This paper discusses the theory of dithered and noise-shaped quantisation, and in particular their application to Nyquist rate digital audio. Dither is shown to be essential if quantisation-related distortion is to be avoided. Careful application of noise-shaping is shown to be of audible beneet by increasing the perceived dynamic range of a signal. Various drawbacks of the technique are discus...

We study measures in Banach space which arise as the skew convolution product of two other measures where the convolution is deformed by a skew map. This is the structure that underlies both the theory of Mehler semigroups and operator selfdecomposable measures. We show how that given such a set-up the skew map can be lifted to an operator that acts at the level of function spaces and demonstra...

This paper compares the latency, accuracy, training time and hardware costs of neural networks compressed with our new multi-objective evolutionary algorithm called NEMOKD, quantisation. We evaluate NEMOKD on Intel’s Movidius Myriad X VPU processor, quantisation Xilinx’s programmable Z7020 FPGA hardware. Evolving models increases inference accuracy by up to 82% at cost 38% increased throughput ...

This study considers linear filtering methods for minimising the end-to-end average distortion of a fixed-rate source quantisation system. For the source encoder, both scalar and vector quantisation are considered. The codebook index output by the encoder is sent over a noisy discrete memoryless channel whose statistics could be unknown at the transmitter. At the receiver, the code vector corre...

one of unsolved problems in quantum measurement theory is to characterize coexistence of quantum effects. in this paper, applying positive operator matrix theory, we give a mathematical characterization of the witness set of coexistence of quantum effects and obtain a series of properties of coexistence. we also devote to characterizing bijective morphisms on quantum effects leaving the witness...

Colour-based retrieval is one of the major content-based retrieval techniques. The main idea used for colour based retrieval techniques is to store the image in terms of a colour map which has a nite set of colour bins. An eecient retrieval scheme should preserve all the distinct colours of an image with a small number of colour bins. Uniform Quantisation is one of the major quantisation techni...

The discrete cosine transform (DCT) is widely applied in modern codecs to remove spatial redundancies, with the resulting DCT coefficients being quantised to achieve compression as well as bit-rate control. In distributed video coding (DVC) architectures like DISCOVER, DCT coefficient quantisation is traditionally performed using predetermined quantisation matrices (QM), which means the compres...

We discuss semiclassical states in quantum gravity corresponding to Schwarzschild as well as Reissner-Nordström black holes. We show that reduced quantisation of these models is equivalent to Wheeler-DeWitt quantisation with a particular factor ordering. We then demonstrate how the entropy of black holes can be consistently calculated from these states. While this leads to the Bekenstein-Hawkin...

The topological recursion of Eynard and Orantin governs a variety of problems in enumerative geometry and mathematical physics. The recursion uses the data of a spectral curve to define an infinite family of multidifferentials. It has been conjectured that, under certain conditions, the spectral curve possesses a non-commutative quantisation whose associated differential operator annihilates th...