Fully fault tolerant quantum computation with non-deterministic gates

In certain approaches to quantum computing the operations between qubits are non-deterministic and likely to fail. For example, a distributed quantum processor would achieve scalability by networking together many small components; operations between components should assumed to be failure prone. In the logical limit of this architecture each component contains only one qubit. Here we derive thresholds for fault tolerant quantum computation under such extreme paradigms. We find that computation is supported for remarkably high failure rates (exceeding 90%) providing that failures are heralded, meanwhile the rate of unknown errors should not exceed 2 in 10^4 operations.Comment: 5 pages, 3 fig

On the genericity properties in networked estimation: Topology design and sensor placement

In this paper, we consider networked estimation of linear, discrete-time dynamical systems monitored by a network of agents. In order to minimize the power requirement at the (possibly, battery-operated) agents, we require that the agents can exchange information with their neighbors only \emph{once per dynamical system time-step}; in contrast to consensus-based estimation where the agents exchange information until they reach a consensus. It can be verified that with this restriction on information exchange, measurement fusion alone results in an unbounded estimation error at every such agent that does not have an observable set of measurements in its neighborhood. To over come this challenge, state-estimate fusion has been proposed to recover the system observability. However, we show that adding state-estimate fusion may not recover observability when the system matrix is structured-rank ($S$-rank) deficient. In this context, we characterize the state-estimate fusion and measurement fusion under both full $S$-rank and $S$-rank deficient system matrices.Comment: submitted for IEEE journal publicatio

Online Algorithms for Multi-Level Aggregation

In the Multi-Level Aggregation Problem (MLAP), requests arrive at the nodes of an edge-weighted tree T, and have to be served eventually. A service is defined as a subtree X of T that contains its root. This subtree X serves all requests that are pending in the nodes of X, and the cost of this service is equal to the total weight of X. Each request also incurs waiting cost between its arrival and service times. The objective is to minimize the total waiting cost of all requests plus the total cost of all service subtrees. MLAP is a generalization of some well-studied optimization problems; for example, for trees of depth 1, MLAP is equivalent to the TCP Acknowledgment Problem, while for trees of depth 2, it is equivalent to the Joint Replenishment Problem. Aggregation problem for trees of arbitrary depth arise in multicasting, sensor networks, communication in organization hierarchies, and in supply-chain management. The instances of MLAP associated with these applications are naturally online, in the sense that aggregation decisions need to be made without information about future requests. Constant-competitive online algorithms are known for MLAP with one or two levels. However, it has been open whether there exist constant competitive online algorithms for trees of depth more than 2. Addressing this open problem, we give the first constant competitive online algorithm for networks of arbitrary (fixed) number of levels. The competitive ratio is O(D^4 2^D), where D is the depth of T. The algorithm works for arbitrary waiting cost functions, including the variant with deadlines. We also show several additional lower and upper bound results for some special cases of MLAP, including the Single-Phase variant and the case when the tree is a path

The Advocate, May 5, 2011

https://red.mnstate.edu/advocate/1259/thumbnail.jp

Hearing behaviour: social interaction as a means of creating emergent situations in/as/through music

This body of writing serves as accompaniment to a portfolio of musical compositions and visual media composed between September 2013 and August 2014. The work is in three parts. Part one sets the context of the compositions with reference to numerous other artists, explaining the political need for compositions of this kind and how these relate to the topic of emergence in relation to group performance and social enrichment. This part also makes reference to the philosophical influence behind the works and how these ideas might be relevant to wider society. Part two offers a commentary on the works themselves, explaining the thinking that brought them about, and a narrative of the development from one composition to the next. Part three offers a reflection of how well these works relate to the originally stated political agenda, as well as outlining my plans for future artistic direction

Online Algorithms for Multi-Level Aggregation

In the Multi-Level Aggregation Problem (MLAP), requests arrive at the nodes of an edge-weighted tree T, and have to be served eventually. A service is defined as a subtree X of T that contains its root. This subtree X serves all requests that are pending in the nodes of X, and the cost of this service is equal to the total weight of X. Each request also incurs waiting cost between its arrival and service times. The objective is to minimize the total waiting cost of all requests plus the total cost of all service subtrees. MLAP is a generalization of some well-studied optimization problems; for example, for trees of depth 1, MLAP is equivalent to the TCP Acknowledgment Problem, while for trees of depth 2, it is equivalent to the Joint Replenishment Problem. Aggregation problem for trees of arbitrary depth arise in multicasting, sensor networks, communication in organization hierarchies, and in supply-chain management. The instances of MLAP associated with these applications are naturally online, in the sense that aggregation decisions need to be made without information about future requests. Constant-competitive online algorithms are known for MLAP with one or two levels. However, it has been open whether there exist constant competitive online algorithms for trees of depth more than 2. Addressing this open problem, we give the first constant competitive online algorithm for networks of arbitrary (fixed) number of levels. The competitive ratio is O(D^4*2^D), where D is the depth of T. The algorithm works for arbitrary waiting cost functions, including the variant with deadlines. We include several additional results in the paper. We show that a standard lower-bound technique for MLAP, based on so-called Single-Phase instances, cannot give super-constant lower bounds (as a function of the tree depth). This result is established by giving an online algorithm with optimal competitive ratio 4 for such instances on arbitrary trees. We also study the MLAP variant when the tree is a path, for which we give a lower bound of 4 on the competitive ratio, improving the lower bound known for general MLAP. We complement this with a matching upper bound for the deadline setting

Aesthetically driven design of network based multi-user instruments.

Digital networking technologies open up a new world of possibilities for music making, allowing performers to collaborate in ways not possible before. Network based Multi-User Instruments (NMIs) are one novel method of musical collaboration that take advantage of networking technology. NMIs are digital musical instruments that exist as a single entity instantiated over several nodes in a network and are performed simultaneously by multiple musicians in realtime. This new avenue is exciting, but it begs the question of how does one design instruments for this new medium? This research explores the use of an aesthetically driven design process to guide the design, construction, rehearsal, and performance of a series of NMIs. This is an iterative process that makes use of a regularly rehearsing and performing ensemble which serves as a test-bed for new instruments, from conception, to design, to implementation, to performance. This research includes details of several NMIs constructed in accordance with this design process. These NMIs have been quantitatively analysed and empirically tested for the presence of interconnectivity and group influence during performance as a method for measuring group collaboration. Furthermore qualitative analyses are applied which test for the perceived e ectiveness of these instruments during real-world performances in front of live audiences. The results of these analyses show that an aesthetically driven method of designing NMIs produces instruments that are interactive and collaborative. Furthermore results show that audiences perceive a measurable impression of interconnectivity and liveness in the ensemble even though most of the performers in the ensemble are not physically present