Limitations on the smooth confinement of an unstretchable manifold

We prove that an m-dimensional unit ball D^m in the Euclidean space {\mathbb R}^m cannot be isometrically embedded into a higher-dimensional Euclidean ball B_r^d \subset {\mathbb R}^d of radius r < 1/2 unless one of two conditions is met -- (1)The embedding manifold has dimension d >= 2m. (2) The embedding is not smooth. The proof uses differential geometry to show that if d<2m and the embedding is smooth and isometric, we can construct a line from the center of D^m to the boundary that is geodesic in both D^m and in the embedding manifold {\mathbb R}^d. Since such a line has length 1, the diameter of the embedding ball must exceed 1.Comment: 20 Pages, 3 Figure

Thoughts of self-harm in early and late pregnancy in urban South Africa: Investigating prevalence, predictors and screening options

Background. Thoughts of self-harm (TSH) are an important marker of mental health risk, and risk for attempted and completed suicide. While there is increasing attention being paid to mental health problems in pregnancy in South Africa (SA), TSH have received less attention despite some cross-sectional studies suggesting that prevalence may be high (12 - 39%). There is a dearth of longitudinal research to inform prevention and treatment.Objectives. To examine the rates of TSH across pregnancy in a longitudinal SA cohort and to investigate factors associated with the onset and persistence of TSH, as well as the relationship between TSH, depression and/or anxiety.Methods. Women were enrolled in a prospective pregnancy cohort (S1000) in Soweto, SA between 2014 and 2016, and assessed using validated screening measures (Edinburgh Postnatal Depression Scale (EPDS) and State Trait Anxiety Index short form) in early and later pregnancy. Data were available for 649 women. TSH were determined using EPDS item 10. Logistic regression and bifactor models were used to determine factors associated with TSH across pregnancy.Results. Of the 649 women, 18% reported TSH at some stage during their pregnancy. Prevalence of TSH was slightly higher in early pregnancy (12.5%) than later in pregnancy (11.6%). TSH were associated with a history of mental illness (adjusted odds ratio (aOR) 4.17; 95% confidence interval (CI) 1.3 - 13.7; p=0.020), concurrent depression (aOR 4.8; 95%CI 2.7 - 8.6; p&lt;0.001); marital stress (aOR 1.74; 95% CI 1.0 - 3.0; p=0.040); and practical support (aOR 0.43; 95% CI 0.2 - 1.0; p=0.040) using a multivariate logistic regression. Bifactor analysis examining depression and anxiety scales showed that TSH contributed the highest variance to a shared depression and anxiety factor in early pregnancy. Logistic regressions showed that early depression was a strong predictor of later reports of TSH.Conclusions. The present study shows that the risk of TSH during pregnancy is relatively common, and starts early during pregnancy. Screening approaches could be simplified to encourage healthcare practitioners working in busy and over-burdened public healthcare settings to engage in identifying at-risk women. Efforts in improving early identification of mental health risk in pregnancy should be matched with strengthening of current treatment and referral options. Since practical support and a good marital relationship reduce the risk of TSH, these may be important avenues of focus for designing interventions

Soil weathering rates in 21 catchments of the Canadian Shield

Soil mineral weathering represents an essential source of nutrient base cation (Ca, Mg and K) for forest growth in addition to provide a buffering power against precipitation acidity for soils and surface waters. Weathering rates of base cations were obtained for 21 catchments located within the temperate and the boreal forest of the Canadian Shield with the geochemical model PROFILE. Weathering rates ranged from 0.58 to 4.46 kmol&lt;sub&gt;c&lt;/sub&gt; ha&lt;sup&gt;−1&lt;/sup&gt; yr&lt;sup&gt;−1&lt;/sup&gt; and their spatial variation within the studied area was mostly in agreement with spatial variations in soil mineralogy. Weathering rates of Ca and Mg were significantly correlated (&lt;i&gt;r&lt;/i&gt; = 0.80 and 0.64) with their respective lake concentrations. Weathering rates of K and Na did not correlate with lake concentrations of K and Na. The modeled weathering rates for each catchment were also compared with estimations of net catchment exportations. The result show that modeled weathering rates of Ca were not significantly different than the net catchment exportations while modeled weathering rates of Mg were higher by 51%. Larger differences were observed for K and Na weathering rates that were significantly different than net catchment exportations being 6.9 and 2.2 times higher than net exportations, respectively. The results for K were expected given its high reactivity with biotic compartments and suggest that most of the K produced by weathering reactions was retained within soil catchments and/or above ground biomass. This explanation does not apply to Na, however, which is a conservative element in forest ecosystems because of the insignificant needs of Na for soil microorganisms and above ground vegetations. It raises concern about the liability of the PROFILE model to provide reliable values of Na weathering rates. Overall, we concluded that the PROFILE model is powerful enough to reproduce spatial geographical gradients in weathering rates for relatively large areas as well as adequately predict absolute weathering rates values for the sum of base cations, Ca and Mg

PMH40 How do Patients Describe Their Depression? - Incorporating the Patient's Voice Into Instrument Development

Letter from CGIAR Chairman Ismail Serageldin to CGIAR heads of delegation, board chairs, center directors and the TAC chairman and secretariat, leading up to ICW94. Serageldin described the work of various ad hoc and standing bodies in preparation for International Centers Week 1994 and the Ministerial-level Meeting being planned for early 1995. He also announced that as a result of additional funding by donors and matching funds from the World Bank, the 1994 core program was fully funded

Physical and psychological factors associated with walking capacity in patients with lumbar spinal stenosis with neurogenic claudication: A systematic scoping review

Objective: The purpose of this study was to evaluate the current state of scientific knowledge regarding physical and psychological factors associated with walking capacity in patients with lumbar spinal stenosis (LSS) with neurogenic claudication. Design: Systematic scoping review. Literature Search: We searched CINAHL (Cumulative Index to Nursing and Allied Health Literature), MEDLINE, Cochrane, PsycINFO, and SPORTDiscus databases. Study Selection Criteria: Cohorts and cross-sectional studies reporting on associations between physical or psychological factors and impaired walking capacity in patients with symptomatic LSS were included. Data Synthesis: Data were synthetized to identify associations between physical or psychological factors and either walking capacity, gait pattern characteristics, or functional tasks. Results: Twenty-four studies were included. Walking capacity was significantly correlated with several pain outcomes, disability, estimated walking distance, and cross-sectional area of the lumbar spine. Gait pattern characteristics such as speed and stride were strongly and positively correlated with disability outcomes. Functional tasks were significantly correlated with lower back and upper limb disability, lower limb endurance strength, ranges of motion, and speed. Associations with psychological factors were mostly conflicting except for the Rasch-based Depression Screener and the Pain Anxiety Symptom Scale (PASS-20) questionnaire that were associated with a decreased performance in functional tasks. Conclusion: Physical and psychological factors that are associated with walking capacity in patients with symptomatic LSS were identified. However, many associations reported between physical or psychological factors and walking capacity were conflicting, even more so when correlated with walking capacity specifically