A Penalty Method for the Numerical Solution of Hamilton-Jacobi-Bellman (HJB) Equations in Finance

We present a simple and easy to implement method for the numerical solution of a rather general class of Hamilton-Jacobi-Bellman (HJB) equations. In many cases, the considered problems have only a viscosity solution, to which, fortunately, many intuitive (e.g. finite difference based) discretisations can be shown to converge. However, especially when using fully implicit time stepping schemes with their desirable stability properties, one is still faced with the considerable task of solving the resulting nonlinear discrete system. In this paper, we introduce a penalty method which approximates the nonlinear discrete system to first order in the penalty parameter, and we show that an iterative scheme can be used to solve the penalised discrete problem in finitely many steps. We include a number of examples from mathematical finance for which the described approach yields a rigorous numerical scheme and present numerical results.Comment: 18 Pages, 4 Figures. This updated version has a slightly more detailed introduction. In the current form, the paper will appear in SIAM Journal on Numerical Analysi

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

Addition of 5-fluorouracil to doxorubicin-paclitaxel sequence increases caspase-dependent apoptosis in breast cancer cell lines

INTRODUCTION: The aim of the study was to evaluate the activity of a combination of doxorubicin (Dox), paclitaxel (Pacl) and 5-fluorouracil (5-FU), to define the most effective schedule, and to investigate the mechanisms of action in human breast cancer cells. METHODS: The study was performed on MCF-7 and BRC-230 cell lines. The cytotoxic activity was evaluated by sulphorhodamine B assay and the type of drug interaction was assessed by the median effect principle. Cell cycle perturbation and apoptosis were evaluated by flow cytometry, and apoptosis-related marker (p53, bcl-2, bax, p21), caspase and thymidylate synthase (TS) expression were assessed by western blot. RESULTS: 5-FU, used as a single agent, exerted a low cytotoxic activity in both cell lines. The Dox→Pacl sequence produced a synergistic cytocidal effect and enhanced the efficacy of subsequent exposure to 5-FU in both cell lines. Specifically, the Dox→Pacl sequence blocked cells in the G2-M phase, and the addition of 5-FU forced the cells to progress through the cell cycle or killed them. Furthermore, Dox→Pacl pretreatment produced a significant reduction in basal TS expression in both cell lines, probably favoring the increase in 5-FU activity. The sequence Dox→Pacl→48-h washout→5-FU produced a synergistic and highly schedule-dependent interaction (combination index < 1), resulting in an induction of apoptosis in both experimental models regardless of hormonal, p53, bcl-2 or bax status. Apoptosis in MCF-7 cells was induced through caspase-9 activation and anti-apoptosis-inducing factor hyperexpression. In the BRC-230 cell line, the apoptotic process was triggered only by a caspase-dependent mechanism. In particular, at the end of the three-drug treatment, caspase-8 activation triggered downstream executioner caspase-3 and, to a lesser degree, caspase-7. CONCLUSION: In our experimental models, characterized by different biomolecular profiles representing the different biology of human breast cancers, the schedule Dox→Pacl→48-h washout→5-FU was highly active and schedule-dependent and has recently been used to plan a phase I/II clinical protocol

Clinical symptoms and chemotherapy completion in elderly patients with newly diagnosed acute leukemia: a retrospective comparison study with a younger cohort

<p>Abstract</p> <p>Background</p> <p>Cancer affects older adults disproportionately. The disease is often difficult to diagnose and treat due to co-morbidities and performance status, and patients tend to discontinue chemotherapy prematurely. There are no systemic studies of the reasons and factors that create a higher withdrawal rate in older acute leukemia patients. This study tried to understand the initial characteristics, blood counts and bone marrow measurements in older acute leukemia patients by comparing them with a younger group to provide information and assistance in early clinical diagnosis, treatment and reasons for treatment withdrawal.</p> <p>Methods</p> <p>Using retrospective medical record reviews, we examined clinical characteristics and chemotherapy completion status in the patients of two groups (age ≥ 60, n = 183 and age <60, n = 183) who were diagnosed with acute leukemia for the first time and were hospitalized in Union Hospital Affiliated with Fujian Medical University from 2004 to 2008.</p> <p>Results</p> <p>There were no statistical differences in initial presenting symptoms of fatigue (67.2% vs. 57.9%, <it>P</it>>0.05) and pallor (53% vs. 59.6%, <it>P</it>>0.05) between the two groups, but older patients demonstrated more underlying diseases including lung infections (25.7%, <it>P </it>= <0.001), cardiovascular disease (4.4%, <it>P </it>= 0.007), and hypertension (20.8%, <it>P </it>=< 0.001). The complete remission rate after chemotherapy (1 to 2 courses) was 49.5% in the older group and 66.7% in the younger group (χ²= 6.202, <it>P </it>= 0.013). The percentage of patients age 60 and older who prematurely discontinued chemotherapy (50.3%), mainly due to the influences of traditional Chinese concept of critical illness, financial difficulties, and intolerance to adverse reactions to chemotherapy, was significantly higher than that of younger patients (37.7%) (χ²= 5.866, <it>P </it>= 0.015).</p> <p>Conclusions</p> <p>A comprehensive approach to diagnosis, treatment selection, and toxicity management, and implementing strategies to enhance treatment compliance may improve outcomes in older adults with acute leukemia.</p

A one-mutation mathematical model can explain the age incidence of acute myeloid leukemia with mutated nucleophosmin (NPM1).

Acute myeloid leukemia with mutated NPM1 gene and aberrant cytoplasmic expression of nucleophosmin (NPMc(+) acute myeloid leukemia) shows distinctive biological and clinical features. Experimental evidence of the oncogenic potential of the nucleophosmin mutant is, however, still lacking, and it is unclear whether other genetic lesion(s), e.g. FLT3 internal tandem duplication, cooperate with NPM1 mutations in acute myeloid leukemia development. An analysis of age-specific incidence, together with mathematical modeling of acute myeloid leukemia epidemiology, can help to uncover the number of genetic events needed to cause leukemia. We collected data on age at diagnosis of acute myeloid leukemia patients from five European Centers in Germany, The Netherlands and Italy, and determined the age-specific incidence of AML with mutated NPM1 (a total of 1,444 cases) for each country. Linear regression of the curves representing age-specific rates of diagnosis per year showed similar slopes of about 4 on a double logarithmic scale. We then adapted a previously designed mathematical model of hematopoietic tumorigenesis to analyze the age incidence of acute myeloid leukemia with mutated NPM1 and found that a one-mutation model can explain the incidence curve of this leukemia entity. This model fits with the hypothesis that NPMc(+) acute myeloid leukemia arises from an NPM1 mutation with haploinsufficiency of the wild-type NPM1 allele

A one-mutation mathematical model can explain the age incidence of acute myeloid leukemia with mutated nucleophosmin (NPM1)

Acute myeloid leukemia with mutated NPM1 gene and aberrant cytoplasmic expression of nucleophosmin (NPMc+acute myeloid leukemia) shows distinctive biological and clinical features. Experimental evidence of the oncogenic potential of the nucleophosmin mutant is, however, still lacking, and it is unclear whether other genetic lesion(s), e.g. FLT3 internal tandem duplication, cooperate with NPM1 mutations in acute myeloid leukemia development. An analysis of age-specific incidence, together with mathematical modeling of acute myeloid leukemia epidemiology, can help to uncover the number of genetic events needed to cause leukemia. We collected data on age at diagnosis of acute myeloid leukemia patients from five European Centers in Germany, The Netherlands and Italy, and determined the age-specific incidence of AML with mutated NPM1 (a total of 1,444 cases) for each country. Linear regression of the curves representing age-specific rates of diagnosis per year showed similar slopes of about 4 on a double logarithmic scale. We then adapted a previously designed mathematical model of hematopoietic tumorigenesis to analyze the age incidence of acute myeloid leukemia with mutated NPM1 and found that a one-mutation model can explain the incidence curve of this leukemia entity. This model fits with the hypothesis that NPMc+acute myeloid leukemia arises from an NPM1 mutation with haploinsufficiency of the wild-type NPM1 allele

Docetaxel and gemcitabine activity in NSCLC cell lines and in primary cultures from human lung cancer

The activity of the following drugs was investigated in two established NSCLC cell lines: docetaxel, gemcitabine, vinorelbine, paclitaxel, doxorubicin (0.01, 0.1, 1 μg ml−1), cisplatin, ifosfamide (1, 2, 3 μg ml−1) and carboplatin (2, 4, 6 μg ml−1). The cytotoxic activity was evaluated by the sulphorhodamine B assay. The two most active drugs, docetaxel and gemcitabine, used singly and in association, were investigated as a function of treatment schedule. The sequence docetaxel→gemcitabine produced only a weak synergistic interaction in RAL but a strong synergism in CAEP cells. The synergistic interaction increased in both cell lines after a 48-h washout between the drug administrations. Flow cytometric analysis showed that in docetaxel→gemcitabine sequence, docetaxel produced a block in G2/M phase and, after 48 h, provided gemcitabine with a large fraction of recovered synchronized cells in the G1/S boundary, which is the specific target phase for gemcitabine. Conversely, simultaneous treatment induced an antagonistic effect in both cell lines, and the sequential scheme gemcitabine→docetaxel produced a weak synergistic effect only in RAL cells. Moreover, the synergistic interaction disappeared when washout periods of 24 or 48 h between two drug administrations were adopted. The synergistic activity of docetaxel→ 48-h washout→gemcitabine was confirmed in 11 of 14 primary cultures, which represents an important means of validating experimental results before translating them into clinical practice. © 1999 Cancer Research Campaig

An overview on the approximation of boundary Riemann problems through physical viscosity

This note aims at providing an overview of some recent results concerning the viscous approximation of so-called boundary Riemann problems for nonlinear systems of conservation laws in small total variation regimes. \ua9 2016, Sociedade Brasileira de Matem\ue1tica

Molecular landscape and prognostic impact of FLT3 -ITD insertion site in acute myeloid leukemia : RATIFY study results

In acute myeloid leukemia (AML) internal tandem duplications of the FLT3 gene (FLT3- ITD) are associated with poor prognosis. Retrospectively, we investigated the prognostic and predictive impact of FLT3 -ITD insertion site (IS) in 452 patients randomized within the RATIFY trial, which evaluated midostaurin additionally to intensive chemotherapy. Next-generation sequencing identified 908 ITDs, with 643 IS in the juxtamembrane domain (JMD) and 265 IS in the tyrosine kinase domain-1 (TKD1). According to IS, patients were categorized as JMDsole (n = 251, 55%), JMD and TKD1 (JMD/TKD1; n = 117, 26%), and TKD1sole (n = 84, 19%). While clinical variables did not differ among the 3 groups, NPM1 mutation was correlated with JMDsole (P = 0.028). Overall survival (OS) differed significantly, with estimated 4-year OS probabilities of 0.44, 0.50, and 0.30 for JMDsole, JMD/TKD1, and TKD1sole, respectively (P = 0.032). Multivariate (cause-specific) Cox models for OS and cumulative incidence of relapse using allogeneic hematopoietic cell transplantation (HCT) in first complete remission as a time-dependent variable identified TKD1sole as unfavorable and HCT as favorable factors. In addition, Midostaurin exerted a significant benefit only for JMDsole. Our results confirm the distinct molecular heterogeneity of FLT3 -ITD and the negative prognostic impact of TKD1 IS in AML that was not overcome by midostaurin