On the arithmetic sums of Cantor sets

Let C_\la and C_\ga be two affine Cantor sets in $\mathbb{R}$ with similarity dimensions d_\la and d_\ga, respectively. We define an analog of the Bandt-Graf condition for self-similar systems and use it to give necessary and sufficient conditions for having \Ha^{d_\la+d_\ga}(C_\la + C_\ga)>0 where C_\la + C_\ga denotes the arithmetic sum of the sets. We use this result to analyze the orthogonal projection properties of sets of the form C_\la \times C_\ga. We prove that for Lebesgue almost all directions $\theta$ for which the projection is not one-to-one, the projection has zero (d_\la + d_\ga)-dimensional Hausdorff measure. We demonstrate the results on the case when C_\la and C_\ga are the middle-(1-2\la) and middle-(1-2\ga) sets

Can the United States Afford a “No-Fault” System of Compensation for Medical Injury?

One of the key issues separating US critics of a no-fault alternative to the tort system for compensating victims of medical injury from supporters is its anticipated cost. Results from a study are presented that estimate the costs of a no-fault system, one that is similar to the system now in operation in Sweden, within the context of the US health care system

Variability within individuals of plasma ionic magnesium concentrations

BACKGROUND: With the invention of the ion-selective electrode (ISE), ionic magnesium (iMg) is a common blood assay. This could be advantageous, as iMg is the biologically active form of Mg. There is some evidence that iMg has considerable within subject variability. RESULTS: Individual ranges averaged .08 mmol/L (range .05 to .14). Coefficients of variation (CV) ranged from 3% to 7% (mean 4%) while analytical variation was determined to be 2.3%. Biological variability thus accounts for almost half of the variability, which is clinically significant, as 9 of the 13 subjects recorded at least one value below a reference range of .46 – .60 mmol/L. A significant within-day variation (p < .001) was noted, with differences between 7:00 and 10:00 as well as 10:00 and 22:00. Between day variations were not significant (p = .56). CONCLUSIONS: A plausible explanation of this data is that iMg has a circadian rhythm. Thus, cautious interpretation of single iMg values is warranted until future research determines the nature of iMg variability

Spectra of Discrete Schr\"odinger Operators with Primitive Invertible Substitution Potentials

We study the spectral properties of discrete Schr\"odinger operators with potentials given by primitive invertible substitution sequences (or by Sturmian sequences whose rotation angle has an eventually periodic continued fraction expansion, a strictly larger class than primitive invertible substitution sequences). It is known that operators from this family have spectra which are Cantor sets of zero Lebesgue measure. We show that the Hausdorff dimension of this set tends to $1$ as coupling constant $\lambda$ tends to $0$. Moreover, we also show that at small coupling constant, all gaps allowed by the gap labeling theorem are open and furthermore open linearly with respect to $\lambda$. Additionally, we show that, in the small coupling regime, the density of states measure for an operator in this family is exact dimensional. The dimension of the density of states measure is strictly smaller than the Hausdorff dimension of the spectrum and tends to $1$ as $\lambda$ tends to $0$

On stochastic sea of the standard map

Consider a generic one-parameter unfolding of a homoclinic tangency of an area preserving surface diffeomorphism. We show that for many parameters (residual subset in an open set approaching the critical value) the corresponding diffeomorphism has a transitive invariant set $\Omega$ of full Hausdorff dimension. The set $\Omega$ is a topological limit of hyperbolic sets and is accumulated by elliptic islands. As an application we prove that stochastic sea of the standard map has full Hausdorff dimension for sufficiently large topologically generic parameters.Comment: 36 pages, 5 figure

The Lagrange and Markov spectra from the dynamical point of view

This text grew out of my lecture notes for a 4-hours minicourse delivered on October 17 \& 19, 2016 during the research school "Applications of Ergodic Theory in Number Theory" -- an activity related to the Jean-Molet Chair project of Mariusz Lema\'nczyk and S\'ebastien Ferenczi -- realized at CIRM, Marseille, France. The subject of this text is the same of my minicourse, namely, the structure of the so-called Lagrange and Markov spectra (with an special emphasis on a recent theorem of C. G. Moreira).Comment: 27 pages, 6 figures. Survey articl

Perspectives from deductible plan enrollees: plan knowledge and anticipated care-seeking changes

<p>Abstract</p> <p>Background</p> <p>Consumer directed health care proposes that patients will engage as informed consumers of health care services by sharing in more of their medical costs, often through deductibles. We examined knowledge of deductible plan details among new enrollees, as well as anticipated care-seeking changes in response to the deductible.</p> <p>Methods</p> <p>In a large integrated delivery system with a range of deductible-based health plans which varied in services included or exempted from deductible, we conducted a mixed-method, cross-sectional telephone interview study.</p> <p>Results</p> <p>Among 458 adults newly enrolled in a deductible plan (71% response rate), 51% knew they had a deductible, 26% knew the deductible amount, and 6% knew which medical services were included or exempted from their deductible. After adjusting for respondent characteristics, those with more deductible-applicable services and those with lower self-reported health status were significantly more likely to know they had a deductible. Among those who knew of their deductible, half anticipated that it would cause them to delay or avoid medical care, including avoiding doctor's office visits and medical tests, even services that they believed were medically necessary. Many expressed concern about their costs, anticipating the inability to afford care and expressing the desire to change plans.</p> <p>Conclusion</p> <p>Early in their experience with a deductible, patients had limited awareness of the deductible and little knowledge of the details. Many who knew of the deductible reported that it would cause them to delay or avoid seeking care and were concerned about their healthcare costs.</p

Daily or weekly? The role of treatment frequency in the effectiveness of grammar treatment for children with specific language impairment.

This study compared the effectiveness of a school-based treatment for expressive grammar in 5-year-olds with specific language impairment delivered in two different dose frequencies: eight sessions delivered daily over 8 consecutive school days or eight sessions delivered weekly over 8 consecutive weeks. Eighteen children received treatment daily and 13 children received treatment weekly. In both groups, treatment consisted of eight 1-hour sessions of small group activities in a classroom setting. Techniques included explicit instruction, focused stimulation, recasting, and imitation. Results were analysed at the group level and as a case series with each child as their own control in a single-subject design. The 8-weeks group showed significantly greater gain in test scores over the treatment period than in an equal time period prior to treatment, whereas the 8-days group did not (Cohen's d = 1.64 for 8-weeks group). Single-subject analyses indicated that 46% of children in the 8-week group and 17% of children in the 8-day group showed a significant treatment effect. It is concluded that expressive grammar treatment was most effective when dose frequency was weekly over 8 weeks rather than daily over 8 days for 5-year-old children with specific language impairment.13 page(s

Solar fuel photoanodes prepared by inkjet printing of copper vanadates

Widespread deployment of solar fuel generators requires the development of efficient and scalable functional materials, especially for photoelectrocatalysis of the oxygen evolution reaction. Metal oxides comprise the most promising class of photoanode materials, but no known material meets the demanding photoelectrochemical requirements. Copper vanadates have recently been identified as a promising class of photoanode materials with several phases exhibiting an indirect band gap near 2 eV and stable photoelectrocatalysis of the oxygen evolution reaction in a pH 9.2 electrolyte. By employing combinatorial inkjet printing of metal precursors and applying both calcination and rapid thermal processing, we characterize the phase behaviour of the entire CuO–V_2O_5 composition space for different thermal treatments via automated analysis of approximately 100 000 Raman spectra acquired using a novel Raman imaging technique. These results enable the establishment of structure–property relationships for optical absorption and photoelectrochemical properties, revealing that highly active photoelectrocatalysts containing α-Cu_2V_2O_7 or α-CuV_2O_6 can be prepared using scalable solution processing techniques. An additional discovery results from the formation of an off-stoichiometric β-Cu_2V_2O_7 material that exhibits high photoelectroactivity in the presence of a ferri/ferrocyanide redox couple with excellent stability in a pH 13 electrolyte, demonstrating that copper vanadates may be viable photoanodes in strong alkaline electrolytes

Polymorphisms in the WNK1 gene are asociated with blood pressure variation and urinary potassium excretion

WNK1 - a serine/threonine kinase involved in electrolyte homeostasis and blood pressure (BP) control - is an excellent candidate gene for essential hypertension (EH). We and others have previously reported association between WNK1 and BP variation. Using tag SNPs (tSNPs) that capture 100% of common WNK1 variation in HapMap, we aimed to replicate our findings with BP and to test for association with phenotypes relating to WNK1 function in the British Genetics of Hypertension (BRIGHT) study case-control resource (1700 hypertensive cases and 1700 normotensive controls). We found multiple variants to be associated with systolic blood pressure, SBP (7/28 tSNPs min-p = 0.0005), diastolic blood pressure, DBP (7/28 tSNPs min-p = 0.002) and 24 hour urinary potassium excretion (10/28 tSNPs min-p = 0.0004). Associations with SBP and urine potassium remained significant after correction for multiple testing (p = 0.02 and p = 0.01 respectively). The major allele (A) of rs765250, located in intron 1, demonstrated the strongest evidence for association with SBP, effect size 3.14 mmHg (95%CI:1.23–4.9), DBP 1.9 mmHg (95%CI:0.7–3.2) and hypertension, odds ratio (OR: 1.3 [95%CI: 1.0–1.7]).We genotyped this variant in six independent populations (n = 14,451) and replicated the association between rs765250 and SBP in a meta-analysis (p = 7×10−3, combined with BRIGHT data-set p = 2×10−4, n = 17,851). The associations of WNK1 with DBP and EH were not confirmed. Haplotype analysis revealed striking associations with hypertension and BP variation (global permutation p10 mmHg reduction) and risk for hypertension (OR<0.60). Our data indicates that multiple rare and common WNK1 variants contribute to BP variation and hypertension, and provide compelling evidence to initiate further genetic and functional studies to explore the role of WNK1 in BP regulation and EH