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We present an efficient procedure for computing resonances and resonant modes of Helmholtz problems posed in exterior domains. The problem is formulated as a nonlinear eigenvalue problem (NEP), where the nonlinearity arises from the use of a Dirichlet-to-Neumann map, which accounts for modeling unbounded domains. We consider a variational formulation and show that the spectrum consists of isolated eigenvalues of finite multiplicity that only can accumulate at infinity. The proposed method is based on a high order finite element discretization combined with a specialization of the Tensor Infinite Arnoldi method (TIAR). Using Toeplitz matrices, we show how to specialize this method to our specific structure. In particular we introduce a pole cancellation technique in order to increase the radius of convergence for computation of eigenvalues that lie close to the poles of the matrix-valued function. The solution scheme can be applied to multiple resonators with a varying refractive index that is not necessarily piecewise constant. We present two test cases to show stability, performance and numerical accuracy of the method. In particular the use of a high order finite element discretization together with TIAR results in an efficient and reliable method to compute resonances., QC 20171205

Objectives: The aim of this study was to examine whether personality i.e. temperament and character interacts with age of onset in bipolar disorder. Methods: Bipolar patients were recruited among in- and outpatients from lithium dispensaries of northern Sweden. Patients were diagnosed according to DSM-IV criteria for bipolar disorder type I and II. Temperament and Character Inventory (TCI) was used for measuring personality. TCI was administered to 100 lithium treated bipolar patients and 100 controls. Results: Treatment response was significantly lower (p = 0.005) in patients with early onset compared with late onset. Family history (p = 0.013) and suicide attempts (p = 0.001) were also significantly more common in patients with early onset. Further, patients with early onset were significantly higher (p = 0.045) in the temperament factor harm avoidance (HA) than patients with late onset, but the difference was weak. Patients with early onset had more fear of uncertainty (HA2, P = 0.022) and were more shy (HA3, p = 0.030). Bipolar I patients showed similar results as those in the total bipolar group (I and II), with significantly higher HA (p = 0.019, moderate difference), HA2 (p = 0.015) and HA3 (p = 0.043) in patients with early onset compared with late onset. Bipolar II patients showed no differences between early and late age of onset but the groups are small and the results are therefore uncertain. Conclusions: Early age of onset in bipolar disorder was correlated to an increase in severity, family history, poorer treatment response and poorer prognosis. Early onset was also correlated to personality.

An association between bipolar affective disorder and CAG/CTG trinucleotide repeat expansions (TRE) has previously been detected using the repeat expansion detection (RED) method. Here we report that 89% of RED products (CAG/CTG repeats) > 120 nt (n = 202) detected in affective disorder patients as well as unaffected family members and controls correlate with expansions at two repeat loci, ERDA1 on chromosome 17q21.3 and CTG18.1 on 18q21.1. In a set of patients and controls in which we had previously found a significant difference in RED size distribution, the frequency of expansions at the CTG18.1 locus was 13% in bipolar patients (n = 60) and 5% in controls (n = 114) (P < 0.07) with a significantly different size distribution (P < 0.03). A second set of patients were ascertained from 14 affective disorder families showing anticipation. Twelve of the families had members with RED products > 120 nt. The RED product distribution was significantly different (P < 0.0007) between affected (n = 53) and unaffected (n = 123) offspring. Using PCR, a higher frequency (P < 0.04) of CTG18.1 expansions as well as a different (P < 0.02) repeat size distribution was seen between affected and unaffected offspring. In addition, a negative correlation between RED product size and the age-of-onset could be seen in affected offspring (rs = -0.3, P = 0.05, n = 43). This effect was due to an earlier onset in individuals with long CTG18.1 expansions. No difference in ERDA1 expansion frequency was seen either between bipolar patients (35%, n = 60) and matched controls (29%, n = 114), or between affected and unaffected offspring in the families. We conclude that expanded alleles at the CTG18.1 locus confers an odds ratio of 2.6-2.8 and may thus act as a vulnerability factor for affective disorder, while the ERDA1 locus seems unrelated to disease.

Anticipation describes an inheritance pattern within a pedigree with an increase in disease severity and/or decrease in age at onset in successive generations. The phenomenon of anticipation has recently been shown to be correlated with the expansion of trinucleotide repeat sequences in a neuromuscular disease, various neurodegenerative disorders and mental retardation. We have studied parent-offspring differences in age at onset and disease severity in 31 pairs with unilineal inheritance of unipolar affective disorder (UPAD). Life-table analyses showed a significant decrease in survival to 1st episode of major depression in the offspring generation compared with the parental generation (P = 0.0007). There was also a significant difference in age at onset (P < 0.001) between parents and offsprings. The offspring generation experienced onset 15.6 years earlier and illness 1.5 x more severe than did the parent generation. Furthermore, there was a significant correlation (P < 0.05) in age at onset between parent and offspring generations. When we excluded pairs where the affected parent has an age of onset greater than the age of the child at the time of ascertainment (i.e., 23 pairs left), there was still a significant (P = 0.02) decrease in age at onset (8.4 years) and 1.5 x more severe disease in the offspring generation. No evidence for specific maternal or paternal inheritance was found. We found evidence of anticipation in 75-80% of this sample of unilineal family pairs of UPAD. Anticipation is, thus, an inheritance pattern in a large group of UPAD which suggests that the expansion of trinucleotide repeat sequences is a possible mode of inheritance in this group of UPAD. The findings of anticipation in this study of families with UPAD and previous findings in families with BPAD suggest that the variable expression of unstable expansions of trinucleotide repeats may turn out to be the basis of the continuum of liability in affective disorders.

Nineteen parent-offspring pairs obtained from 14 two-generation families with available medical records and diagnosis of schizophrenia were studied to compare the ages of onset of the parent generation with those of the offspring generation. The mean age of onset for the parent generation was 37.3 +/- 6.0 years and for the offspring generation was 20.8 +/- 4.4. The mean difference was thus 16.5 +/- 6.2, suggesting the occurrence of anticipation in schizophrenia (p < 0.001). Although some ascertainment biases (like reduced fertility in early-onset parents or early detection of symptoms in offsprings of affected parents) may partially contribute to the occurrence of anticipation, this study replicates recent reports of anticipation in several neuropsychiatric disorders, some of which have been shown to be associated with unstable expansions of trinucleotide repeats in the genomic DNA.

Genetic factors are of major aetiological importance in Bipolar Affective Disorder (BPAD type I and II). The exact mode of inheritance of BPAD is unknown, but the recent demonstration of anticipation suggests that dynamic mutations could be involved in the clinical expression of the disease. We have used the repeat expansion detection (RED) method to test whether the anticipation in BPAD could be explained by the presence of expanded trinucleotide repeat sequences. Using a (CTG)10 oligonucleotide a significantly higher number of expanded CAG repeats were found in the genomic DNA of two independent samples of unrelated BPAD patients of Swedish and Belgian ancestry as compared with normal controls. The difference in repeat number was more consistent if data of the two samples of patients was pooled. In this study a CAG trinucleotide repeat expansion was associated for the first time with a major psychiatric disorder. It is possible that the CAG trinucleotide repeat expansion is involved in the clinical expression of BPAD and that it is the molecular basis explaining the phenomenon of anticipation observed in this disorder.

Anticipation describes an inheritance pattern within a pedigree with an increase in disease severity or decrease in age at onset or both in successive generations. The phenomenon of anticipation has recently been shown to be correlated with the expansion of trinucleotide repeat sequences in different disorders. We have studied differences of age at onset and disease severity between two generations in 14 families with unilinear inheritance of bipolar affective disorder (BPAD). There was a significant difference in age at onset (p < 0.008), in episodes per year with (p < 0.006) and without (p < 0.03) lithium treatment, and in total episodes per year (p < 0.002) between generations I and II. Furthermore, there was a highly significant correlation (p < 0.001) in age at onset between generations I and II. No evidence for specific paternal or maternal inheritance was found. We found evidence of anticipation and could rule out ascertainment bias or some other artefact. Anticipation is thus an inheritance pattern in BPAD which suggests that the expansion of trinucleotide repeat sequences is a possible mode of inheritance in BPAD.