Should we teach linear algebra through geometry?

AbstractCan geometry help students learn linear algebra? I study this question and demonstrate that there is no obvious clear answer: geometry can be an obstacle to learning linear algebra; or it can be helpful. Geometry is helpful only under certain conditions and with a specific use of drawings. These special requirements for using geometry are apparently not much recognized in our teaching of linear algebra courses, at least in France, where my educational studies have taken place

Characterisation of 11β-hydroxysteroid dehydrogenase 1 in human orbital adipose tissue: a comparison with subcutaneous and omental fat

Glucocorticoids (GCs) have a profound effect on adipose biology increasing tissue mass causing central obesity. The pre-receptor regulation of GCs by 11β-hydroxysteroid dehydrogenase type 1 (11β-HSD1) that activates cortisol from cortisone has been postulated as a fundamental mechanism underlying the metabolic syndrome mediating adipocyte hyperplasia and hypertrophy in the omental (OM) depot. Orbital adipose tissue (OF) is the site of intense inflammation and tissue remodelling in several orbital inflammatory disease states. In this study, we describe features of the GC metabolic pathways in normal human OF depot and compare it with subcutaneous (SC) and OM depots. Using an automated histological characterisation technique, OF adipocytes were found to be significantly smaller (parameters: area, maximum diameter and perimeter) than OM and SC adipocytes (P<0·001). Although immunohistochemical analyses demonstrated resident CD68+ cells in all three whole tissue adipose depots, OF CD68 mRNA and protein expression exceeded that of OM and SC (mRNA, P<0·05; protein, P<0·001). In addition, there was higher expression of glucocorticoid receptor (GR)α mRNA in the OF whole tissue depot (P<0·05). Conversely, 11β-HSD1 mRNA together with the markers of late adipocyte differentiation (FABP4 and G3PDH) were significantly lower in OF. Primary cultures of OF preadipocytes demonstrated predominant 11β-HSD1 oxo-reductase activity with minimal dehydrogenase activity. Orbital adipocytes are smaller, less differentiated, and express low levels of 11β-HSD1 but abundant GRα compared with SC and OM. OF harbours a large CD68+ population. These characteristics define an orbital microenvironment that has the potential to respond to sight-threatening orbital inflammatory disease

Higher education delays and shortens cognitive impairment. A multistate life table analysis of the US Health and Retirement Study

Improved health may extend or shorten the duration of cognitive impairment by postponing incidence or death. We assess the duration of cognitive impairment in the US Health and Retirement Study (1992–2004) by self reported BMI, smoking and levels of education in men and women and three ethnic groups. We define multistate life tables by the transition rates to cognitive impairment, recovery and death and estimate Cox proportional hazard ratios for the studied determinants. 95% confidence intervals are obtained by bootstrapping. 55 year old white men and women expect to live 25.4 and 30.0 years, of which 1.7 [95% confidence intervals 1.5; 1.9] years and 2.7 [2.4; 2.9] years with cognitive impairment. Both black men and women live 3.7 [2.9; 4.5] years longer with cognitive impairment than whites, Hispanic men and women 3.2 [1.9; 4.6] and 5.8 [4.2; 7.5] years. BMI makes no difference. Smoking decreases the duration of cognitive impairment with 0.8 [0.4; 1.3] years by high mortality. Highly educated men and women live longer, but 1.6 years [1.1; 2.2] and 1.9 years [1.6; 2.6] shorter with cognitive impairment than lowly educated men and women. The effect of education is more pronounced among ethnic minorities. Higher life expectancy goes together with a longer period of cognitive impairment, but not for higher levels of education: that extends life in good cognitive health but shortens the period of cognitive impairment. The increased duration of cognitive impairment in minority ethnic groups needs further study, also in Europe

Hearing loss in Pompe disease revisited: results from a study of 24 children

Little information is available regarding the auditory function in Pompe patients. Hearing loss has been reported in classic infantile patients, but it is still unknown whether central nervous system involvement interferes with auditory function and whether enzyme replacement therapy can improve hearing. Audi

文献目録

Background: As little information is available on children with non-classic presentations of Pompe disease, we wished to gain knowledge of specific clinical characteristics and genotypes. We included all patients younger than 18 years, who had been evaluated at the Pompe Center in Rotterdam, the Netherlands, between 1975 and 2012, excluding those with the classic-infantile form. None were treated with enzyme replacement therapy at the time of evaluation. We collected information on first symptoms, diagnosis, use of a wheelchair and/or respirator, and enzyme and mutation analysis and assessed muscle strength, pulmonary function, and cardiac parameters. Results: Thirty-one patients participated. Median age at symptom onset was 2.6 years (range 0.5-13y) and at diagnosis 4.0 years. Most first problems were delayed motor development and problems related to limb-girdle weakness. Fatigue, persistent diarrhea and problems in raising the head in supine position were other first complaints. Ten patients were asymptomatic at time of diagnosis. Five of them developed symptoms before inclusion in this study. Over 50 % of all patients had low or absent reflexes, a myopathic face, and scoliosis; 29 % were underweight. Muscle strength of the neck flexors, hip extensors, hip flexors, and shoulder abductors were most frequently reduced. Pulmonary function was decreased in over 48 % of the patients; 2 patients had cardiac hypertrophy. Patients with mutations other than the c.-32-13T > G were overall more severely affected, while 18 out of the 21 patients (86 %) with the c.-32-13T > G/`null' genotype were male. Conclusions: Our study shows that Pompe disease can present with severe mobility and respiratory problems during childhood. Pompe disease should be considered in the differential diagnosis of children with less familiar signs such as disproportional weakness of the neck flexors, unexplained fatigue, persistent diarrhea and unexplained high CK/ASAT/ALAT. Disease presentation appears to be different from adult patients. The majority of affected children with GAA genotype c.-32-13T > G/`null' appeared to be male

Hearing in adults with Pompe disease

Hearing loss has been recognized as an important cause of morbidity in infants with Pompe disease, a metabolic disorder caused by deficiency of acid α-glucosidase. It is unknown whether hearing is also affected in adult Pompe patients. We have studied the prevalence, severity, and type of hearing loss in 58 adult patients using tympanometry and pure-tone audiometry. Compared to normative data (International Organisation for Standardisation standard 7029), 72% of patients had impaired hearing thresholds at one or more frequencies in at least one ear. All measured frequencies were equally affected. All patients had a sensorineural type of hearing loss, pointing to cochlear or retrocochlear pathology. Categorised according to the standards of the World Health Organisation 21% of patients had a clinically relevant hearing loss (16% slight, 3% moderate, 2% profound). Though this suggests that hearing loss occurs in a considerable number of patients with Pompe disease, this prevalence is similar to that in the general population. Therefore, we conclude that hearing loss is not a specific feature of Pompe disease in adults

PAS-positive lymphocyte vacuoles can be used as diagnostic screening test for Pompe disease

Screening of blood films for the presence of periodic acid-Schiff (PAS)-positive lymphocyte vacuoles is sometimes used to support the diagnosis of Pompe disease, but the actual diagnostic value is still unknown. We collected peripheral blood films from 65 untreated Pompe patients and 51 controls. Lymphocyte vacuolization was quantified using three methods: percentage vacuolated lymphocytes, percentage PAS-positive lymphocytes, and a PAS score depending on staining intensity. Diagnostic accuracy of the tests was assessed using receiver operating characteristic (ROC) curves. All three methods fully discerned classic infantile patients from controls. The mean values of patients with milder forms of Pompe disease were significantly higher than those of controls, but full separation was not obtained. The area under the ROC curve was 0.98 for the percentage vacuolated lymphocytes (optimal cutoff value 3; sensitivity 91%, specificity 96%) and 0.99 for the percentage PAS-positive lymphocytes and PAS score (optimal cutoff value 9; sensitivity 100%, specificity 98%). Our data indicate that PAS-stained blood films can be used as a reliable screening tool to support a diagnosis of Pompe disease. The percentage of PAS-positive lymphocytes is convenient for use in clinical practice but should always be interpreted in combination with other clinical and laboratory parameters

Facial-muscle weakness, speech disorders and dysphagia are common in patients with classic infantile Pompe disease treated with enzyme therapy

Classic infantile Pompe disease is an inherited generalized glycogen storage disorder caused by deficiency of lysosomal acid α-glucosidase. If left untreated, patients die before one year of age. Although enzyme-replacement therapy (ERT) has significantly prolonged lifespan, it has also revealed new aspects of the disease. For up to 11 years, we investigated the frequency and consequences of facial-muscle weakness, speech disorders and dysphagia in long-term survivors. Sequential photographs were used to determine the timing and severity of facial-muscle weakness. Using standardized articulation tests and fibreoptic endoscopic evaluation of swallowing, we investigated speech and swallowing function in a subset of patients. This study included 11 patients with classic infantile Pompe disease. Median age at the start of ERT was 2.4 months (range 0.1-8.3 months), and median age at the end of the study was 4.3 years (range 7.7 months −12.2 years). All patients developed facial-muscle weakness before the age of 15 months. Speech was studied in four patients. Articulation was disordered, with hypernasal resonance and reduced speech intelligibility in all four. Swallowing function was studied in six patients, the most important findings being ineffective swallowing with residues of food (5/6), penetration or aspiration (3/6), and reduced pharyngeal and/or laryngeal sensibility (2/6). We conclude that facial-muscle weakness, speech disorders and dysphagia are common in long-term survivors receiving ERT for classic infantile Pompe disease. To improve speech and reduce the risk for aspiration, early treatment by a speech therapist and regular swallowing assessments are recommended