Counting and computing regions of DD-decomposition: algebro-geometric approach

New methods for $D$-decomposition analysis are presented. They are based on topology of real algebraic varieties and computational real algebraic geometry. The estimate of number of root invariant regions for polynomial parametric families of polynomial and matrices is given. For the case of two parametric family more sharp estimate is proven. Theoretic results are supported by various numerical simulations that show higher precision of presented methods with respect to traditional ones. The presented methods are inherently global and could be applied for studying $D$-decomposition for the space of parameters as a whole instead of some prescribed regions. For symbolic computations the Maple v.14 software and its package RegularChains are used.Comment: 16 pages, 8 figure

Analytic Metaphysics versus Naturalized Metaphysics: The Relevance of Applied Ontology

The relevance of analytic metaphysics has come under criticism: Ladyman & Ross, for instance, have suggested do discontinue the field. French & McKenzie have argued in defense of analytic metaphysics that it develops tools that could turn out to be useful for philosophy of physics. In this article, we show first that this heuristic defense of metaphysics can be extended to the scientific field of applied ontology, which uses constructs from analytic metaphysics. Second, we elaborate on a parallel by French & McKenzie between mathematics and metaphysics to show that the whole field of analytic metaphysics, being useful not only for philosophy but also for science, should continue to exist as a largely autonomous field

Associations between mothers’ perceptions of the cost of fruit and vegetables and children’s diets : Will children pay the price?

Background/Objectives: Perceptions that fruit and vegetables are expensive are more common among the socio-economically disadvantaged groups and are linked to poor dietary outcomes. Such perceptions may be exacerbated in countries recently affected by natural disasters, where devastation of fruit and vegetable crops has resulted in increase in prices of fruit and vegetables. Examining the associations of perceptions of fruit and vegetable affordability and children\u27s diets can offer insights into how the high prices of fruit and vegetables might have an impact on the diets of children.Subjects/Methods: We analysed the data from 546 socio-economically disadvantaged mother&ndash;child pairs to assess the relationship between maternal perceptions of fruit and vegetable affordability and the diets of their children.Results: Fruit consumption was lower among children whose mothers felt the cost of fruit was too high. Maternal perceptions of fruit and vegetable affordability were not associated with any other aspect of child\u27s diet.Conclusions: Our results suggest a possible role for maternal perceptions of fruit affordability in children\u27s diet, though further research is warranted.<br /

Design of high-magnetic field gradient sources for controlling magnetically induced flow of ferrofluids in microfluidic systems

The use of miniature electromagnets for ferrofluid-actuated liquid dispensing into microfluidic channels has been investigated by numerical simulations using the finite element method and measurements of fluid displacement and flow rate. The simulations illustrate the effect of structural and geometrical parameters of single and paired solenoid coils on the magnetic force experienced by the ferrofluid. Dual solenoids were used for extended fluid displacement. Ferrofluid positioning and flow rates were controlled also by using a solenoid with an iron core. The experimental measurements of fluidflow in capillaries were used to validate the modeling calculations. The results can be used as a basis for the development of on-chip ferrofluid-based devices integrated with microfluidic architectures

Non-Parametric Approximations for Anisotropy Estimation in Two-dimensional Differentiable Gaussian Random Fields

Spatially referenced data often have autocovariance functions with elliptical isolevel contours, a property known as geometric anisotropy. The anisotropy parameters include the tilt of the ellipse (orientation angle) with respect to a reference axis and the aspect ratio of the principal correlation lengths. Since these parameters are unknown a priori, sample estimates are needed to define suitable spatial models for the interpolation of incomplete data. The distribution of the anisotropy statistics is determined by a non-Gaussian sampling joint probability density. By means of analytical calculations, we derive an explicit expression for the joint probability density function of the anisotropy statistics for Gaussian, stationary and differentiable random fields. Based on this expression, we obtain an approximate joint density which we use to formulate a statistical test for isotropy. The approximate joint density is independent of the autocovariance function and provides conservative probability and confidence regions for the anisotropy parameters. We validate the theoretical analysis by means of simulations using synthetic data, and we illustrate the detection of anisotropy changes with a case study involving background radiation exposure data. The approximate joint density provides (i) a stand-alone approximate estimate of the anisotropy statistics distribution (ii) informed initial values for maximum likelihood estimation, and (iii) a useful prior for Bayesian anisotropy inference.Comment: 39 pages; 8 figure

Price Setting in the Euro Area: Some Stylized Facts from Individual Consumer Price Data.

This paper documents patterns of price setting at the retail level in the euro area. A set of stylized facts on the frequency and size of price changes is presented along with an econometric investigation of their main determinants. Price adjustment in the euro area can be summarized in six stylized facts. First, prices of most products change rarely. The average monthly frequency of price adjustment is 15 p.c., compared to about 25 p.c. in the US. Second, the frequency of price changes is characterized by substantial cross-product heterogeneity and pronounced sectoral patterns: prices of (oil-related) energy and unprocessed food products change very often, while price adjustments are less frequent for processed food products, non-energy industrial goods and services. Third, cross-country heterogeneity exists but is less pronounced. Fourth, price decreases are not uncommon. Fifth, price increases and decreases are sizeable compared to aggregate and sectoral inflation rates. Sixth, price changes are not highly synchronized across price-setters. Moreover, the frequency of price changes in the euro area is related to a number of factors, in particular seasonality, outlet type, indirect taxation, use of attractive prices as well as aggregate or product-specific inflation.Price-setting ; consumer price ; frequency of price change.

Nanoscale temperature measurements using non-equilibrium Brownian dynamics of a levitated nanosphere

Einstein realised that the fluctuations of a Brownian particle can be used to ascertain properties of its environment. A large number of experiments have since exploited the Brownian motion of colloidal particles for studies of dissipative processes, providing insight into soft matter physics, and leading to applications from energy harvesting to medical imaging. Here we use optically levitated nanospheres that are heated to investigate the non-equilibrium properties of the gas surrounding them. Analysing the sphere's Brownian motion allows us to determine the temperature of the centre-of-mass motion of the sphere, its surface temperature and the heated gas temperature in two spatial dimensions. We observe asymmetric heating of the sphere and gas, with temperatures reaching the melting point of the material. This method offers new opportunities for accurate temperature measurements with spatial resolution on the nanoscale, and a new means for testing non-equilibrium thermodynamicsComment: 5 pages, 4 figures, supplementary material available upon reques

Microstructural damage of the posterior corpus callosum contributes to the clinical severity of neglect

One theory to account for neglect symptoms in patients with right focal damage invokes a release of inhibition of the right parietal cortex over the left parieto-frontal circuits, by disconnection mechanism. This theory is supported by transcranial magnetic stimulation studies showing the existence of asymmetric inhibitory interactions between the left and right posterior parietal cortex, with a right hemispheric advantage. These inhibitory mechanisms are mediated by direct transcallosal projections located in the posterior portions of the corpus callosum. The current study, using diffusion imaging and tract-based spatial statistics (TBSS), aims at assessing, in a data-driven fashion, the contribution of structural disconnection between hemispheres in determining the presence and severity of neglect. Eleven patients with right acute stroke and 11 healthy matched controls underwent MRI at 3T, including diffusion imaging, and T1-weighted volumes. TBSS was modified to account for the presence of the lesion and used to assess the presence and extension of changes in diffusion indices of microscopic white matter integrity in the left hemisphere of patients compared to controls, and to investigate, by correlation analysis, whether this damage might account for the presence and severity of patients' neglect, as assessed by the Behavioural Inattention Test (BIT). None of the patients had any macroscopic abnormality in the left hemisphere; however, 3 cases were discarded due to image artefacts in the MRI data. Conversely, TBSS analysis revealed widespread changes in diffusion indices in most of their left hemisphere tracts, with a predominant involvement of the corpus callosum and its projections on the parietal white matter. A region of association between patients' scores at BIT and brain FA values was found in the posterior part of the corpus callosum. This study strongly supports the hypothesis of a major role of structural disconnection between the right and left parietal cortex in determining 'neglect'