A geometric approach to quantum circuit lower bounds

What is the minimal size quantum circuit required to exactly implement a specified n-qubit unitary operation, U, without the use of ancilla qubits? We show that a lower bound on the minimal size is provided by the length of the minimal geodesic between U and the identity, I, where length is defined by a suitable Finsler metric on the manifold SU(2(n)). The geodesic curves on these manifolds have the striking property that once an initial position and velocity are set, the remainder of the geodesic is completely determined by a second order differential equation known as the geodesic equation. This is in contrast with the usual case in circuit design, either classical or quantum, where being given part of an optimal circuit does not obviously assist in the design of the rest of the circuit. Geodesic analysis thus offers a potentially powerful approach to the problem of proving quantum circuit lower bounds. In this paper we construct several Finsler metrics whose minimal length geodesics provide lower bounds on quantum circuit size. For each Finsler metric we give a procedure to compute the corresponding geodesic equation. We also construct a large class of solutions to the geodesic equation, which we call Pauli geodesics, since they arise from isometries generated by the Pauli group. For any unitary U diagonal in the computational basis, we show that: (a) provided the minimal length geodesic is unique, it must be a Pauli geodesic; (b) finding the length of the minimal Pauli geodesic passing from I to U is equivalent to solving an exponential size instance of the closest vector in a lattice problem (CVP); and (c) all but a doubly exponentially small fraction of such unitaries have minimal Pauli geodesics of exponential length.

Advances in distributed parameter approach to the dynamics and control of activated sludge processes for wastewater treatment

This paper presents a review of modelling and control of biological nutrient removal (BNR)-activated sludge processes for wastewater treatment using distributed parameter models described by partial differential equations (PDE). Numerical methods for solution to the BNR-activated sludge process dynamics are reviewed and these include method of lines, global orthogonal collocation and orthogonal collocation on finite elements. Fundamental techniques and conceptual advances of the distributed parameter approach to the dynamics and control of activated sludge processes are briefly described. A critical analysis on the advantages of the distributed parameter approach over the conventional modelling strategy in this paper shows that the activated sludge process is more adequately described by the former and the method is recommended for application to the wastewater industry (c) 2006 Elsevier Ltd. All rights reserved.

Stochastic dynamic programming for election timing: A game theory approach

In this paper, we consider dynamic programming for the election timing in the majoritarian parliamentary system such as in Australia, where the government has a constitutional right to call an early election. This right can give the government an advantage to remain in power for as long as possible by calling an election, when its popularity is high. On the other hand, the opposition's natural objective is to gain power, and it will apply controls termed as "boosts" to reduce the chance of the government being re-elected by introducing policy and economic responses. In this paper, we explore equilibrium solutions to the government, and the opposition strategies in a political game using stochastic dynamic programming. Results are given in terms of the expected remaining life in power, call and boost probabilities at each time at any level of popularity.

A core vocabulary approach for management of inconsistent speech disorder

Developmental speech disorder is accounted for by theories derived from psychology, psycholinguistics, linguistics and medicine, with researchers developing assessment protocols that reflect their theoretical perspective. How theory and data analyses lead to different therapy approaches, however, is sometimes unclear. Here, we present a case management plan for a 7 year old boy with unintelligible speech. Assessment data were analysed to address seven case management questions regarding need for intervention, service delivery, differential diagnosis, intervention goals, generalization of therapeutic gains, discharge criteria and evaluation of efficacy. Jarrod was diagnosed as having inconsistent speech disorder that required intervention. He pronounced 88% of words differently when asked to name each word in the 25 word inconsistency test of the Diagnostic Evaluation of Articulation and Phonology three times, each trial separated by another activity. Other standardized assessments supported the diagnosis of inconsistent speech disorder that, according to previous research, is associated with a deficit in phonological assembly. Core vocabulary intervention was chosen as the most appropriate therapy technique. Its nature and a possible protocol for implementation is described.

Stochastic delay differential equations for genetic regulatory networks

Time delay is an important aspect in the modelling of genetic regulation due to slow biochemical reactions such as gene transcription and translation, and protein diffusion between the cytosol and nucleus. In this paper we introduce a general mathematical formalism via stochastic delay differential equations for describing time delays in genetic regulatory networks. Based on recent developments with the delay stochastic simulation algorithm, the delay chemical masterequation and the delay reaction rate equation are developed for describing biological reactions with time delay, which leads to stochastic delay differential equations derived from the Langevin approach. Two simple genetic regulatory networks are used to study the impact of' intrinsic noise on the system dynamics where there are delays. (c) 2006 Elsevier B.V. All rights reserved.

Optimising profitability and environmental trade-offs in managing cropping systems using differential evolution

Whilst traditional optimisation techniques based on mathematical programming techniques are in common use, they suffer from their inability to explore the complexity of decision problems addressed using agricultural system models. In these models, the full decision space is usually very large while the solution space is characterized by many local optima. Methods to search such large decision spaces rely on effective sampling of the problem domain. Nevertheless, problem reduction based on insight into agronomic relations and farming practice is necessary to safeguard computational feasibility. Here, we present a global search approach based on an Evolutionary Algorithm (EA). We introduce a multi-objective evaluation technique within this EA framework, linking the optimisation procedure to the APSIM cropping systems model. The approach addresses the issue of system management when faced with a trade-off between economic and ecological consequences.

Differential evolution based total transfer capability assessment with optimal dispatch

In this paper, a new differential evolution (DE) based power system optimal available transfer capability (ATC) assessment is presented. Power system total transfer capability (TTC) is traditionally solved by the repeated power flow (RPF) method and the continuation power flow (CPF) method. These methods are based on the assumption that the productions of the source area generators are increased in identical proportion to balance the load increment in the sink area. A new approach based on DE algorithm to generate optimal dispatch both in source area generators and sink area loads is proposed in this paper. This new method can compute ATC between two areas with significant improvement in accuracy compared with the traditional RPF and CPF based methods. A case study using a 30 bus system is given to verify the efficiency and effectiveness of this new DE based ATC optimization approach.

Systems biology approach to study permeability of paracetamol and its solid dispersion

Physiological changes that take place at cellular level are usually reflective of their level of gene expression. Different formulation excipients have an impact on physiological behavior of the exposed cells and in turn affect transporter genes, enterocyte-mediated metabolism and toxicity biomarkers. The aim of this study was to prepare solid dispersion of paracetamol and evaluate genetic changes that occur in Caco-2 cell lines during the permeability of paracetamol alone and paracetamol solid dispersion formulations. Paracetamol-PEG 8000 solid dispersion was prepared by melt fusion method and the formulation was characterised using differential scanning calorimetry (DSC), scanning electron microscopy (SEM) and Fourier transform infrared spectroscopy (FTIR). Formulation of solid dispersion resulted in the conversion of crystalline drug into an amorphous form. Permeability studies showed that paracetamol absorption was higher from the solid dispersion formulation. DNA microarrays analysis was carried out in order to investigate the involvement of any efflux/uptake transporters in paracetamol or its solid dispersion permeability. Neither transporter carriers nor efflux proteins were found to be involved in the absorption of paracetamol or its PEG solid dispersion. Gene expression analysis established that paracetamol toxicity was potentially reduced upon formulation into solid dispersion when ATP binding cassette (ABC) and solute carrier transporter (SLC) genes were analyzed.

Estimating parameters in stochastic systems:a variational Bayesian approach

This work is concerned with approximate inference in dynamical systems, from a variational Bayesian perspective. When modelling real world dynamical systems, stochastic differential equations appear as a natural choice, mainly because of their ability to model the noise of the system by adding a variation of some stochastic process to the deterministic dynamics. Hence, inference in such processes has drawn much attention. Here a new extended framework is derived that is based on a local polynomial approximation of a recently proposed variational Bayesian algorithm. The paper begins by showing that the new extension of this variational algorithm can be used for state estimation (smoothing) and converges to the original algorithm. However, the main focus is on estimating the (hyper-) parameters of these systems (i.e. drift parameters and diffusion coefficients). The new approach is validated on a range of different systems which vary in dimensionality and non-linearity. These are the Ornstein–Uhlenbeck process, the exact likelihood of which can be computed analytically, the univariate and highly non-linear, stochastic double well and the multivariate chaotic stochastic Lorenz ’63 (3D model). As a special case the algorithm is also applied to the 40 dimensional stochastic Lorenz ’96 system. In our investigation we compare this new approach with a variety of other well known methods, such as the hybrid Monte Carlo, dual unscented Kalman filter, full weak-constraint 4D-Var algorithm and analyse empirically their asymptotic behaviour as a function of observation density or length of time window increases. In particular we show that we are able to estimate parameters in both the drift (deterministic) and the diffusion (stochastic) part of the model evolution equations using our new methods.

A systems approach to students' motivation and academic achievement

This research followed earlier work (reported in a thesis presented in 1970) on factors associated with the academic performance of a sample of technical college students, which recommended the further study of students' motivation. The technical college then became part of a polytechnic, but the courses chosen for the continuation of the research were all of a specifically vocational character. The approach was influenced by Angyal (1941) in seeking to relate symbolic processes to broader behaviour patterns within a systems framework. Forms of semantic differential were developed to obtain the students' responses to words representing various activities and various people both within and outside the academic environment. Also, a "!growth motivation questionnaire" was produced using ideas from self-actualisation, job satisfaction and expectancy theory and examination marks were recorded. From pre-coded responses to the growth motivation questionnaire, scores on a 'study satisfaction' factor were calculated, and subsamples of students were taken at the extremes of this scale. Wriitten responses from the same questionnaire and semantic differential factor scores showed contrasting patterns between the two subsamples. Interpretation of these patterns suggested a diversity of approach to academic work among the students which calls for greater flexibility in the educational system serving them.

Combining temporal and spectral information with spatial mapping to identify differences between phonological and semantic networks:a magnetoencephalographic approach

Early, lesion-based models of language processing suggested that semantic and phonological processes are associated with distinct temporal and parietal regions respectively, with frontal areas more indirectly involved. Contemporary spatial brain mapping techniques have not supported such clear-cut segregation, with strong evidence of activation in left temporal areas by both processes and disputed evidence of involvement of frontal areas in both processes. We suggest that combining spatial information with temporal and spectral data may allow a closer scrutiny of the differential involvement of closely overlapping cortical areas in language processing. Using beamforming techniques to analyze magnetoencephalography data, we localized the neuronal substrates underlying primed responses to nouns requiring either phonological or semantic processing, and examined the associated measures of time and frequency in those areas where activation was common to both tasks. Power changes in the beta (14-30 Hz) and gamma (30-50 Hz) frequency bandswere analyzed in pre-selected time windows of 350-550 and 500-700ms In left temporal regions, both tasks elicited power changes in the same time window (350-550 ms), but with different spectral characteristics, low beta (14-20 Hz) for the phonological task and high beta (20-30 Hz) for the semantic task. In frontal areas (BA10), both tasks elicited power changes in the gamma band (30-50 Hz), but in different time windows, 500-700ms for the phonological task and 350-550ms for the semantic task. In the left inferior parietal area (BA40), both tasks elicited changes in the 20-30 Hz beta frequency band but in different time windows, 350-550ms for the phonological task and 500-700ms for the semantic task. Our findings suggest that, where spatial measures may indicate overlapping areas of involvement, additional beamforming techniques can demonstrate differential activation in time and frequency domains. © 2012 McNab, Hillebrand, Swithenby and Rippon.

Variational mean-field algorithm for efficient inference in large systems of stochastic differential equations

This work introduces a Gaussian variational mean-field approximation for inference in dynamical systems which can be modeled by ordinary stochastic differential equations. This new approach allows one to express the variational free energy as a functional of the marginal moments of the approximating Gaussian process. A restriction of the moment equations to piecewise polynomial functions, over time, dramatically reduces the complexity of approximate inference for stochastic differential equation models and makes it comparable to that of discrete time hidden Markov models. The algorithm is demonstrated on state and parameter estimation for nonlinear problems with up to 1000 dimensional state vectors and compares the results empirically with various well-known inference methodologies.

On a Differential Equation with Left and Right Fractional Derivatives

Mathematics Subject Classification: 26A33; 70H03, 70H25, 70S05; 49S05

Hypoellipticity of Anisotropic Partial Differential Equations

2002 Mathematics Subject Classification: 35S05

A holistic multi evidence approach to study the fragmentation behaviour of crystalline mannitol

Mannitol is an essential excipient employed in orally disintegrating tablets due to its high palatability. However its fundamental disadvantage is its fragmentation during direct compression, producing mechanically weak tablets. The primary aim of this study was to assess the fracture behaviour of crystalline mannitol in relation to the energy input during direct compression, utilising ball milling as the method of energy input, whilst assessing tablet characteristics of post-milled powders. Results indicated that crystalline mannitol fractured at the hydrophilic (011) plane, as observed through SEM, alongside a reduction in dispersive surface energy. Disintegration times of post-milled tablets were reduced due to the exposure of the hydrophilic plane, whilst more robust tablets were produced. This was shown through higher tablet hardness and increased plastic deformation profiles of the post-milled powders, as observed with a lower yield pressure through an out-of-die Heckel analysis. Evaluation of crystal state using x-ray diffraction/differential scanning calorimetry showed that mannitol predominantly retained the β-polymorph; however x-ray diffraction provided a novel method to calculate energy input into the powders during ball milling. It can be concluded that particle size reduction is a pragmatic strategy to overcome the current limitation of mannitol fragmentation and provide improvements in tablet properties.