![]() In this paper, we report experimental evidence and the corresponding theoretical foundation for harnessing the continuous time dynamics of a system of coupled relaxation oscillators to solve vertex coloring of a random graphs, a combinatorial optimization problem of large-scale importance. ![]() ![]() This has motivated active research in alternative computing models, where dynamical systems have been shown to provide a fundamentally new platform to address these increasingly important problem classes 7, 8, 9, 10, 11. In spite of the success of the von Neumann computing architecture, its limitations become apparent 1, 2 when dealing with certain classes of problems such as associative computing 3, 4, optimizations 5, pattern matching and recognition 6. Processing is distributed in all parts of the machine memory and processors are integrated clear distinguishable atomic instructions are replaced by continuous time dynamics and information is encoded in physically meaningful quantities instead of their symbolic interpretations. On the contrary, computation in nature, our brain included, follows a radically different approach. Computation is carried out through a sequence of instructions with periodic loads and stores to the memory. The semiconductor industry is pivoted upon the Von Neumann computer architecture which implements the “Turing Machine” model of computation with a clear distinction between processing units and memory. Our work not only elucidates a physics-based computing approach but also presents tantalizing opportunities for building customized analog co-processors for solving hard problems efficiently. We further indicate a fundamental connection between spectral properties of linear dynamical systems and spectral algorithms for graph coloring. The proposed VO 2 oscillator network harnesses the natural analogue between optimization problems and energy minimization processes in highly parallel, interconnected dynamical systems to approximate optimal coloring of graphs. Pairwise coupled VO 2 oscillator circuits have been analyzed before for basic computing operations, but using complex networks of VO 2 oscillators, or any other oscillators, for more complex tasks have been challenging in theory as well as in experiments. Here we demonstrate a coupled relaxation oscillator based dynamical system that exploits insulator-metal transition in Vanadium Dioxide (VO 2) to efficiently solve vertex coloring of graphs. ![]() It is well studied for its applications in data sciences, life sciences, social sciences and technology, and hence, motivates alternate, more efficient non-Boolean pathways towards its solution. Vertex coloring of graphs, belonging to the class of combinatorial optimization, represents one such problem. Interfaces of his kind lend themselves particularly to electroacoustic and computer music performance where timbre, texture and morphology may be paramount.While Boolean logic has been the backbone of digital information processing, there exist classes of computationally hard problems wherein this paradigm is fundamentally inefficient. The author will argue that interfaces need to communicate something of their task and that cognitive affordances (Gibson 1979) associated with the performance interface become paramount if the musical outcomes are to be perceived as clearly tied to real-time performance gestures – in other words, that the audience are witnessing the creation of the music in that moment as distinct to the manipulation of pre-recorded or pre-sequenced events. Critics argue that performances of this nature fail to engage audiences because many performers use the mouse and/or computer keyboard to control their musical works, leaving no visual cues to guide the audience as to the correlation between performance gestures and musical outcomes. It brings with it many issues pertaining to the communication of musical intent. The use of a laptop computer for musical performance has become widespread in the electronic music community. ![]()
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