Some Results on the Boundary Control of Systems of Conservation Laws

This note is concerned with the study of the initial boundary value problem for systems of conservation laws from the point of view of control theory, where the initial data is fixed and the boundary data are regarded as control functions. We first consider the problem of controllability at a fixed time for genuinely nonlinear Temple class systems, and present a description of the set of attainable configurations of the corresponding solutions in terms of suitable Oleinik-type estimates. We next present a result concerning the asymptotic stabilization near a constant state for general $n\times n$ systems. Finally we show with an example that in general one cannot achieve exact controllability to a constant state in finite time.Comment: 10 pages, 4 figures, conferenc

Genetic Features of Metachronous Esophageal Cancer Developed in Hodgkin's Lymphoma or Breast Cancer Long-Term Survivors: An Exploratory Study.

Background Development of novel therapeutic drugs and regimens for cancer treatment has led to improvements in patient long-term survival. This success has, however, been accompanied by the increased occurrence of second primary cancers. Indeed, patients who received regional radiotherapy for Hodgkin's Lymphoma (HL) or breast cancer may develop, many years later, a solid metachronous tumor in the irradiated field. Despite extensive epidemiological studies, little information is available on the genetic changes involved in the pathogenesis of these solid therapy-related neoplasms. Methods Using microsatellite markers located in 7 chromosomal regions frequently deleted in sporadic esophageal cancer, we investigated loss of heterozygosity (LOH) and microsatellite instability (MSI) in 46 paired (normal and tumor) samples. Twenty samples were of esophageal carcinoma developed in HL or breast cancer long-term survivors: 14 squamous cell carcinomas (ESCC) and 6 adenocarcinomas (EADC), while 26 samples, used as control, were of sporadic esophageal cancer (15 ESCC and 11 EADC). Results We found that, though the overall LOH frequency at the studied chromosomal regions was similar among metachronous and sporadic tumors, the latter exhibited a statistically different higher LOH frequency at 17q21.31 (p = 0.018). By stratifying for tumor histotype we observed that LOH at 3p24.1, 5q11.2 and 9p21.3 were more frequent in ESCC than in EADC suggesting a different role of the genetic determinants located nearby these regions in the development of the two esophageal cancer histotypes. Conclusions Altogether, our results strengthen the genetic diversity among ESCC and EADC whether they occurred spontaneously or after therapeutic treatments. The presence of histotype-specific alterations in esophageal carcinoma arisen in HL or breast cancer long-term survivors suggests that their transformation process, though the putative different etiological origin, may retrace sporadic ESCC and EADC carcinogenesis

The boundary Riemann solver coming from the real vanishing viscosity approximation

We study a family of initial boundary value problems associated to mixed hyperbolic-parabolic systems: v^{\epsilon} _t + A (v^{\epsilon}, \epsilon v^{\epsilon}_x ) v^{\epsilon}_x = \epsilon B (v^{\epsilon} ) v^{\epsilon}_{xx} The conservative case is, in particular, included in the previous formulation. We suppose that the solutions $v^{\epsilon}$ to these problems converge to a unique limit. Also, it is assumed smallness of the total variation and other technical hypotheses and it is provided a complete characterization of the limit. The most interesting points are the following two. First, the boundary characteristic case is considered, i.e. one eigenvalue of $A$ can be $0$. Second, we take into account the possibility that $B$ is not invertible. To deal with this case, we take as hypotheses conditions that were introduced by Kawashima and Shizuta relying on physically meaningful examples. We also introduce a new condition of block linear degeneracy. We prove that, if it is not satisfied, then pathological behaviours may occur.Comment: 84 pages, 6 figures. Text changes in Sections 1 and 3.2.3. Added Section 3.1.2. Minor changes in other section

Holomorphic transforms with application to affine processes

In a rather general setting of It\^o-L\'evy processes we study a class of transforms (Fourier for example) of the state variable of a process which are holomorphic in some disc around time zero in the complex plane. We show that such transforms are related to a system of analytic vectors for the generator of the process, and we state conditions which allow for holomorphic extension of these transforms into a strip which contains the positive real axis. Based on these extensions we develop a functional series expansion of these transforms in terms of the constituents of the generator. As application, we show that for multidimensional affine It\^o-L\'evy processes with state dependent jump part the Fourier transform is holomorphic in a time strip under some stationarity conditions, and give log-affine series representations for the transform.Comment: 30 page

A Semi-Lagrangian scheme for a modified version of the Hughes model for pedestrian flow

In this paper we present a Semi-Lagrangian scheme for a regularized version of the Hughes model for pedestrian flow. Hughes originally proposed a coupled nonlinear PDE system describing the evolution of a large pedestrian group trying to exit a domain as fast as possible. The original model corresponds to a system of a conservation law for the pedestrian density and an Eikonal equation to determine the weighted distance to the exit. We consider this model in presence of small diffusion and discuss the numerical analysis of the proposed Semi-Lagrangian scheme. Furthermore we illustrate the effect of small diffusion on the exit time with various numerical experiments

An Integro-Differential Conservation Law arising in a Model of Granular Flow

We study a scalar integro-differential conservation law. The equation was first derived in [2] as the slow erosion limit of granular flow. Considering a set of more general erosion functions, we study the initial boundary value problem for which one can not adapt the standard theory of conservation laws. We construct approximate solutions with a fractional step method, by recomputing the integral term at each time step. A-priori L^\infty bounds and BV estimates yield convergence and global existence of BV solutions. Furthermore, we present a well-posedness analysis, showing that the solutions are stable in L^1 with respect to the initial data

Recombinant human erythropoietin in the treatment of chemotherapy-induced anemia and prevention of transfusion requirement associated with solid tumors: A randomized, controlled study

Background: Anemia is a common side effect of anticancer chemotherapy. Blood transfusion, previously the only available treatment for chemotherapy-induced anemia, may result insome clinical or subclinical adverse effects in the recipients. Recombinant human erythropoietin (rhEPO) provides a new treatment modality for chemotherapy-induced anemia. Patients and methods: To evaluate the effect of rhEPO onthe need for blood transfusions and on hemoglobin (Hb)concentrations, 227 patients with solid tumors and chemotherapy-induced anemia were enrolled in a randomized, controlled, clinical trial. Of 189 patients evaluable for efficacy, 101 received 5000 IU rhEPO daily s.c, while 88 patients received no treatment during the 12-week controlled phase of the study. Results: The results demonstrate a statistically significant reduction in the need for blood transfusions (28% vs. 42%, P = 0.028) and in the mean volume of packed red blood cells transfused (152 ml vs. 190 ml, p = 0.044) in patients treated with rhEPO compared to untreated controls. This effect was even more pronounced in patients receiving platinum-based chemotherapy (26% vs. 45%, % 0.038). During the controlled treatment phase, the median Hb values increased in the rhEPO patients while remaining unchanged in the control group. The response was seen in all tumor types. Conclusions: RhEPO administration at a dose of 5000 IU daily s.c. increases hemoglobin levels and reduces transfusionrequirements in chemotherapy-induced anemia, especially during platinum-based chemotherap

Randomized Phase II Trial of weekly paclitaxel alone versus trastuzumab plus weekly paclitaxel as first-line therapy of patients with Her-2 positive advanced breast cancer.

BACKGROUND: A randomized Phase II study evaluated the activity of weekly paclitaxel versus its combination with trastuzumab for treatment of patients with advanced breast cancer overexpressing HER-2. PATIENTS AND METHODS: Among 124 patients randomized, 123 are assessable for toxicity and 118 for response. Patients received weekly paclitaxel single agent (80 mg/m2) or combined with trastuzumab (4 mg/kg loading dose, then weekly 2 mg/kg). HER-2 overexpression was determined by immunohistochemistry (IHC). Patients with 2+/3+ IHC scores were eligible. IHC was compared with HER-2 serum extracellular domain (ECD). RESULTS: Patient characteristics were similar in the two arms. Both treatments were feasible and well tolerated with no grade 4 hematologic toxicity. No patient developed cardiac toxicity. The combined treatment was statistically significant superior for overall response rate (ORR) (75% vs. 56.9%; P = 0.037), particularly in the subset of IHC 3+ patients (84.5% vs. 47.5%; P = 0.00050). A statistically significant better median time to progression was seen in the subgroup with IHC 3+ (369 vs. 272 days; P = 0.030) and visceral disease (301 vs. 183 days; P = 0.0080) treated with combination. Multivariable analysis of predictive factors showed that only IHC score retained statistically significant value for ORR (P = 0.0035). CONCLUSION: Weekly paclitaxel plus trastuzumab is highly active and safe and it is superior to paclitaxel alone in patients with IHC score of 3+

Treatment of Acute Myeloid Leukemia with 20-30% Bone Marrow Blasts

The transition of patients with ≥20% <30% bone marrow (BM) blast from the FAB category of myelodysplasia to the family of acute myeloid leukemia (AML) according to the recent WHO classification has not resolved the argument as to whether the natural history and responsiveness to therapy of these diseases is comparable to that of AML with > 30% BM blast. These controversies are even more manifest when it comes to elderly patients in whom concern for intensive chemotherapy (IC) related toxicity is the critical determinant for the therapeutic choice. In fact, due to concerns of treatment-related morbidity and mortality associated with delivery of IC, approximately only 30% of all patients ≥65 years are considered eligible for this approach. Therefore, a great deal of attention has been dedicated to alternative agents such as hypomethylators (azacitidine and decitabine). Actually, these agents have shown efficacy with reduced toxicity when administered to elderly patients with 20–30% BM blasts and not eligible for IC. In the present review, we will discuss the clinical results achieved in the treatment of elderly patients with 20%–30% BM blasts AML using intensive chemotherapy (IC) or hypomethylating agents. Overall, our survey of the literature suggests that only controlled, randomized, clinical trials will answer the question as to whether hypomethylating agents has the potential to substitute for IC even in elderly patients with an optimal functional status