Pragmatic Considerations in Mixed Music: a Case Study of La Rage

With access to powerful real-time DSP languages now easier than ever, the new generation of mixed music composers are able to manage both sides of the coin: they have the programming skills and the compositional concerns that were traditionally the responsibility of two different persons. This brings more and more sophisticated integration of technical resources and compositional gestures. A good example of such integration is the author’s piece La Rage. In the light of general comments on the seamless integration of technology in this piece, the author, by discussing how compositional and technical concerns interact in his process of creation, tries to pinpoint key considerations that help him achieve this. He proposes two major categories, portability and adaptability, and explains how they were addressed in this specific work

Multiplying a Gaussian Matrix by a Gaussian Vector

We provide a new and simple characterization of the multivariate generalized Laplace distribution. In particular, this result implies that the product of a Gaussian matrix with independent and identically distributed columns by an independent isotropic Gaussian vector follows a symmetric multivariate generalized Laplace distribution

Exact Dimensionality Selection for Bayesian PCA

We present a Bayesian model selection approach to estimate the intrinsic dimensionality of a high-dimensional dataset. To this end, we introduce a novel formulation of the probabilisitic principal component analysis model based on a normal-gamma prior distribution. In this context, we exhibit a closed-form expression of the marginal likelihood which allows to infer an optimal number of components. We also propose a heuristic based on the expected shape of the marginal likelihood curve in order to choose the hyperparameters. In non-asymptotic frameworks, we show on simulated data that this exact dimensionality selection approach is competitive with both Bayesian and frequentist state-of-the-art methods

Thinking Inside the Box: A New Integrated Approach to Mixed Music Composition and Performance

The Thinking Inside the Box project (TItB) seeks to address pragmatic concerns inherent to mixed music performance, and proposes ways to better consider the sound of the acoustic reality of the concert space at studio composition time. This is achieved through empirical investigation into subversive use of recent developments in hardware and software technologies. The primary concerns are (1) optimising the integration of live instruments and electroacoustic sound in the concert hall environment for both the performers and the public, by carefully choosing loudspeaker types and placement at commission time, and by avoiding sound reinforcement; (2) minimizing for studio composers the insitu trauma of the first live rendition of the piece, by bringing the concert hall acoustic environment into the studio composition process, using convolution reverb to reproduce in the studio the given loudspeaker setup through its impulse responses. This paper presents the conclusions of the project's early experiments in the form of three case study sets, and describes how this approach will be of use for any composer of mixed music

Linear statistics and pushed Coulomb gas at the edge of beta random matrices: four paths to large deviations

The Airy$_\beta$ point process, $a_i \equiv N^{2/3} (\lambda_i-2)$, describes the eigenvalues $\lambda_i$ at the edge of the Gaussian $\beta$ ensembles of random matrices for large matrix size $N \to \infty$. We study the probability distribution function (PDF) of linear statistics ${\sf L}= \sum_i t \varphi(t^{-2/3} a_i)$ for large parameter $t$. We show the large deviation forms $\mathbb{E}_{{\rm Airy},\beta}[\exp(-{\sf L})] \sim \exp(- t^2 \Sigma[\varphi])$ and $P({\sf L}) \sim \exp(- t^2 G(L/t^2))$ for the cumulant generating function and the PDF. We obtain the exact rate function $\Sigma[\varphi]$ using four apparently different methods (i) the electrostatics of a Coulomb gas (ii) a random Schr\"odinger problem, i.e. the stochastic Airy operator (iii) a cumulant expansion (iv) a non-local non-linear differential Painlev\'e type equation. Each method was independently introduced to obtain the lower tail of the KPZ equation. Here we show their equivalence in a more general framework. Our results are obtained for a class of functions $\varphi$, the monotonous soft walls, containing the monomials $\varphi(x)=(u+x)_+^\gamma$ and the exponential $\varphi(x)=e^{u+x}$ and equivalently describe the response of a Coulomb gas pushed at its edge. The small $u$ behavior of the excess energy $\Sigma[\varphi]$ exhibits a change at $\gamma=3/2$ between a non-perturbative hard wall like regime for $\gamma<3/2$ (third order free-to-pushed transition) and a perturbative deformation of the edge for $\gamma>3/2$ (higher order transition). Applications are given, among them: (i) truncated linear statistics such as $\sum_{i=1}^{N_1} a_i$, leading to a formula for the PDF of the ground state energy of $N_1 \gg 1$ noninteracting fermions in a linear plus random potential (ii) $(\beta-2)/r^2$ interacting spinless fermions in a trap at the edge of a Fermi gas (iii) traces of large powers of random matrices.Comment: Main text : 8 pages. Supp mat : 49 page

Convergence speed of unsteady distributed consensus: decay estimate along the settling spanning-trees

Results for estimating the convergence rate of non-stationary distributed consensus algorithms are provided, on the basis of qualitative (mainly topological) as well as basic quantitative information (lower-bounds on the matrix entries). The results appear to be tight in a number of instances and are illustrated through simple as well as more sophisticated examples. The main idea is to follow propagation of information along certain spanning trees which arise in the communication graph.Comment: 27 pages, 5 figure