Combinatorial characterization of pseudometrics

Let X, Y be sets and let similar to, similar to be mappings with the domains X2 and Y 2 respectively. We say that similar to is combinatorially similar to similar to if there are bijections f : similar to(X2) similar to similar to(Y 2) and g : Y similar to X such that similar to (x, y) = f(similar to(g(x), g(y))) for all x, y similar to Y. It is shown that the semigroups of binary relations generated by sets {similar to-1 (a): a similar to similar to(X 2)} and {similar to-1 (b): b similar to similar to(Y 2)} are isomorphic for combinatorially similar similar to and similar to. The necessary and sufficient conditions under which a given mapping is combinatorially similar to a pseudometric, or strongly rigid pseudometric, or discrete pseudometric are found. The algebraic structure of semigroups generated by {d-1 (r): r similar to d(X 2)} is completely described for nondiscrete, strongly rigid pseudometrics and, also, for discrete pseudometrics d: X2 similar to R.Peer reviewe

Generalised Cantor sets and the dimension of products

In this paper we consider the relationship between the Assouad and box-counting dimension and how both behave under the operation of taking products. We introduce the notion of ‘equi-homogeneity’ of a set, which requires a uniformity in the cardinality of local covers at all length-scales and at all points, and we show that a large class of homogeneous Moran sets have this property. We prove that the Assouad and box-counting dimensions coincide for sets that have equal upper and lower box-counting dimensions provided that the set ‘attains’ these dimensions (analogous to ‘s-sets’ when considering the Hausdorff dimension), and the set is equi-homogeneous. Using this fact we show that for any α ∈ (0, 1) and any β, γ ∈ (0, 1) such that β + γ ≥ 1 we can construct two generalised Cantor sets C and D such that dimBC = αβ, dimBD = α γ, and dimAC = dimAD = dimA (C × D) = dimB (C × D) = α

Immune cell profiles of metastatic HER2-positive breast cancer patients according to the sites of metastasis

Purpose Recent works have characterized that metastatic site can affect the tumour immune profiles and efficiency of cancer immunotherapies. The prognosis of HER2-positive breast cancer is associated with the characteristics of the tumour immune microenvironment, with immunological cells playing a central role in efficiency of HER2-targeted antibodies. Here we investigated the prognostic significance of different metastatic sites and their correlation to tumour immune profiles in HER2-positive breast cancer treated with trastuzumab. Methods We collected all (n = 54) HER2-positive metastatic breast cancer patients treated with trastuzumab containing regimens at Oulu University Hospital 2009-2014. Pathological and clinical data were collected from electronic patient records. The tumour immune profiles were analysed from pre-treatment primary tumours using well-characterized immunological markers with computer-assisted immune cell counting. Results Of the metastatic sites, only liver metastases were associated with poor prognosis (hazard ratio 1.809, 95% confidence interval 1.004-3.262), especially when presented as the primary site of metastases. Of the other sites, pulmonary metastases characterized a patient profile with trend to improved survival. Of the studied tumour immunological markers, patients with liver metastases had low densities of CD3(+) T cells (p = 0.030) and M1-like macrophages in their primary tumours (p = 0.025). Of the other studied markers and sites, patients with pulmonary metastases had low STAB1(+)-immunosuppressive macrophage density in their primary tumours. Conclusion Our results suggest that the site of metastasis is associated with prognosis in HER2-positive breast cancer, highlighted by the poor prognosis of liver metastases. Furthermore, liver metastases were associated with adverse tumour immune cell profiles.Peer reviewe

Immune cell profiles of metastatic HER2-positive breast cancer patients according to the sites of metastasis

Purpose Recent works have characterized that metastatic site can affect the tumour immune profiles and efficiency of cancer immunotherapies. The prognosis of HER2-positive breast cancer is associated with the characteristics of the tumour immune microenvironment, with immunological cells playing a central role in efficiency of HER2-targeted antibodies. Here we investigated the prognostic significance of different metastatic sites and their correlation to tumour immune profiles in HER2-positive breast cancer treated with trastuzumab. Methods We collected all (n = 54) HER2-positive metastatic breast cancer patients treated with trastuzumab containing regimens at Oulu University Hospital 2009-2014. Pathological and clinical data were collected from electronic patient records. The tumour immune profiles were analysed from pre-treatment primary tumours using well-characterized immunological markers with computer-assisted immune cell counting. Results Of the metastatic sites, only liver metastases were associated with poor prognosis (hazard ratio 1.809, 95% confidence interval 1.004-3.262), especially when presented as the primary site of metastases. Of the other sites, pulmonary metastases characterized a patient profile with trend to improved survival. Of the studied tumour immunological markers, patients with liver metastases had low densities of CD3(+) T cells (p = 0.030) and M1-like macrophages in their primary tumours (p = 0.025). Of the other studied markers and sites, patients with pulmonary metastases had low STAB1(+)-immunosuppressive macrophage density in their primary tumours. Conclusion Our results suggest that the site of metastasis is associated with prognosis in HER2-positive breast cancer, highlighted by the poor prognosis of liver metastases. Furthermore, liver metastases were associated with adverse tumour immune cell profiles.Peer reviewe

Patient satisfaction in the long-term effects of Eustachian tube balloon dilation is encouraging

Object: To investigate the long-term effects of balloon Eustachian tuboplasty (BET) from patient’s perspective and to discover which symptoms of Eustachian tube dysfunction (ETD) benefit the most from BET.Method: We designed a retrospective postal questionnaire based on the seven-item ETD questionnaire (ETDQ-7). Our questionnaire covered the severity of present ETD symptoms in comparison with the preoperative situation, the severity of current overall ear symptoms, and possible surgical interventions after BET. Forty-six patients treated in our institution between 2011 and 2013 fulfilled the inclusion criteria and 74% (34 patients; total 52 ears treated with BET) returned the questionnaire with a mean follow-up time of 3.1 years (range 1.8-4.6 years).Results: Pain in the ears, feeling of pressure in the ears, and feeling that ears are clogged had reduced in 75% of the ears that suffered from these symptoms preoperatively. Seventy-seven percent of all the responders felt that their overall ear symptoms were reduced. Altogether, 82% of all the patients stated that they would undergo BET again if their ear symptoms returned to the preoperative level.Conclusion: Patient satisfaction in the long-term effects of BET is encouraging. These results may help clinicians in preoperative patient selection and counselling.</p

Systematic review of fatty acid composition of human milk from mothers of preterm compared to full-term infants

Background: Fatty acid composition of human milk serves as guidance for the composition of infant formulae. The aim of the study was to systematically review data on the fatty acid composition of human milk of mothers of preterm compared to full-term infants. Methods: An electronic literature search was performed in English (Medline and Medscape) and German (SpringerLink) databases and via the Google utility. Fatty acid compositional data for preterm and fullterm human milk were converted to differences between means and 95% confidence intervals. Results: We identified five relevant studies publishing direct comparison of fatty acid composition of preterm versus full-term human milk. There were no significant differences between the values of the principal saturated and monounsaturated fatty acids. In three independent studies covering three different time points of lactation, however, docosahexaenoic acid (DHA) values were significantly higher in milk of mothers of preterm as compared to those of full-term infants, with an extent of difference considered nutritionally relevant. Conclusion: Higher DHA values in preterm than in full-term human milk underlines the importance of using own mother's milk for feeding preterm babies and raises the question whether DHA contents in preterm formulae should be higher than in formulae for full-term infants. Copyright (c) 2008 S. Karger AG, Basel