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In this work we present a modified neural network model which is capable to simulate Markov Chains. We show how to express and train such a network, how to ensure given statistical properties reflected in the training data and we…
Traditionally, music was treated as an analogue signal and was generated manually. In recent years, music is conspicuous to technology which can generate a suite of music automatically without any human intervention. To accomplish this…
We introduce a general method for the study of memory in symbolic sequences based on higher-order Markov analysis. The Markov process that best represents a sequence is expressed as a mixture of matrices of minimal orders, enabling the…
We study the properties of the two-point spectral form factor for classically chaotic systems with spin 1/2 in the semiclassical limit, with a suitable semiclassical trace formula as our principal tool. To this end we introduce a…
Stephen Wolfram proclaimed in his 2003 seminal work "A New Kind Of Science" that simple recursive programs in the form of Cellular Automata (CA) are a promising approach to replace currently used mathematical formalizations, e.g.…
Neural Cellular Automata (NCAs) are a promising new approach to model self-organizing processes, with potential applications in life science. However, their deterministic nature limits their ability to capture the stochasticity of…
The bijection between composition structures and random closed subsets of the unit interval implies that the composition structures associated with $S \cap [0,1]$ for a self-similar random set $S\subset {\mathbb R}_+$ are those which are…
A program is a finite piece of data that produces a (possibly infinite) sequence of primitive instructions. From scratch we develop a linear notation for sequential, imperative programs, using a familiar class of primitive instructions and…
We propose a randomized first order optimization method--SEGA (SkEtched GrAdient method)-- which progressively throughout its iterations builds a variance-reduced estimate of the gradient from random linear measurements (sketches) of the…
Principal component analysis (PCA) is a widely used dimension reduction technique in machine learning and multivariate statistics. To improve the interpretability of PCA, various approaches to obtain sparse principal direction loadings have…
We study the problem of sequentially testing whether a given stochastic process is generated by a known Markov chain. Formally, given access to a stream of random variables, we want to quickly determine whether this sequence is a trajectory…
Hidden Markov Models (HMMs) are a ubiquitous tool to model time series data, and have been widely used in two main tasks of Automatic Music Transcription (AMT): note segmentation, i.e. identifying the played notes after a multi-pitch…
Studying the neurological, genetic and evolutionary basis of human vocal communication mechanisms using animal vocalization models is an important field of neuroscience. The data sets typically comprise structured sequences of syllables or…
Spike-sorting techniques attempt to classify a series of noisy electrical waveforms according to the identity of the neurons that generated them. Existing techniques perform this classification ignoring several properties of actual neurons…
In Hindustani classical music, the tabla plays an important role as a rhythmic backbone and accompaniment. In applications like computer-based music analysis, learning singing, and learning musical instruments, tabla stroke transcription,…
In this paper, we study smooth stochastic multi-level composition optimization problems, where the objective function is a nested composition of $T$ functions. We assume access to noisy evaluations of the functions and their gradients,…
RNA molecules are known to form complex secondary structures including pseudoknots. A systematic framework for the enumeration, classification and prediction of secondary structures is critical to determine the biological significance of…
Graph convolutional networks (GCNs) have gained popularity due to high performance achievable on several downstream tasks including node classification. Several architectural variants of these networks have been proposed and investigated…
We consider how to generate chemical reaction networks (CRNs) from functional specifications. We propose a two-stage approach that combines synthesis by satisfiability modulo theories and Markov chain Monte Carlo based optimisation. First,…
Recurrent Neural Networks (RNNS) are now widely used on sequence generation tasks due to their ability to learn long-range dependencies and to generate sequences of arbitrary length. However, their left-to-right generation procedure only…