Linear feedback shift registers and the minimal realization problem

[EN] The Berlekamp-Massey algorithm solves the problem of finding the shortest linear feedback shift register which generates a given finite sequence of scalars. This problem is reinterpreted from the point of view of the realization theory and several extensions to sequences of matrices are analyzed. We give a generalization of the result on which the Berlekamp-Massey algorithm is based in terms of the partial Brunovsky indices of a sequence of matrices and propose an algorithm to obtain them for sequences of vectors. The results we obtain hold for arbitrary fields.The first author is partially supported by grants MINECO MTM2017-83624-P, MTM2017-90682-REDT, and UPV/EHU GIU16/42. The second author is partially supported by grants MINECO MTM2017-83624-P and MTM2017-90682-REDT.Baragana, I.; Roca Martinez, A. (2019). Linear feedback shift registers and the minimal realization problem. Linear Algebra and its Applications. 576:200-227. https://doi.org/10.1016/j.laa.2018.06.009S20022757

Weierstrass Structure and Eigenvalue Placement of Regular Matrix Pencils under Low Rank Perturbations

[EN] We solve the problem of determining the Weierstrass structure of a regular matrix pencil obtained by a low rank perturbation of another regular matrix pencil. We apply the result to find necessary and sufficient conditions for the existence of a low rank perturbation such that the perturbed pencil has prescribed eigenvalues and algebraic multiplicities. The results hold over fields with sufficient number of elements.The work of the first and second authors was partially supported by MINECO grants MTM2017-83624-P and MTM2017-90682-REDT. The work of the first author was also partially supported by UPV/EHU grant GIU16/42.Baragana Garate, I.; Roca Martinez, A. (2019). Weierstrass Structure and Eigenvalue Placement of Regular Matrix Pencils under Low Rank Perturbations. SIAM Journal on Matrix Analysis and Applications. 40(2):440-453. https://doi.org/10.1137/18M120024544045340

The lattice of characteristic subspaces of an endomorphism with Jordan-Chevalley decomposition

[EN] Given an endomorphism A over a finite dimensional vector space having Jordan-Chevalley decomposition, the lattices of invariant and hyperinvariant subspaces of A can be obtained from the nilpotent part of this decomposition. We extend this result for lattices of characteristic subspaces. We also obtain a generalization of Shoda's theorem about the characterization of the existence of characteristic non hyperinvariant subspaces. (C) 2018 Elsevier Inc. All rights reserved.The second author is partially supported by grant MTM2015-65361-P MINECO/FEDER, UE and MTM2017-90682-REDT. The third author is partially supported by grants MTM2017-83624-P and MTM2017-90682-REDT.Mingueza, D.; Montoro, ME.; Roca Martinez, A. (2018). The lattice of characteristic subspaces of an endomorphism with Jordan-Chevalley decomposition. Linear Algebra and its Applications. 558:63-73. https://doi.org/10.1016/j.laa.2018.08.005S637355

The characteristic subspace lattice of a linear transformation

[EN] Given a square matrix A in Mn(F), the lattices of the hyper-invariant (Hinv(A)) and characteristic (Chinv(A)) subspaces coincide whenever Fis not GF(2). If the characteristic polynomial of A splits over F, A can be considered nilpotent. In this paper we investigate the properties of the lattice Chinv(J) when F =GF(2) for a nilpotent matrix J. In particular, we prove it to be self-dual.The second author is partially supported by MINECO, grant MTM2015-65361-P and third author is partially supported by MINECO, grant MTM2013-40960-P, and by Gobierno Vasco, grant GIC13/IT-710-13.Mingueza, D.; Montoro, ME.; Roca Martinez, A. (2016). The characteristic subspace lattice of a linear transformation. Linear Algebra and its Applications. 506:329-341. https://doi.org/10.1016/j.laa.2016.06.003S32934150

La probabilidad y el sistema de clasificación de la Federación Internacional de Ajedrez

En este artículo mostramos una aplicación de algunas nociones de la probabilidad. Se presenta para ello el cálculo del elo, sistema de puntuación empleado por la Federación Internacional de Ajedrez (FIDE) para medir el nivel de juego de un jugador federado de ajedrez.A medida que nos vamos aproximando al cálculo del elo, aparece la necesidad de introducir las nociones de variable aleatoria y distribución normal y de analizar algunas de sus propiedades.Benítez López, J.; Roca Martinez, A. (2020). La probabilidad y el sistema de clasificación de la Federación Internacional de Ajedrez. http://hdl.handle.net/10251/146643DE

Las matemáticas escondidas en la puntuación Elo del ajedrez

[EN] El sistema Elo es el método usado por la FIDE (Federación Internacional de Ajedrez) para clasificar a los jugadores de ajedrez en función de su calidad. Este sistema tiene una fuerte componente matemática: la teoría de la probabilidad. Con algunas modificaciones sencillas, este trabajo puede usarse como ejemplo en una asignatura de Probabilidad, en cualquier estudio universitario, como una aplicación de esta rama de las matemáticas.Benítez López, J.; Roca Martinez, A. (2018). Las matemáticas escondidas en la puntuación Elo del ajedrez. La Gaceta de la Real Sociedad Matemática Española. 21(3):517-525. http://hdl.handle.net/10251/120543S51752521

Evaluación de los test de diagnóstico clínicos: análisis estadístico

En este artículo se muestra una aplicación de la probabilidad condicional (teoremas de Bayes y de la probabilidad total). Se evalúa la fiabilidad de los test de diagnóstico clínicos. Se presentan para ello las nociones de sensibilidad y especificidad de un test, conceptos clave para evaluar la fiabilidad de un test. Después de efectuar algunos cálculos, se analizan los resultados numéricos obtenidos. Finalmente, se estudia la bondad de las pruebas múltiples en función de la fiabilidad de cada una por separado.Benítez López, J.; Roca Martinez, A. (2022). Evaluación de los test de diagnóstico clínicos: análisis estadístico. http://hdl.handle.net/10251/183235DE

Treatment Of A Patient With Thoracolumbar Scoliosis Utilizing A Regional Interdependence Approach Including Components Of The Schroth Method: A Case Report

Background and Purpose: Spinal deformity is a challenging spinal disorder in adults. A scoliotic curve of \u3e10 degrees exists in up to 12% of the population and while surgery is the definitive measure, there is limited evidence to guide non-surgical treatment. This case investigated traditional physical therapy (PT) treatment utilizing a Regional Interdependence Approach (RIA) and components of the Schroth method for a patient with chronic low back pain (CLBP). Case Description: A 66 year old male presented with CLBP, worst upon rising in the AM with (6/10 NPRS). Imaging demonstrated thoracolumbar dextroscoliosis, bilateral foraminal narrowing and associated spondylolisthesis of the fifth lumbar vertebrae. A RIA exam revealed mobility deficits of thoracolumbar spine, instability of L5-S1, and a 1.38” leg length discrepancy. A comprehensive treatment approach was used including lumbar stabilization exercises and postural therapy, including components of the Schroth method. Outcomes: Following 12 weeks, pain improved from 6/10 to 4/105, with the patient reporting no pain when arising from bed. 30-second sit to stand improved from five to eight. Following implementation of a shoe lift visible changes were noted in pelvic symmetry. However, the degree of scoliosis appeared unchanged and no subjective improvements were noted on the Roland-Morris Low Back Pain Questionnaire (RMLBPQ)

Barriers of mental health treatment utilization among first-year college students: First cross-national results from the WHO World Mental Health International College Student Initiative.

BACKGROUND: Although mental disorders and suicidal thoughts-behaviors (suicidal thoughts and behaviors) are common among university students, the majority of students with these problems remain untreated. It is unclear what the barriers are to these students seeking treatment. AIMS: The aim of this study is to examine the barriers to future help-seeking and the associations of clinical characteristics with these barriers in a cross-national sample of first-year college students. METHOD: As part of the World Mental Health International College Student (WMH-ICS) initiative, web-based self-report surveys were obtained from 13,984 first-year students in eight countries across the world. Clinical characteristics examined included screens for common mental disorders and reports about suicidal thoughts and behaviors. Multivariate regression models adjusted for socio-demographic, college-, and treatment-related variables were used to examine correlates of help-seeking intention and barriers to seeking treatment. RESULTS: Only 24.6% of students reported that they would definitely seek treatment if they had a future emotional problem. The most commonly reported reasons not to seek treatment among students who failed to report that they would definitely seek help were the preference to handle the problem alone (56.4%) and wanting to talk with friends or relatives instead (48.0%). Preference to handle the problem alone and feeling too embarrassed were also associated with significantly reduced odds of having at least some intention to seek help among students who failed to report that they would definitely seek help. Having 12-month major depression, alcohol use disorder, and suicidal thoughts and behaviors were also associated with significantly reduced reported odds of the latter outcome. CONCLUSIONS: The majority of first-year college students in the WMH-ICS surveys report that they would be hesitant to seek help in case of future emotional problems. Attitudinal barriers and not structural barriers were found to be the most important reported reasons for this hesitation. Experimental research is needed to determine whether intention to seek help and, more importantly, actual help-seeking behavior could be increased with the extent to which intervention strategies need to be tailored to particular student characteristics. Given that the preference to handle problems alone and stigma and appear to be critical, there could be value in determining if internet-based psychological treatments, which can be accessed privately and are often build as self-help approaches, would be more acceptable than other types of treatments to student who report hesitation about seeking treatment.status: publishe

WHO World Mental Health Surveys International College Student Project: Prevalence and Distribution of Mental Disorders

Increasingly, colleges across the world are contending with rising rates of mental disorders, and in many cases, the demand for services on campus far exceeds the available resources. The present study reports initial results from the first stage of the WHO World Mental Health International College Student project, in which a series of surveys in 19 colleges across 8 countries (Australia, Belgium, Germany, Mexico, Northern Ireland, South Africa, Spain, United States) were carried out with the aim of estimating prevalence and basic sociodemographic correlates of common mental disorders among first-year college students. Web-based self-report questionnaires administered to incoming first-year students (45.5% pooled response rate) screened for six common lifetime and 12-month DSM-IV mental disorders: major depression, mania/hypomania, generalized anxiety disorder, panic disorder, alcohol use disorder, and substance use disorder. We focus on the 13,984 respondents who were full-time students: 35% of whom screened positive for at least one of the common lifetime disorders assessed and 31% screened positive for at least one 12-month disorder. Syndromes typically had onsets in early to middle adolescence and persisted into the year of the survey. Although relatively modest, the strongest correlates of screening positive were older age, female sex, unmarried-deceased parents, no religious affiliation, nonheterosexual identification and behavior, low secondary school ranking, and extrinsic motivation for college enrollment. The weakness of these associations means that the syndromes considered are widely distributed with respect to these variables in the student population. Although the extent to which cost-effective treatment would reduce these risks is unclear, the high level of need for mental health services implied by these results represents a major challenge to institutions of higher education and governments. (PsycINFO Database Record (c) 2018 APA, all rights reserved).status: publishe