An efficient and exact dynamic programming algorithm is introduced to quantise a continuous random variable into a discrete random variable that maximises the likelihood of the quantised probability distribution for the original continuous random variable. Quantisation is often useful before statistical analysis and modelling of large discrete network models from observations of multiple contin...

where p is an empirically chosen constant (0 < 1-1 < 2). The modification in the MBTS algorithm is in the last step where the quantisation levels are calculated. In the BTS algorithm the quantisation levels are selected at cluster centres. In MBTS, they are displaced from the cluster centres to facilitate the representation of more colours within a cluster with closer quantisation colours (eqn....

In digital systems, the amplitude of a time series is quantised with finite resolution. This is a nonlinear process which introduces distortion. We develop a Bayesian, model-based approach to reducing the quantisation distortion when moving a time series, such as an audio signal, to a higher resolution medium. The signal is modelled as a discrete-time, continuous-valued autoregressive (AR) proc...

We develop a categorical compositional distributional semantics for Lambek Calculus with Relevant Modality !L*, which has limited edition of the contraction and permutation rules. The part is monoidal biclosed category coalgebra modality, very similar to structure Differential Category. instantiate this finite dimensional vector spaces linear maps via "quantisation" functors work three concrete...

Sigma-delta modulation, where a single-bit quantiser is embedded within a negative feedback loop (Fig. 1), is now a commonly-used technique for implementing high-resolution analogue-to-digital and digital-toanalogue converters (DACs), principally because of a favourable insensitivity to component tolerancing [1]. Single-bit quantisation generates relatively high levels of quantisation noise, he...

Two types of neural networks were trained and tested on a real robot for a natural landmark recognition task. The neural networks investigated were the multilayer perceptron (MLP) and learning vector quantisation (LVQ). The intended application is for autonomous vacuuming robots in completely unknown indoor environments, using a novel topological world model and region filling algorithm. A topo...

The discrimination powers of Multilayer perceptron (MLP) and Learning Vector Quantisation (LVQ) networks are compared for overlapping Gaussian distributions. It is shown, both analytically and with Monte Carlo studies, that the MLP network handles high dimensional problems in a more eecient way than LVQ. This is mainly due to the sigmoidal form of the MLP transfer function, but also to the the ...

We investigate quantisations of line bundles $\mathcal{L}$ on derived Lagrangians $X$ over $0$-shifted symplectic Artin $N$-stacks $Y$. In our setting, a deformation quantisation consists curved $A_{\infty}$ the structure sheaf $\mathcal{O}_{Y}$, equipped with morphism to ring differential operators $\mathcal{L}$; for smooth Lagrangian subvarieties algebraic varieties, this simplifies deforming...