Rank-revealing top-down ULV factorizations

Rank-revealing ULV and URV factorizations are useful tools to determine the rank and to compute bases for null-spaces of a matrix. However, in the practical ULV (resp. URV ) factorization each left (resp. right) null vector is recomputed from its corresponding right (resp. left) null vector via triangular solves. Triangular solves are required at initial factorization, refinement and updating. As a result, algorithms based on these factorizations may be expensive, especially on parallel computers where triangular solves are expensive. In this paper we propose an alternative approach. Our new rank-revealing ULV factorization, which we call ¨top-down¨ ULV factorization ( TDULV -factorization) is based on right null vectors of lower triangular matrices and therefore no triangular solves are required. Right null vectors are easy to estimate accurately using condition estimators such as incremental condition estimator (ICE). The TDULV factorization is shown to be equivalent to the URV factorization with the advantage of circumventing triangular solves

Analytical Solutions for Systems of Singular Partial Differential-Algebraic Equations

This paper proposes power series method (PSM) in order to find solutions for singular partial differential-algebraic equations (SPDAEs). We will solve three examples to show that PSM method can be used to search for analytical solutions of SPDAEs. What is more, we will see that, in some cases, Padé posttreatment, besides enlarging the domain of convergence, may be employed in order to get the exact solution from the truncated series solutions of PSM

Analytical Solutions for Systems of Singular Partial Differential-Algebraic Equations

This paper proposes power series method (PSM) in order to find solutions for singular partial differential-algebraic equations (SPDAEs). We will solve three examples to show that PSM method can be used to search for analytical solutions of SPDAEs. What is more, we will see that, in some cases, Padé posttreatment, besides enlarging the domain of convergence, may be employed in order to get the exact solution from the truncated series solutions of PSM

Central Configurations and Action Minimizing Orbits in Kite Four-Body Problem

In the current article, we study the kite four-body problems with the goal of identifying global regions in the mass parameter space which admits a corresponding central configuration of the four masses. We consider two different types of symmetrical configurations. In each of the two cases, the existence of a continuous family of central configurations for positive masses is shown. We address the dynamical aspect of periodic solutions in the settings considered and show that the minimizers of the classical action functional restricted to the homographic solutions are the Keplerian elliptical solutions. Finally, we provide numerical explorations via Poincaré cross-sections, to show the existence of periodic and quasiperiodic solutions within the broader dynamical context of the four-body problem

Differential Operators Homotopy Perturbation Method (DOHPM): an automated selection procedure for Adjustment Parameters

This paper proposes a modified version of HPM method (DOHPM method), introducing in a systematic fashion, adjustment parameters in order to obtain analytical approximate solutions for nonlinear differential equations by using certain differential operators to turn a nonlinear differential equation into other of higher order. Comparison with exact solution shows that DOHPM method is highly efficient if the initial guess is chosen adequatel

Modified Hyperspheres Algorithm to Trace Homotopy Curves of Nonlinear Circuits Composed by Piecewise Linear Modelled Devices

We present a homotopy continuation method (HCM) for finding multiple operating points of nonlinear circuits composed of devices modelled by using piecewise linear (PWL) representations. We propose an adaptation of the modified spheres path tracking algorithm to trace the homotopy trajectories of PWL circuits. In order to assess the benefits of this proposal, four nonlinear circuits composed of piecewise linear modelled devices are analysed to determine their multiple operating points. The results show that HCM can find multiple solutions within a single homotopy trajectory. Furthermore, we take advantage of the fact that homotopy trajectories are PWL curves meant to replace the multidimensional interpolation and fine tuning stages of the path tracking algorithm with a simple and highly accurate procedure based on the parametric straight line equation

Survival of patients with advanced melanoma enrolled in phase II trials involving hogh dose II-2: A case record based analysis

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Results of interleukin-2-based treatment in advanced melanoma: a case record-based analysis of 631 patients

In patients with stage IV melanoma, durable responses have been reported with treatment regimens that involve high-dose interleukin-2 (IL-2). We analyze long-term results of 631 melanoma patients from 12 institutions who had received IL-2 alone, in combination with interferon alfa 2a or 2b (IFNalpha), or with cytotoxic drugs. Case records that contained pretreatment parameters, response data, and updated survival information were collected. After univariate analysis, the multivariate evaluation of the impact of pretreatment parameters on response and survival was performed by logistic regression and Cox's regression, respectively. Patients were divided into four groups according to treatment: IL-2 alone (n=117), IL-2 and chemotherapy (n=49), IL-2 and IFNalpha (n=153), and IL-2, chemotherapy, and IFNalpha (n=312). The median survival of all patients was 10.5 months and the 2- and 5-year survival rates were 19.9% and 10.4%, respectively. Independent prognostic factors for response and survival were entirely different, treatment group being the only significant factor for response, and serum lactate dehydrogenase (LDH), metastatic site, and performance predicting survival. The addition of IFNalpha to IL-2 was associated with prolonged survival, but the effect of additional chemotherapy was less obvious. Serum LDH, metastatic site, and performance status are useful stratification factors for randomized trials in metastatic melanoma. The improved long-term survival rates observed in melanoma patients treated with IL-2/IFNalpha-containing regimens are notable in contrast to the reported 5-year survival rates of 2% to 6% achieved with chemotherapy, but because selection bias cannot be ruled out, the impact of IL-2, as well as all other components of the treatment regimens, on survival needs to be confirmed in prospective randomized trial