Boundaries of Disk-like Self-affine Tiles

Let $T:= T(A, {\mathcal D})$ be a disk-like self-affine tile generated by an integral expanding matrix $A$ and a consecutive collinear digit set ${\mathcal D}$, and let $f(x)=x^{2}+px+q$ be the characteristic polynomial of $A$. In the paper, we identify the boundary $\partial T$ with a sofic system by constructing a neighbor graph and derive equivalent conditions for the pair $(A,{\mathcal D})$ to be a number system. Moreover, by using the graph-directed construction and a device of pseudo-norm $\omega$, we find the generalized Hausdorff dimension $\dim_H^{\omega} (\partial T)=2\log \rho(M)/\log |q|$ where $\rho(M)$ is the spectral radius of certain contact matrix $M$. Especially, when $A$ is a similarity, we obtain the standard Hausdorff dimension $\dim_H (\partial T)=2\log \rho/\log |q|$ where $\rho$ is the largest positive zero of the cubic polynomial $x^{3}-(|p|-1)x^{2}-(|q|-|p|)x-|q|$, which is simpler than the known result.Comment: 26 pages, 11 figure

Experiencing sense of place in virtual and physical Avebury.

This paper discusses the findings from a project to construct a simulation of Avebury henge, a Late Neolithic/ Early Bronze Age monument in SW Britain, in a 3D, virtual world environment. The aims of the study were to explore the archaeological research and interpretation necessary to plan and construct such a simulation in an interactive, online environment, to identify which aspects of visualisation and soundscape design appear to have the greatest impact upon users’ sense of place in the virtual simulation and to explore the experiences of a small group of users in the virtual simulation and the effects of those experiences upon their sense of place at the physical site. The findings from this project demonstrated that in undertaking a simulation of an ancient site, a core set of sources need to be selected to create the main parts of the simulation. There is often much debate in archaeological literature regarding the way in which archaeological findings are interpreted, and a different virtual Avebury would be constructed if different interpretations had been chosen. Any simulation of an ancient site should therefore clearly recognise and state the basis upon which it has been designed. The evaluation showed that responses to virtual environments, and the resulting effect upon responses to physical environments, are complex and personal, resulting in a range of experiences and perceptions, suggesting that the range of users’ experiences might be a more significant issue than attempting to find any general consensus on user reactions to simulated ancient sites

Ictal Behaviors During Nonepileptic Seizures Differ in Patients with Temporal Lobe Interictal Epileptiform EEG Activity and Patients Without Interictal Epileptiform EEG Abnormalities

Purpose: Ictal behaviors during psychogenic non-epileptic seizures (NES) vary considerably among individuals, and can closely resemble common semiologies of epileptic seizures (ES). We tested the hypothesis that behaviors during NES in patients who have temporal spikes would more closely resemble behaviors during ES in patients with temporal lobe epilepsy than would behaviors during NES in patients who do not have EEG spikes. Methods: We identified 20 patients who had interictal temporal EEG spikes and EEG-video recorded NES (Study Group), 133 patients with temporal EEG spikes and recorded ES, without NES (Epileptic Group), and 24 patients with recorded NES and no epileptiform EEG abnormalities, without ES (Nonepileptic Group). Results: The hypothesis was supported with regard to ictal motor behaviors. Motionless staring or complex automatisms occurred mainly during NES in the Study Group and during ES in the Epileptic Group. In contrast, convulsive movements or flaccid falls were most common during NES in the Nonepileptic Group. Duration of unresponsiveness was longer, and there were fewer postictal states in NES both in the Study and Non-epileptic Groups. Unresponsiveness was briefer and postictal states were more consistent in ES in the Epileptic Group, however. Conclusions: Stereotyped motor activities during NES presumably represent learned behaviors. Processes underlying acquisition of ictal behaviors of NES probably differ in patients with interictal epileptiform EEG abnormalities compared to those without. Prior experiences and temporal lobe dysfunctions that are associated with epilepsy, and psychological characteristics that are unrelated to interictal epileptic dysfunctions, may determine ictal behaviors during NES.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/65913/1/j.1528-1157.1998.tb01355.x.pd

Accuracy of Predicting the Genetic Risk of Disease Using a Genome-Wide Approach

Background - The prediction of the genetic disease risk of an individual is a powerful public health tool. While predicting risk has been successful in diseases which follow simple Mendelian inheritance, it has proven challenging in complex diseases for which a large number of loci contribute to the genetic variance. The large numbers of single nucleotide polymorphisms now available provide new opportunities for predicting genetic risk of complex diseases with high accuracy. Methodology/Principal Findings - We have derived simple deterministic formulae to predict the accuracy of predicted genetic risk from population or case control studies using a genome-wide approach and assuming a dichotomous disease phenotype with an underlying continuous liability. We show that the prediction equations are special cases of the more general problem of predicting the accuracy of estimates of genetic values of a continuous phenotype. Our predictive equations are responsive to all parameters that affect accuracy and they are independent of allele frequency and effect distributions. Deterministic prediction errors when tested by simulation were generally small. The common link among the expressions for accuracy is that they are best summarized as the product of the ratio of number of phenotypic records per number of risk loci and the observed heritability. Conclusions/Significance - This study advances the understanding of the relative power of case control and population studies of disease. The predictions represent an upper bound of accuracy which may be achievable with improved effect estimation methods. The formulae derived will help researchers determine an appropriate sample size to attain a certain accuracy when predicting genetic ris

The contribution of genetic variants to disease depends on the ruler

Our understanding of the genetic basis of disease has evolved from descriptions of overall heritability or familiality to the identification of large numbers of risk loci. One can quantify the impact of such loci on disease using a plethora of measures, which can guide future research decisions. However, different measures can attribute varying degrees of importance to a variant. In this Analysis, we consider and contrast the most commonly used measures-specifically, the heritability of disease liability, approximate heritability, sibling recurrence risk, overall genetic variance using a logarithmic relative risk scale, the area under the receiver-operating curve for risk prediction and the population attributable fraction-and give guidelines for their use that should be explicitly considered when assessing the contribution of genetic variants to disease

Extending the rapeseed gene pool with resynthesized Brassica napus II: Heterosis

Hybrid breeding relies on the combination of parents from two differing heterotic groups. However, the genetic diversity in adapted oilseed rape breeding material is rather limited. Therefore, the use of resynthesized Brassica napus as a distant gene pool was investigated. Hybrids were derived from crosses between 44 resynthesized lines with a diverse genetic background and two male sterile winter oilseed rape tester lines. The hybrids were evaluated together with their parents and check cultivars in 2 years and five locations in Germany. Yield, plant height, seed oil, and protein content were monitored, and genetic distances were estimated with molecular markers (127 polymorphic RFLP fragments). Resynthesized lines varied in yield between 40.9 dt/ha and 21.5 dt/ha, or between 85.1 and 44.6% of check cultivar yields. Relative to check cultivars, hybrids varied from 91.6 to 116.6% in yield and from 94.5 to 103.3% in seed oil content. Mid-parent heterosis varied from −3.5 to 47.2% for yield. The genetic distance of parental lines was not significantly correlated with heterosis or hybrid yield. Although resynthesized lines do not meet the elite rapeseed standards, they are a valuable source for hybrid breeding due to their large distance from present breeding material and their high heterosis when combined with European winter oilseed rape

Genetic parameters for faecal egg count, packed-cell volume and body-weight in Santa Inês lambs

Worm infection is one of the main factors responsible for economic losses in sheep breeding in Brazil. Random regression analysis was used to estimate genetic parameters for the factors faecal egg-count (FEC), packed-cell volume (PCV) and body weight (BW) in Santa Inês lambs. Data from 119 female, offspring of nine rams, were collected between December, 2005 and December, 2006, from the experimental flock of Embrapa Tabuleiros Costeiros, the Brazilian Agricultural Research Corporation located in Frei Paulo, SE, Brazil. After weaning, females were drenched until the faecal egg count had dropped to zero. Two natural challenges were undertaken. FEC heritability was extremely variable, this increasing from 0.04 to 0.27 in the first challenge and from 0.01 to 0.52 during the second. PCV heritability peaks were 0.31 and 0.12 in the first and second challenges, respectively. In the second challenge, BW heritability was close to 0.90. The genetic correlations among these traits did not differ from zero. There is the possibility of increasing parasite resistance in Santa Inês by selecting those animals with lower FEC. Selection to increase resistance will not adversely affect lamb-growth, although lambs with a slow growth-rate may be more susceptible to infection

The Heritability of Amyotrophic Lateral Sclerosis in a Clinically Ascertained United States Research Registry

The genetic basis of amyotrophic lateral sclerosis (ALS) is not entirely clear. While there are families with rare highly penetrant mutations in Cu/Zn superoxide dismutase 1 and several other genes that cause apparent Mendelian inheritance of the disease, most ALS occurs in families without another affected individual. However, twin studies suggest that all ALS has a substantial genetic basis. Herein, we estimate the genetic contribution to ALS in a clinically ascertained case series from the United States.We used the database of the Emory ALS Center to ascertain individuals with ALS along with their family histories to determine the concordance among parents and offspring for the disease. We found that concordance for all parent-offspring pairs was low (<2%). With this concordance we found that ALS heritability, or the proportion of the disease explained by genetic factors, is between 40 and 45% for all likely estimates of ALS lifetime prevalence.We found the lifetime risk of ALS is 1.1% in first-degree relatives of those with ALS. Environmental and genetic factors appear nearly equally important for the development of ALS