We investigate the critical phenomena emerging from a statistical mechanics model of musical harmony on a three-dimensional (3D) lattice, and the resulting structure of the ordered phase. In this model, each lattice site represents a tone, with nearest neighbors interacting via the perception of dissonance between them. With dissonance assumed to be an octave-wise periodic function of pitch difference, this model is a 3D XY system with the same symmetry and dimensionality as superfluid helium and models of the cosmological axion field. We use numerical simulation to observe a phase transition from disordered sound to ordered arrangements of musical pitches as a parameter analogous to the temperature is quenched towards zero. We observe the divergence of correlation length and relaxation time at the phase boundary, consistent with the critical exponents in similar systems. Furthermore, the quenched low-temperature phase of these systems displays topological defects in the form of vortex strings that thread throughout the system volume. We observe the formation of these vortex strings in accordance with the Kibble-Zurek mechanism, and discuss the structure of these vortex strings in the context of the theory of musical harmony, finding both similarities to established music theory, and uncovering new avenues to explore.
Traditionally the image quality of a particular imaging system has been limited by the particular protocol and hardware. These limits appear as bounds to the resolution, accuracy, acquisition and processing time, and much more. More recently, deep learning and other artificial intelligence methods have emerged to overcome such bounds by outsourcing information from previous scans from the same, or similar imaging systems. Tasks such as segmentation, deconvolution, multi-modality models, and overall image quality have been greatly aided and have found broad clinical application in both therapy and diagnostic imaging. We propose that super resolution (SR) is another potential application, more specifically in the situation where multiple images of the same object are obtained at once. This study investigates the relative performance difference of single image inputs vs multilayer image inputs via a convolutional neural network (CNN), in particular for a dual-layer flat panel detector. We simulate the data acquisition process through the known modulation transfer function and noise power spectrum of the detector and aim to demonstrate that SR may greatly benefit from even a single additional lossy image. To verify the effectiveness and efficiency of multilayer image SR, we benchmark against a variety of classical CNN-based SR algorithms. Our tests demonstrate that SR for radiography is an attractive and readily realisable application to the image processing process.
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