Diagonalizing operators with reflection symmetry

Let $U$ be an operator in a Hilbert space $\mathcal{H}_{0}$, and let $\mathcal{K}\subset\mathcal{H}_{0}$ be a closed and invariant subspace. Suppose there is a period-2 unitary operator $J$ in $\mathcal{H}_{0}$ such that $JUJ=U^*$, and $PJP \geq 0$, where $P$ denotes the projection of $\mathcal{H}_{0}$ onto $\mathcal{K}$. We show that there is then a Hilbert space $\mathcal{H}(\mathcal{K})$, a contractive operator $W:\mathcal{K}\to\mathcal{H}(\mathcal{K})$, and a selfadjoint operator $S=S(U)$ in $\mathcal{H}(\mathcal{K})$ such that $W^*W=PJP$, $W$ has dense range, and $SW=WUP$. Moreover, given $(\mathcal{K},J)$ with the stated properties, the system $(\mathcal{H}(\mathcal{K}),W,S)$ is unique up to unitary equivalence, and subject to the three conditions in the conclusion. We also provide an operator-theoretic model of this structure where $U|_{\mathcal{K}}$ is a pure shift of infinite multiplicity, and where we show that $\ker(W)=0$. For that case, we describe the spectrum of the selfadjoint operator $S(U)$ in terms of structural properties of $U$. In the model, $U$ will be realized as a unitary scaling operator of the form $f(x)\mapsto f(cx)$, $c>1$, and the spectrum of $S(U_{c})$ is then computed in terms of the given number $c$.Comment: 30 pages; Dedicated to the memory of I.E. Sega

Intelligence of very preterm or very low birthweight infants in young adulthood

Contains fulltext : 80142.pdf (publisher's version ) (Closed access)OBJECTIVE: To examine the effect of intrauterine and neonatal growth, prematurity and personal and environmental risk factors on intelligence in adulthood in survivors of the early neonatal intensive care era. METHODS: A large geographically based cohort comprised 94% of all babies born alive in the Netherlands in 1983 with a gestational age below 32 weeks and/or a birth weight >1500 g (POPS study). Intelligence was assessed in 596 participants at 19 years of age. Intrauterine and neonatal growth were assessed at birth and 3 months of corrected age. Environmental and personal risk factors were maternal age, education of the parent, sex and origin. RESULTS: The mean (SD) IQ of the cohort was 97.8 (15.6). In multiple regression analysis, participants with highly educated parents had a 14.2-point higher IQ than those with less well-educated parents. A 1 SD increase in birth weight was associated with a 2.6-point higher IQ, and a 1-week increase in gestational age was associated with a 1.3-point higher IQ. Participants born to young mothers (<25 years) had a 2.7-point lower IQ, and men had a 2.1-point higher IQ than women. The effect on intelligence after early (symmetric) intrauterine growth retardation was more pronounced than after later (asymmetric) intrauterine or neonatal growth retardation. These differences in mean IQ remained when participants with overt handicaps were excluded. CONCLUSIONS: Prematurity as well as the timing of growth retardation are important for later intelligence. Parental education, however, best predicted later intelligence in very preterm or very low birthweight infants

Effects of Acute Febrile Diseases on the Periodontium of Rhesus Monkeys with Reference to Poliomyelitis

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/67269/2/10.1177_00220345510300050301.pd

Gender differences in respiratory symptoms in 19-year-old adults born preterm

Objective: To study the prevalence of respiratory and atopic symptoms in (young) adults born prematurely, differences between those who did and did not develop Bronchopulmonary Disease (BPD) at neonatal age and differences in respiratory health between males and females. Methods: Design: Prospective cohort study. Setting: Nation wide follow-up study, the Netherlands. Participants: 690 adults (19 year old) born with a gestational age below 32 completed weeks and/or with a birth weight less than 1500g. Controls were Dutch participants of the European Community Respiratory Health Survey (ECRHS). Main outcome measures: Presence of wheeze, shortness of breath, asthma, hay fever and eczema using the ECRHS-questionnaire

Nonresponse bias in a follow-up study of 19-year-old adolescents born as preterm infants

Objective. To assess the effect of demographic and neonatal risk factors and outcome at the last available assessment on the probability of full responders, postal responders (those who only responded to the mailed questionnaire), or nonresponders in a follow-up study of 19-year-old adolescents who were born as preterm infants. Design. The 19-year follow-up program was part of a large ongoing collaborative study in the Netherlands on the long-term effect of prematurity and dysmaturity on various medical, psychological, and social parameters. In the original cohort, 1338 infants (94%) with a gestational age of <32 weeks and/or a birth weight of <1500 g were enrolled. Neonatal mortality was 23% (n = 312), and another 67 children had died between the ages of 28 days and 19 years, leaving 959 survivors (72% of the original cohort) for follow-up at the present assessment. To study the effect of nonresponse, we divided the 959 survivors into 3 groups: full responders (596 [62.1%]), postal responders (109 [11.4%]), and nonresponders (254 [26.5%]). In the 3 groups we compared demographic and neonatal data, as well as outcome at the last available assessment. Results. The odds ratios (ORs) for male versus female for the probabilities of nonresponse and postal response were statistically significant: 2.7 (95% CI: 1.9-3.9) and 1.6 (95% CI: 1.0-2.5), respectively. The same holds for the ORs for non-Dutch versus Dutch and low versus high maternal education for nonresponse: 2.0 (95% CI: 1.3-3.2) and 3.7 (95% CI: 2.0-6.7), respectively. Special education and severe handicap showed a statistically significant influence on nonresponse (OR: 1.6; 95% CI: 1.1-2.4 and OR: 2.6; 95% CI: 1.3-5.2) and postal response (OR: 2.0; 95% CI: 1.2-3.3 and OR: 4.4; 95% CI: 2.0-9.9), respectively. At the age of 19 years, primary school and special education were found significantly more frequent in the postal responders than in the full-response group (20% and 21% vs 6% and 12%). The full responders, on the other hand, were higher educated than were the postal responders. Conclusions. In this follow-up study at the age of 19 years, boys, non-Dutch adolescents, and low maternal education were overrepresented in the nonresponse and postal-response groups. Nonresponse decreased the proportion of infants with adverse outcome in assessed children. To be able to present reliable results for the total group of survivors in long-term follow-up studies, the nonresponse bias needs to be quantified. Therefore, it is evident that more research using statistical methods such as imputation of missing data is needed. Copyrigh

Functional outcomes and participation in young adulthood for very preterm and very low birth weight infants: the Dutch Project on Preterm and Small for Gestational Age Infants at 19 years of age.

Contains fulltext : 53562.pdf (publisher's version ) (Closed access)OBJECTIVE: Young adults who were born very preterm or with a very low birth weight remain at risk for physical and neurodevelopmental problems and lower academic achievement scores. Data, however, are scarce, hospital based, mostly done in small populations, and need additional confirmation. METHODS: Infants who were born at or = 3 affected areas in activities and participation. Special education or lesser level was completed by 24%, and 7.6% neither had a paid job nor followed any education. Overall, 31.7% had > or = 1 moderate or severe problems in the assessed areas. CONCLUSIONS: A total of 12.6% of young adults who were born very preterm and/or with a very low birth weight had moderate or severe problems in cognitive or neurosensory functioning. Compared with the general Dutch population, twice as many young adults who were born very preterm and/or with a very low birth weight were poorly educated, and 3 times as many were neither employed nor in school at age 19

Elderly postmenopausal patients with breast cancer are at increased risk for distant recurrence: A Tamoxifen Exemestane Adjuvant Multinational Study Analysis

Introduction. For postmenopausal patients with hormonesensitive breast cancer, outcome is worse with increasing age at diagnosis. The aim of this study was to assess the incidenceof breast cancer recurrence (locoregionalanddistant), and contralateral breast cancer by age at diagnosis. Methods. Patients enrolled in the Tamoxifen Exemestane Adjuvant Multinational (TEAM) trial were included. Primary endpoints were locoregional recurrence, distant recurrence, and contralateralbreastcancer.Ageatdiagnosiswascategorizedas younger than 65 years, 65-74 years, and 75 years or older. Results. Overall, 9,766 patients were included, of which 5,349 were younger than 65 years (reference group), 3,060 were 65-74 years, and 1,357 were 75 years or older. With increasing age, a decreased administration of radiotherapy after breast conserving surgery (94%, 92%, and 88%, respectively) and adjuvant chemotherapy (51%, 23%, and 5%, respectively) was observed. Risk of distant recurrence increased with age at diagnosis; multivariable hazard ratio for p