The Banach–Tarski paradox and its implications on the problem of measure

Vi presenterar ett bevis av en sats av Stefan Banach och Alfred Tarski, som bygger på resultat av Felix Hausdorff: Det finns två ändliga samlingar av disjunkta delmängder av enhetsbollen i R3 sådana att varje samling kan transformeras till en ny enhetsboll under verkan av stela rörelser (ändliga kombinationer av translationer och rotationer). Detta resultat förlängs sedan till dess starka form: Om A;B är två begränsade delmängder av R3 med icketomt inre så finns två partitioner fAign i=1; fBigni =1 av A och B respektive, och stela rörelser _1; _2; :::; _n sådana att _i(Ai) = Bi för varje i = 1; 2; :::; n. Dessa satser kallas för Banach– Tarski paradoxen. Måttproblemet ställer frågan huruvida man kan tilldela en volym till varje delmängd av Rn för n 2 N så att volym bevaras under stela rörelser och partitionering. Vi visar att, som en konsekvens av Banach–Tarski paradoxen, kan man inte ge ett jakande svar till måttproblemet för n > 2. Vi diskuterar om detta kan ges i en och två dimensioner, och i allmänhet hur problemet att tilldela en volym till varje delmängd av en mängd X relaterar till existensen av dekomposititoner av delmängder av X liknande dem ovan, där elementen som transformerar dekompositionerna kan höra till vilken klass som helst av bijektioner av

Nyblivna skogsägares riskperception

På den svenska marknaden för skogsmark växer andelen köpare som investerar i sin första skogsfastighet. Både för de nyblivna och för de erfarna skogsägarna medför investeringen risker som kan påverka dess lönsamhet. Studier indikerar att skogsskadefrekvens och -effekt kommer öka i framtiden. Den här studiens syfte är att undersöka riskperception inom gruppen nyblivna skogsägare bland Handelsbankens kunder. Detta innebär att undersöka vilka risker som identifieras, hur dessa upplevs, värderas och hanteras. Ett delsyfte är att undersöka vilka bakomliggande faktorer som kan påverka skogsägarnas riskperception. Kvalitativ data är insamlad genom telefonintervjuer med fem av bankens kunder. Resultaten visar att inte alla nyblivna skogsägare identifierar risker, men de tre framträdande riskerna är storma, prisförändringar och ränteosäkerhet. Riskens konsekvens och sannolikhet, så väl som skogsägarens erfarenhet och kunskap visar sig påverka riskperception. Inte alla upplever att man aktivt kan påverka riskerna och en förhållandevis låg orosgrad förklaras genom attityden “händer det, så händer det”. Trots detta påstår vissa skogsägare att bättre planering av skötselåtgärder samt försäkring kan påverka riskerna. En väsentlig slutsats är att kunder med låg kunskap kring riskhantering utgör en osäkerhet för bankens försäkringsverksamhet. Riskperception är ett synnerligen komplext fenomen som lämnar stort utrymme för fortsatt forskning.In the Swedish market for forest properties the proportion of buyers who invest in their first forest estate is growing. For both the newly-become and the experienced forest owners the investment involves risks that can affect its profitability. Studies indicate that forest damage frequency and effect will increase in the future. The purpose of this study is to examine risk perception within the group of newly-become forest owners, among Handelsbanken's customers. This means examining which risks are identified, how they are experienced, valued and managed. One aim is to examine which underlying factors that can influence forest owners' risk perception. Qualitative data are collected through telephone interviews with five of the bank's customers. The results show that not all new forest owners identify risks, but three prominent risks are storms, price fluctuations and interest rate uncertainty. Risk effect and probability, as well as the forest owner's experience and knowledge are found to influence risk perception. Not everyone feels that they can actively influence the risks and a relatively low degree of concern is explained through the attitude "if it happens, it happens". Despite this, some forest owners claim that better planning of silvicultural measures and insurance may affect the risks. A significant conclusion is that customers with a low degree of knowledge concerning risk management constitute an uncertainty for the bank's insurance business. Risk perception is a highly complex phenomenon which leaves wide scope for further research

Banach–Tarski paradoxen och dess implikationer på måttproblemet

Vi presenterar ett bevis av en sats av Stefan Banach och Alfred Tarski, som bygger på resultat av Felix Hausdorff: Det finns två ändliga samlingar av disjunkta delmängder av enhetsbollen i R3 sådana att varje samling kan transformeras till en ny enhetsboll under verkan av stela rörelser (ändliga kombinationer av translationer och rotationer). Detta resultat förlängs sedan till dess starka form: Om A;B är två begränsade delmängder av R3 med icketomt inre så finns två partitioner fAign i=1; fBigni =1 av A och B respektive, och stela rörelser _1; _2; :::; _n sådana att _i(Ai) = Bi för varje i = 1; 2; :::; n. Dessa satser kallas för Banach– Tarski paradoxen. Måttproblemet ställer frågan huruvida man kan tilldela en volym till varje delmängd av Rn för n 2 N så att volym bevaras under stela rörelser och partitionering. Vi visar att, som en konsekvens av Banach–Tarski paradoxen, kan man inte ge ett jakande svar till måttproblemet för n > 2. Vi diskuterar om detta kan ges i en och två dimensioner, och i allmänhet hur problemet att tilldela en volym till varje delmängd av en mängd X relaterar till existensen av dekomposititoner av delmängder av X liknande dem ovan, där elementen som transformerar dekompositionerna kan höra till vilken klass som helst av bijektioner av

Oxygen provision to severely ill COVID-19 patients at the peak of the 2020 pandemic in a Swedish district hospital.

Oxygen is a low-cost and life-saving therapy for patients with COVID-19. Yet, it is a limited resource in many hospitals in low income countries and in the 2020 pandemic even hospitals in richer countries reported oxygen shortages. An accurate understanding of oxygen requirements is needed for capacity planning. The World Health Organization estimates the average flow-rate of oxygen to severe COVID-19-patients to be 10 l/min. However, there is a lack of empirical data about the oxygen provision to patients. This study aimed to estimate the oxygen provision to COVID-19 patients with severe disease in a Swedish district hospital. A retrospective, medical records-based cohort study was conducted in March to May 2020 in a Swedish district hospital. All adult patients with severe COVID-19 -those who received oxygen in the ward and had no ICU-admission during their hospital stay-were included. Data were collected on the oxygen flow-rates provided to the patients throughout their hospital stay, and summary measures of oxygen provision calculated. One-hundred and twenty-six patients were included, median age was 70 years and 43% were female. On admission, 27% had a peripheral oxygen saturation of ≤91% and 54% had a respiratory rate of ≥25/min. The mean oxygen flow-rate to patients while receiving oxygen therapy was 3.0 l/min (SD 2.9) and the mean total volume of oxygen provided per patient admission was 16,000 l (SD 23,000). In conclusion, the provision of oxygen to severely ill COVID-19-patients was lower than previously estimated. Further research is required before global estimates are adjusted

“They can do whatever they want”: Meanings of receiving psychiatric care based on a common staff approach

This study deepens our understanding of how patients, when cared for in a psychiatric ward, experience situations that involve being handled according to a common staff approach. Interviews with nine former psychiatric in-patients were analyzed using a phenomenological–hermeneutic method to illuminate the lived experience of receiving care based on a common staff approach. The results revealed several meanings: discovering that you are as subjected to a common staff approach, becoming aware that no one cares, becoming aware that your freedom is restricted, being afflicted, becoming aware that a common staff approach is not applied by all staff, and feeling safe because someone else is responsible. The comprehensive understanding was that the patient's understanding of being cared for according to a common staff approach was to be seen and treated in accordance with others' beliefs and valuations, not in line with the patients' own self-image, while experiencing feelings of affliction

Accumulation of CCR4+ CTLA-4hi FOXP3+CD25hi Regulatory T Cells in Colon Adenocarcinomas Correlate to Reduced Activation of Conventional T Cells

BACKGROUND: Colorectal cancer usually gives rise to a specific anti-tumor immune response, but for unknown reasons the resulting immunity is not able to clear the tumor. Recruitment of activated effector lymphocytes to the tumor is important for efficient anti-tumor responses, while the presence of regulatory T cells (Treg) down-modulate tumor-specific immunity. We therefore aimed to determine homing mechanisms and activation stage of Treg and effector T cell infiltrating colon tumors compared to cells from the unaffected mucosa in patients suffering from colon adenocarcinoma. METHODOLOGY/PRINCIPAL FINDINGS: Lymphocytes were isolated from unaffected and tumor mucosa from patients with colon adenocarcinoma, and flow cytometry, immunohistochemistry, and quantitative PCR was used to investigate the homing mechanisms and activation stage of infiltrating Treg and conventional lymphocytes. We detected significantly higher frequencies of CD25(high)FOXP3⁺CD127(low) putative Treg in tumors than unaffected mucosa, which had a complete demethylation in the FOXP3 promotor. Tumor-associated Treg had a high expression of CTLA-4, and some appeared to be antigen experienced effector/memory cells based on their expression of αEβ7 (CD103). There were also significantly fewer activated T cells and more CTLA-4⁺ conventional T cells susceptible to immune regulation in the tumor-associated mucosa. In contrast, CD8⁺granzyme B⁺ putative cytotoxic cells were efficiently recruited to the tumors. The frequencies of cells expressing α4β7 and the Th1 associated chemokine receptor CXCR3 were significantly decreased among CD4⁺ T cells in the tumor, while frequencies of CD4⁺CCR4⁺ lymphocytes were significantly increased. CONCLUSIONS/SIGNIFICANCE: This study shows that CCR4⁺CTLA4(hi) Treg accumulate in colon tumors, while the frequencies of activated conventional Th1 type T cells are decreased. The altered lymphocyte composition in colon tumors will probably diminish the ability of the immune system to effectively attack tumor cells, and reducing the Treg activity is an important challenge for future immunotherapy protocols

Stromal regulatory T-cells are associated with a favourable prognosis in gastric cancer of the cardia

<p>Abstract</p> <p>Background</p> <p>Recent evidence suggests that CD4⁺CD25⁺FoxP3⁺regulatory T-cells (Treg) may be responsible for the failure of host anti-tumour immunity by suppressing cytotoxic T- cells. We assessed the prognostic significance of tumour infiltrating lymphocytes (TIL) in intestinal-type gastric cardiac cancer.</p> <p>Methods</p> <p>Tumour infiltrating lymphocyte (TIL) subsets and tumour infiltrating macrophages (TIM) were investigated in 52 cases using tissue microarrays. The interrelationship between the cell populations (CD3+, CD8+, CD20+, CD68+, GranzymeB+, FoxP3+) in different compartments and NED-survival was investigated (median follow-up time: 61 months).</p> <p>Results</p> <p>Intraepithelial infiltration with TIL and TIM including Treg was generally low and not related to NED-survival. However, patients with large numbers of FoxP3⁺Treg in the tumour stroma (>125.9 FoxP3⁺TILs/mm²) had a median survival time of 58 months while those with low FoxP3⁺TIL counts (<125.9 FoxP3⁺TILs/mm²) had a median survival time of 32 months (p = 0.006). Patients with high versus low stromal CD68⁺/FoxP3⁺cell ratios in primary tumour displayed median survivals of 32 and 55 months, respectively (p = 0.008).</p> <p>Conclusion</p> <p>Our results suggest that inflammatory processes within the tumour stroma of gastric intestinal-type adenocarcinomas located at the gastric cardia may affect outcome in two ways. Tumour-infiltrating macrophages are likely to promote carcinogenesis while large numbers of Treg are associated with improved outcome probably by inhibiting local inflammatory processes promoting carcinogenesis. Thus, inhibition of Treg may not be a feasible treatment option in gastric adenocarcinoma.</p

Prognostic impact of peritumoral lymphocyte infiltration in soft tissue sarcomas

<p>Abstract</p> <p>Background</p> <p>The purpose of this study was to clarify the prognostic significance of peritumoral lymphocyte infiltration in the capsule of soft tissue sarcomas (STS). Multiple observations in preclinical and clinical studies have shown that the immune system has a role in controlling tumor growth and progression. Prognostic markers in potentially curable STS should guide therapy after surgical resection. The immune status at the time of resection may be important, but the prognostic significance of peritumoral lymphocytes is unknown.</p> <p>Methods</p> <p>Tissue microarrays from 80 patients with STS were constructed from duplicate cores of tissue from the tumor and the peritumoral capsule. Immunohistochemistry was used to evaluate the CD3+, CD4+, CD8+ and CD20+ lymphocytes in the tumor and the peritumoral capsule.</p> <p>Results</p> <p>In univariate analyses, increasing numbers of CD20+ (<it>P </it>= 0.032) peritumoral lymphocytes were associated with a reduced disease free survival (DSS). In multivariate analyses, a high number of CD20+ peritumoral lymphocytes (<it>P </it>= 0.030) in the capsule was an independent negative prognostic factor for DSS. There were no such associations of lymphocyte infiltration in the tumor.</p> <p>Conclusions</p> <p>A high density of CD20+ peritumoral lymphocytes is an independent negative prognostic indicator for patients with STS. Further research is needed to determine whether CD20 cells in the peritumoral capsule of STS may promote tumor invasion in the surrounding tissue and increase the metastatic potential.</p