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

Piecewise Linear Models for the Quasiperiodic Transition to Chaos

We formulate and study analytically and computationally two families of piecewise linear degree one circle maps. These families offer the rare advantage of being non-trivial but essentially solvable models for the phenomenon of mode-locking and the quasi-periodic transition to chaos. For instance, for these families, we obtain complete solutions to several questions still largely unanswered for families of smooth circle maps. Our main results describe (1) the sets of maps in these families having some prescribed rotation interval; (2) the boundaries between zero and positive topological entropy and between zero length and non-zero length rotation interval; and (3) the structure and bifurcations of the attractors in one of these families. We discuss the interpretation of these maps as low-order spline approximations to the classic ``sine-circle'' map and examine more generally the implications of our results for the case of smooth circle maps. We also mention a possible connection to recent experiments on models of a driven Josephson junction.Comment: 75 pages, plain TeX, 47 figures (available on request

The Exact Ground State of the Frenkel-Kontorova Model with Repeated Parabolic Potential: I. Basic Results

The problem of finding the exact energies and configurations for the Frenkel-Kontorova model consisting of particles in one dimension connected to their nearest-neighbors by springs and placed in a periodic potential consisting of segments from parabolas of identical (positive) curvature but arbitrary height and spacing, is reduced to that of minimizing a certain convex function defined on a finite simplex.Comment: 12 RevTeX pages, using AMS-Fonts (amssym.tex,amssym.def), 6 Postscript figures, accepted by Phys. Rev.

Addition of serum-containing medium to cerebrospinal fluid prevents cellular loss over time

Immediately after sampling, leukocyte counts in native cerebrospinal fluid (CSF) start to decrease rapidly. As the time lapse between CSF collection to analysis is not routinely registered, the clinical significance of decreasing cell counts in native CSF is not known. Earlier data suggest that addition of serum-containing medium to CSF directly after sampling prevents this rapid decrease in leukocyte counts and, thus, may improve the accuracy of CSF cell counting and cell characterization. Here, we prospectively examined the effect of storage time after lumbar puncture on counts of leukocytes and their major subsets in both native CSF and after immediate addition of serum-containing medium, measured by flow cytometry and microscopy. We collected CSF samples of 69 patients in tubes with and tubes without serum-containing medium and determined counts of leukocytes and subsets at 30 minutes, 1 hour, and 5 hours after sampling. Compared to cell counts at 30 minutes, no significant decrease in cell number was observed in CSF with serum-containing medium 1 and 5 hours after sampling, except for the granulocytes at 1 hour. In native CSF, approximately 50% of leukocytes and all their subsets were lost after 1 hour, both in flow cytometric and microscopic counting. In 6/7 (86%) samples with mild pleocytosis (5–15 × 106 leukocytes/l), native CSF at 1 hour was incorrectly diagnosed as normocellular. In conclusion, addition of serum-containing medium to CSF directly after sampling prevents cell loss and allows longer preservation of CSF cells prior to analysis, both for microscopic and flow cytometric enumeration. We suggest that this protocol results in more accurate CSF cell counts and may prevent incorrect conclusions based on underestimated CSF cell counts

Long-term effects of cranial irradiation and intrathecal chemotherapy in treatment of childhood leukemia: a MEG study of power spectrum and correlated cognitive dysfunction

<p>Abstract</p> <p>Background</p> <p>Prophylaxis to prevent relapses in the central nervous system after childhood acute lymphoblastic leukemia (ALL) used to consist of both intrathecal chemotherapy (CT) and cranial irradiation (CRT). CRT was mostly abolished in the eighties because of its neurotoxicity, and replaced with more intensive intrathecal CT. In this study, a group of survivors treated with CRT before 1983 and another group treated without CRT thereafter are investigated 20–25 years later, giving a much stronger perspective on long-term quality of life than previous studies. The outcomes will help to better understand these groups’ current needs and will aid in anticipating late effects of prophylactic CRT that is currently applied for other diseases. This study evaluates oscillatory neuronal activity in these long-term survivors. Power spectrum deviations are hypothesized to correlate with cognitive dysfunction.</p> <p>Methods</p> <p>Resting state eyes-closed magnetoencephalography (MEG) recordings were obtained from 14 ALL survivors treated with CT + CRT, 18 treated with CT alone and 35 controls. Relative spectral power was calculated in the δ, θ, α1, α2, β and γ frequency bands. The Amsterdam Neuropsychological Tasks (ANT) program was used to assess cognition in the executive functions domain. MEG data and ANT scores were correlated.</p> <p>Results</p> <p>In the CT + CRT group, relative θ power was slightly increased (p = 0.069) and α2 power was significantly decreased (p = 0.006). The CT + CRT group performed worse on various cognitive tests. A deficiency in visuomotor accuracy, especially of the right hand, could be clearly associated with the deviating regional θ and α2 powers (0.471 < r < 0.697). A significant association between decreased regional α2 power and less attentional fluctuations was found for CT + CRT patients as well as controls (0.078 < r < 0.666). Patients treated with CT alone displayed a power spectrum similar to controls, except for a significantly increased level of left frontal α2 power (p = 0.030).</p> <p>Conclusions</p> <p>The tendency towards global slowing of brain oscillatory activity, together with the fact that dementia has been reported as a late effect of CRT and the neuropsychological deficiencies currently present, suggest that the irradiated brain might be aging faster and could be at risk for early‐onset dementia. The CT group showed no signs of early aging.</p

Genome-wide association analyses of symptom severity among clozapine-treated patients with schizophrenia spectrum disorders

Clozapine is the most effective antipsychotic for patients with treatment-resistant schizophrenia. However, response is highly variable and possible genetic underpinnings of this variability remain unknown. Here, we performed polygenic risk score (PRS) analyses to estimate the amount of variance in symptom severity among clozapine-treated patients explained by PRSs (R2) and examined the association between symptom severity and genotype-predicted CYP1A2, CYP2D6, and CYP2C19 enzyme activity. Genome-wide association (GWA) analyses were performed to explore loci associated with symptom severity. A multicenter cohort of 804 patients (after quality control N = 684) with schizophrenia spectrum disorder treated with clozapine were cross-sectionally assessed using the Positive and Negative Syndrome Scale and/or the Clinical Global Impression-Severity (CGI-S) scale. GWA and PRS regression analyses were conducted. Genotype-predicted CYP1A2, CYP2D6, and CYP2C19 enzyme activities were calculated. Schizophrenia-PRS was most significantly and positively associated with low symptom severity (p = 1.03 × 10−3; R2 = 1.85). Cross-disorder-PRS was also positively associated with lower CGI-S score (p = 0.01; R2 = 0.81). Compared to the lowest tertile, patients in the highest schizophrenia-PRS tertile had 1.94 times (p = 6.84×10−4) increased probability of low symptom severity. Higher genotype-predicted CYP2C19 enzyme activity was independently associated with lower symptom severity (p = 8.44×10−3). While no locus surpassed the genome-wide significance threshold, rs1923778 within NFIB showed a suggestive association (p = 3.78×10−7) with symptom severity. We show that high schizophrenia-PRS and genotype-predicted CYP2C19 enzyme activity are independently associated with lower symptom severity among individuals treated with clozapine. Our findings open avenues for future pharmacogenomic projects investigating the potential of PRS and genotype-predicted CYP-activity in schizophrenia

Global, regional, and national comparative risk assessment of 79 behavioural, environmental and occupational, and metabolic risks or clusters of risks, 1990-2015: a systematic analysis for the Global Burden of Disease Study 2015

SummaryBackground The Global Burden of Diseases, Injuries, and Risk Factors Study 2015 provides an up-to-date synthesis of the evidence for risk factor exposure and the attributable burden of disease. By providing national and subnational assessments spanning the past 25 years, this study can inform debates on the importance of addressing risks in context. Methods We used the comparative risk assessment framework developed for previous iterations of the Global Burden of Disease Study to estimate attributable deaths, disability-adjusted life-years (DALYs), and trends in exposure by age group, sex, year, and geography for 79 behavioural, environmental and occupational, and metabolic risks or clusters of risks from 1990 to 2015. This study included 388 risk-outcome pairs that met World Cancer Research Fund-defined criteria for convincing or probable evidence. We extracted relative risk and exposure estimates from randomised controlled trials, cohorts, pooled cohorts, household surveys, census data, satellite data, and other sources. We used statistical models to pool data, adjust for bias, and incorporate covariates. We developed a metric that allows comparisons of exposure across risk factors—the summary exposure value. Using the counterfactual scenario of theoretical minimum risk level, we estimated the portion of deaths and DALYs that could be attributed to a given risk. We decomposed trends in attributable burden into contributions from population growth, population age structure, risk exposure, and risk-deleted cause-specific DALY rates. We characterised risk exposure in relation to a Socio-demographic Index (SDI). Findings Between 1990 and 2015, global exposure to unsafe sanitation, household air pollution, childhood underweight, childhood stunting, and smoking each decreased by more than 25%. Global exposure for several occupational risks, high body-mass index (BMI), and drug use increased by more than 25% over the same period. All risks jointly evaluated in 2015 accounted for 57·8% (95% CI 56·6–58·8) of global deaths and 41·2% (39·8–42·8) of DALYs. In 2015, the ten largest contributors to global DALYs among Level 3 risks were high systolic blood pressure (211·8 million [192·7 million to 231·1 million] global DALYs), smoking (148·6 million [134·2 million to 163·1 million]), high fasting plasma glucose (143·1 million [125·1 million to 163·5 million]), high BMI (120·1 million [83·8 million to 158·4 million]), childhood undernutrition (113·3 million [103·9 million to 123·4 million]), ambient particulate matter (103·1 million [90·8 million to 115·1 million]), high total cholesterol (88·7 million [74·6 million to 105·7 million]), household air pollution (85·6 million [66·7 million to 106·1 million]), alcohol use (85·0 million [77·2 million to 93·0 million]), and diets high in sodium (83·0 million [49·3 million to 127·5 million]). From 1990 to 2015, attributable DALYs declined for micronutrient deficiencies, childhood undernutrition, unsafe sanitation and water, and household air pollution; reductions in risk-deleted DALY rates rather than reductions in exposure drove these declines. Rising exposure contributed to notable increases in attributable DALYs from high BMI, high fasting plasma glucose, occupational carcinogens, and drug use. Environmental risks and childhood undernutrition declined steadily with SDI; low physical activity, high BMI, and high fasting plasma glucose increased with SDI. In 119 countries, metabolic risks, such as high BMI and fasting plasma glucose, contributed the most attributable DALYs in 2015. Regionally, smoking still ranked among the leading five risk factors for attributable DALYs in 109 countries; childhood underweight and unsafe sex remained primary drivers of early death and disability in much of sub-Saharan Africa. Interpretation Declines in some key environmental risks have contributed to declines in critical infectious diseases. Some risks appear to be invariant to SDI. Increasing risks, including high BMI, high fasting plasma glucose, drug use, and some occupational exposures, contribute to rising burden from some conditions, but also provide opportunities for intervention. Some highly preventable risks, such as smoking, remain major causes of attributable DALYs, even as exposure is declining. Public policy makers need to pay attention to the risks that are increasingly major contributors to global burden. Funding Bill & Melinda Gates Foundation

Effect of Solution Composition on the Energy Production by Capacitive Mixing in Membrane-Electrode Assembly

The final edited version of the paper can be found at: http://pubs.acs.org/articlesonrequest/AOR-c9UMxSzGY3eiU5SENNgT The complete citation is: Ahualli, S.; et al. Effect of Solution Composition on the Energy Production by Capacitive Mixing in Membrane-Electrode Assembly. Journal of Physical Chemistry, 118(29): 15590-15599 (2014). DOI:10.1021/jp504461mOpen access in the Journal on May 26, 2015In this work we consider the extent to which the presence of multi-valent ions in solution modifies the equilibrium and dynamics of the energy production in a capacitive cell built with ion-exchange membranes in contact with high surface area electrodes. The cell potential in open circuit (OCV) is controlled by the difference between both membrane potentials, simulated as constant volume charge regions. A theoretical model is elaborated for steady state OCV, first in the case of monovalent solutions, as a reference. This is compared to the results in multi-ionic systems, containing divalent cations in concentrations similar to those in real sea water. It is found that the OCV is reduced by about 25 % (as compared to the results in pure NaCl solutions) due to the presence of the divalent ions, even in low concentrations. Interestingly, this can be related to the “uphill” transport of such ions against their concentration gradients. On the contrary, their effect on the dynamics of the cell potential is negligible in the case of highly charged membranes. The comparison between model predictions and experimental results shows a very satisfactory agreement, and gives clues for the practical application of these recently introduced energy production methods.The research leading to these results received funding from the European Union 7th Framework Programme (FP7/2007-2013) under agreement No. 256868. Further financial support from Junta de Andalucia, Spain (PE2012-FQM 694) is also acknowledged. One of us, M.M.F., received financial support throughan FPU grant from the Universityof Granada