Mappings preserving locations of movable poles: a new extension of the truncation method to ordinary differential equations

The truncation method is a collective name for techniques that arise from truncating a Laurent series expansion (with leading term) of generic solutions of nonlinear partial differential equations (PDEs). Despite its utility in finding Backlund transformations and other remarkable properties of integrable PDEs, it has not been generally extended to ordinary differential equations (ODEs). Here we give a new general method that provides such an extension and show how to apply it to the classical nonlinear ODEs called the Painleve equations. Our main new idea is to consider mappings that preserve the locations of a natural subset of the movable poles admitted by the equation. In this way we are able to recover all known fundamental Backlund transformations for the equations considered. We are also able to derive Backlund transformations onto other ODEs in the Painleve classification.Comment: To appear in Nonlinearity (22 pages

Non-classical symmetries and the singular manifold method: A further two examples

This paper discusses two equations with the conditional Painleve property. The usefulness of the singular manifold method as a tool for determining the non-classical symmetries that reduce the equations to ordinary differential equations with the Painleve property is confirmed once moreComment: 9 pages (latex), to appear in Journal of Physics

B\"acklund transformations for the second Painlev\'e hierarchy: a modified truncation approach

The second Painlev\'e hierarchy is defined as the hierarchy of ordinary differential equations obtained by similarity reduction from the modified Korteweg-de Vries hierarchy. Its first member is the well-known second Painlev\'e equation, P2. In this paper we use this hierarchy in order to illustrate our application of the truncation procedure in Painlev\'e analysis to ordinary differential equations. We extend these techniques in order to derive auto-B\"acklund transformations for the second Painlev\'e hierarchy. We also derive a number of other B\"acklund transformations, including a B\"acklund transformation onto a hierarchy of P34 equations, and a little known B\"acklund transformation for P2 itself. We then use our results on B\"acklund transformations to obtain, for each member of the P2 hierarchy, a sequence of special integrals.Comment: 12 pages in LaTeX 2.09 (uses ioplppt.sty), to appear in Inverse Problem

Lattice modified KdV hierarchy from a Lax pair expansion

We produce a hierarchiy of integrable equations by systematically adding terms to the Lax pair for the lattice modified KdV equation. The equations in the hierarchy are related to one aonother by recursion relations. These recursion relations are solved explicitly so that every equation in the hierarchy along with its Lax pair is known

Abundance of Pelagia noctiluca early life stages in the western Mediterranean Sea scales with surface chlorophyll

Pelagia noctiluca is the most successful and well-studied jellyfish in the Mediterranean Sea. This species tolerates a wide range of water temperatures and succeeds in low to medium food regimes, but factors driving its distribution and population dynamics remain poorly understood. Here we applied a multiscale analytical approach using survey data and a physical-biochemical coupled model to assess how environmental factors affect the 3-dimensional distribution and seasonal abundance of P. noctiluca early life stages. The surveys took place after the spring bloom, when warm water favors fecundity and growth, but food shortage limits the reproductive investment and early survival. We found that most early life stages of P. noctiluca remained above the shallow thermocline and upper mixed layer where temperature is warm. Their spatial distribution was positively correlated with surface chlorophyll concentration, and over 90% of the variation in interannual abundance was explained by basin-scale productivity in June. Warmer water during winter and spring seasons coupled with protracted spring blooms increase the population of P. noctiluca, and this explains the trend of increasing outbreaks observed in the western Mediterranean Sea over the past decades.Postprin

2022 Proposed base case model for eastern Atlantic and Mediterranean bluefin tuna assessment using stock synthesis.

This document presents the proposed base case for the assessment of Eastern Atlantic and Mediterranean population of bluefin tuna using Stock Synthesis in 2022. The model runs from 1950 to 2020 and was fitted to length composition data, conditional age-at-length (otolith and spines–length-age pairs), 16 fishing fleets and 11 indices of abundance. Growth is modeled by a Richards function with Linf fixed at 271 cm, K fixed at 0.23387, and the shape parameter is estimated by the model. A Beverton-Holt stock recruitment relationship was estimated in the model with the steepness and sigmaR fixed at 0.9 and 0.6, respectively. R0 is freely estimated. Although the diagnostics indicate an acceptable stability of the model, there are important conflicts between the catch information, length composition and index data. The model fits to length compositions were not good, but the model followed most of the indices fairly fine. The model results showed that the SSB decreased since 1950 until 1970s, remaining relatively stable at low values during the 1980-2009 period, and showing a sharp and steady increased since 2010. Model diagnostics indicated that the different source of data provides contradicting information about the stock, resulting in biases in the results

Atezolizumab in locally advanced or metastatic urothelial cancer : a pooled analysis from the Spanish patients of the IMvigor 210 cohort 2 and 211 studies

Funding: This study was funded by Roche Farma, Spain.The studies IMvigor 210 cohort 2 and IMvigor211 evaluated the efficacy of atezolizumab in patients with locally advanced or metastatic urothelial cancer (mUC) upon progression to platinum-based chemotherapy worldwide. Yet, the real impact of this drug in specific geographical regions is unknown. We combined individual-level data from the 131 patients recruited in Spain from IMvigor210 cohort 2 and IMvigor211 in a pooled analysis. Efficacy and safety outcomes were assessed in the overall study population and according to PD-L1 expression on tumour-infiltrating immune cells. Full data were available for 127 patients; 74 (58%) received atezolizumab and 53 (42%) chemotherapy. Atezolizumab patients had a numerically superior median overall survival although not reaching statistical significance (9.2 months vs 7.7 months). No statistically significant differences between arms were observed in overall response rates (20.3% vs 37.0%) or progression-free survival (2.1 months vs 5.3 months). Nonetheless, median duration of response was superior for the immunotherapy arm (non-reached vs 6.4 months; p = 0.005). Additionally, among the responders, the 12-month survival rates seemed to favour atezolizumab (66.7% vs 19.9%). When efficacy was analyzed based on PD-L1 expression status, no significant differences were found. Treatment-related adverse events of any grade occurred more frequently in the chemotherapy arm [46/57 (81%) vs 44/74 (59%)]. Patients who achieved an objective response on atezolizumab presented a longer median duration of response and numerically superior 12 month survival rates when compared with chemotherapy responders along with a more favorable safety profile. PD-L1 expression did not discriminate patients who might benefit from atezolizumab

Data and initial model set-up for the 2022 stock synthesis stock assessment of the eastern Atlantic and Mediterranean bluefin tuna.

This paper describes the data used for Stock Synthesis assessment for the Eastern Atlantic and Mediterranean bluefin tuna. The initial model configuration, fleet definitions, selectivity modeling and main parameterization are also outlined. The model runs from 1950 to 2020 and is fit to length composition data and pair age-length data treated as conditional age-at-length

DATA AND INITIAL MODEL SET-UP FOR THE 2022 STOCK SYNTHESIS STOCK ASSESSMENT OF THE EASTERN ATLANTIC AND MEDITERRANEAN BLUEFIN TUNA

This document describes the data used for Stock Synthesis assessment for the Eastern Atlantic and Mediterranean bluefin tuna. The initial model configuration, fleet definitions, selectivity modeling and main parameterization are also outlined. The model runs from 1950 to 2020 and is fit to length composition data and pair age-length data treated as conditional age-at-length.En prens