The musicologist is confronted with many situations during the analysis of electroacoustic music, whether on support media, mixed, or real-time. Musical genres and styles vary greatly, and the collection of electronic musical instruments has also proven to be very heterogeneous. The intrinsic characteristics of the electroacoustic parts and their scoring create serious limitations. Furthermore, many sources remain inaccessible or are already lost. Thus the preoccupation with documentary sources related to the acts of creation, interpretation, and technological context becomes more and more pressing. It is now essential to formulate a synthetic vision of this music, which has existed for half a century, and to pursue the search for invariants. This work must be based on a rigorous methodology that has yet to be developed. More generally speaking, the goal is to establish the terms and conditions of a systematic musicology of electroacoustics.

The word ‘noise’ has taken on various meanings throughout the course of twentieth-century music. Technology has had direct influence on the presence of noise, as phenomenon and as concept, both through its newfound ubiquity in modernity and through its use directly in music production – in electroacoustics. The creative use of technologies has lead to new representation systems for music, and noise – considered as that outside of a given representation – was brought into meaning. This paper examines several moments in which a change in representation brought noise into musical consideration – leading to a ‘noise music’ for its time before simply becoming understood as music.

An electroacoustic musical work is a complex network of processes and elements: technical, musical, human, etc.; therefore, while the aesthetic perception is unified, its definition is fragmentary. This observation compels us to intensify our study of a taxonomy of agents and processes, with the aim of clarifying the identity of this music.

The discussion is positioned according to two different vantage points: (i) analysis of works, and (ii) the writings devoted to the aesthetics of electroacoustic music. Musicological analysis is simultaneously the means, the goal and the motivation for getting to know this arborescent reality. It allows us to arrive at the identification of six agents and four processes associated with the work, whose main properties we will describe. These elements are used as a methodological and theoretical grid for organising the discussion about the works. The question centres on a paradigm which is created from the analysis and returns to it, as an essential link between hermeneutic knowledge and the knowledge of the internal logic of an electroacoustic work.

One of the most remarkable achievements of Pierre Schaeffer's musical thought is his proposal of the sonorous object as the focus of research. The sonorous object is a fragment of sound, typically in the range of a few seconds (often even less), perceived as a unit. Sonorous objects are constituted, studied, and evaluated according to various criteria, and sonorous objects that are found suitable are regarded as musical objects that may be used in musical composition. In the selection and qualification of these sonorous objects, we are encouraged to practise what Schaeffer called ‘reduced listening’, meaning disregarding the original context of the sound, including its source and signification, and instead focus our listening on the sonorous features.

However, it can be argued that this principle of ‘reduced listening’ is not in conflict with more fundamental principles of embodied cognition, and that the criteria for the constitution, and the various feature qualifications, of sonorous objects can be linked to gestural images. Also, there are several similarities between studying sound and gestures from a phenomenological perspective, and it is suggested that Schaeffer's theoretical concepts may be extended to what is called gestural-sonorous objects.

Electroacoustic music has been of great interest to Latin American composers since its inception. Hundreds of composers have been working in this field, creating thousands of pieces. However, there is a significant lack of information and recordings in this respect, and little research has been conducted in this area until recently. One step forward to advance the exploration of a somewhat lost sound world is The Latin American Electroacoustic Music Collection, a documentation, preservation and dissemination project, developed by the author.

Art always does more than subsist upon technical progress; for centuries its practice has merged with it, and we should never forget that the first meaning of the word art was technê. However, never before has the relationship between art and technology raised so many questions and provoked so much misunderstanding. As a matter of fact, at the same time as the frontiers of technique continue to recede, the frontiers of art seem more and more difficult to grasp. (Couchot and Hillaire 2003: 15)

Motivated by a property of linear resistive electrical networks, we introduce the class of Rayleigh matroids. These form a subclass of the balanced matroids defined by Feder and Mihail [9] in 1992. We prove a variety of results relating Rayleigh matroids to other well-known classes – in particular, we show that a binary matroid is Rayleigh if and only if it does not contain $\mathcal{S}_{8}$ as a minor. This has the consequence that a binary matroid is balanced if and only if it is Rayleigh, and provides the first complete proof in print that $\mathcal{S}_{8}$ is the only minor-minimal binary non-balanced matroid, as claimed in [9]. We also give an example of a balanced matroid which is not Rayleigh.

Bootstrap percolation on an arbitrary graph has a random initial configuration, where each vertex is occupied with probability $p$, independently of each other, and a deterministic spreading rule with a fixed parameter $k$: if a vacant site has at least $k$ occupied neighbours at a certain time step, then it becomes occupied in the next step. This process is well studied on ${\mathbb Z}^d$; here we investigate it on regular and general infinite trees and on non-amenable Cayley graphs. The critical probability is the infimum of those values of $p$ for which the process achieves complete occupation with positive probability. On trees we find the following discontinuity: if the branching number of a tree is strictly smaller than $k$, then the critical probability is 1, while it is $1-1/k$ on the $k$-ary tree. A related result is that in any rooted tree $T$ there is a way of erasing $k$ children of the root, together with all their descendants, and repeating this for all remaining children, and so on, such that the remaining tree $T'$ has branching number $\mbox{\rm br}(T')\leq \max\{\mbox{\rm br}(T)-k,\,0\}$. We also prove that on any $2k$-regular non-amenable graph, the critical probability for the $k$-rule is strictly positive.

A graph is $k$-linked if for every list of $2k$ vertices $\{s_1,{\ldots}\,s_k, t_1,{\ldots}\,t_k\}$, there exist internally disjoint paths $P_1,{\ldots}\, P_k$ such that each $P_i$ is an $s_i,t_i$-path. We consider degree conditions and connectivity conditions sufficient to force a graph to be $k$-linked.

Let $D(n,k)$ be the minimum positive integer $d$ such that every $n$-vertex graph with minimum degree at least $d$ is $k$-linked and let $R(n,k)$ be the minimum positive integer $r$ such that every $n$-vertex graph in which the sum of degrees of each pair of non-adjacent vertices is at least $r$ is $k$-linked. The main result of the paper is finding the exact values of $D(n,k)$ and $R(n,k)$ for every $n$ and $k$.

Thomas and Wollan [14] used the bound $D(n,k)\leq (n+3k)/2-2$ to give sufficient conditions for a graph to be $k$-linked in terms of connectivity. Our bound allows us to modify the Thomas–Wollan proof slightly to show that every $2k$-connected graph with average degree at least $12k$ is $k$-linked.

Let $p_c({\mathbb Q}_n)$ and $p_c({\mathbb Z}^n)$ denote the critical values for nearest-neighbour bond percolation on the $n$-cube ${\mathbb Q}_n = \{0,1\}^n$ and on ${\mathbb Z}^n$, respectively. Let $\Omega = n$ for ${\mathbb G} = {\mathbb Q}_n$ and $\Omega = 2n$ for ${\mathbb G} = {\mathbb Z}^n$ denote the degree of ${\mathbb G}$. We use the lace expansion to prove that for both ${\mathbb G} = {\mathbb Q}_n$ and ${\mathbb G} = {\mathbb Z}^n$, \[p_c({\mathbb G}) = \Omega^{-1} + \Omega^{-2} + \frac{7}{2} \Omega^{-3} + O(\Omega^{-4}).\] This extends by two terms the result $p_c({\mathbb Q}_n) = \Omega^{-1} + O(\Omega^{-2})$ of Borgs, Chayes, van der Hofstad, Slade and Spencer, and provides a simplified proof of a previous result of Hara and Slade for ${\mathbb Z}^n$.

We give results for the age-dependent distribution of vertex degree and number of vertices of given degree in the undirected web-graph process, a discrete random graph process introduced in [8]. For such processes we show that as $k \rightarrow \infty$, the expected proportion of vertices of degree $k$ has power law parameter $1+1/\eta$ where $\eta$ is the limiting ratio of the expected number of edge endpoints inserted by preferential attachment to the expected total degree. The proof for the undirected process generalizes naturally to give similar results for the directed hub-authority process, and an undirected hypergraph process.

We consider instances of the maximum independent set problem that are constructed according to the following semirandom model. Let $G_{n,p}$ be a random graph, and let $S$ be a set of $k$ vertices, chosen uniformly at random. Then, let $G_0$ be the graph obtained by deleting all edges connecting two vertices in $S$. Finally, an adversary may add edges to $G_0$ that do not connect two vertices in $S$, thereby producing the instance $G=G_{n,p,k}^*$. We present an algorithm that on input $G=G_{n,p,k}^*$ finds an independent set of size $\geq k$ within polynomial expected time, provided that $k\geq C(n/p)^{1/2}$ for a certain constant $C>0$. Moreover, we prove that in the case $k\leq (1-\varepsilon)\ln(n)/p$ this problem is hard.

We will study the best way to reveal a hidden perfect matching in a balanced bipartite graph by eliminating edges, one by one, in the hope that the eliminated edge is not part of the mystery perfect matching. We will look for the strategy that maximizes the odds of finding the perfect matching without revealing a fixed number of the edges in that perfect matching. For a complete bipartite graph, this is equivalent to finding a mystery permutation via negative guesses with only a fixed number of incorrect negative guesses.

We define ${\mathcal B}_n$ to be the set of $n$-tuples of the form $(a_0, {\ldots}\,, a_{n-1})$ where $a_j = \pm 1$. If $A \in {\mathcal B}_n$, then we call $A$ a binary sequence and define the autocorrelations of $A$ by $c_k := \sum_{j=0}^{n-k-1} a_j a_{j+k}$ for $0 \leq k \leq n-1$. The problem of finding binary sequences with autocorrelations ‘near zero’ has arisen in communications engineering and is also relevant to conjectures of Littlewood and Erdős on ‘flat’ polynomials with $\pm 1$ coefficients. Following Turyn, we define \[ b(n) := \min_{A \in {\mathcal B}_n} \max_{1 \leq k \leq n-1} |c_k|.\] The purpose of this article is to show that, using some known techniques from discrete probability, we can improve upon the best upper bound on $b(n)$ appearing in the previous literature, and we can obtain both asymptotic and exact expressions for the expected value of $c_k^m$ if the $a_j$ are independent $\pm 1$ random variables with mean 0. We also include some brief heuristic remarks in support of the unproved conjecture that $b(n) = O(\sqrt{n})$.

Motivated by a scheduling problem that arises in the study of optical networks, we prove the following result, which is a variation of a conjecture of Haxell, Wilfong and Winkler.

Let $k,n$ be two positive integers, let $w_{sj}, 1 \leq s \leq n, 1 \leq j \leq k$ be nonnegative reals satisfying $\sum_{j=1}^k w_{sj}< 1/n$ for every $1 \leq s \leq n$ and let $d_{sj}$ be arbitrary nonnegative reals. Then there are real numbers $x_1, x_2, {\ldots}\,,x_n$ such that for every $j$, $1 \leq j \leq k$, the $n$ cyclic closed intervals $I_s^{(j)}=[x_s+d_{sj},x_s+d_{sj}+w_{sj}]$, $(1 \leq s \leq n)$, where the endpoints are reduced modulo 1, are pairwise disjoint on the unit circle.

The proof is based on some properties of multivariate polynomials and on the validity of the Dyson conjecture.

We observe returns of a simple random walk on a finite graph to a fixed node, and would like to infer properties of the graph, in particular properties of the spectrum of the transition matrix. This is not possible in general, but at least the set of eigenvalues can be recovered under fairly general conditions, e.g., when the graph has a node-transitive automorphism group. The main result is that by observing polynomially many returns, it is possible to estimate the spectral gap of such a graph up to a constant factor.

It is reasonable to assume that quantum computations take place under the control of the classical world. For modelling this standard situation, we introduce a Classically controlled Quantum Turing Machine (CQTM), which is a Turing machine with a quantum tape for acting on quantum data, and a classical transition function for formalised classical control. In a CQTM, unitary transformations and quantum measurements are allowed. We show that any classical Turing machine can be simulated by a CQTM without loss of efficiency. Furthermore, we show that any $k$-tape CQTM can be simulated by a 2-tape CQTM with a quadratic loss of efficiency. In order to compare CQTMs with existing models of quantum computation, we prove that any uniform family of quantum circuits (Yao 1993) is efficiently approximated by a CQTM. Moreover, we prove that any semi-uniform family of quantum circuits (Nishimura and Ozawa 2002), and any measurement calculus pattern (Danos et al. 2004) are efficiently simulated by a CQTM. Finally, we introduce a Measurement-based Quantum Turing Machine (MQTM), which is a restriction of CQTMs in which only projective measurements are allowed. We prove that any CQTM is efficiently simulated by a MQTM. In order to appreciate the similarity between programming classical Turing machines and programming CQTMs, some examples of CQTMs are given.

Recently, encodings in interaction nets of the call-by-name and call-by-value strategies of the $\lambda$-calculus have been proposed. The purpose of these encodings is to bridge the gap between interaction nets and traditional abstract machines, which are both used to provide lower-level specifications of strategies of the $\lambda$-calculus, but in radically different ways. The strength of these encodings is their simplicity, which comes from the simple idea of introducing an explicit syntactic object to represent the evaluation flow. Another benefit of this approach is that no artifact is needed to represent boxes. However, these encodings deliberately follow the implemented strategies (call-by-name and call-by-value) as closely as possible, and hence do not benefit from the ability of interaction nets to represent sharing easily. The aim of this paper is to show that better sharing (hence efficiency) can indeed be achieved without adding much structure. We thus present the call-by-need strategy following the same philosophy, which is, indeed, no more complicated than call-by-name. We also extend our approach to fully lazy reduction. This continues the task of bridging the gap between interaction nets and abstract machines, thus pushing forward a more uniform framework for implementations of the $\lambda$-calculus.