In this paper, we present a neural network approach for synchronizing audio recordings of human piano performances with their corresponding loosely aligned MIDI files. The task is addressed using a Convolutional Recurrent Neural Network (CRNN) architecture, which effectively captures spectral and temporal features by processing an unaligned piano roll and a spectrogram as inputs to estimate the aligned piano roll. To train the network, we create a dataset of piano pieces with augmented MIDI files that simulate common human timing errors. The proposed model achieves up to 20
Despite the increasing availability of recorded music, people continue to engage in live musical experiences such as multimodal live concerts. However, the dynamics of audience engagement in such contexts are largely understudied. In a classical concert experiment, we presented audiences with audio-only (AO) and audio-visual (AV) piano performances while cardiorespiratory measures were continuously recorded. To investigate engagement, cardiorespiratory synchrony was calculated using both correlation and phase coherence methods. Only correlation measures remained significant in comparison to control (circular-shifted) data. Significant synchrony measures were then assessed between modalities, both across and within music pieces. AV performances evoked higher inter-subject correlation of heart rate (ISC-HR). However, self-reported engagement did not correspond to synchrony when averaged across music pieces. On the other hand, synchronized deceleration-acceleration heart rate (HR) patterns, typical of an ‘orienting response’ (an index of directed attention), occurred within music pieces at salient events (i.e., at section boundaries). In other words, seeing musicians perform heightened audience engagement at structurally important moments in the music. These results highlight the multimodal effects of music in real-world contexts, calling for future studies to explore wider-ranging genres and contexts to better understand dynamics of audience synchrony and engagement. ### Competing Interest Statement The authors have declared no competing interest.
We consider the oblique boundary value problem of the Laplace equation for the earth’s surface as of the boundary surface, which originates e.g. from the linearized fixed boundary value problem using gravity as boundary data. We transform this problem into a strongly singular integral equation of the second kind, where its integral part exists in the sense of Cauchy’s principal value under weak conditions for the boundary surface and the oblique direction field. For its numerical solution we use the boundary element method, which has proved to be a powerful tool in engineering sciences. The boundary integral equation is discretized using both mathematical collocation and the Galerkin—Bubnov method. We discuss the pros and cons of these discretization methods and compare the results for a local solution, i.e. a solution for a bounded part of the earth’s surface. We concentrate on the numerical expenditure, the conditioning of the linear system of equations and the differences between both the single layer density values and the disturbing potential in the external space of the earth. It results that mathematical collocation is superior to Galerkin if we only consider computational expense. But for the considered strongly singular integral equation on the smoothed earth’s surface we do not have any proof of convergence at the present time. However, for all Galerkin methods asymptotic convergence of quasioptimal order have successfully been proved if the oblique direction field is not tangent anywhere to the earth’s surface.
The second order design problem is defined as the problem of finding the observational weight matrix from the configuration of the network and the dispersion matrix of its absolute or relative coordinates. In part I, the second order design problem was introduced in its canonical form and solved for a diagonal weight matrix in order to avoid correlations between the observations. Here, it is applied for model networks and the real testnet Karlsruhe. Sufficiency conditions for the existence of a diagonal observational weight matrix computed from the given matrices of configuration and coordinate dispersion are tested. Inconsistent models are approximated by a solution of type least-squares minimum-norm. The dispersion matrix of Taylor-Karman or unit type is discussed. The power of the method is demonstrated by a complete optimization of the testnet Karlsruhe.
The drawback of the classical way to construct criterion matrices for the second order design (SOD) of geodetic networks by the use of distance-dependent correlation functions is the fact, that the observation plan has no influence upon the “ideal” correlation between points. This is obvious in the case, when the coordinates of two points situated far away from each other get correlations near zero, even if they are connected by direct measurements, which implies relatively high correlations after the net adjustment itself. The paper demonstrates an alternative approach based on graph theory, which uses as parameter for the computation of ideal correlation coefficients the degree of neighbourhood between two points in the network graph, which can be determined by minimal path algorithms. The paper includes empirical correlation studies and examples for the application of the new approach. It can be shown that the SOD-approximation of criterion matrices, which have been constructed under the neighbourhood principle, is much better than that of conventional criterion matrices, especially for networks with inhomogeneous geometry.
