Relative systoles of relative-essential 2-complexes

We prove a systolic inequality for the phi-relative 1-systole of a phi-essential 2-complex, where phi is a homomorphism from the fundamental group of the complex, to a finitely presented group G. Indeed we show that universally for any phi-essential Riemannian 2-complex, and any G, the area of X is bounded below by 1/8 of sys(X,phi)^2. Combining our results with a method of Larry Guth, we obtain new quantitative results for certain 3-manifolds: in particular for Sigma the Poincare homology sphere, we have sys(Sigma)^3 < 24 vol(Sigma).Comment: 20 pages, to appear in Algebraic and Geometric Topolog

Fermat, Leibniz, Euler, and the gang: The true history of the concepts of limit and shadow

Fermat, Leibniz, Euler, and Cauchy all used one or another form of approximate equality, or the idea of discarding "negligible" terms, so as to obtain a correct analytic answer. Their inferential moves find suitable proxies in the context of modern theories of infinitesimals, and specifically the concept of shadow. We give an application to decreasing rearrangements of real functions.Comment: 35 pages, 2 figures, to appear in Notices of the American Mathematical Society 61 (2014), no.

Primary stenting of the superficial femoral and popliteal artery

ObjectivesOver the last decade, the number of endovascular procedures performed on the superficial femoral (SFA) and popliteal arteries (PA) has significantly increased. There is no consensus on the optimal form of intervention used in this arterial segment. While some have advocated balloon angioplasty alone, others have championed either selective or primary stenting of these lesions. It is the purpose of this study to determine the efficacy and durability of primary stenting of the superficial femoral and popliteal artery.MethodsAll patients undergoing peripheral angioplasty by a single vascular surgeon were prospectively enrolled in an Institutional Review Board-approved, primary-stenting protocol. During a 44-month period, all patients undergoing percutaneous transluminal angioplasty of the SFA or PA also received primary arterial stenting with bare, self-expanding nitinol stents. Patient demographics and risk factors were identified. TransAtlantic InterSociety Consensus (TASC) classifications were determined for all lesions. Loss of primary patency was said to have occurred when an occlusion or a 50% or greater stenosis in any treated arterial segment was diagnosed by arterial duplex or angiography. Only time to loss of primary patency was recorded. Kaplan-Meier survival curves were plotted and differences between groups tested by log rank method.ResultsBetween January 16, 2004 and August 13, 2007, 201 angioplasties with primary stenting were performed on 161 patients. One hundred twenty-three stents were placed for claudication, and 78 for critical limb ischemia. Forty-six segments treated were TASC A, 82 were TASC B, 38 were TASC C, and 35 were TASC D. Patient follow-up ranged from three to 1329 days (mean: 426 days). Primary patency rates for TASC A and B lesions were 79%, 67%, and 57% at 12, 24, and 36 months. For TASC C and D lesions, primary patency rates were 52.7%, 36%, and 19% at the same time intervals. Primary patency rates for TASC A and B lesions were significantly higher than for C and D lesions (P < .001). The limb salvage rate was 88.5% in patients with critical limb ischemia. Distal runoff did not influence patency (P = .827).ConclusionsPrimary stenting of the SFA and PA provides durable results in patients with TASC A and B lesions and may be an effective treatment strategy. This approach is significantly less effective when used in treating those with TASC C and D disease. Based on the results in this series, the use of primary stenting does not extend the anatomic limits of the current treatment recommendations for catheter-based intervention in patients with infrainguinal occlusive disease

Indoor Particulate Matter Concentration, Water Boiling Time, and Fuel Use of Selected Alternative Cookstoves in a Home-Like Setting in Rural Nepal

Alternative cookstoves are designed to improve biomass fuel combustion efficiency to reduce the amount of fuel used and lower emission of air pollutants. The Nepal Cookstove Trial (NCT) studies effects of alternative cookstoves on family health. Our study measured indoor particulate matter concentration (PM2.5), boiling time, and fuel use of cookstoves during a water-boiling test in a house-like setting in rural Nepal. Study I was designed to select a stove to be used in the NCT; Study II evaluated stoves used in the NCT. In Study I, mean indoor PM2.5 using wood fuel was 4584 μg/m3 , 1657 μg/m3 , and 2414 μg/m3 for the traditional, alternative mud brick stove (AMBS-I) and Envirofit G-series, respectively. The AMBS-I reduced PM2.5 concentration but increased boiling time compared to the traditional stove (p-values \u3c 0.001). Unlike AMBS-I, Envirofit G-series did not significantly increase overall fuel consumption. In Phase II, the manufacturer altered Envirofit stove (MAES) and Nepal Nutrition Intervention Project Sarlahi (NNIPS) altered Envirofit stove (NAES), produced lower mean PM2.5, 1573 μg/m3 and 1341 μg/m3 , respectively, relative to AMBS-II 3488 μg/m3 for wood tests. The liquid propane gas stove had the lowest mean PM2.5 concentrations, with measurements indistinguishable from background levels. Results from Study I and II showed significant reduction in PM2.5 for all alternative stoves in a controlled setting. In study I, the AMBS-I stove required more fuel than the traditional stove. In contrast, in study II, the MAES and NAES stoves required statistically less fuel than the AMBS-II. Reductions and increases in fuel use should be interpreted with caution because the composition of fuels was not standardized—an issue which may have implications for generalizability of other findings as well. Boiling times for alternative stoves in Study I were significantly longer than the traditional stove—a trade-off that may have implications for acceptability of the stoves among end users. These extended cooking times may increase cumulative exposure during cooking events where emission rates are lower; these differences must be carefully considered in the evaluation of alternative stove designs

Human arachnoid granulations Part I: a technique for quantifying area and distribution on the superior surface of the cerebral cortex

<p>Abstract</p> <p>Background</p> <p>The arachnoid granulations (AGs) are herniations of the arachnoid membrane into the dural venous sinuses on the surface of the brain. Previous morphological studies of AGs have been limited in scope and only one has mentioned surface area measurements. The purpose of this study was to investigate the topographic distribution of AGs on the superior surface of the cerebral cortex.</p> <p>Methods</p> <p><it>En face </it>images were taken of the superior surface of 35 formalin-fixed human brains. AGs were manually identified using Adobe Photoshop, with a pixel location containing an AG defined as 'positive'. A set of 25 standard fiducial points was marked on each hemisphere for a total of 50 points on each image. The points were connected on each hemisphere to create a segmented image. A standard template was created for each hemisphere by calculating the average position of the 25 fiducial points from all brains. Each segmented image was mapped to the standard template using a linear transformation. A topographic distribution map was produced by calculating the proportion of AG positive images at each pixel in the standard template. The AG surface area was calculated for each hemisphere and for the total brain superior surface. To adjust for different brain sizes, the proportional involvement of AGs was calculated by dividing the AG area by the total area.</p> <p>Results</p> <p>The total brain average surface area of AGs was 78.53 ± 13.13 mm²(n = 35) and average AG proportional involvement was 57.71 × 10^-4± 7.65 × 10^-4. Regression analysis confirmed the reproducibility of AG identification between independent researchers with r²= 0.97. The surface AGs were localized in the parasagittal planes that coincide with the region of the lateral lacunae.</p> <p>Conclusion</p> <p>The data obtained on the spatial distribution and <it>en face </it>surface area of AGs will be used in an <it>in vitro </it>model of CSF outflow. With an increase in the number of samples, this analysis technique can be used to study the relationship between AG surface area and variables such as age, race and gender.</p

Aorto-venous fistula between an abdominal aortic aneurysm and an aberrant renal vein: a case report

<p>Abstract</p> <p>Introduction</p> <p>The potential complications of an abdominal aortic aneurysm include rupture, compression of surrounding structures, thrombo-embolic events and fistula. The most common site of arterio-venous fistula is the inferior vena cava. Fistula involving a renal vein is particularly uncommon.</p> <p>Case presentation</p> <p>This report describes a 54-year-old Caucasian woman who was admitted to the emergency department with fatigue, severe dyspnea and bilateral lower limb edema. In the first instance this anamnesis suggested possible heart failure. In fact, our patient presented with multi-organ system failure due to a fistula between an infra-renal aortic aneurysm and an aberrant retro-aortic renal vein.</p> <p>Conclusions</p> <p>To our knowledge, this is the first report of a woman with a fistula between an infra-renal aortic aneurysm and an aberrant retro-aortic left renal vein. Aorto-venous fistulas may be asymptomatic or may present with symptoms characteristic of arterio-venous shunting and/or aneurysm rupture. This type of fistula is a rare cause of heart failure. Clinical examination and imaging are essential for detection.</p

Development and validation of a computerized expert system for evaluation of automated visual fields from the Ischemic Optic Neuropathy Decompression Trial

BACKGROUND: The objective of this report is to describe the methods used to develop and validate a computerized system to analyze Humphrey visual fields obtained from patients with non-arteritic anterior ischemic optic neuropathy (NAION) and enrolled in the Ischemic Optic Neuropathy Decompression Trial (IONDT). The IONDT was a multicenter study that included randomized and non-randomized patients with newly diagnosed NAION in the study eye. At baseline, randomized eyes had visual acuity of 20/64 or worse and non-randomized eyes had visual acuity of better than 20/64 or were associated with patients refusing randomization. Visual fields were measured before treatment using the Humphrey Field Analyzer with the 24-2 program, foveal threshold, and size III stimulus. METHODS: We used visual fields from 189 non-IONDT eyes with NAION to develop the computerized classification system. Six neuro-ophthalmologists ("expert panel") described definitions for visual field patterns defects using 19 visual fields representing a range of pattern defect types. The expert panel then used 120 visual fields, classified using these definitions, to refine the rules, generating revised definitions for 13 visual field pattern defects and 3 levels of severity. These definitions were incorporated into a rule-based computerized classification system run on Excel(® )software. The computerized classification system was used to categorize visual field defects for an additional 95 NAION visual fields, and the expert panel was asked to independently classify the new fields and subsequently whether they agreed with the computer classification. To account for test variability over time, we derived an adjustment factor from the pooled short term fluctuation. We examined change in defects with and without adjustment in visual fields of study participants who demonstrated a visual acuity decrease within 30 days of NAION onset (progressive NAION). RESULTS: Despite an agreed upon set of rules, there was not good agreement among the expert panel when their independent visual classifications were compared. A majority did concur with the computer classification for 91 of 95 visual fields. Remaining classification discrepancies could not be resolved without modifying existing definitions. Without using the adjustment factor, visual fields of 63.6% (14/22) patients with progressive NAION and no central defect, and all (7/7) patients with a paracentral defect, worsened within 30 days of NAION onset. After applying the adjustment factor, the visual fields of the same patients with no initial central defect and 5/7 of the patients with a paracentral defect were seen to worsen. CONCLUSION: The IONDT developed a rule-based computerized system that consistently defines pattern and severity of visual fields of NAION patients for use in a research setting