Artículos de revista DM - MS Aldizkari artikuluak
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Publication Open Access An algorithm for group decision making using n -dimensional fuzzy sets, admissible orders and OWA operators(Elsevier, 2017) Miguel Turullols, Laura de; Sesma Sara, Mikel; Elkano Ilintxeta, Mikel; Asiain Ollo, María José; Bustince Sola, Humberto; Automatika eta Konputazioa; Matematika; Institute of Smart Cities - ISC; Automática y Computación; Matemáticas; Universidad Pública de Navarra / Nafarroako Unibertsitate PublikoaIn this paper we propose an algorithm to solve group decision making problems using n-dimensional fuzzy sets, namely, sets in which the membership degree of each element to the set is given by an in- creasing tuple of n elements. The use of these sets has naturally led us to define admissible orders for n-dimensional fuzzy sets, to present a construction method for those orders and to study OWA operators for aggregating the tuples used to represent the membership degrees of the elements. In these condi- tions, we present an algorithm and apply it to a case study, in which we show that the exploitation phase which appears in many decision making methods can be omitted by just considering linear orders between tuples.Publication Open Access Assessment of asymmetric leg loading before and after total hip arthroplasty using instrumented shoes(BioMed Central, 2014) Martínez Ramírez, Alicia; Weenk, Dirk; Lecumberri Villamediana, Pablo; Verdonschot, Nico; Pakvis, Dean; Veltink, Peter H.; Matemáticas; MatematikaBackground: Total hip arthroplasty is a successful surgical treatment in patients with osteoarthritis of the hip. Different questionnaires are used by the clinicians to assess functional capacity and the patient's pain, despite these questionnaires are known to be subjective. Furthermore, many studies agree that kinematic and kinetic parameters are crucial to evaluate and to provide useful information about the patient’s evolution for clinicians and rehabilitation specialists. However, these quantities can currently only be obtained in a fully equipped gait laboratory. Instrumented shoes can quantify gait velocity, kinetic, kinematic and symmetry parameters. The aim of this study was to investigate whether the instrumented shoes is a sufficiently sensitive instrument to show differences in mobility performance before and after total hip arthroplasty. Methods: In this study, patients undergoing total hip arthroplasty were measured before and 6–8 months after total hip arthroplasty. Both measurement sessions include 2 functional mobility tasks while the subject was wearing instrumented shoes. Before each measurement the Harris Hip Score and the Traditional Western Ontario and McMaster Universities osteoarthritis index were administered as well. Results: The stance time and the average vertical ground reaction force measured with the instrumented shoes during walking, and their symmetry index, showed significant differences before and after total hip arthroplasty. However, the data obtained with the sit to stand test did not reveal this improvement after surgery. Conclusions: Our results show that inter-limb asymmetry during a walking activity can be evaluated with the instrumented shoes before and after total hip arthroplasty in an outpatient clinical setting.Publication Embargo Binary relations coming from solutions of functional equations: orderings and fuzzy subsets(World Scientific Publishing Company, 2017) Campión Arrastia, María Jesús; Miguel Turullols, Laura de; García Catalán, Olga Raquel; Induráin Eraso, Esteban; Abrísqueta Usaola, Francisco Javier; Automatika eta Konputazioa; Matematika; Institute of Smart Cities - ISC; Institute for Advanced Research in Business and Economics - INARBE; Institute for Advanced Materials and Mathematics - INAMAT2; Automática y Computación; Matemáticas; Universidad Pública de Navarra / Nafarroako Unibertsitate PublikoaWe analyze the main properties of binary relations, defined on a nonempty set, that arise in a natural way when dealing with real-valued functions that satisfy certain classical functional equations on two variables. We also consider the converse setting, namely, given binary relations that accomplish some typical properties, we study whether or not they come from solutions of some functional equation. Applications to the numerical representability theory of ordered structures are also furnished as a by-product. Further interpretations of this approach as well as possible generalizations to the fuzzy setting are also commented. In particular, we discuss how the values taken for bivariate functions that are bounded solutions of some classical functional equations define, in a natural way, fuzzy binary relations on a set.Publication Open Access Comparison meaningful operators and ordinal invariant preferences(Elsevier, 2015) Candeal, Juan Carlos; Induráin Eraso, Esteban; Matemáticas; MatematikaThe existence of a continuous and order-preserving real-valued function, for the class of continuous and ordinal invariant total preorders, defined on the Banach space of all bounded real-valued functions, which are in turn defined on a given set Ω, is characterized. Whenever the total preorder is nontrivial, the type of representation obtained leads to a functional equation that is closely related to the concept of comparison meaningfulness, and is studied in detail in this setting. In particular, when restricted to the space of bounded and measurable real-valued functions, with respect to some algebra of subsets of Ω, we prove that, if the total preorder is also weakly Paretian, then it can be represented as a Choquet integral with respect to a {0,1}-valued capacity. Some interdisciplinary applications to measurement theory and social choice are also considered.Publication Open Access Construction of admissible linear orders for interval-valued Atanassov intuitionistic fuzzy sets with an application to decision making(Elsevier, 2015) Miguel Turullols, Laura de; Bustince Sola, Humberto; Fernández Fernández, Francisco Javier; Induráin Eraso, Esteban; Kolesárová, Anna; Mesiar, Radko; Matemáticas; Matematika; Automática y Computación; Automatika eta Konputazioa; Universidad Pública de Navarra / Nafarroako Unibertsitate PublikoaIn this work we introduce a method for constructing linear orders between pairs of intervals by using aggregation functions. We adapt this method to the case of interval-valued Atanassov intuitionistic fuzzy sets and we apply these sets and the considered orders to a decision making problem.Publication Open Access Desarrollo de la competencia de análisis ontosemiótico de futuros profesores de matemáticas(Universidad Complutense de Madrid, 2018) Giacomone, Belén; Godino, Juan D.; Wilhelmi, Miguel R.; Blanco, Teresa F.; Matemáticas; MatematikaUna enseñanza adecuada de las matemáticas requiere el conocimiento y la competencia de los profesores para identificar la variedad de objetos y significados involucrados en la resolución de tareas escolares. En este artículo se describe el diseño, la implementación y análisis retrospectivo de un proceso formativo dirigido a futuros profesores de matemáticas, centrado en desarrollar esta llamada competencia de análisis ontosemiótico. Para esto, se utilizan algunas herramientas teóricas y metodológicas del Enfoque Ontosemiótico del conocimiento y la instrucción matemáticos. En esta experiencia, los futuros profesores primero resuelven tareas matemáticas sobre visualización y razonamiento diagramático; luego, analizan los objetos y significados puestos en juego en la resolución de cada tarea implementada. Además, las estrategias que los estudiantes producen en sus soluciones se discuten y comparten en entornos reales de clase. El análisis de los datos es cualitativo y está orientado a la identificación de prácticas didácticas significativas sobre el estado inicial de los significados personales de los estudiantes, el reconocimiento de conflictos y progresos en el desarrollo de la competencia pretendida. Los datos se recogen de las respuestas escritas de los estudiantes, las notas del investigador observador y las grabaciones en audio de las clases. Los resultados revelan la complejidad involucrada en el desarrollo de esta competencia de análisis ontosemiótico, así como su relevancia para lograr una enseñanza de las matemáticas de alta calidad. Finalmente, el análisis retrospectivo del diseño formativo permite al profesor y al investigador reflexionar sobre cada uno de los factores que condicionan los procesos de enseñanza y así, determinar mejoras potenciales para futuras implementaciones.Publication Open Access Diseño de un cuestionario para evaluar conocimientos didáctico-matemáticos sobre razonamiento algebraico elemental(Universitat Autònoma de Barcelona, 2015) Godino, Juan D.; Aké, Lilia P.; Lacasta Zabalza, Eduardo; Lasa Oyarbide, Aitzol; Wilhelmi, Miguel R.; Matemáticas; MatematikaLa promoción del pensamiento algebraico en alumnos de primaria requiere implementar acciones formativas específicas para los profesores, lo que a su vez implica elaborar instrumentos de evaluación del estado de sus conocimientos didáctico-matemáticos sobre el tema. En este trabajo presentamos resultados del estudio realizado para la construcción de un cuestionario de evaluación de los conocimientos didáctico-matemáticos de estudiantes de magisterio sobre razonamiento algebraico elemental. Describimos las categorías de conocimientos algebraicos tenidas en cuenta (estructuras, funciones y modelización) y las categorías de conocimientos didácticos (facetas epistémica, cognitiva, instruccional y ecológica). Así mismo se describen y analizan las tareas incluidas en el cuestionario informando de su validez de contenido.Publication Open Access Distribution patterns of infection with multiple types of human papillomaviruses and their association with risk factors(Public Library of Science, 2011) Soto de León, Sara; Camargo, Milena; Sánchez, Ricardo; Muñoz, Marina; Pérez Prados, Antonio; Purroy Unanua, Antonio; Patarroyo, Manuel Elkin; Patarroyo, Manuel Alfonso; Matemáticas; MatematikaBackground: Infection with multiple types of human papillomavirus (HPV) is one of the main risk factors associated with the development of cervical lesions. In this study, cervical samples collected from 1, 810 women with diverse sociocultural backgrounds, who attended to their cervical screening program in different geographical regions of Colombia, were examined for the presence of cervical lesions and HPV by Papanicolau testing and DNA PCR detection, respectively. Principal Findings: The negative binomial distribution model used in this study showed differences between the observed and expected values within some risk factor categories analyzed. Particularly in the case of single infection and coinfection with more than 4 HPV types, observed frequencies were smaller than expected, while the number of women infected with 2 to 4 viral types were higher than expected. Data analysis according to a negative binomial regression showed an increase in the risk of acquiring more HPV types in women who were of indigenous ethnicity (+37.8%), while this risk decreased in women who had given birth more than 4 times (-31.1%), or were of mestizo (-24.6%) or black (-40.9%) ethnicity. Conclusions: According to a theoretical probability distribution, the observed number of women having either a single infection or more than 4 viral types was smaller than expected, while for those infected with 2-4 HPV types it was larger than expected. Taking into account that this study showed a higher HPV coinfection rate in the indigenous ethnicity, the role of underlying factors should be assessed in detail in future studies.Publication Open Access La educación musical en la formación básica en España. El problema de la dispersión curricular(Pontificia Universidad Católica de Valparaíso, 2016) Belletich Ruiz, Olga; Wilhelmi, Miguel R.; Ángel Alvarado, Rolando Alfredo; Psicología y Pedagogía; Psikologia eta Pedagogia; Matemáticas; MatematikaEn España la Educación Artística pierde su carácter obligatorio en Educación Primaria con la entrada en vigencia de la Ley Orgánica para la Mejora de la Calidad Educativa [LOMCE], relegando la decisión curricular a las Comunidades Autónomas. Este estudio pretende establecer la concreción de las estipulaciones de la LOMCE, relativas a la Educación Musical, en las distintas comunidades y explicar el problema de la dispersión del currículo entre los enfoques eficientista y humanista de la educación. Como estudio cualitativo de diseño socio-crítico, se enmarca en el modelo de análisis de la ingeniería didáctica. Los resultados demuestran que las comunidades hacen esfuerzos por impartir la asignatura más allá de lo normado por la LOMCE y, que existe una intención educativa de facto para incorporar la asignatura en forma transversal y obligatoria en la Educación Primaria, a partir de una articulación basada en las competencias clave internacionales.Publication Open Access Ensembles of adaptive spatial filters increase BCI performance: an online evaluation(IOP, 2016) Sannelli, Claudia; Vidaurre, Carmen; Müller, Klaus Robert; Blankertz, Benjamin; Matemáticas; MatematikaObjective: In electroencephalographic (EEG) data, signals from distinct sources within the brain are widely spread by volume conduction and superimposed such that sensors receive mixtures of a multitude of signals. This reduction of spatial information strongly hampers single-trial analysis of EEG data as, for example, required for brain–computer interfacing (BCI) when using features from spontaneous brain rhythms. Spatial filtering techniques are therefore greatly needed to extract meaningful information from EEG. Our goal is to show, in online operation, that common spatial pattern patches (CSPP) are valuable to counteract this problem. Approach: Even though the effect of spatial mixing can be encountered by spatial filters, there is a trade-off between performance and the requirement of calibration data. Laplacian derivations do not require calibration data at all, but their performance for single-trial classification is limited. Conversely, data-driven spatial filters, such as common spatial patterns (CSP), can lead to highly distinctive features; however they require a considerable amount of training data. Recently, we showed in an offline analysis that CSPP can establish a valuable compromise. In this paper, we confirm these results in an online BCI study. In order to demonstrate the paramount feature that CSPP requires little training data, we used them in an adaptive setting with 20 participants and focused on users who did not have success with previous BCI approaches. Main results: The results of the study show that CSPP adapts faster and thereby allows users to achieve better feedback within a shorter time than previous approaches performed with Laplacian derivations and CSP filters. The success of the experiment highlights that CSPP has the potential to further reduce BCI inefficiency. Significance: CSPP are a valuable compromise between CSP and Laplacian filters. They allow users to attain better feedback within a shorter time and thus reduce BCI inefficiency to one-fourth in comparison to previous non-adaptive paradigms.Publication Open Access Evaluación de conocimientos didáctico-matemáticos sobre razonamiento algebraico elemental de futuros maestros(Ministerio de Educación, Cultura y Deporte, 2015) Díaz Godino, Juan; Wilhelmi, Miguel R.; Neto, Teresa; Fernández Blanco, María Teresa; Contreras de la Fuente, Ángel; Díaz Batanero, María Carmen; Estepa, Antonio; Lasa Oyarbide, Aitzol; Matemáticas; MatematikaDiferentes estudios sugieren la necesidad de incorporar desde edades tempranas el razonamiento algebraico elemental, que en las propuestas curriculares clásicas se inicia en la Educación Secundaria Obligatoria. En este trabajo se analizan los resultados de aplicar un cuestionario de evaluación de conocimientos didáctico-matemáticos sobre razonamiento algebraico elemental a una muestra de estudiantes del Grado en Maestro en Educación Primaria. El objetivo es la elaboración de un diagnóstico sobre la competencia algebraica elemental y su didáctica de los futuros maestros, que permita enmarcar un programa formativo para estos, que garantice finalmente procesos de estudio efectivos en la educación primaria. La muestra está compuesta por 597 estudiantes de las Universidades de Granada, Jaén, Pública de Navarra, Santiago de Compostela en España y de Aveiro en Portugal. En estas universidades, los grupos se constituyen homogéneos ad extra y heterogéneos ad intro. Se propone pues la selección intencional de grupos completos en cada universidad. El cuestionario consta de 25 ítems que evalúan tanto conocimientos algebraicos como conocimientos sobre la enseñanza y aprendizaje del álgebra en Educación Primaria. El análisis cuantitativo de los resultados ha permitido explorar las características psicométricas del instrumento (índices de dificultad, discriminación, fiabilidad y validez). La comparación de los programas de formación en matemáticas y su didáctica entre las distintas universidades participantes revela el énfasis psicopedagógico del Plan de estudios vigente y muestra una formación disciplinar deficiente, que, en particular, no incluye el bloque de razonamiento algebraico. Los resultados muestran un bajo nivel de conocimientos generalizado en las distintas componentes del conocimiento didáctico-matemático, con diferencias significativas entre las universidades. Se concluye que es necesario revisar los programas de formación y planificar el diseño de acciones formativas específicas sobre los contenidos algebraicos elementales, a fin de capacitar a los futuros maestros para que puedan promover en los alumnos de primaria el progresivo desarrollo del pensamiento algebraico.Publication Open Access An evaluation of the 30-s chair stand test in older adults: frailty detection based on kinematic parameters from a single inertial unit(BioMed Central, 2013) Millor Muruzábal, Nora; Lecumberri Villamediana, Pablo; Gómez Fernández, Marisol; Martínez Ramírez, Alicia; Izquierdo Redín, Mikel; Matemáticas; Ciencias de la Salud; Matematika; Osasun Zientziak; Gobierno de Navarra / Nafarroako GobernuaBackground: A growing interest in frailty syndrome exists because it is regarded as a major predictor of co-morbidities and mortality in older populations. Nevertheless, frailty assessment has been controversial, particularly when identifying this syndrome in a community setting. Performance tests such as the 30-second chair stand test (30-s CST) are a cornerstone for detecting early declines in functional independence. Additionally, recent advances in body-fixed sensors have enhanced the sensors’ ability to automatically and accurately evaluate kinematic parameters related to a specific movement performance. The purpose of this study is to use this new technology to obtain kinematic parameters that can identify frailty in an aged population through the performance the 30-s CST. Methods: Eighteen adults with a mean age of 54 years, as well as sixteen pre-frail and thirteen frail patients with mean ages of 78 and 85 years, respectively, performed the 30-s CST while threir trunk movements were measured by a sensor-unit at vertebra L3. Sit-stand-sit cycles were determined using both acceleration and orientation information to detect failed attempts. Movement-related phases (i.e. impulse, stand-up, and sit-down) were differentiated based on seat off and seat on events. Finally, the kinematic parameters of the impulse, stand-up and sit-down phases were obtained to identify potential differences across the three frailty groups. Results: For the stand-up and sit-down phases, velocity peaks and “modified impulse” parameters clearly differentiated subjects with different frailty levels (p < 0.001). The trunk orientation range during the impulse phase was also able to classify a subject according to his frail syndrome (p < 0.001). Furthermore, these parameters derived from the inertial units (IUs) are sensitive enough to detect frailty differences not registered by the number of completed cycles which is the standard test outcome. Conclusions: This study shows that IUs can enhance the information gained from tests currently used in clinical practice, such as the 30-s CST. Parameters such as velocity peaks, impulse, and orientation range are able to differentiate between adults and older populations with different frailty levels. This study indicates that early frailty detection could be possible in clinical environments, and the subsequent interventions to correct these disabilities could be prescribed before further degradation occurs.Publication Open Access Frailty assessment based on trunk kinematic parameters during walking(BioMed Central, 2015) Martínez Ramírez, Alicia; Martinikorena Aranburu, Ion; Gómez Fernández, Marisol; Lecumberri Villamediana, Pablo; Millor Muruzábal, Nora; Rodríguez Mañas, Leocadio; García García, Francisco José; Izquierdo Redín, Mikel; Matemáticas; MatematikaBackground: Physical frailty has become the center of attention of basic, clinical and demographic research due to its incidence level and gravity of adverse outcomes with age. Frailty syndrome is estimated to affect 20 % of the population older than 75 years. Thus, one of the greatest current challenges in this field is to identify parameters that can discriminate between vulnerable and robust subjects. Gait analysis has been widely used to predict frailty. The aim of the present study was to investigate whether a collection of parameters extracted from the trunk acceleration signals could provide additional accurate information about frailty syndrome. Methods: A total of 718 subjects from an elderly population (319 males, 399 females; age: 75.4 ± 6.1 years, mass: 71.8 ± 12.4 kg, height: 158 ± 6 cm) volunteered to participate in this study. The subjects completed a 3-m walk test at their own gait velocity. Kinematic data were acquired from a tri-axial inertial orientation tracker. Findings: The spatio-temporal and frequency parameters measured in this study with an inertial sensor are related to gait disorders and showed significant differences among groups (frail, pre-frail and robust). A selection of those parameters improves frailty classification obtained to gait velocity, compared to classification model based on gait velocity solely. Interpretation: Gait parameters simultaneously used with gait velocity are able to provide useful information for a more accurate frailty classification. Moreover, this technique could improve the early detection of pre-frail status, allowing clinicians to perform measurements outside of a laboratory environment with the potential to prescribe a treatment for reversing their physical decline.Publication Open Access Grupos primitivos con subgrupos maximales pequeños(Universidad Autónoma de Barcelona, Departamento de Matemáticas, 1985) Lafuente López, Julio; Matemáticas; MatematikaPublication Open Access Interval-valued Atanassov intuitionistic OWA aggregations using admissible linear orders and their application to decision making(IEEE, 2016) Miguel Turullols, Laura de; Bustince Sola, Humberto; Pekala, Barbara; Bentkowska, Urszula; Silva, Ivanoska da; Bedregal, Benjamin; Mesiar, Radko; Ochoa Lezaun, Gustavo; Automatika eta Konputazioa; Matematika; Institute of Smart Cities - ISC; Automática y Computación; MatemáticasBased on the definition of admissible order for interval-valued Atanassov intuitionistic fuzzy sets, we study OWA operators in these sets distinguishing between the weights associated to the membership and those associated to the nonmembership degree which may differ from the latter. We also study Choquet integrals for aggregating information which is represented using interval-valued Atanassov intuitionistic fuzzy sets. We conclude with two algorithms to choose the best alternative in a decision making problem when we use this kind of sets to represent information.Publication Open Access A large scale screening study with a SMR-based BCI: Categorization of BCI users and differences in their SMR activity(Plos one, 2019) Sannelli, Claudia; Vidaurre, Carmen; Müller, Klaus Robert; Blankertz, Benjamin; Matemáticas; MatematikaBrain-Computer Interfaces (BCIs) are inefficient for a non-negligible part of the population, estimated around 25%. To understand this phenomenon in Sensorimotor Rhythm (SMR) based BCIs, data from a large-scale screening study conducted on 80 novice participants with the Berlin BCI system and its standard machine-learning approach were investigated. Each participant performed one BCI session with resting state Encephalography, Motor Observation, Motor Execution and Motor Imagery recordings and 128 electrodes. A significant portion of the participants (40%) could not achieve BCI control (feedback performance > 70%). Based on the performance of the calibration and feedback runs, BCI users were stratified in three groups. Analyses directed to detect and elucidate the differences in the SMR activity of these groups were performed. Statistics on reactive frequencies, task prevalence and classification results are reported. Based on their SMR activity, also a systematic list of potential reasons leading to performance drops and thus hints for possible improvements of BCI experimental design are given. The categorization of BCI users has several advantages, allowing researchers 1) to select subjects for further analyses as well as for testing new BCI paradigms or algorithms, 2) to adopt a better subject-dependent training strategy and 3) easier comparisons between different studies.Publication Open Access The lattice of fitting classes which are right extensible by soluble groups(Universidad Autónoma de Barcelona, Departamento de Matemáticas, 2005) Iranzo, M.J.; Lafuente López, Julio; Pérez Monasor, F.; Matemáticas; MatematikaIn this paper we study the set of fitting classes which are right extensible by soluble groups ordered by the inclusion relation. The consideration of the associated lattices gives rise to new fitting classes and it allows to obtain some injectivity criteria for general fitting classes.Publication Open Access Long live to triangles!: dynamic models for trigonometry(Pontifícia Universidade Católica de São Paulo, 2016) Lasa Oyarbide, Aitzol; Belloso Sancet, Nahia; Abaurrea Larrayoz, Jaione; Matemáticas; MatematikaSe presenta en este trabajo un Libro-GGB para asistir situaciones de enseñanza y aprendizaje de la trigonometría. En primer lugar, se justifica la decisión de utilizar el software de geometría dinámica como instrumento para organizar la actividad matemática, basada en la clasificación de modelos dinámicos por “momentos de la actividad matemática”. En segundo lugar, se presenta una propuesta teórica detallada junto con indicaciones de uso. Finalmente, se muestran los resultados de una experiencia práctica con estudiantes de educación secundaria (15-16 años).Publication Open Access Motor abnormalities and cognitive impairment in first-episode psychosis patients, their unaffected siblings and healthy controls(Elsevier, 2018) Cuesta, Manuel J.; Moreno-Izco, Lucía; Ribeiro Fernández, María; López-Ilundain, José M.; Lecumberri Villamediana, Pablo; Cabada Giadás, Teresa; Lorente Omeñaca, Ruth; Sánchez Torres, Ana María; Gómez Fernández, Marisol; Peralta Martín, Víctor; Ciencias de la Salud; Osasun Zientziak; Matemáticas; MatematikaMotor abnormalities (MAs) may be already evidenced long before the beginning of illness and are highly prevalent in psychosis. However, the extent to which the whole range of MAs are related to cognitive impairment in psychosis remains understudied. This study aimed to examine comparatively the relationships between the whole range of motor abnormalities and cognitive impairments in the first-episode of psychosis (FEP), their unaffected siblings and healthy control subjects. Fifty FEP patients, 21 of their healthy siblings and 24 age- and sex matched healthy controls were included. Motor assessment included catatonic, extrapyramidal and neurological soft signs (NSS) by means of standardized instruments. An exhaustive neuropsychological battery was also performed to extract the 7 cognitive dimensions of MATRICS initiative. Higher scores on NSS but not on extrapyramidal and catatonic signs showed significant associations with worse cognitive performance in the three study groups. However, the pattern of associations regarding specific cognitive functions was different among the three groups. Moreover, extrapyramidal signs showed significant associations with cognitive impairment only in FEP patients but not in their unaffected siblings and healthy controls. Catatonic signs did not show any significant association with cognitive functioning in the three study groups. These findings add evidence to the associations between motor abnormalities, particularly NSS and extrapyramidal signs, and cognitive impairment in first-episode psychosis patients. In addition, our results suggest that the specific pattern of associations between MAs and cognitive functioning is different in FEP patients from those of the unaffected siblings and healthy subjects.Publication Open Access Naturaleza del razonamiento algebraico elemental(UNESP, 2012) Godino, Juan D.; Castro, Walter F.; Aké, Lilia P.; Wilhelmi, Miguel R.; Matemáticas; MatematikaLa introducción del razonamiento algebraico en educación primaria es un tema de interés para la investigación e innovación curricular en didáctica de las matemáticas, y presupone una visión ampliada de la naturaleza del álgebra escolar. En este trabajo proponemos una manera de concebir el razonamiento algebraico, basada en los tipos de objetos y procesos matemáticos introducidos en el enfoque ontosemiótico del conocimiento matemático. En síntesis, la consideración de una práctica matemática como algebraica se basará en la intervención de procesos de generalización y simbolización, junto con otros objetos usualmente considerados como algebraicos, tales como relaciones binarias, operaciones, funciones y estructuras. Esta forma de concebir el álgebra elemental es contrastada con las caracterizaciones dadas por otros autores. Asimismo, proponemos una tipología de configuraciones algebraicas que permite definir grados de algebrización de la actividad matemática.