An Overview on Some Results Concerning the Transport Equation and its Applications to Conservation Laws

We provide an informal overview on the theory of transport equations with non smooth velocity fields, and on some applications of this theory to the well-posedness of hyperbolic systems of conservation laws.Comment: 12 page

On the singular local limit for conservation laws with nonlocal fluxes

We give an answer to a question posed in [P. Amorim, R. Colombo, and A. Teixeira, ESAIM Math. Model. Numerics. Anal. 2015], which can be loosely speaking formulated as follows. Consider a family of continuity equations where the velocity depends on the solution via the convolution by a regular kernel. In the singular limit where the convolution kernel is replaced by a Dirac delta, one formally recovers a conservation law: can we rigorously justify this formal limit? We exhibit counterexamples showing that, despite numerical evidence suggesting a positive answer, one in general does not have convergence of the solutions. We also show that the answer is positive if we consider viscous perturbations of the nonlocal equations. In this case, in the singular local limit the solutions converge to the solution of the viscous conservation law.Comment: 26 page

Initial-boundary value problems for continuity equations with BV coefficients

We establish well-posedness of initial-boundary value problems for continuity equations with BV (bounded total variation) coefficients. We do not prescribe any condition on the orientation of the coefficients at the boundary of the domain. We also discuss some examples showing that, regardless the orientation of the coefficients at the boundary, uniqueness may be violated as soon as the BV regularity deteriorates at the boundary.Comment: 25 pages, 5 figure

Some new well-posedness results for continuity and transport equations, and applications to the chromatography system

We obtain various new well-posedness results for continuity and transport equations, among them an existence and uniqueness theorem (in the class of strongly continuous solutions) in the case of nearly incompressible vector fields, possibly having a blow-up of the BV norm at the initial time. We apply these results (valid in any space dimension) to the k x k chromatography system of conservation laws and to the k x k Keyfitz and Kranzer system, both in one space dimension.Comment: 33 pages, minor change

Diagnosing social anxiety in Parkinson’s disease: Characteristics and frequencies according to two diagnostic criteria

BACKGROUND: Studies found inconsistent frequencies of social anxiety disorder (SAD) in Parkinson’s disease (PD) (9.7%-50%). Previous reports did not test the impact of applying DSM-IV restrictive criteria that recommends the exclusion of secondary cases when diagnosing SAD in PD. OBJECTIVE: Our aim is to estimate the frequency of social anxiety according to DSM-IV criteria and according to an inclusive broader approach. Methods: One hundred and ten PD patients were assessed for the presence of SAD using SCID-I, diagnosis of social anxiety were determined according to two different criteria: following and not following DSM-IV recommendation for exclusion of cases though to be secondary to a general medical condition. RESULTS: SAD was present in 34 (31%) of patients, but 17 (15.5%) were secondary to a general medical condition. Patients with SAD were significantly younger, had earlier disease onset, had more severe PD symptoms, and were more frequently depressed. There was no difference in demographic and clinical features between primary and secondary SAD. DISCUSSION: We conclude that the use of different diagnostic criteria may have a massive impact in the estimation of frequency of SAD in PD

Fokker-Planck type equations with Sobolev diffusion coefficients and BV drift coefficients

In this paper we give an affirmative answer to an open question mentioned in [Le Bris and Lions, Comm. Partial Differential Equations 33 (2008), 1272--1317], that is, we prove the well-posedness of the Fokker-Planck type equations with Sobolev diffusion coefficients and BV drift coefficients.Comment: 11 pages. The proof has been modifie

Neoadjuvant eribulin mesylate following anthracycline and taxane in triple negative breast cancer: Results from the HOPE study

Background Eribulin mesylate (E) is indicated for metastatic breast cancer patients previously treated with anthracycline and taxane. We argued that E could also benefit patients eligible for neoadjuvant chemotherapy. Methods Patients with primary triple negative breast cancer 2 cm received doxorubicin 60 mg/m2 and paclitaxel 200 mg/m2 x 4 cycles (AT) followed by E 1.4 mg/m2 x 4 cycles. Primary endpoint was pathological complete response (pCR) rate; secondary and explorative endpoints included clinical/metabolic response rates and safety, and biomarker analysis, respectively. Using a two-stage Simon design, 43 patients were to be included provided that 4 of 13 patients had achieved pCR in the first stage of the study. Results In stage I of the study 13 women were enrolled, median age 43 years, tumor size 2–5 cm in 9/13 (69%), positive nodal status in 8/13 (61%). Main grade 3 adverse event was neutropenia (related to AT and E in 4 and 2 cases, respectively). AT followed by E induced clinical complete + partial responses in 11/13 patients (85%), pCR in 3/13 (23%). Median measurements of maximum standardized uptake value (SUVmax) resulted 13, 3, and 1.9 at baseline, after AT and E, respectively. Complete metabolic response (CMR) occurred after AT and after E in 2 and 3 cases, respectively. Notably, 2 of the 5 (40%) patients with CMR achieved pCR at surgery. Immunostaining of paired pre-/post-treatment tumor specimens showed a reduction of β-catenin, CyclinD1, Zeb-1, and c-myc expression, in the absence of N-cadherin modulation. The study was interrupted at stage I due to the lack of the required patients with pCR. Conclusions Despite the early study closure, preoperative E following AT showed clinical and biological activity in triple negative breast cancer patients. Furthermore, the modulation of β-catenin pathway core proteins, supposedly outside the domain of epithelial–mesenchymal transition, claims for further investigation. Trial registration EU Clinical Trial Register, EudraCT number 2012-004956-12

Phase III studies on novel oral anticoagulants for stroke prevention in atrial fibrillation -a look beyond the excellent results

In this overview we address the three phase III studies that compared new oral anticoagulants (dabigatran, rivaroxaban and apixaban) with warfarin in the setting of stroke prevention in atrial fibrillation. Strengths and weaknesses of the studies were examined in detail through indirect comparison. We analyze and comment the inclusion and exclusion criteria, the characteristics of randomized patients, the primary efficacy and safety end points and side effects. All new oral anticoagulants resulted in being non-inferior to vitamin K antagonists in reducing stroke or systemic embolism in patients with atrial fibrillation. Dabigatran 150 mg and apixaban were superior to vitamin K antagonists. Importantly, new oral anticoagulants significantly reduced hemorrhagic stroke in all three studies. Major differences among new oral anticoagulants include the way they are eliminated and side effects. Both dabigatran and apixaban were tested in low- to moderate-risk patients (mean CHADS2 [Congestive heart failure, Hypertension, Age, Diabetes, Stroke] score = 2.1-2.2) whereas rivaroxaban was tested in high-risk patients (mean CHADS2 score = 3.48) and at variance with dabigatran and apixaban was administered once daily. Apixaban significantly reduced mortality from any cause. The choice of a new oral anticoagulant should take into account these and other differences between the new drugs