Existence of Probability Measures With Given Marginals

We show that if f is a probability density on Rn wrt Lebesgue measure (or any absolutely continuous measure) and 0 ≤ f ≤ 1, then there is another density g with only the values 0 and 1 and with the same (n−1)-dimensional marginals in any finite number of directions. This sharpens, unifies and extends the results of Lorentz and of Kellerer. Given a pair of independent random variables 0 ≤ X, Y ≤ 1, we further study functions 0 ≤ ϕ ≤ 1 such that Z = ϕ (X,Y) satisfies E(Z|X) = X and E(Z|Y) = Y. If there is a solution then there also is a nondecreasing solution ϕ(x,y). These results are applied to tomography and baseball

Skin Distress Screening: Validation of an Efficient One-question Tool

Skin diseases are often accompanied by physical, emotional and social problems, which may negatively impact health-related quality of life and result in skin-related distress. It is essential to identify patients with skin-related distress within the short time-window of an outpatient dermatological visit. Therefore the one-question screening tool, the Distress Thermometer adjusted for skin conditions, was validated in a cross-sectional questionnaire study. In 2 medical centres in Amsterdam, 214 patients with a chronic skin disease were invited to complete the Distress Thermometer and additional health-related quality of life questionnaires. To validate the Distress Thermometer, the Skindex29 was used as gold standard. To test test-retest reliability, the questionnaires were answered at 2 different time-points. Severely impaired health-related quality of life was present in 30% of respondents according to the Skindex29 using a cut-off score of 44. Receiver operating characteristic curve analyses yielded an area under the curve of 0.813 (standard error 0.04, 95% confidence interval 0.74-0.89). A cut-off score ≥ 4 on the Distress Thermometer provided the optimal ratio of sensitivity (90.7%) to specificity (56.1%). Therefore, for general practice, a cut-off score of ≥ 4 on the Distress Thermometer is advised. The Distress Thermometer seems to be a rapid, valid and reliable screening tool for identifying skin-related distress in patients with a chronic skin disease in the outpatient dermatology setting

On the critical pair theory in abelian groups : Beyond Chowla's Theorem

We obtain critical pair theorems for subsets S and T of an abelian group such that |S+T| < |S|+|T|+1. We generalize some results of Chowla, Vosper, Kemperman and a more recent result due to Rodseth and one of the authors.Comment: Submitted to Combinatorica, 23 pages, revised versio

The impact of loco-regional recurrences on metastatic progression in early-stage breast cancer: a multistate model

To study whether the effects of prognostic factors associated with the occurrence of distant metastases (DM) at primary diagnosis change after the incidence of loco-regional recurrences (LRR) among women treated for invasive stage I or II breast cancer. The study population consisted of 3,601 women, enrolled in EORTC trials 10801, 10854, or 10902 treated for early-stage breast cancer. Data were analysed in a multivariate, multistate model by using multivariate Cox regression models, including a state-dependent covariate. The presence of a LRR in itself is a significant prognostic risk factor (HR: 3.64; 95%-CI: 2.02-6.5) for the occurrence of DM. Main prognostic risk factors for a DM are young age at diagnosis (</=40: HR: 1.79; 95%-CI: 1.28-2.51), larger tumour size (HR: 1.58; 95%-CI: 1.35-1.84) and node positivity (HR: 2.00; 95%-CI: 1.74-2.30). Adjuvant chemotherapy is protective for a DM (HR: 0.66; 95%-CI: 0.55-0.80). After the occurrence of a LRR the latter protective effect has disappeared (P = 0.009). The presence of LRR in itself is a significant risk factor for DM. For patients who are at risk of developing LRR, effective local control should be the main target of therapy

Characteristic functional equations of polynomials and the morera-carleman theorem

Several characteristic functional equations satisfied by classes of polynomials of bounded degree are examined in connection with certain generalizations of the Morera-Carleman Theorem. Certain functional equations which have nonanalytic polynomial solutions are also considered.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/43923/1/10_2005_Article_BF02188016.pd

The Prometastatic Microenvironment of the Liver

The liver is a major metastasis-susceptible site and majority of patients with hepatic metastasis die from the disease in the absence of efficient treatments. The intrahepatic circulation and microvascular arrest of cancer cells trigger a local inflammatory reaction leading to cancer cell apoptosis and cytotoxicity via oxidative stress mediators (mainly nitric oxide and hydrogen peroxide) and hepatic natural killer cells. However, certain cancer cells that resist or even deactivate these anti-tumoral defense mechanisms still can adhere to endothelial cells of the hepatic microvasculature through proinflammatory cytokine-mediated mechanisms. During their temporary residence, some of these cancer cells ignore growth-inhibitory factors while respond to proliferation-stimulating factors released from tumor-activated hepatocytes and sinusoidal cells. This leads to avascular micrometastasis generation in periportal areas of hepatic lobules. Hepatocytes and myofibroblasts derived from portal tracts and activated hepatic stellate cells are next recruited into some of these avascular micrometastases. These create a private microenvironment that supports their development through the specific release of both proangiogenic factors and cancer cell invasion- and proliferation-stimulating factors. Moreover, both soluble factors from tumor-activated hepatocytes and myofibroblasts also contribute to the regulation of metastatic cancer cell genes. Therefore, the liver offers a prometastatic microenvironment to circulating cancer cells that supports metastasis development. The ability to resist anti-tumor hepatic defense and to take advantage of hepatic cell-derived factors are key phenotypic properties of liver-metastasizing cancer cells. Knowledge on hepatic metastasis regulation by microenvironment opens multiple opportunities for metastasis inhibition at both subclinical and advanced stages. In addition, together with metastasis-related gene profiles revealing the existence of liver metastasis potential in primary tumors, new biomarkers on the prometastatic microenvironment of the liver may be helpful for the individual assessment of hepatic metastasis risk in cancer patients