An review of automatic drum transcription

In Western popular music, drums and percussion are an important means to emphasize and shape the rhythm, often defining the musical style. If computers were able to analyze the drum part in recorded music, it would enable a variety of rhythm-related music processing tasks. Especially the detection and classification of drum sound events by computational methods is considered to be an important and challenging research problem in the broader field of Music Information Retrieval. Over the last two decades, several authors have attempted to tackle this problem under the umbrella term Automatic Drum Transcription(ADT).This paper presents a comprehensive review of ADT research, including a thorough discussion of the task-specific challenges, categorization of existing techniques, and evaluation of several state-of-the-art systems. To provide more insights on the practice of ADT systems, we focus on two families of ADT techniques, namely methods based on Nonnegative Matrix Factorization and Recurrent Neural Networks. We explain the methods’ technical details and drum-specific variations and evaluate these approaches on publicly available datasets with a consistent experimental setup. Finally, the open issues and under-explored areas in ADT research are identified and discussed, providing future directions in this fiel

Spin Matrix Theory: A quantum mechanical model of the AdS/CFT correspondence

We introduce a new quantum mechanical theory called Spin Matrix theory (SMT). The theory is interacting with a single coupling constant g and is based on a Hilbert space of harmonic oscillators with a spin index taking values in a Lie (super)algebra representation as well as matrix indices for the adjoint representation of U(N). We show that SMT describes N=4 super-Yang-Mills theory (SYM) near zero-temperature critical points in the grand canonical phase diagram. Equivalently, SMT arises from non-relativistic limits of N=4 SYM. Even though SMT is a non-relativistic quantum mechanical theory it contains a variety of phases mimicking the AdS/CFT correspondence. Moreover, the infinite g limit of SMT can be mapped to the supersymmetric sector of string theory on AdS_5 x S^5. We study SU(2) SMT in detail. At large N and low temperatures it is a theory of spin chains that for small g resembles planar gauge theory and for large g a non-relativistic string theory. When raising the temperature a partial deconfinement transition occurs due to finite-N effects. For sufficiently high temperatures the partially deconfined phase has a classical regime. We find a matrix model description of this regime at any coupling g. Setting g=0 it is a theory of N^2+1 harmonic oscillators while for large g it becomes 2N harmonic oscillators.Comment: 36 pages, 3 figures. v2: Refs. adde

Algebra, coalgebra, and minimization in polynomial differential equations

We consider reasoning and minimization in systems of polynomial ordinary differential equations (ode's). The ring of multivariate polynomials is employed as a syntax for denoting system behaviours. We endow this set with a transition system structure based on the concept of Lie-derivative, thus inducing a notion of L-bisimulation. We prove that two states (variables) are L-bisimilar if and only if they correspond to the same solution in the ode's system. We then characterize L-bisimilarity algebraically, in terms of certain ideals in the polynomial ring that are invariant under Lie-derivation. This characterization allows us to develop a complete algorithm, based on building an ascending chain of ideals, for computing the largest L-bisimulation containing all valid identities that are instances of a user-specified template. A specific largest L-bisimulation can be used to build a reduced system of ode's, equivalent to the original one, but minimal among all those obtainable by linear aggregation of the original equations. A computationally less demanding approximate reduction and linearization technique is also proposed.Comment: 27 pages, extended and revised version of FOSSACS 2017 pape

The Geometry of Statistical Machine Translation

This is the author accepted manuscript. The final version is available from ACL via http://www.aclweb.org/anthology/N15-1041Most modern statistical machine translation systems are based on linear statistical models. One extremely effective method for estimating the model parameters is minimum error rate training (MERT), which is an efficient form of line optimisation adapted to the highly nonlinear objective functions used in machine translation. We describe a polynomial-time generalisation of line optimisation that computes the error surface over a plane embedded in parameter space. The description of this algorithm relies on convex geometry, which is the mathematics of polytopes and their faces. Using this geometric representation of MERT we investigate whether the optimisation of linear models is tractable in general. Previous work on finding optimal solutions in MERT (Galley and Quirk, 2011) established a worstcase complexity that was exponential in the number of sentences, in contrast we show that exponential dependence in the worst-case complexity is mainly in the number of features. Although our work is framed with respect to MERT, the convex geometric description is also applicable to other error-based training methods for linear models. We believe our analysis has important ramifications because it suggests that the current trend in building statistical machine translation systems by introducing a very large number of sparse features is inherently not robust.This research was supported by a doctoral training account from the Engineering and Physical Sciences Research Council