Geometric Finite Element Discretization of Maxwell Equations in Primal and Dual Spaces

Based on a geometric discretization scheme for Maxwell equations, we unveil a mathematical\textit{\}transformation between the electric field intensity $E$ and the magnetic field intensity $H$, denoted as Galerkin duality. Using Galerkin duality and discrete Hodge operators, we construct two system matrices, $[ X_{E}]$ (primal formulation) and $[ X_{H}$ (dual formulation) respectively, that discretize the second-order vector wave equations. We show that the primal formulation recovers the conventional (edge-element) finite element method (FEM) and suggests a geometric foundation for it. On the other hand, the dual formulation suggests a new (dual) type of FEM. Although both formulations give identical dynamical physical solutions, the dimensions of the null spaces are different.Comment: 22 pages and 4 figure

Color-coordinate system from a 13th-century account of rainbows.

We present a new analysis of Robert Grosseteste’s account of color in his treatise De iride (On the Rainbow), dating from the early 13th century. The work explores color within the 3D framework set out in Grosseteste’s De colore [see J. Opt. Soc. Am. A 29, A346 (2012)], but now links the axes of variation to observable properties of rainbows. We combine a modern understanding of the physics of rainbows and of human color perception to resolve the linguistic ambiguities of the medieval text and to interpret Grosseteste’s key terms

On the degrees of freedom of lattice electrodynamics

Using Euler's formula for a network of polygons for 2D case (or polyhedra for 3D case), we show that the number of dynamic\textit{\}degrees of freedom of the electric field equals the number of dynamic degrees of freedom of the magnetic field for electrodynamics formulated on a lattice. Instrumental to this identity is the use (at least implicitly) of a dual lattice and of a (spatial) geometric discretization scheme based on discrete differential forms. As a by-product, this analysis also unveils a physical interpretation for Euler's formula and a geometric interpretation for the Hodge decomposition.Comment: 14 pages, 6 figure

Processing carbon nanotubes with holographic optical tweezers

We report the first demonstration that carbon nanotubes can be trapped and manipulated by optical tweezers. This observation is surprising because individual nanotubes are substantially smaller than the wavelength of light, and thus should not be amenable to optical trapping. Even so, nanotube bundles, and perhaps even individual nanotubes, can be transported at high speeds, deposited onto substrates, untangled, and selectively ablated, all with visible light. The use of holographic optical tweezers, capable of creating hundreds of independent traps simultaneously, suggests opportunities for highly parallel nanotube processing with light.Comment: 3 pages, 1 figur

Expression and characterization of a histidine-rich protein, Hpn: Potential for Ni2+ storage in Helicobacter pylori

Hpn is a small cytoplasmic protein found in Helicobacter pylori, which binds Ni2+ ions with moderate affinity. Consisting of 60 amino acids, the protein is rich in histidine (28 residues, 46.7%), as well as glutamate, glycine and serine residues (in total 31.7%), and contains short repeating motifs. In the present study, we report the detailed biophysical characterization of the multimeric status and Ni2+-binding properties of purified recombinant Hpn under physiologically relevant conditions. The protein exists as an equilibration of multimeric forms in solution, with 20-mers (approx. 136 kDa) being the predominant species. Using equilibrium dialysis, ICP-MS (inductively coupled plasma MS) and UV/visible spectroscopy, Hpn was found to bind five Ni2+ ions per monomer at pH 7.4, with a dissociation constant (Kd) of 7.1 μM. Importantly, Ni2+ binding to Hpn is reversible: metal is released either in the presence of a chelating ligand such as EDTA, or at a slightly acidic pH (pH for half dissociation, pH1/2 ∼6.3). Ni2+ binding induces conformational changes within the protein, increasing β-sheet and reducing α-helical content, from 22% to 37%, and 20% to 10% respectively. Growth curves of Escherichia coli BL21(DE3) both with and without the hpn gene performed under Ni2+ pressure clearly implied a role for Hpn to protect the cells from higher concentrations of external metal ions. Similarly, the accumulation of Ni2+ in these cells expressing Hpn from a plasmid was approx. 4-fold higher than in uninduced controls or control cultures that lacked the plasmid. Similarly, levels of Ni2+ in wild-type H. pylori 26695 cells were higher than those in H. pylori hpn-deletion mutant strains. Hpn may potentially serve multiple roles inside the bacterium: storage of Ni 2+ ions in a 'reservoir'; donation of Ni2+ to other proteins; and detoxification via sequestration of excess Ni2+. © 2006 Biochemical Society.published_or_final_versio

How early can myocardial iron overload occur in Beta thalassemia major?

BACKGROUND: Myocardial siderosis is the most common cause of death in patients with beta thalassemia major(TM). This study aimed at investigating the occurrence, prevalence and severity of cardiac iron overload in a young Chinese population with beta TM. METHODS AND RESULTS: We analyzed T2* cardiac magnetic resonance (CMR), left ventricular ejection fraction (LVEF) and serum ferritin (SF) in 201 beta TM patients. The median age was 9 years old. Patients received an average of 13 units of blood per year. The median SF level was 4536 ng/ml and 165 patients (82.1%) had SF>2500 ng/ml. Myocardial iron overload was detected in 68 patients (33.8%) and severe myocardial iron overload was detected in 26 patients (12.6%). Twenty-two patients ≤10 years old had myocardial iron overload, three of whom were only 6 years old. No myocardial iron overload was detected under the age of 6 years. Median LVEF was 64% (measured by CMR in 175 patients). Five of 6 patients with a LVEF<56% and 8 of 10 patients with cardiac disease had myocardial iron overload. CONCLUSIONS: The TM patients under follow-up at this regional centre in China patients are younger than other reported cohorts, more poorly-chelated, and have a high burden of iron overload. Myocardial siderosis occurred in patients younger than previously reported, and was strongly associated with impaired LVEF and cardiac disease. For such poorly-chelated TM patients, our data shows that the first assessment of cardiac T2* should be performed as early as 6 years old

Understanding Medical Mistrust in Black Women at Risk of BRCA 1/2 Mutations

The benefits of genetic counseling and testing for hereditary breast and/or ovarian cancer (HBOC) are well documented; however, Black women are less likely to use these services compared to White women. Mistrust of the medical system has been associated with Black women’s use of genetic counseling and testing (GCT). However, relatively little is known about the correlates of medical mistrust in Black women at increased risk of HBOC. In this study, we examined the prevalence and predictors of medical mistrust in 94 Black women at-risk of HBOC. Most women were married (48.7%) and had at least some collegiate education (57.1%). While no predisposing characteristics were significantly related to medical mistrust, bivariate analysis indicated significant relationships between mistrust and fatalism (p=0.04), perceptions of discrimination in the healthcare setting (p=0.01), and self-efficacy in obtaining GCT (p=0.01). Multivariable analysis revealed that women who reported more discriminatory experiences and women with less confidence in obtaining GCT expressed greater medical mistrust. Multilevel approaches are needed to address psychosocial factors associated with feelings of mistrust. Future efforts must not solely focus on educating women on the importance of and need for GCT; addressing structural barriers, such as patient-provider interactions, that contribute to mistrust must become a priority

A Randomized Controlled Trial of Angiotensin-Converting Enzyme Inhibition for Skeletal Muscle Dysfunction in COPD

BACKGROUND: Skeletal muscle impairment is a recognized complication of COPD, predicting mortality in severe disease. Increasing evidence implicates the renin-angiotensin system in control of muscle phenotype. We hypothesized that angiotensin-converting enzyme (ACE) inhibition would improve quadriceps function and exercise performance in COPD. METHODS: This double-blind, randomized placebo-controlled trial investigated the effect of the ACE inhibitor, fosinopril, on quadriceps function in patients with COPD with quadriceps weakness. Primary outcomes were change in quadriceps endurance and atrophy signaling at 3 months. Quadriceps maximum voluntary contraction (QMVC), mid-thigh CT scan of the cross-sectional area (MTCSA), and incremental shuttle walk distance (ISWD) were secondary outcomes. RESULTS: Eighty patients were enrolled (mean [SD], 65 [8] years, FEV1 43% [21%] predicted, 53% men). Sixty-seven patients (31 fosinopril, 36 placebo) completed the trial. The treatment group demonstrated a significant reduction in systolic BP (Δ−10.5 mm Hg; 95% CI, −19.9 to −1.1; P = .03) and serum ACE activity (Δ−20.4 IU/L; 95% CI, −31.0 to −9.8; P < .001) compared with placebo. No significant between-group differences were observed in the primary end points of quadriceps endurance half-time (Δ0.5 s; 95% CI, −13.3-14.3; P = .94) or atrogin-1 messenger RNA expression (Δ−0.03 arbitrary units; 95% CI, −0.32-0.26; P = .84). QMVC improved in both groups (fosinopril: Δ1.1 kg; 95% CI, 0.03-2.2; P = .045 vs placebo: Δ3.6 kg; 95% CI, 2.1-5.0; P < .0001) with a greater increase in the placebo arm (between-group, P = .009). No change was shown in the MTCSA (P = .09) or ISWD (P = .51). CONCLUSIONS: This randomized controlled trial found that ACE inhibition, using fosinopril for 3 months, did not improve quadriceps function or exercise performance in patients with COPD with quadriceps weakness

Calibration of myocardial T2 and T1 against iron concentration.

BACKGROUND: The assessment of myocardial iron using T2* cardiovascular magnetic resonance (CMR) has been validated and calibrated, and is in clinical use. However, there is very limited data assessing the relaxation parameters T1 and T2 for measurement of human myocardial iron. METHODS: Twelve hearts were examined from transfusion-dependent patients: 11 with end-stage heart failure, either following death (n=7) or cardiac transplantation (n=4), and 1 heart from a patient who died from a stroke with no cardiac iron loading. Ex-vivo R1 and R2 measurements (R1=1/T1 and R2=1/T2) at 1.5 Tesla were compared with myocardial iron concentration measured using inductively coupled plasma atomic emission spectroscopy. RESULTS: From a single myocardial slice in formalin which was repeatedly examined, a modest decrease in T2 was observed with time, from mean (± SD) 23.7 ± 0.93 ms at baseline (13 days after death and formalin fixation) to 18.5 ± 1.41 ms at day 566 (p<0.001). Raw T2 values were therefore adjusted to correct for this fall over time. Myocardial R2 was correlated with iron concentration [Fe] (R2 0.566, p<0.001), but the correlation was stronger between LnR2 and Ln[Fe] (R2 0.790, p<0.001). The relation was [Fe] = 5081•(T2)-2.22 between T2 (ms) and myocardial iron (mg/g dry weight). Analysis of T1 proved challenging with a dichotomous distribution of T1, with very short T1 (mean 72.3 ± 25.8 ms) that was independent of iron concentration in all hearts stored in formalin for greater than 12 months. In the remaining hearts stored for <10 weeks prior to scanning, LnR1 and iron concentration were correlated but with marked scatter (R2 0.517, p<0.001). A linear relationship was present between T1 and T2 in the hearts stored for a short period (R2 0.657, p<0.001). CONCLUSION: Myocardial T2 correlates well with myocardial iron concentration, which raises the possibility that T2 may provide additive information to T2* for patients with myocardial siderosis. However, ex-vivo T1 measurements are less reliable due to the severe chemical effects of formalin on T1 shortening, and therefore T1 calibration may only be practical from in-vivo human studies