Certification of Bounds of Non-linear Functions: the Templates Method

The aim of this work is to certify lower bounds for real-valued multivariate functions, defined by semialgebraic or transcendental expressions. The certificate must be, eventually, formally provable in a proof system such as Coq. The application range for such a tool is widespread; for instance Hales' proof of Kepler's conjecture yields thousands of inequalities. We introduce an approximation algorithm, which combines ideas of the max-plus basis method (in optimal control) and of the linear templates method developed by Manna et al. (in static analysis). This algorithm consists in bounding some of the constituents of the function by suprema of quadratic forms with a well chosen curvature. This leads to semialgebraic optimization problems, solved by sum-of-squares relaxations. Templates limit the blow up of these relaxations at the price of coarsening the approximation. We illustrate the efficiency of our framework with various examples from the literature and discuss the interfacing with Coq.Comment: 16 pages, 3 figures, 2 table

The Thermal Explosion Synthesis of AlNi Monitored by Neutron Thermodiffractometry

The synthesis of AlNi from thermally activated equimolar powder mixtures of aluminium and nickel was monitored in situ and acquired diffraction patterns every 2 s or less. The analysis of diffraction patterns permitted establishment of its kinetics, which could be modeled according to an equation expressed as kt=[α/(1-α)]3/2. From 1530 to an activation energy of 9 ± 2 kJ mol−1 was estimated. Also, the crystallite size evolution on cooling was established to vary from ≈14 nm at 1530 °C to ≈28 nm at 180 °C. Finally, the reaction was found to occur through the melting of aluminium and the subsequent dissolving of nickel to form the polycrystalline single-phase product, AlNi

Exploiting Evolution for an Adaptive Drift-Robust Classifier in Chemical Sensing

Gas chemical sensors are strongly affected by drift, i.e., changes in sensors' response with time, that may turn statistical models commonly used for classification completely useless after a period of time. This paper presents a new classifier that embeds an adaptive stage able to reduce drift effects. The proposed system exploits a state-of-the-art evolutionary strategy to iteratively tweak the coefficients of a linear transformation able to transparently transform raw measures in order to mitigate the negative effects of the drift. The system operates continuously. The optimal correction strategy is learnt without a-priori models or other hypothesis on the behavior of physical-chemical sensors. Experimental results demonstrate the efficacy of the approach on a real problem

Magnetic properties of the Kagom mixed compounds CoxNi1 x 3V2O8

The magnetic properties of the mixed compounds CoxNi1 x 3 V2O8 CNVO investigated by magnetization and neutron diffraction measurements are presented. Unlike their parent compounds Ni3V2O8 NVO and Co3V2O8 CVO , only one magnetic phase transition into an antiferromagnetic phase was detected for powder samples with x 0.27, 0.52, and 0.76. The magnetic structures are modulated according to a propagation vector k delta,0,0 with delta being dependent on the composition parameter x. Furthermore, magnetization data of a CVO single crystal is featured, which is qualitatively different from previous publications and exhibits a controversial aspect concerning the behavior of the curve under an applied magnetic field along the b axi

Current Distribution in the Three-Dimensional Random Resistor Network at the Percolation Threshold

We study the multifractal properties of the current distribution of the three-dimensional random resistor network at the percolation threshold. For lattices ranging in size from $8^3$ to $80^3$ we measure the second, fourth and sixth moments of the current distribution, finding {\it e.g.\/} that $t/\nu=2.282(5)$ where $t$ is the conductivity exponent and $\nu$ is the correlation length exponent.Comment: 10 pages, latex, 8 figures in separate uuencoded fil

High-resolution transthoracic echocardiography accurately detects pulmonary arterial pressure and decreased right ventricular contractility in a mouse model of pulmonary fibrosis and secondary pulmonary hypertension

BACKGROUND: To date, assessment of right ventricular (RV) function in mice has relied extensively on invasive measurements. Echocardiographic advances have allowed adaptation of measures used in humans for serial, noninvasive RV functional assessment in mice. We evaluated the diagnostic performance of tricuspid annular plane systolic excursion (TAPSE), RV peak systolic myocardial velocity (s'), RV myocardial performance index (MPI), and RV fractional area change (FAC) in a mouse model of pulmonary hypertension. METHODS AND RESULTS: Echocardiography was performed on mice at baseline and 3 weeks after induction of pulmonary hypertension using inhaled bleomycin or saline, including adapted measures of TAPSE, s', MPI, and FAC. RV systolic pressure was measured by invasive catheterization, and RV contractility was measured as the peak slope of the RV systolic pressure recording (maximum change pressure/change time). Postmortem morphological assessment of RV hypertrophy was performed. RV systolic pressure was elevated and maximum change pressure/change time was reduced in bleomycin versus control (n=8; P=0.002). Compared with controls, bleomycin mice had reduced TAPSE (0.79±0.05 versus 1.06±0.04 mm; P=0.003), s' (21.3±1.2 versus 29.2±1.3 mm/s; P<0.001), and FAC (20.3±0.7% versus 31.0±1.3%; P<0.001), whereas MPI was increased (0.51±0.03 versus 0.37±0.01; P=0.006). All measures correlated with RV systolic pressure and maximum change pressure/change time. Intraobserver and interobserver variability were minimal. Receiver operating characteristic curves demonstrated that TAPSE (<0.84 mm), s'(<23.3 mm/s), MPI (0.42), and FAC (<23.3%) identified maximum change pressure/change time ≤2100 mm Hg/s with high accuracy. CONSLUSIONS: TAPSE, s', MPI, and FAC are measurable consistently using high-resolution echocardiography in mice, and are sensitive and specific measures of pulmonary pressure and RV function. This validation opens the opportunity for serial noninvasive measures in mouse models of pulmonary hypertension, enhancing the statistical power of preclinical studies of novel therapeutics

Low-temperature electron dephasing time in AuPd revisited

Ever since the first discoveries of the quantum-interference transport in mesoscopic systems, the electron dephasing times, $\tau_\phi$, in the concentrated AuPd alloys have been extensively measured. The samples were made from different sources with different compositions, prepared by different deposition methods, and various geometries (1D narrow wires, 2D thin films, and 3D thickfilms) were studied. Surprisingly, the low-temperature behavior of $\tau_\phi$ inferred by different groups over two decades reveals a systematic correlation with the level of disorder of the sample. At low temperatures, where $\tau_\phi$ is (nearly) independent of temperature, a scaling $\tau_\phi^{\rm max} \propto D^{-\alpha}$ is found, where $tau_\phi^{\rm max}$ is the maximum value of $\tau_\phi$ measured in the experiment, $D$ is the electron diffusion constant, and the exponent $\alpha$ is close to or slightly larger than 1. We address this nontrivial scaling behavior and suggest that the most possible origin for this unusual dephasing is due to dynamical structure defects, while other theoretical explanations may not be totally ruled out.Comment: to appear in Physica E, Proceedings for the International Seminar and Workshop "Quantum Coherence, Noise, and Decoherence in Nanostructures", 15-26 May 2006, Dresde

Elucidating Individual Magnetic Contributions in Bi-Magnetic Fe3O4/Mn3O4 Core/Shell Nanoparticles by Polarized Powder Neutron Diffraction

Heterogeneous bi-magnetic nanostructured systems have had a sustained interest during the last decades owing to their unique magnetic properties and the wide range of derived potential applications. However, elucidating the details of their magnetic properties can be rather complex. Here, a comprehensive study of Fe3O4/Mn3O4 core/shell nanoparticles using polarized neutron powder diffraction, which allows disentangling the magnetic contributions of each of the components, is presented. The results show that while at low fields the Fe3O4 and Mn3O4 magnetic moments averaged over the unit cell are antiferromagnetically coupled, at high fields, they orient parallel to each other. This magnetic reorientation of the Mn3O4 shell moments is associated with a gradual evolution with the applied field of the local magnetic susceptibility from anisotropic to isotropic. Additionally, the magnetic coherence length of the Fe3O4 cores shows some unusual field dependence due to the competition between the antiferromagnetic interface interaction and the Zeeman energies. The results demonstrate the great potential of the quantitative analysis of polarized neutron powder diffraction for the study of complex multiphase magnetic materials

Phase transitions in a ferrofluid at magnetic field induced microphase separation

In the presence of a magnetic field applied perpendicular to a thin sample layer, a suspension of magnetic colloidal particles (ferrofluid) can form spatially modulated phases with a characteristic length determined by the competition between dipolar forces and short-range forces opposing density variations. We introduce models for thin-film ferrofluids in which magnetization and particle density are viewed as independent variables and in which the non-magnetic properties of the colloidal particles are described either by a lattice-gas entropy or by the Carnahan-Starling free energy. Our description is particularly well suited to the low-particle density regions studied in many experiments. Within mean-field theory, we find isotropic, hexagonal and stripe phases, separated in general by first-order phase boundaries.Comment: 12 pages, RevTex, to appear in PR

Elucidating Individual Magnetic Contributions in Bi-Magnetic Fe3O4/Mn3O4 Core/Shell Nanoparticles by Polarized Powder Neutron Diffraction

Heterogeneous bi-magnetic nanostructured systems have had a sustained interest during the last decades owing to their unique magnetic properties and the wide range of derived potential applications. However, elucidating the details of their magnetic properties can be rather complex. Here, a comprehensive study of FeO/MnO core/shell nanoparticles using polarized neutron powder diffraction, which allows disentangling the magnetic contributions of each of the components, is presented. The results show that while at low fields the FeO and MnO magnetic moments averaged over the unit cell are antiferromagnetically coupled, at high fields, they orient parallel to each other. This magnetic reorientation of the MnO shell moments is associated with a gradual evolution with the applied field of the local magnetic susceptibility from anisotropic to isotropic. Additionally, the magnetic coherence length of the FeO cores shows some unusual field dependence due to the competition between the antiferromagnetic interface interaction and the Zeeman energies. The results demonstrate the great potential of the quantitative analysis of polarized neutron powder diffraction for the study of complex multiphase magnetic materials