Punctured polygons and polyominoes on the square lattice

We use the finite lattice method to count the number of punctured staircase and self-avoiding polygons with up to three holes on the square lattice. New or radically extended series have been derived for both the perimeter and area generating functions. We show that the critical point is unchanged by a finite number of punctures, and that the critical exponent increases by a fixed amount for each puncture. The increase is 1.5 per puncture when enumerating by perimeter and 1.0 when enumerating by area. A refined estimate of the connective constant for polygons by area is given. A similar set of results is obtained for finitely punctured polyominoes. The exponent increase is proved to be 1.0 per puncture for polyominoes.Comment: 36 pages, 11 figure

Assessing the Information Content in Environmental Modelling: A Carbon Cycle Perspective

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Carbon dioxide and climate impulse response functions for the computation of greenhouse gas metrics: a multi-model analysis

The responses of carbon dioxide (CO2) and other climate variables to an emissionpulse of CO2into the atmosphere are often used to compute the Global WarmingPotential (GWP) and Global Temperature change Potential (GTP), to characterizethe response time scales of Earth System models, and to build reduced-form mod-5els. In this carbon cycle-climate model intercomparison project, which spans the fullmodel hierarchy, we quantify responses to emission pulses of different magnitudes in-jected under different conditions. The CO2response shows the known rapid declinein the first few decades followed by a millennium-scale tail. For a 100 GtC emissionpulse, 24±10 % is still found in the atmosphere after 1000 yr; the ocean has absorbed1060±18 % and the land the remainder. The response in global mean surface air tem-perature is an increase by 0.19±0.10◦C within the first twenty years; thereafter anduntil year 1000, temperature decreases only slightly, whereas ocean heat content andsea level continue to rise. Our best estimate for the Absolute Global Warming Po-tential, given by the time-integrated response in CO2at year 100 times its radiative15efficiency, is 92.7×10−15yr Wm−2per kg CO2. This value very likely (5 to 95% confi-dence) lies within the range of (70 to 115)×10−15yr Wm−2per kg CO2. Estimates fortime-integrated response in CO2published in the IPCC First, Second, and Fourth As-sessment and our multi-model best estimate all agree within 15%. The integrated CO2response is lower for pre-industrial conditions, compared to present day, and lower for20smaller pulses than larger pulses. In contrast, the response in temperature, sea leveland ocean heat content is less sensitive to these choices. Although, choices in pulsesize, background concentration, and model lead to uncertainties, the most importantand subjective choice to determine AGWP of CO2and GWP is the time horizon.ISSN:1680-7375ISSN:1680-736

Marital status, living arrangement, and survival among individuals with advanced prostate cancer in the International Registry for Men with Advanced Prostate Cancer

BACKGROUND: Studies have shown improved survival among individuals with cancer with higher levels of social support. Few studies have investigated social support and overall survival (OS) in individuals with advanced prostate cancer in an international cohort. We investigated the associations of marital status and living arrangements with OS among individuals with advanced prostate cancer in the International Registry for Men with Advanced Prostate Cancer (IRONMAN).METHODS: IRONMAN is enrolling participants diagnosed with advanced prostate cancer (metastatic hormone-sensitive prostate cancer, mHSPC; castration resistant prostate cancer, CRPC) from 16 countries. Participants in this analysis were recruited between July 2017 and January 2023. Adjusting for demographics and tumor characteristics, the associations were estimated using Cox regression and stratified by disease state (mHSPC, CRPC), age (&lt;70, 70+ years), and continent of enrollment (North America, Europe, Other).RESULTS: We included 2,119 participants with advanced prostate cancer, of whom 427 died during up to 5 years of follow-up (median 6 months). Two-thirds had mHSPC. Most were married/in a civil partnership (79%) and 6% were widowed. Very few married participants were living alone (1%), while most unmarried participants were living alone (70%). Married participants had better OS than unmarried participants (adjusted HR: 1.44; 95% CI: 1.02, 2.02). Widowed participants had the worst survival compared to married individuals (adjusted HR: 1.89; 95% CI: 1.22, 2.94).CONCLUSIONS: Among those with advanced prostate cancer, unmarried and widowed participants had worse OS compared to married participants.IMPACT: This research highlighted the importance of social support in OS within this vulnerable population.</p