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

IRONMAN: A Novel International Registry of Men With Advanced Prostate Cancer

To describe a newly established international registry recruiting diverse patients with advanced prostate cancer across academic and community practices to address unmet needs in this population. PATIENTS AND METHODS: Initiated in 2017, IRONMAN (International Registry for Men with Advanced Prostate Cancer) is a prospective cohort of patients with advanced prostate cancer. The study will enroll 5,000 patients with metastatic hormone-sensitive prostate cancer (mHSPC) or castration-resistant prostate cancer (CRPC), recruited from Australia, the Bahamas, Barbados, Brazil, Canada, Ireland, Jamaica, Kenya, Nigeria, Norway, South Africa, Spain, Sweden, Switzerland, the United Kingdom, and the United States. The study is collecting datatypes to study variation in care and treatment of advanced prostate cancer across countries and across academic, community-based, and government practices with a focus on clinical outcomes, patient-reported outcomes, epidemiologic data, biologic subtypes, and clinician questionnaires. RESULTS: Through July 2022, 2,682 eligible patients were enrolled in 11 of 12 active countries. Sixty-six percent of patients have mHSPC, and 34% have CRPC. On the basis of self-report, 11% of patients are Black and 9% are Hispanic. Five Veterans Affairs Medical Centers are enrolling patients. Globally, 23% of patients report being veterans of military service. CONCLUSION: To our knowledge, this is the first international cohort of people newly diagnosed with advanced prostate cancer designed to describe variations in patient management, experiences, and outcomes. IRONMAN aims to identify optimal treatment sequences to improve survival, understand patient-reported outcomes, and explore novel biomarkers to understand treatment resistance mechanisms. Insights from IRONMAN will inform and guide future clinical management of people with mHSPC and CRPC. This cohort study will provide real-world evidence to facilitate a better understanding of the survivorship of people with advanced prostate cancer

Response function analysis of carbon dioxide and climate using the Padé-Laplace technique

&lt;abstract&gt;&lt;p&gt;The Padé-Laplace technique consists of approximating impulse response relations by fitting the Laplace transforms of such relations as ratios of polynomials in the transform variable. This can be used to define "reduced models" that capture the dominant behaviour of more complex systems. This approach is illustrated by analysing various aspects of the carbon cycle and its connection to climate, providing a way to capture how the interactions depend on the timescales involved. The Padé-Laplace technique is used to relate descriptions of the carbon cycle in terms of impulse response functions versus descriptions in terms of feedbacks. It is also used to discuss the concept of CO$_2$-emission equivalence. A further example analyses the gain of the climate-carbon feedback loop. This is approximated with a simple parameterization that captures the results of more complex model results and shows that the gain on timescales of centuries is as much as 3 times the gain on decadal timescales. The scope for extensions to more general aspects of the carbon system, such as the distribution of radiocarbon, is noted along with other potential extensions of this approach.&lt;/p&gt;&lt;/abstract&gt;</jats:p

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

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