On solutions of the transport equation in the presence of singularities

We consider the transport equation on $[0,T]\times \R^n$ in the situation where the vector field is $BV$ off a set $S\subset [0,T]\times \R^n$. We demonstrate that solutions exist and are unique provided that the set of singularities has a sufficiently small anisotropic fractal dimension and the normal component of the vector field is sufficiently integrable near the singularities. This result improves upon recent results of Ambrosio who requires the vector field to be of bounded variation everywhere. In addition, we demonstrate that under these conditions almost every trajectory of the associated regular Lagrangian flow does not intersect the set $S$ of singularities. Finally, we consider the particular case of an initial set of singularities that evolve in time so the singularities consists of curves in the phase space, which is typical in applications such as vortex dynamics. We demonstrate that solutions of the transport equation exist and are unique provided that the box-counting dimension of the singularities is bounded in terms of the H\"older exponent of the curves

The EU and US : friends or rivals

As boas relações entre a União Europeia e os EUA são essenciais para a estabilidade global. Mas as actuais relações transatlânticas permanecem constrangidas sobretudo como resultado da guerra no Iraque e da abordagem unilateral da primeira administração George W. Bush. As divergências entre UE-EUA têm aumentado nas áreas políticas e estratégicas bem como nas áreas económicas e sociais. Uma das maiores divergências incide sobre a governação global e sobre o papel atribuído à ONU e a outras instituições multilaterais. Também existe um elevado grau de anti-americanismo (ou de oposição às políticas da administração Bush) na Europa, e de ressentimento para com a Europa (ou melhor, para com a França e Alemanha) nos EUA. A UE não tem ideia de como lidar com a única superpotência mundial. Normalmente prefere- se o bilateral aos canais europeus. Mas as actuais estruturas UE-EUA não permitem uma discussão séria sobre muitas destas diferenças. Nem a OTAN é uma estrutura adequada para um diálogo estratégico transatlântico, como o chanceler Schroeder referiu na Conferencia Wehrkunde, em Munique, em Janeiro de 2005

The Cauchy problem for the 3-D Vlasov-Poisson system with point charges

In this paper we establish global existence and uniqueness of the solution to the three-dimensional Vlasov-Poisson system in presence of point charges in case of repulsive interaction. The present analysis extends an analogeous two-dimensional result by Caprino and Marchioro [On the plasma-charge model, to appear in Kinetic and Related Models (2010)].Comment: 28 page

Human thyroid tumours, the puzzling lessons from E7 and RET/PTC3 transgenic mice

Human rearranged RET/PTC3 (papillary thyroid carcinoma) proto-oncogene and high-risk human papillomavirus (HPV) type 16 E7 oncogene induces in the mouse a neoplastic transformation of thyroid follicular cells. We present a detailed immuno-histological study (170 mouse thyroids: RET/PTC3, E7, wild type, 2- to 10-month-old) with cell cycle proliferation and signalling pathway indicators. The characteristics of both models are different. There is an ‘oncogene dependent' cellular signature, maintained at all studied ages in the E7 model, less in the RET/PTC3 model. During tumour development a large heterogeneity occurred in the Tg-RET/PTC3 model within a same tumour or within a same thyroid lobe. The Tg-E7 model was less heterogeneous, with a dominant goitrous pattern. The solid tumour already described in the RET/PTC3 models associated with cribriform patterns, suggested ‘PTC spindle cell changes' as in humans PTC rather than the equivalent of the solid human PTC. Proliferation and apoptosis in the two thyroid models are related to the causal oncogene rather than reflect a general tumorigenic process. The thyroids of RET/PTC3 mice appeared as a partial and transient model of human PTCs, whereas the Tg-E7 mice do not belong to the usual PTC type

Tc-99m-NTP 15-5 assessment of the early therapeutic response of chondrosarcoma to zoledronic acid in the Swarm rat orthotopic model

Background: Since proteoglycans (PGs) appear as key partners in chondrosarcoma biology, PG-targeted imaging using the radiotracer 99mTc-N-(triethylammonium)-3-propyl-[15]ane-N5 (99mTc-NTP 15-5) developed by our group was previously demonstrated to be a good single-photon emission computed tomography tracer for cartilage neoplasms. We therefore initiated this new preclinical study to evaluate the relevance of 99mTc-NTP 15-5 imaging for the in vivo monitoring and quantitative assessment of chondrosarcoma response to zoledronic acid (ZOL) in the Swarm rat orthotopic model. Findings: Rats bearing chondrosarcoma in the orthotopic paratibial location were treated by ZOL (100 μg/kg, subcutaneously) or phosphate-buffered saline, twice a week, from day 4 to day 48 post-tumor implantation. 99mTc-NTP 15-5 imaging was performed at regular intervals with the target-to-background ratio (TBR) determined. Tumor volume was monitored using a calliper, and histology was performed at the end of the study. From day 11 to day 48, mean TBR values ranged from 1.7 ± 0.6 to 2.3 ± 0.6 in ZOL-treated rats and from 2.1 ± 1.0 to 4.9 ± 0.9 in controls. Tumor growth inhibition was evidenced using a calliper from day 24 and associated to a decrease in PG content in treated tumor tissues (confirmed by histology). Conclusions: This work demonstrated two proofs of concept: (1) biphosphonate therapy could be a promising therapeutic approach for chondrosarcoma; (2) 99mTc-NTP 15-5 is expected to offer a novel imaging modality for the in vivo evaluation of the extracellular matrix features of chondrosarcoma, which could be useful for the follow-up and quantitative assessment of proteoglycan ‘downregulation’ associated to the response to therapeutic attempts

Ginzburg-Landau vortex dynamics with pinning and strong applied currents

We study a mixed heat and Schr\"odinger Ginzburg-Landau evolution equation on a bounded two-dimensional domain with an electric current applied on the boundary and a pinning potential term. This is meant to model a superconductor subjected to an applied electric current and electromagnetic field and containing impurities. Such a current is expected to set the vortices in motion, while the pinning term drives them toward minima of the pinning potential and "pins" them there. We derive the limiting dynamics of a finite number of vortices in the limit of a large Ginzburg-Landau parameter, or \ep \to 0, when the intensity of the electric current and applied magnetic field on the boundary scale like \lep. We show that the limiting velocity of the vortices is the sum of a Lorentz force, due to the current, and a pinning force. We state an analogous result for a model Ginzburg-Landau equation without magnetic field but with forcing terms. Our proof provides a unified approach to various proofs of dynamics of Ginzburg-Landau vortices.Comment: 48 pages; v2: minor errors and typos correcte

Follicular thyroid lesions: Is there a discriminatory potential in the computerized nuclear analysis?

Background: Computerized image analysis seems to represent a promising diagnostic possibility for thyroid tumors. Our aim was to evaluate the discriminatory diagnostic efficiency of computerized image analysis of cell nuclei from histological materials of follicular tumors. Methods: We studied paraffin-embedded materials from 42 follicular adenomas (FA), 47 follicular variants of papillary carcinomas (FVPC) and 20 follicular carcinomas (FC) by the software ImageJ. Based on the nuclear morphometry and chromatin texture, the samples were classified as FA, FC or FVPC using the Classification and Regression Trees method. Results: We observed high diagnostic sensitivity and specificity rates (FVPC: 89.4% and 100%; FC: 95.0% and 92.1%; FA: 90.5 and 95.5%, respectively). When the tumors were compared by pairs (FC vs FA, FVPC vs FA), 100% of the cases were classified correctly. Conclusion: The computerized image analysis of nuclear features showed to be a useful diagnostic support tool for the histological differentiation between follicular adenomas, follicular variants of papillary carcinomas and follicular carcinomas.This study received financial support from Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP; process number 2014/10028-2), and PIBIC/PROPE-Unesp (process number 33347). The authors thank to Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP; process number 2014/10028-2), and PIBIC/PROPE-Unesp (process number 33347) for the research support and to Marcos Roberto Franchi and Luiz Fernando Franchi for the help in processing the histological material

Promising pre-clinical validation of targeted radionuclide therapy using a [131I] labelled iodoquinoxaline derivative for an effective melanoma treatment

Targeted internal radionuclide therapy (TRT) would be an effective alternative to current therapies for dissemi- nated melanoma treatment. At our institution, a class of iodobenzamides has been developed as potent melanoma- seeking agents. This review described the preclinical vali- dations of a quinoxaline derivative molecule (ICF01012) as tracer for TRT application. It was selected for its high, specific and long-lasting uptake in tumour with rapid clear- ance from non-target organs providing suitable dosimetry parameters for TRT. Extended in vivo study of metabolic profiles confirmed durable tumoural concentration of the unchanged molecule form. Moreover melanin specificity of ICF01012 was determined by binding assay with syn- thetic melanin and in vivo by SIMS imaging. Then, we showed in vivo that [131I] ICF01012 treatment drastically inhibited growth of B16F0, B16Bl6 and M4Beu tumours whereas [131I] NaI or unlabelled ICF01012 treatment was without significant effect. Histological analysis showed that residual tumour cells exhibit a significant loss of aggres- siveness after treatment. This anti-tumoural effect was associated with a lengthening of the treated-mice survival time and an inhibition of lung dissemination for B16Bl6 model. Results presented here support the concept of TRT using a [131I] labelled iodoquinoxaline derivative for an effective melanoma treatment.<br /