Computation of an integral basis of quartic number field

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Fast numerical algorithms for the computation of invariant tori in Hamiltonian systems

In this paper, we develop numerical algorithms that use small requirements of storage and operations for the computation of invariant tori in Hamiltonian systems (exact symplectic maps and Hamiltonian vector fields). The algorithms are based on the parameterization method and follow closely the proof of the KAM theorem given in [LGJV05] and [FLS07]. They essentially consist in solving a functional equation satisfied by the invariant tori by using a Newton method. Using some geometric identities, it is possible to perform a Newton step using little storage and few operations. In this paper we focus on the numerical issues of the algorithms (speed, storage and stability) and we refer to the mentioned papers for the rigorous results. We show how to compute efficiently both maximal invariant tori and whiskered tori, together with the associated invariant stable and unstable manifolds of whiskered tori. Moreover, we present fast algorithms for the iteration of the quasi-periodic cocycles and the computation of the invariant bundles, which is a preliminary step for the computation of invariant whiskered tori. Since quasi-periodic cocycles appear in other contexts, this section may be of independent interest. The numerical methods presented here allow to compute in a unified way primary and secondary invariant KAM tori. Secondary tori are invariant tori which can be contracted to a periodic orbit. We present some preliminary results that ensure that the methods are indeed implementable and fast. We postpone to a future paper optimized implementations and results on the breakdown of invariant tori.

Reduced quality of life associated adverse events in intermediate hepatocellular carcinoma patients treated with PRECISION TACE with drug eluting beads: Results from the PRECISION V randomized trial : B-241

Purpose: To evaluate the extent of quality of life (QoL) associated adverse events (AEs) following PRECISION TACE with DC Bead compared with conventional transarterial chemoembolisation (cTACE). Methods and Materials: 201 intermediate HCC patients were treated with DC Bead (PRECISION TACE) or conventional TACE (cTACE) with doxorubicin in the PRECISION V clinical study. 93 patients were treated with DC Bead and 108 Patients with cTACE every 2 months and followed up for 6 months. AEs were classified according to the South West Oncology Group criteria. QoL associated AEs were defined as alopecia, constipation, nausea, vomiting, pyrexia, chills, asthenia, fatigue, and headache. Results: The biggest difference in QoL associated AEs was for alopecia: 2 patients (2.2%) for DC-Bead versus 21 patients (19.4%) for cTACE. For other clinical symptoms, constipation (n=10; 10.8% vs. n=13; 12%), vomiting (n=10; 10.8% vs. n=14; 13.0%), pyrexia (n=16; 17.2% vs. n=26; 24.1%), chills (n=1; 1.1% vs. n=5; 4.6%), and headache (n=2; 2.2% vs. n=8; 7.4%) showed lower incidence in the DC Bead group versus cTACE. Nausea, n= 15; 13.9% (n=15; 16.1%) and fatigue, n=6; 5.6% (n=13; 14.0%) were lower for cTACE. Total dose of doxorubicin was on average 35% higher in the DC Bead group. Conclusion: Although patients in the DC Bead group received a higher doxorubicin dose, less QoL associated AEs were reported for this group. Alopecia, the most obvious outward sign of toxicity, was only reported in a tenth of DC Bead patients. Thus, PRECISION TACE with DC Bead improves quality of life associated adverse events.

Repositioning precision of coronary arteries measured on X-ray angiography and its implications for coronary MR angiography.

BACKGROUND: To test the hypothesis that intervals with superior beat-to-beat coronary artery repositioning precision exist in the cardiac cycle, to design a coronary MR angiography (MRA) methodology in response, and to ascertain its performance. METHODS: Coronary repositioning precision in consecutive heartbeats was measured on x-ray coronary angiograms of 17 patients and periods with the highest repositioning precision were identified. In response, the temporal order of coronary MRA pulse sequence elements required modification and the T2 -prep now follows (T2 -post) rather than precedes the imaging part of the sequence. The performance of T2 -post was quantitatively compared (signal-to-noise [SNR], contrast-to-noise [CNR], vessel sharpness) to that of T2 -prep in vivo. RESULTS: Coronary repositioning precision is <1 mm at peak systole and in mid diastole. When comparing systolic T2 -post to diastolic T2 -prep, CNR and vessel sharpness remained unchanged (both P = NS) but SNR for muscle and blood increased by 104% and 36% (both P < 0.05), respectively. CONCLUSION: Windows with improved coronary repositioning precision exist in the cardiac cycle: one in peak systole and one in mid diastole. Peak-systolic imaging necessitates a re-design of conventional coronary MRA pulse sequences and leads to image quality very similar to that of conventional mid-diastolic data acquisition but improved SNR. J. Magn. Reson. Imaging 2015;41:1251-1258. © 2014 Wiley Periodicals, Inc.

A mixed finite element method for nonlinear diffusion equations

We propose a mixed finite element method for a class of nonlinear diffusion equations, which is based on their interpretation as gradient flows in optimal transportation metrics. We introduce an appropriate linearization of the optimal transport problem, which leads to a mixed symmetric formulation. This formulation preserves the maximum principle in case of the semi-discrete scheme as well as the fully discrete scheme for a certain class of problems. In addition solutions of the mixed formulation maintain exponential convergence in the relative entropy towards the steady state in case of a nonlinear Fokker-Planck equation with uniformly convex potential. We demonstrate the behavior of the proposed scheme with 2D simulations of the porous medium equations and blow-up questions in the Patlak-Keller-Segel model.

Nash equilibrium strategies in discrete-time finite-horizon dynamic games with risk-and effort-averse players

The objective of this paper is to re-examine the risk-and effort attitude in the context of strategic dynamic interactions stated as a discrete-time finite-horizon Nash game. The analysis is based on the assumption that players are endogenously risk-and effort-averse. Each player is characterized by distinct risk-and effort-aversion types that are unknown to his opponent. The goal of the game is the optimal risk-and effort-sharing between the players. It generally depends on the individual strategies adopted and, implicitly, on the the players' types or characteristics.

Prospective randomized study of doxorubicin-eluting-bead embolization in the treatment of hepatocellular carcinoma: results of the PRECISION V study.

Transcatheter arterial chemoembolization (TACE) offers a survival benefit to patients with intermediate hepatocellular carcinoma (HCC). A widely accepted TACE regimen includes administration of doxorubicin-oil emulsion followed by gelatine sponge-conventional TACE. Recently, a drug-eluting bead (DC Bead) has been developed to enhance tumor drug delivery and reduce systemic availability. This randomized trial compares conventional TACE (cTACE) with TACE with DC Bead for the treatment of cirrhotic patients with HCC. Two hundred twelve patients with Child-Pugh A/B cirrhosis and large and/or multinodular, unresectable, N0, M0 HCCs were randomized to receive TACE with DC Bead loaded with doxorubicin or cTACE with doxorubicin. Randomization was stratified according to Child-Pugh status (A/B), performance status (ECOG 0/1), bilobar disease (yes/no), and prior curative treatment (yes/no). The primary endpoint was tumor response (EASL) at 6 months following independent, blinded review of MRI studies. The drug-eluting bead group showed higher rates of complete response, objective response, and disease control compared with the cTACE group (27% vs. 22%, 52% vs. 44%, and 63% vs. 52%, respectively). The hypothesis of superiority was not met (one-sided P = 0.11). However, patients with Child-Pugh B, ECOG 1, bilobar disease, and recurrent disease showed a significant increase in objective response (P = 0.038) compared to cTACE. DC Bead was associated with improved tolerability, with a significant reduction in serious liver toxicity (P < 0.001) and a significantly lower rate of doxorubicin-related side effects (P = 0.0001). TACE with DC Bead and doxorubicin is safe and effective in the treatment of HCC and offers a benefit to patients with more advanced disease.

Analysis of a finite volume element method for the Stokes problem

In this paper we propose a stabilized conforming finite volume element method for the Stokes equations. On stating the convergence of the method, optimal a priori error estimates in different norms are obtained by establishing the adequate connection between the finite volume and stabilized finite element formulations. A superconvergence result is also derived by using a postprocessing projection method. In particular, the stabilization of the continuous lowest equal order pair finite volume element discretization is achieved by enriching the velocity space with local functions that do not necessarily vanish on the element boundaries. Finally, some numerical experiments that confirm the predicted behavior of the method are provided.

Evolutionary and convergence stability for continuous phenotypes in finite populations derived from two-allele models.

The evolution of a quantitative phenotype is often envisioned as a trait substitution sequence where mutant alleles repeatedly replace resident ones. In infinite populations, the invasion fitness of a mutant in this two-allele representation of the evolutionary process is used to characterize features about long-term phenotypic evolution, such as singular points, convergence stability (established from first-order effects of selection), branching points, and evolutionary stability (established from second-order effects of selection). Here, we try to characterize long-term phenotypic evolution in finite populations from this two-allele representation of the evolutionary process. We construct a stochastic model describing evolutionary dynamics at non-rare mutant allele frequency. We then derive stability conditions based on stationary average mutant frequencies in the presence of vanishing mutation rates. We find that the second-order stability condition obtained from second-order effects of selection is identical to convergence stability. Thus, in two-allele systems in finite populations, convergence stability is enough to characterize long-term evolution under the trait substitution sequence assumption. We perform individual-based simulations to confirm our analytic results.

3D gait assessment in young and elderly subjects using foot-worn inertial sensors.

This study describes the validation of a new wearable system for assessment of 3D spatial parameters of gait. The new method is based on the detection of temporal parameters, coupled to optimized fusion and de-drifted integration of inertial signals. Composed of two wirelesses inertial modules attached on feet, the system provides stride length, stride velocity, foot clearance, and turning angle parameters at each gait cycle, based on the computation of 3D foot kinematics. Accuracy and precision of the proposed system were compared to an optical motion capture system as reference. Its repeatability across measurements (test-retest reliability) was also evaluated. Measurements were performed in 10 young (mean age 26.1±2.8 years) and 10 elderly volunteers (mean age 71.6±4.6 years) who were asked to perform U-shaped and 8-shaped walking trials, and then a 6-min walking test (6MWT). A total of 974 gait cycles were used to compare gait parameters with the reference system. Mean accuracy±precision was 1.5±6.8cm for stride length, 1.4±5.6cm/s for stride velocity, 1.9±2.0cm for foot clearance, and 1.6±6.1° for turning angle. Difference in gait performance was observed between young and elderly volunteers during the 6MWT particularly in foot clearance. The proposed method allows to analyze various aspects of gait, including turns, gait initiation and termination, or inter-cycle variability. The system is lightweight, easy to wear and use, and suitable for clinical application requiring objective evaluation of gait outside of the lab environment.

On finite unions and finite products with the D-property

We show that the product of a subparacompact C-scattered space and a Lindelöf D-space is D. In addition, we show that every regular locally D-space which is the union of a finite collection of subparacompact spaces and metacompact spaces has the D-property. Also, we extend this result from the class of locally D-spaces to the wider class of D-scattered spaces. All the results are shown in a direct way.

Hybrid Multiscale Finite Volume method for two-phase flow in porous media

We present a novel hybrid (or multiphysics) algorithm, which couples pore-scale and Darcy descriptions of two-phase flow in porous media. The flow at the pore-scale is described by the Navier?Stokes equations, and the Volume of Fluid (VOF) method is used to model the evolution of the fluid?fluid interface. An extension of the Multiscale Finite Volume (MsFV) method is employed to construct the Darcy-scale problem. First, a set of local interpolators for pressure and velocity is constructed by solving the Navier?Stokes equations; then, a coarse mass-conservation problem is constructed by averaging the pore-scale velocity over the cells of a coarse grid, which act as control volumes; finally, a conservative pore-scale velocity field is reconstructed and used to advect the fluid?fluid interface. The method relies on the localization assumptions used to compute the interpolators (which are quite straightforward extensions of the standard MsFV) and on the postulate that the coarse-scale fluxes are proportional to the coarse-pressure differences. By numerical simulations of two-phase problems, we demonstrate that these assumptions provide hybrid solutions that are in good agreement with reference pore-scale solutions and are able to model the transition from stable to unstable flow regimes. Our hybrid method can naturally take advantage of several adaptive strategies and allows considering pore-scale fluxes only in some regions, while Darcy fluxes are used in the rest of the domain. Moreover, since the method relies on the assumption that the relationship between coarse-scale fluxes and pressure differences is local, it can be used as a numerical tool to investigate the limits of validity of Darcy's law and to understand the link between pore-scale quantities and their corresponding Darcy-scale variables.

Random mating with a finite number of matings.

Random mating is the null model central to population genetics. One assumption behind random mating is that individuals mate an infinite number of times. This is obviously unrealistic. Here we show that when each female mates a finite number of times, the effective size of the population is substantially decreased.

Reduced quality of life associated adverse events in intermediate hepatocellular carcinoma patients treated with PRECISION TACE with drug eluting beads: Results from the PRECISION V randomized trial

Purpose: To evaluate the extent of quality of life (QoL) associated adverse events (AEs) following PRECISION TACE with DC Bead compared with conventional transarterial chemoembolisation (cTACE). Methods and Materials: 201 intermediate HCC patients were treated with DC Bead (PRECISION TACE) or conventional TACE (cTACE) with doxorubicin in the PRECISION V clinical study. 93 patients were treated with DC Bead and 108 Patients with cTACE every 2 months and followed up for 6 months. AEs were classified according to the South West Oncology Group criteria. QoL associated AEs were defined as alopecia, constipation, nausea, vomiting, pyrexia, chills, asthenia, fatigue, and headache. Results: The biggest difference in QoL associated AEs was for alopecia: 2 patients (2.2%) for DC-Bead versus 21 patients (19.4%) for cTACE. For other clinical symptoms, constipation (n=10; 10.8% vs. n=13; 12%), vomiting (n=10; 10.8% vs. n=14; 13.0%), pyrexia (n=16; 17.2% vs. n=26; 24.1%), chills (n=1; 1.1% vs. n=5; 4.6%), and headache (n=2; 2.2% vs. n=8; 7.4%) showed lower incidence in the DC Bead group versus cTACE. Nausea, n= 15; 13.9% (n=15; 16.1%) and fatigue, n=6; 5.6% (n=13; 14.0%) were lower for cTACE. Total dose of doxorubicin was on average 35% higher in the DC Bead group. Conclusion: Although patients in the DC Bead group received a higher doxorubicin dose, less QoL associated AEs were reported for this group. Alopecia, the most obvious outward sign of toxicity, was only reported in a tenth of DC Bead patients. Thus, PRECISION TACE with DC Bead improves quality of life associated adverse events.