Solution to the Equations of the Moment Expansions

We develop a formula for matching a Taylor series about the origin and an asymptotic exponential expansion for large values of the coordinate. We test it on the expansion of the generating functions for the moments and connected moments of the Hamiltonian operator. In the former case the formula produces the energies and overlaps for the Rayleigh-Ritz method in the Krylov space. We choose the harmonic oscillator and a strongly anharmonic oscillator as illustrative examples for numerical test. Our results reveal some features of the connected-moments expansion that were overlooked in earlier studies and applications of the approach

Deep Optimisation:Solving Combinatorial Optimisation Problems using Deep Neural Networks

Deep Optimisation (DO) combines evolutionary search with Deep Neural Networks (DNNs) in a novel way - not for optimising a learning algorithm, but for finding a solution to an optimisation problem. Deep learning has been successfully applied to classification, regression, decision and generative tasks and in this paper we extend its application to solving optimisation problems. Model Building Optimisation Algorithms (MBOAs), a branch of evolutionary algorithms, have been successful in combining machine learning methods and evolutionary search but, until now, they have not utilised DNNs. DO is the first algorithm to use a DNN to learn and exploit the problem structure to adapt the variation operator (changing the neighbourhood structure of the search process). We demonstrate the performance of DO using two theoretical optimisation problems within the MAXSAT class. The Hierarchical Transformation Optimisation Problem (HTOP) has controllable deep structure that provides a clear evaluation of how DO works and why using a layerwise technique is essential for learning and exploiting problem structure. The Parity Modular Constraint Problem (MCparity) is a simplistic example of a problem containing higher-order dependencies (greater than pairwise) which DO can solve and state of the art MBOAs cannot. Further, we show that DO can exploit deep structure in TSP instances. Together these results show that there exists problems that DO can find and exploit deep problem structure that other algorithms cannot. Making this connection between DNNs and optimisation allows for the utilisation of advanced tools applicable to DNNs that current MBOAs are unable to use

Effect of silver content on the structure and antibacterial activity of silver-doped phosphate-based glasses

Staphylococcus aureus can cause a range of diseases, such as osteomyelitis, as well as colonize implanted medical devices. In most instances the organism forms biofilms that not only are resistant to the body's defense mechanisms but also display decreased susceptibilities to antibiotics. In the present study, we have examined the effect of increasing silver contents in phosphate-based glasses to prevent the formation of S. aureus biofilms. Silver was found to be an effective bactericidal agent against S. aureus biofilms, and the rate of silver ion release (0.42 to 1.22 µg·mm–2·h–1) from phosphate-based glass was found to account for the variation in its bactericidal effect. Analysis of biofilms by confocal microscopy indicated that they consisted of an upper layer of viable bacteria together with a layer (20 µm) of nonviable cells on the glass surface. Our results showed that regardless of the silver contents in these glasses (10, 15, or 20 mol%) the silver exists in its +1 oxidation state, which is known to be a highly effective bactericidal agent compared to that of silver in other oxidation states (+2 or +3). Analysis of the glasses by 31P nuclear magnetic resonance imaging and high-energy X-ray diffraction showed that it is the structural rearrangement of the phosphate network that is responsible for the variation in silver ion release and the associated bactericidal effectiveness. Thus, an understanding of the glass structure is important in interpreting the in vitro data and also has important clinical implications for the potential use of the phosphate-based glasses in orthopedic applications to deliver silver ions to combat S. aureus biofilm infections

Why, what, and how? case study on law, risk, and decision making as necessary themes in built environment teaching

The paper considers (and defends) the necessity of including legal studies as a core part of built environment undergraduate and postgraduate curricula. The writer reflects upon his own experience as a lawyer working alongside and advising built environment professionals in complex land remediation and site safety management situations in the United Kingdom and explains how themes of liability, risk, and decision making can be integrated into a practical simulation in order to underpin more traditional lecture-based law teaching. Through reflection upon the writer's experiments with simulation-based teaching, the paper suggests some innovations that may better orientate law teaching to engage these themes and, thereby, enhance the relevance of law studies to the future needs of built environment professionals in practice.</p

Combining qualitative and quantitative operational research methods to inform quality improvement in pathways that span multiple settings

BACKGROUND: Improving integration and continuity of care across sectors within resource constraints is a priority in many health systems. Qualitative operational research methods of problem structuring have been used to address quality improvement in services involving multiple sectors but not in combination with quantitative operational research methods that enable targeting of interventions according to patient risk. We aimed to combine these methods to augment and inform an improvement initiative concerning infants with congenital heart disease (CHD) whose complex care pathway spans multiple sectors. METHODS: Soft systems methodology was used to consider systematically changes to services from the perspectives of community, primary, secondary and tertiary care professionals and a patient group, incorporating relevant evidence. Classification and regression tree (CART) analysis of national audit datasets was conducted along with data visualisation designed to inform service improvement within the context of limited resources. RESULTS: A 'Rich Picture' was developed capturing the main features of services for infants with CHD pertinent to service improvement. This was used, along with a graphical summary of the CART analysis, to guide discussions about targeting interventions at specific patient risk groups. Agreement was reached across representatives of relevant health professions and patients on a coherent set of targeted recommendations for quality improvement. These fed into national decisions about service provision and commissioning. CONCLUSIONS: When tackling complex problems in service provision across multiple settings, it is important to acknowledge and work with multiple perspectives systematically and to consider targeting service improvements in response to confined resources. Our research demonstrates that applying a combination of qualitative and quantitative operational research methods is one approach to doing so that warrants further consideration

High--order connected moments expansion for the Rabi Hamiltonian

We analyze the convergence properties of the connected moments expansion (CMX) for the Rabi Hamiltonian. To this end we calculate the moments and connected moments of the Hamiltonian operator to a sufficiently large order. Our large--order results suggest that the CMX is not reliable for most practical purposes because the expansion exhibits considerable oscillations.Comment: 12 pages, 5 figures, 1 tabl

Correlation effects in MgO and CaO: Cohesive energies and lattice constants

A recently proposed computational scheme based on local increments has been applied to the calculation of correlation contributions to the cohesive energy of the CaO crystal. Using ab-initio quantum chemical methods for evaluating individual increments, we obtain 80% of the difference between the experimental and Hartree-Fock cohesive energies. Lattice constants corrected for correlation effects deviate by less than 1% from experimental values, in the case of MgO and CaO.Comment: LaTeX, 4 figure

A New Technique for Finding Needles in Haystacks: A Geometric Approach to Distinguishing Between a New Source and Random Fluctuations

We propose a new test statistic based on a score process for determining the statistical significance of a putative signal that may be a small perturbation to a noisy experimental background. We derive the reference distribution for this score test statistic; it has an elegant geometrical interpretation as well as broad applicability. We illustrate the technique in the context of a model problem from high-energy particle physics. Monte Carlo experimental results confirm that the score test results in a significantly improved rate of signal detection.Comment: 5 pages, 4 figure