Common parietal activation in musical mental transformations across pitch and time

We previously observed that mental manipulation of the pitch level or temporal organization of melodies results in functional activation in the human intraparietal sulcus (IPS), a region also associated with visuospatial transformation and numerical calculation. Two outstanding questions about these musical transformations are whether pitch and time depend on separate or common processing in IPS, and whether IPS recruitment in melodic tasks varies depending upon the degree of transformation required (as it does in mental rotation). In the present study we sought to answer these questions by applying functional magnetic resonance imaging while musicians performed closely matched mental transposition (pitch transformation) and melody reversal (temporal transformation) tasks. A voxel-wise conjunction analysis showed that in individual subjects, both tasks activated overlapping regions in bilateral IPS, suggesting that a common neural substrate subserves both types of mental transformation. Varying the magnitude of mental pitch transposition resulted in variation of IPS BOLD signal in correlation with the musical key-distance of the transposition, but not with the pitch distance, indicating that the cognitive metric relevant for this type of operation is an abstract one, well described by music-theoretic concepts. These findings support a general role for the IPS in systematically transforming auditory stimulus representations in a nonspatial context. (C) 2013 Elsevier Inc. All rights reserved.

Auditory Imagery and the Poor-Pitch Singer

The vocal imitation of pitch by singing requires one to plan laryngeal movements on the basis of anticipated target pitch events. This process may rely on auditory imagery, which has been shown to activate motor planning areas. As such, we hypothesized that poor-pitch singing, although not typically associated with deficient pitch perception, may be associated with deficient auditory imagery. Participants vocally imitated simple pitch sequences by singing, discriminated pitch pairs on the basis of pitch height, and completed an auditory imagery self-report questionnaire (the Bucknell Auditory Imagery Scale). The percentage of trials participants sung in tune correlated significantly with self-reports of vividness for auditory imagery, although not with the ability to control auditory imagery. Pitch discrimination was not predicted by auditory imagery scores. The results thus support a link between auditory imagery and vocal imitation.

An integral conservative gridding--algorithm using Hermitian curve interpolation

The problem of re-sampling spatially distributed data organized into regular or irregular grids to finer or coarser resolution is a common task in data processing. This procedure is known as 'gridding' or 're-binning'. Depending on the quantity the data represents, the gridding-algorithm has to meet different requirements. For example, histogrammed physical quantities such as mass or energy have to be re-binned in order to conserve the overall integral. Moreover, if the quantity is positive definite, negative sampling values should be avoided. The gridding process requires a re-distribution of the original data set to a user-requested grid according to a distribution function. The distribution function can be determined on the basis of the given data by interpolation methods. In general, accurate interpolation with respect to multiple boundary conditions of heavily fluctuating data requires polynomial interpolation functions of second or even higher order. However, this may result in unrealistic deviations (overshoots or undershoots) of the interpolation function from the data. Accordingly, the re-sampled data may overestimate or underestimate the given data by a significant amount. The gridding-algorithm presented in this work was developed in order to overcome these problems. Instead of a straightforward interpolation of the given data using high-order polynomials, a parametrized Hermitian interpolation curve was used to approximate the integrated data set. A single parameter is determined by which the user can control the behavior of the interpolation function, i.e. the amount of overshoot and undershoot. Furthermore, it is shown how the algorithm can be extended to multidimensional grids. The algorithm was compared to commonly used gridding-algorithms using linear and cubic interpolation functions. It is shown that such interpolation functions may overestimate or underestimate the source data by about 10-20%, while the new algorithm can be tuned to significantly reduce these interpolation errors. The accuracy of the new algorithm was tested on a series of x-ray CT-images (head and neck, lung, pelvis). The new algorithm significantly improves the accuracy of the sampled images in terms of the mean square error and a quality index introduced by Wang and Bovik (2002 IEEE Signal Process. Lett. 9 81-4).

Hermitian curve interpolation for CT-data re-sampling

Purpose: Development of an interpolation algorithm for re‐sampling spatially distributed CT‐data with the following features: global and local integral conservation, avoidance of negative interpolation values for positively defined datasets and the ability to control re‐sampling artifacts. Method and Materials: The interpolation can be separated into two steps: first, the discrete CT‐data has to be continuously distributed by an analytic function considering the boundary conditions. Generally, this function is determined by piecewise interpolation. Instead of using linear or high order polynomialinterpolations, which do not fulfill all the above mentioned features, a special form of Hermitian curve interpolation is used to solve the interpolation problem with respect to the required boundary conditions. A single parameter is determined, by which the behavior of the interpolation function is controlled. Second, the interpolated data have to be re‐distributed with respect to the requested grid. Results: The new algorithm was compared with commonly used interpolation functions based on linear and second order polynomial. It is demonstrated that these interpolation functions may over‐ or underestimate the source data by about 10%–20% while the parameter of the new algorithm can be adjusted in order to significantly reduce these interpolation errors. Finally, the performance and accuracy of the algorithm was tested by re‐gridding a series of X‐ray CT‐images. Conclusion: Inaccurate sampling values may occur due to the lack of integral conservation. Re‐sampling algorithms using high order polynomialinterpolation functions may result in significant artifacts of the re‐sampled data. Such artifacts can be avoided by using the new algorithm based on Hermitian curve interpolation

Effect of high order interpolation in the stability and efficiency of the time-integration process in vorticity-velocity CFD algorithms

The numerical solution of the incompressible Navier-Stokes Equations offers an effective alternative to the experimental analysis of Fluid-Structure interaction i.e. dynamical coupling between a fluid and a solid which otherwise is very complex, time consuming and very expensive. To have a method which can accurately model these types of mechanical systems by numerical solutions becomes a great option, since these advantages are even more obvious when considering huge structures like bridges, high rise buildings, or even wind turbine blades with diameters as large as 200 meters. The modeling of such processes, however, involves complex multiphysics problems along with complex geometries. This thesis focuses on a novel vorticity-velocity formulation called the KLE to solve the incompressible Navier-stokes equations for such FSI problems. This scheme allows for the implementation of robust adaptive ODE time integration schemes and thus allows us to tackle the various multiphysics problems as separate modules. The current algorithm for KLE employs a structured or unstructured mesh for spatial discretization and it allows the use of a self-adaptive or fixed time step ODE solver while dealing with unsteady problems. This research deals with the analysis of the effects of the Courant-Friedrichs-Lewy (CFL) condition for KLE when applied to unsteady Stoke’s problem. The objective is to conduct a numerical analysis for stability and, hence, for convergence. Our results confirmthat the time step ∆t is constrained by the CFL-like condition ∆t ≤ const. hα, where h denotes the variable that represents spatial discretization.

Some Notes on the Composition of "Copper Pitch"

A supply of so-called "copper pitch" ore was received by the Montana Bureau of Mines and Geology in response to a request by them from a resident of Kalispell, who had previously sent a specimen to the Bureau for a mineralogical analysis. Since this material was little known and had apparently received but little study under a reflec­ting microscope, it was thought that such a study might throw some light on the mineralogical and chemical composition of the material.

Amalgamation and interpolation in ordered algebras

The first part of this paper provides a comprehensive and self-contained account of the interrelationships between algebraic properties of varieties and properties of their free algebras and equational consequence relations. In particular, proofs are given of known equivalences between the amalgamation property and the Robinson property, the congruence extension property and the extension property, and the flat amalgamation property and the deductive interpolation property, as well as various dependencies between these properties. These relationships are then exploited in the second part of the paper in order to provide new proofs of amalgamation and deductive interpolation for the varieties of lattice-ordered abelian groups and MV-algebras, and to determine important subvarieties of residuated lattices where these properties hold or fail. In particular, a full description is given of all subvarieties of commutative GMV-algebras possessing the amalgamation property.

Precipitation isoscape of high reliefs: interpolation scheme designed and tested for monthly resolved precipitation oxygen isotope records of an Alpine domain

Stable oxygen isotope composition of atmospheric precipitation (δ18Op) was scrutinized from 39 stations distributed over Switzerland and its border zone. Monthly amount-weighted δ18Op values averaged over the 1995–2000 period showed the expected strong linear altitude dependence (−0.15 to −0.22‰ per 100 m) only during the summer season (May–September). Steeper gradients (~ −0.56 to −0.60‰ per 100 m) were observed for winter months over a low elevation belt, while hardly any altitudinal difference was seen for high elevation stations. This dichotomous pattern could be explained by the characteristically shallower vertical atmospheric mixing height during winter season and provides empirical evidence for recently simulated effects of stratified atmospheric flow on orographic precipitation isotopic ratios. This helps explain "anomalous" deflected altitudinal water isotope profiles reported from many other high relief regions. Grids and isotope distribution maps of the monthly δ18Op have been calculated over the study region for 1995–1996. The adopted interpolation method took into account both the variable mixing heights and the seasonal difference in the isotopic lapse rate and combined them with residual kriging. The presented data set allows a point estimation of δ18Op with monthly resolution. According to the test calculations executed on subsets, this biannual data set can be extended back to 1992 with maintained fidelity and, with a reduced station subset, even back to 1983 at the expense of faded reliability of the derived δ18Op estimates, mainly in the eastern part of Switzerland. Before 1983, reliable results can only be expected for the Swiss Plateau since important stations representing eastern and south-western Switzerland were not yet in operation.