Algoritmos primais-duais de ponto fixo aplicados ao problema Ridge Regression

In this work we propose algorithms for solving a fixed-point general primal-dual formulation applied to the Ridge Regression problem. We study the primal formulation for regularized least squares problems, especially L2-norm, named Ridge Regression and then describe convex duality for that class of problems. Our strategy was to consider together primal and dual formulations and minimize the duality gap between them. We established the primal-dual fixed point algorithm, named SRP and a reformulation for this method, the main contribution of the thesis, which was more efficient and robust, called acc-SRP method or accelerated version of the SRP method. The theoretical study of the algorithms was done through the analysis of the spectral properties of the associated iteration matrices. We proved the linear convergence of algorithms and some numerical examples comparing two variants for each algorithm proposed were presented. We also showed that our best method, acc-SRP, has excellent numerical performance for solving very ill-conditioned problems, when compared to the conjugate gradient method, which makes it computationally more attractive.Neste trabalho propomos algoritmos para resolver uma formulação primal-dual geral de ponto fixo aplicada ao problema de Ridge Regression. Estudamos a formulação primal para problemas de quadrados mínimos regularizado, em especial na norma L2, nomeados Ridge Regression e descrevemos a dualidade convexa para essa classe de problemas. Nossa estratégia foi considerar as formulações primal e dual conjuntamente, e minimizar o gap de dualidade entre elas. Estabelecemos o algoritmo de ponto fixo primal-dual, nomeado SRP e uma reformulação para esse método, contribuição principal da tese, a qual mostrou-se mais eficaz e robusta, designada por método acc-SRP, ou versão acelerada do método SRP. O estudo teórico dos algoritmos foi feito por meio da análise de propriedades espectrais das matrizes de iteração associadas. Provamos a convergência linear dos algoritmos e apresentamos alguns exemplos numéricos comparando duas variantes para cada algoritmo proposto. Mostramos também que o nosso melhor método, acc-SRP, possui excelente desempenho numérico na resolução de problemas muito mal-condicionados quando comparado ao Método de Gradientes Conjugados, o que o torna computacionalmente mais atraente

Bannayan–Riley–Ruvalcaba syndrome with posterior subcapsular congenital cataract and a consensus sequence splicing PTEN mutation

This study, combined with the previously reported c.634+1G >T mutation [Agrawal et al., 2005] reveal that exon 6 skipping of PTEN gene produces two different phenotypes of CS and BRRS associated with posterior subcapsular congenital cataract. These data suggest the contribution of other factors that could act downstream of the mutations determining phenotypic variability [Weng et al., 2001]. In conclusion, this study expands our knowledge on the phenotypic variability of BRRS syndrome and suggests a new mechanism for posterior subcapsular congenital cataract due to altered function of the PTEN protein. Further investigations involving a larger number of patients will be required to confirm these data

New mutations in DYNC2H1 and WDR60 genes revealed by whole-exome sequencing in two unrelated Sardinian families with Jeune asphyxiating thoracic dystrophy

Jeune asphyxiating thoracic dystrophy (JATD; Jeune syndrome, MIM 208500) is a rare autosomal recessive chondrodysplasia, phenotypically overlapping with short-rib polydactyly syndromes (SRPS). JATD typical hallmarks include skeletal abnormalities such as narrow chest, shortened ribs, limbs shortened bones, extra fingers and toes (polydactyly), as well as extraskeletal manifestations (renal, liver and retinal disease). To date, disease-causing mutations have been found in several genes, highlighting a marked genetic heterogeneity that prevents a molecular diagnosis of the disease in most families.Here, we report the results of whole-exome sequencing (WES) carried out in four JATD cases, belonging to three unrelated families of Sardinian origin. The exome analysis allowed to identify mutations not previously reported in the DYNC2H1 (MIM 603297) and WDR60 (MIM 615462) genes, both codifying for ciliary intraflagellar transport components whose mutations are known to cause Jeune syndrom

Respiratory sleep disorders in Jeune syndrome: a case description

Purpose: Jeune syndrome (JS, also described as asphyxiating thoracic dystrophy, ATD) is a rare autosomal recessive skeletal dysplasia characterized by a small, narrow chest and variable limb shortness with a considerable neonatal mortality as a result of respiratory distress. Significant life-threatening cervical spine abnormalities can be typical. Method: Here we describe the case of a male infant of Sardinian origin, who developed respiratory distress and feeding difficulties from the first months, correlated with muscle\skeletal dysmorphism prevalent on chest. Nocturnal respiratory sleep alterations were reported from parents. Results: After clinical, genetics, radiographic and cervical MRI investigations, ATD diagnosis with C1 stenosis. A full-night video-polysomnographic study was performed in order to evaluate the sleep apnea condition. The study showed a condition of tachipnea\tachicardia, with several short respiratory events during sleep, both obstructive and central type with apnea-hypopnea index (AHI) 17/ h, mean duration 3.7 sec with longest 20 sec. Conclusion: It can be hypothesized that the combination of altered respiratory and cardiac frequency is related to central type of sleep respiratory disorders consequent to C1 compression, while the obstructive minor component is related to thoracic restrictive disorders. Full night lab-polygraphy is recommended in dysmorphic skeletal disorders like JS

Congenital Joint Dislocations Caused by Carbohydrate Sulfotransferase 3 Deficiency in Recessive Larsen Syndrome and Humero-Spinal Dysostosis

Deficiency of carbohydrate sulfotransferase 3 (CHST3; also known as chondroitin-6-sulfotransferase) has been reported in a single kindred so far and in association with a phenotype of severe chondrodysplasia with progressive spinal involvement. We report eight CHST3 mutations in six unrelated individuals who presented at birth with congenital joint dislocations. These patients had been given a diagnosis of either Larsen syndrome (three individuals) or humero-spinal dysostosis (three individuals), and their clinical features included congenital dislocation of the knees, elbow joint dysplasia with subluxation and limited extension, hip dysplasia or dislocation, clubfoot, short stature, and kyphoscoliosis developing in late childhood. Analysis of chondroitin sulfate proteoglycans in dermal fibroblasts showed markedly decreased 6-O-sulfation but enhanced 4-O-sulfation, confirming functional impairment of CHST3 and distinguishing them from diastrophic dysplasia sulphate transporter (DTDST)-deficient cells. These observations provide a molecular basis for recessive Larsen syndrome and indicate that recessive Larsen syndrome, humero-spinal dysostosis, and spondyloepiphyseal dysplasia Omani type form a phenotypic spectrum

Mutations in CEP290, which encodes a centrosomal protein, cause pleiotropic forms of Joubert syndrome

Joubert syndrome-related disorders (JSRD) are a group of syndromes sharing the neuroradiological features of cerebellar vermis hypoplasia and a peculiar brainstem malformation known as the 'molar tooth sign'. We identified mutations in the CEP290 gene in five families with variable neurological, retinal and renal manifestations. CEP290 expression was detected mostly in proliferating cerebellar granule neuron populations and showed centrosome and ciliary localization, linking JSRDs to other human ciliopathies