the Church Gamut, specific pitches of which form eight harmonic regions that behave like the usual tonalities of major and harmonic minor. Because of the considerable quantity of comparative chant forms, computer-assisted statistical methods are applied to the analysis of chant melodies. The primary chant forms and their respective comparative forms have been pre-processed into reduced chant prototypes and divided into redactions. The analyses are carried out by measuring the formal dissimilarities of the primary chant forms of the Court Chant repertory against each comparative form, and also by measuring the reciprocal dissimilarities of all chant versions in a redaction, the results of which are subjected to agglomerative hierarchical clustering in order to find out how the chant forms relate to each other. The dissimilarities are determined by applying a metric dissimilarity function that is based on the Levenshtein Distance. Chapter 5 provides the melodic and harmonic analyses of generic chants (chants used for multiple texts of different lengths), i.e., chants for stichera samoglasny and troparia, Chapter 6 of pseudo-generic chants (chants that are used for multiple texts but with certain restrictions), i.e., chants for heirmoi, prokeimena, and three other hymns, and Chapter 7 of non-generic chants, covering nine chants that in the Court repertory are not shared by multiple texts. The results are summarized and evaluated in Chapter 8. Accordingly, it can be established that, contrary to previous conceptions, melodically, Court Chant is in effect a full part of the wider Eastern Slavic chant tradition. Even if it is somewhat detached from the chant versions of the Synodal square-note chant books and the local tradition of Moscow, it is particularly close to chant forms of East Ukraine and some vernacular repertories from Russia. Respectively, the harmonization strategies of Court Chant do not show significant individuality in comparison with those of the available polyphonic comparative sources, the main difference being the part-writing, which generally conforms to western common practice standard, whereas the deviations from this tend to be more significant in other analysed repertories of polyphonic chant. Thus, insofar as the subsequent prevalence of Court Chant is not based on its forceful dissemination by authorities (as suggested in previous literature but for which little tangible evidence could be found in Chapter 1), in the present author’s interpretation, Court Chant attained its dominance principally because musically it was considered sufficiently traditional, and as a chant body supported by the government, was conveniently available in print in serviceable harmonizations.

Fatigue and quality of life in breast cancer survivors: a comparative study

PURPOSE: To assess fatigue and quality of life in disease-free breast cancer survivors in relation to a sample of age-matched women with no cancer history and to explore the relationship between fatigue and quality of life.METHODS: A cross-sectional study was conducted in a sample of 202 consecutive disease-free Brazilian breast cancer survivors, all of whom had completed treatment, treated at 2 large hospitals. The patients were compared to age-matched women with no cancer history attending a primary health care center. The Piper Fatigue Scale-Revised and the World Health Organization Quality of Life Instrument (WHOQOL-BREF) were used to measure the fatigue and quality of life, respectively. Socio-demographic and clinical variables were also obtained. The χ2 test, generalized linear model, and Spearman correlation coefficient were used for statistical purposes. The adopted level of significance was 5%.RESULTS: Breast cancer survivors experienced significantly greater total and subscale fatigue scores than comparison group (all p-values<0.05). In addition, survivors reported a poorer quality of life in physical (p=0.002), psychological (p=0.03), and social relationships (p=0.03) domains than comparison group. No difference was found for the environmental domain (p=0.08) for both groups. For survivors of breast cancer and for comparison group, the total and subscale fatigue scores were related to lower quality of life (all p-values<0.01).CONCLUSION: The findings of this study highlight the importance of assessing fatigue and quality of life in breast cancer survivors.

Monostromatic green algae (Ulvales, Chlorophyta) of São Paulo and Paraná states (Brazil): distribution, growth, and reproduction

(Monostromatic green algae (Ulvales, Chlorophyta) of São Paulo and Paraná states (Brazil): distribution, growth, and reproduction). Culture studies were used for taxa identification and to understand aspects of the biology and physiology of monostromatic green blades growing in various sites along the coast of São Paulo state (23º30'-25ºl2'S, 45º10'-48ºW) and one site in Paraná state (25º35'S, 48º21'W), southeast and south Brazil, respectively. Possible variations of the growth rate, age of reproduction and life history were tested under different conditions of temperature, salinity and day length. Two species were found: Ulvaria oxysperma (Kützing) Bliding and Monostroma sp. The first one has been previously reported for many temperate and tropical estuaries around the world. Green monostromatic blades with the same life-history and ontogeny as Monostroma sp. have been reported so far only for the tropical coast of Brazil. Species are distinct in their ontogeny of the thallus (constant under different conditions) and limiting temperatures of survival. U. oxysperma grows and reproduces from 10 to 25ºC and dies when maintained at 30ºC; Monostroma sp. does not reproduce at 15ºC and survives at 30ºC. The different salinities and day lengths that were tested had no significant effect on either species.

Patient and physician evaluation of the severity of acute asthma exacerbations

We studied the ability of patients not experienced in the use of peak expiratory flow meters to assess the severity of their asthma exacerbations and compared it to the assessment of experienced clinicians. We also evaluated which data of physical examination and medical history are used by physicians to subjectively evaluate the severity of asthma attacks. Fifty-seven adult patients (15 men and 42 women, with a mean (± SD) age of 37.3 ± 14.5 years and 24.0 ± 17.9 years of asthma symptoms) with asthma exacerbations were evaluated in a University Hospital Emergency Department. Patients and physicians independently evaluated the severity of the asthma attack using a linear scale. Patient score, physician score and forced expiratory volume at the first second (FEV1) were correlated with history and physical examination variables, and were also considered as dependent variables in multiple linear regression models. FEV1 correlated significantly with the physician score (rho = 0.42, P = 0.001), but not with patient score (rho = 0.03; P = 0.77). Use of neck accessory muscles, expiratory time and wheezing intensity were the explanatory variables in the FEV1 regression model and were also present in the physician score model. We conclude that physicians evaluate asthma exacerbation severity better than patients and that physician's scoring of asthma severity correlated significantly with objective measures of airway obstruction (FEV1). Some variables (the use of neck accessory muscles, expiratory time and wheezing intensity) persisted as explanatory variables in physician score and FEV1 regression models, and should be emphasized in medical schools and emergency settings.

The P48T germline mutation and polymorphism in the CDKN2A gene of patients with melanoma

CDKN2A has been implicated as a melanoma susceptibility gene in some kindreds with a family history of this disease. Mutations in CDKN2A may produce an imbalance between functional p16ink4a and cyclin D causing abnormal cell growth. We searched for germline mutations in this gene in 22 patients with clinical criteria of hereditary cancer (early onset, presence of multiple primary melanoma or 1 or more first- or second-degree relatives affected) by secondary structural content prediction, a mutation scanning method that relies on the propensity for single-strand DNA to take on a three-dimensional structure that is highly sequence dependent, and sequencing the samples with alterations in the electrophoretic mobility. The prevalence of CDKN2A mutation in our study was 4.5% (1/22) and there was a correlation between family history and probability of mutation detection. We found the P48T mutation in 1 patient with 2 melanoma-affected relatives. The patient descends from Italian families and this mutation has been reported previously only in Italian families in two independent studies. This leads us to suggest the presence of a mutational "hotspot" within this gene or a founder mutation. We also detected a high prevalence (59.1%) of polymorphisms, mainly alleles 500 C/G (7/31.8%) or 540 C/T (6/27.3%), in the 3' untranslated region of exon 3. This result reinforces the idea that these rare polymorphic alleles have been significantly associated with the risk of developing melanoma.