The evolution of the orbit distance in the double averaged restricted 3-body problem with crossing singularities

We study the long term evolution of the distance between two Keplerian confocal trajectories in the framework of the averaged restricted 3-body problem. The bodies may represent the Sun, a solar system planet and an asteroid. The secular evolution of the orbital elements of the asteroid is computed by averaging the equations of motion over the mean anomalies of the asteroid and the planet. When an orbit crossing with the planet occurs the averaged equations become singular. However, it is possible to define piecewise differentiable solutions by extending the averaged vector field beyond the singularity from both sides of the orbit crossing set. In this paper we improve the previous results, concerning in particular the singularity extraction technique, and show that the extended vector fields are Lipschitz-continuous. Moreover, we consider the distance between the Keplerian trajectories of the small body and of the planet. Apart from exceptional cases, we can select a sign for this distance so that it becomes an analytic map of the orbital elements near to crossing configurations. We prove that the evolution of the 'signed' distance along the averaged vector field is more regular than that of the elements in a neighborhood of crossing times. A comparison between averaged and non-averaged evolutions and an application of these results are shown using orbits of near-Earth asteroids.Comment: 29 pages, 8 figure

Imatinib in combination with everolimus in patients with progressive advanced chordoma: results form an Italian phase 2 clinical trial

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MICROBIAL PROCESSING OF ORGANIC WASTE STREAMS INTO PHAs AND OTHER HIGH VALUE BIO-PRODUCTS

In the last years, economic and environmental concerns arose for oil shortage and climate change; for these reasons the scientific community focused on possible oil substitutes. In this perspectives, the production of new energy, materials and chemicals of non-fossil origin, could be based on biological resources such as biomasses. The efforts of the microbiology group of DAFNAE are mainly devoted to the exploitation of waste and residual biomasses for the production of high value bio-products such as polyhydroxyalkanoates (PHAs), bioethanol and biohydrogen. PHAs are today considered among the most promising substitutes for petrol-based plastics nevertheless their substitution over the conventional plastics is limited by their expensive manufacturing because of the costly raw materials used as carbon sources and the complex downstream phase of PHAs recovery from bacterial cells. Possible solutions could be i) the utilization of cheap wastes of agro-food origin as carbon sources and ii) the simplification of downstream purification processes. To these aims, Cupriavidus necator DSM545, a well-known PHAs accumulator, has been genetically modified in order to acquire the ability of metabolizing lactose from whey (dairy industry) or lipids (from slaughterhouse) and the capacity to produce nuclease to facilitate downstream processes. In the first case, the modified strains resulted able to grow using whey or lipids as carbon sources, accumulating up to 30 and 60% of PHAs, respectively. In the second case, the recombinant C. necator DSM 545 resulted in an effective decrease of viscosity of bacterial cells lysates, thus avoiding the use of costly commercial nucleases for an efficient downstream. Bioethanol is a fuel obtained from renewable resources and it could be a promising alternative to petrol fuels. First generation bioethanol is mainly produced from corn and sugarcane, thus conflicting with food and feed production . On the contrary, bioethanol from residual and lignocellulosic biomass has environmental impact lower than fossil fuels and would not threaten food supplies. Unfortunately, Saccharomyces cerevisiae, the yeast used for industrial bioethanol production, is not equipped with suitable hydrolytic activities and thus cannot directly utilize starchy and lignocellulosic wastes as feedstock without the use of commercial enzymes. Recent studies were focused to develop a \u201cConsolidated bioprocessing\u201d (CBP), approach where a single yeast is able to hydrolyse starch and lignocellulose and ferment the resulting sugars into ethanol. . With this purpose, novel and robust S. cerevisiae strains were recently engineered at DAFNAE to secrete efficient cellulases and amylases for the efficient saccharification and fermentation of starchy and cellulosic by-products up to 65 g/L ethanol

Euler configurations and quasi-polynomial systems

In the Newtonian 3-body problem, for any choice of the three masses, there are exactly three Euler configurations (also known as the three Euler points). In Helmholtz' problem of 3 point vortices in the plane, there are at most three collinear relative equilibria. The "at most three" part is common to both statements, but the respective arguments for it are usually so different that one could think of a casual coincidence. By proving a statement on a quasi-polynomial system, we show that the "at most three" holds in a general context which includes both cases. We indicate some hard conjectures about the configurations of relative equilibrium and suggest they could be attacked within the quasi-polynomial framework.Comment: 21 pages, 6 figure

Surgical management of retroperitoneal sarcoma and opportunities for global collaboration

Retroperitoneal sarcomas (RPS) are rare cancers that often reach massive size before detection. The mainstay of treatment for RPS is surgical resection, and complete resection is the only chance for potential cure. The management of RPS can be challenging and in individual cases, radiation and systemic therapy may be beneficial in both primary and recurrent disease. Further research through multi-institutional collaboration, ideally on a global level, is needed to better understand RPS and optimize management of this disease

2018 ESMO Sarcoma and GIST Symposium: take-home messages' in soft tissue sarcoma

The 7th edition of the ESMO Sarcoma and GIST Symposium' was held in Milan in February 2018. For the first time, the Symposium brought together representatives from the European Reference Network on rare adult solid cancer (EURACAN) joined by sarcoma experts from the USA, Japan and patient advocacy groups, to share insights and discuss future directions in this rare condition. This commentary will summarise the highlights in soft tissue sarcomas

SYT-SSX fusion genes and prognosis in synovial sarcoma

A case series of 64 synovial sarcomas was characterized for the SYT-SSX fusion transcripts and statistically analysed in order to correlate molecular data with prognosis and morphology. SYT-SSX1 fusion transcript appeared to be an independent, though not reaching statistical significance (P = 0.183), prognostic factor clearly associated with a reduced metastasis-free survival. Regarding the association between transcript type and histologic subtype we found, a borderline P value (P = 0.067) between the SYT-SSX1 transcript and the biphasic subtype which, subsequently expanding the analysis to 70 cases, turned out to be significant. However, we could not confirm the prediction value of the biphasic subtype for the presence of the SYT-SSX1 transcript since in our hands 6 out 33 (18%) biphasic tumours carried the SYT-SSX2 transcript.© 2001 Cancer Research Campaign  http://www.bjcancer.co

Perioperative Management of Extremity Soft Tissue Sarcomas

Biological, physical and clinical aspects of cancer treatment with ionising radiatio

High-Dose Ifosfamide Chemotherapy in a Series of Patients Affected by Myxoid Liposarcoma

Background. To report on the activity of high-dose prolonged-infusion ifosfamide (HDIFX) chemotherapy in a retrospective series of patients affected by myxoid liposarcoma treated at Fondazione IRCCS Istituto Nazionale dei Tumori in Milan, Italy. Patients and Methods. Patients with an advanced myxoid liposarcoma treated with HDIFX (14 g/sqm, i.v., prolonged infusion of 14 days every 28 days) as a single agent between May 2002 and April 2017 were retrospectively reviewed. All pathologic diagnoses were centrally reviewed and molecularly confirmed. Response was evaluated by RECIST, and survival functions were computed by the Kaplan-Meier method. Results. Eleven patients with advanced myxoid liposarcoma were treated with HDIFX (male/female = 9/2, median age 33 years, range 31-75). Among these, 1/11 received HDIFX in first line, 5/11 in second line, 3/11 in third line, and 2/11 in fourth line for a median course number of 3 (range 2-7). No RECIST objective responses were observed. Overall median progression-free survival was 1,9 months. Median overall survival was 37 months. At a median follow-up of 115 months, 1 patient is alive. Conclusions. In this series of patients affected by advanced myxoid liposarcoma, chemotherapy with HDIFX was essentially inactive