Strong-coupling expansion for the momentum distribution of the Bose-Hubbard model with benchmarking against exact numerical results

A strong-coupling expansion for the Green's functions, self-energies, and correlation functions of the Bose-Hubbard model is developed. We illustrate the general formalism, which includes all possible (normal-phase) inhomogeneous effects in the formalism, such as disorder or a trap potential, as well as effects of thermal excitations. The expansion is then employed to calculate the momentum distribution of the bosons in the Mott phase for an infinite homogeneous periodic system at zero temperature through third order in the hopping. By using scaling theory for the critical behavior at zero momentum and at the critical value of the hopping for the Mott insulator–to–superfluid transition along with a generalization of the random-phase-approximation-like form for the momentum distribution, we are able to extrapolate the series to infinite order and produce very accurate quantitative results for the momentum distribution in a simple functional form for one, two, and three dimensions. The accuracy is better in higher dimensions and is on the order of a few percent relative error everywhere except close to the critical value of the hopping divided by the on-site repulsion. In addition, we find simple phenomenological expressions for the Mott-phase lobes in two and three dimensions which are much more accurate than the truncated strong-coupling expansions and any other analytic approximation we are aware of. The strong-coupling expansions and scaling-theory results are benchmarked against numerically exact quantum Monte Carlo simulations in two and three dimensions and against density-matrix renormalization-group calculations in one dimension. These analytic expressions will be useful for quick comparison of experimental results to theory and in many cases can bypass the need for expensive numerical simulations.

Methodological and Empirical Advances in the Quantitative Analysis of Spontaneous Responses in Psychophysiological Time Series

The aim of the present study was to advance the methodology and use of time series analysis to quantify dynamic structures in psychophysiological processes and thereby to produce information on spontaneously coupled physiological responses and their behavioral and experiential correlates. Series of analyses using both simulated and empirical cardiac (IBI), electrodermal (EDA), and facial electromyographic (EMG) data indicated that, despite potential autocorrelated structures, smoothing increased the reliability of detecting response coupling from an interindividual distribution of intraindividual measures and that especially the measures of covariance produced accurate information on the extent of coupled responses. This methodology was applied to analyze spontaneously coupled IBI, EDA, and facial EMG responses and vagal activity in their relation to emotional experience and personality characteristics in a group of middle-aged men (n = 37) during the administration of the Rorschach testing protocol. The results revealed new characteristics in the relationship between phasic end-organ synchronization and vagal activity, on the one hand, and individual differences in emotional adjustment to novel situations on the other. Specifically, it appeared that the vagal system is intimately related to emotional and social responsivity. It was also found that the lack of spontaneously synchronized responses is related to decreased energetic arousal (e.g., depression, mood). These findings indicate that the present process analysis approach has many advantages for use in both experimental and applied research, and that it is a useful new paradigm in psychophysiological research. Keywords: Autonomic Nervous System; Emotion; Facial Electromyography; Individual Differences; Spontaneous Responses; Time Series Analysis; Vagal System

A method for mapping the distribution and density of rabbits and other vertebrate pests in Australia

The European wild rabbit has been considered Australia’s worst vertebrate pest and yet little effort appears to have gone into producing maps of rabbit distribution and density. Mapping the distribution and density of pests is an important step in effective management. A map is essential for estimating the extent of damage caused and for efficiently planning and monitoring the success of pest control operations. This paper describes the use of soil type and point data to prepare a map showing the distribution and density of rabbits in Australia. The potential for the method to be used for mapping other vertebrate pests is explored. The approach used to prepare the map is based on that used for rabbits in Queensland (Berman et al. 1998). An index of rabbit density was determined using the number of Spanish rabbit fleas released per square kilometre for each Soil Map Unit (Atlas of Australian Soils). Spanish rabbit fleas were released into active rabbit warrens at 1606 sites in the early 1990s as an additional vector for myxoma virus and the locations of the releases were recorded using a Global Positioning System (GPS). Releases were predominantly in arid areas but some fleas were released in south east Queensland and the New England Tablelands of New South Wales. The map produced appears to reflect well the distribution and density of rabbits, at least in the areas where Spanish fleas were released. Rabbit pellet counts conducted in 2007 at 54 sites across an area of south east South Australia, south eastern Queensland, and parts of New South Wales (New England Tablelands and south west) in soil Map Units where Spanish fleas were released, provided a preliminary means to ground truth the map. There was a good relationship between mean pellet count score and the index of abundance for soil Map Units. Rabbit pellet counts may allow extension of the map into other parts of Australia where there were no Spanish rabbit fleas released and where there may be no other consistent information on rabbit location and density. The recent Equine Influenza outbreak provided a further test of the value of this mapping method. The distribution and density of domestic horses were mapped to provide estimates of the number of horses in various regions. These estimates were close to the actual numbers of horses subsequently determined from vaccination records and registrations. The soil Map Units are not simply soil types they contain information on landuse and vegetation and the soil classification is relatively localised. These properties make this mapping method useful, not only for rabbits, but also for other species that are not so dependent on soil type for survival.

On the breakdown of the most probable distribution for mayer clusters

We present an analysis of the breakdown of the most probable approximation to the Mayer cluster size distribution for clusters of size comparable to the size of the system. This failure is illustrated by considering an ideal Bose gas for which exact volume dependent reducible cluster integrals are available.

Probabilistic load flow for distribution systems with uncertain PV generation

Large integration of solar Photo Voltaic (PV) in distribution network has resulted in over-voltage problems. Several control techniques are developed to address over-voltage problem using Deterministic Load Flow (DLF). However, intermittent characteristics of PV generation require Probabilistic Load Flow (PLF) to introduce variability in analysis that is ignored in DLF. The traditional PLF techniques are not suitable for distribution systems and suffer from several drawbacks such as computational burden (Monte Carlo, Conventional convolution), sensitive accuracy with the complexity of system (point estimation method), requirement of necessary linearization (multi-linear simulation) and convergence problem (Gram–Charlier expansion, Cornish Fisher expansion). In this research, Latin Hypercube Sampling with Cholesky Decomposition (LHS-CD) is used to quantify the over-voltage issues with and without the voltage control algorithm in the distribution network with active generation. LHS technique is verified with a test network and real system from an Australian distribution network service provider. Accuracy and computational burden of simulated results are also compared with Monte Carlo simulations.

Some aspects of multilevel load-frequency control of a power system

The application of multilevel control strategies for load-frequency control of interconnected power systems is assuming importance. A large multiarea power system may be viewed as an interconnection of several lower-order subsystems, with possible change of interconnection pattern during operation. The solution of the control problem involves the design of a set of local optimal controllers for the individual areas, in a completely decentralised environment, plus a global controller to provide the corrective signal to account for interconnection effects. A global controller, based on the least-square-error principle suggested by Siljak and Sundareshan, has been applied for the LFC problem. A more recent work utilises certain possible beneficial aspects of interconnection to permit more desirable system performances. The paper reports the application of the latter strategy to LFC of a two-area power system. The power-system model studied includes the effects of excitation system and governor controls. A comparison of the two strategies is also made.

Sol → gel transition with rings in a finite polycondensing system in solution

We report a theoretical formulation for the mean cluster size distribution in a finite polycondensing system. Expressions for the mean number of n-mers with j bonds ( nj) are developed. Numerical calculations show that while the non-cyclic molecules make the dominant contribution to the small clusters, the large clusters are dominated by cyclic structures. The number of particles in ringless chains, n n,n-1, decays monotonically with n at all extents of reaction, but n n becomes bimodal near the gel point. We also find that the solvent plays an important role in the cluster size distribution.

Reliability and validity of objective measures of physical activity in youth with cerebral palsy who are ambulatory

BACKGROUND Physical therapy for youth with cerebral palsy (CP) who are ambulatory includes interventions to increase functional mobility and participation in physical activity (PA). Thus, reliable and valid measures are needed to document PA in youth with CP. OBJECTIVE The purpose of this study was to evaluate the inter-instrument reliability and concurrent validity of 3 accelerometer-based motion sensors with indirect calorimetry as the criterion for measuring PA intensity in youth with CP. METHODS Fifty-seven youth with CP (mean age=12.5 years, SD=3.3; 51% female; 49.1% with spastic hemiplegia) participated. Inclusion criteria were: aged 6 to 20 years, ambulatory, Gross Motor Function Classification System (GMFCS) levels I through III, able to follow directions, and able to complete the full PA protocol. Protocol activities included standardized activity trials with increasing PA intensity (resting, writing, household chores, active video games, and walking at 3 self-selected speeds), as measured by weight-relative oxygen uptake (in mL/kg/min). During each trial, participants wore bilateral accelerometers on the upper arms, waist/hip, and ankle and a portable indirect calorimeter. Intraclass coefficient correlations (ICCs) were calculated to evaluate inter-instrument reliability (left-to-right accelerometer placement). Spearman correlations were used to examine concurrent validity between accelerometer output (activity and step counts) and indirect calorimetry. Friedman analyses of variance with post hoc pair-wise analyses were conducted to examine the validity of accelerometers to discriminate PA intensity across activity trials. RESULTS All accelerometers exhibited excellent inter-instrument reliability (ICC=.94-.99) and good concurrent validity (rho=.70-.85). All accelerometers discriminated PA intensity across most activity trials. LIMITATIONS This PA protocol consisted of controlled activity trials. CONCLUSIONS Accelerometers provide valid and reliable measures of PA intensity among youth with CP.

Data distribution and task scheduling for distributed computing of all-to-all comparison problems

This research studied distributed computing of all-to-all comparison problems with big data sets. The thesis formalised the problem, and developed a high-performance and scalable computing framework with a programming model, data distribution strategies and task scheduling policies to solve the problem. The study considered storage usage, data locality and load balancing for performance improvement in solving the problem. The research outcomes can be applied in bioinformatics, biometrics and data mining and other domains in which all-to-all comparisons are a typical computing pattern.

Design of laterally loaded piles in clays based on cone penetration test data: a reliability-based approach

The behaviour of laterally loaded piles is considerably influenced by the uncertainties in soil properties. Hence probabilistic models for assessment of allowable lateral load are necessary. Cone penetration test (CPT) data are often used to determine soil strength parameters, whereby the allowable lateral load of the pile is computed. In the present study, the maximum lateral displacement and moment of the pile are obtained based on the coefficient of subgrade reaction approach, considering the nonlinear soil behaviour in undrained clay. The coefficient of subgrade reaction is related to the undrained shear strength of soil, which can be obtained from CPT data. The soil medium is modelled as a one-dimensional random field along the depth, and it is described by the standard deviation and scale of fluctuation of the undrained shear strength of soil. Inherent soil variability, measurement uncertainty and transformation uncertainty are taken into consideration. The statistics of maximum lateral deflection and moment are obtained using the first-order, second-moment technique. Hasofer-Lind reliability indices for component and system failure criteria, based on the allowable lateral displacement and moment capacity of the pile section, are evaluated. The geotechnical database from the Konaseema site in India is used as a case example. It is shown that the reliability-based design approach for pile foundations, considering the spatial variability of soil, permits a rational choice of allowable lateral loads.

The distribution and abundance of electrosensory pores in two benthic sharks: a comparison of the wobbegong shark, Orectolobus maculatus, and the angel shark, Squatina australis

Electroreception is an ancient sense found in many aquatic animals, including sharks, which may be used in the detection of prey, predators and mates. Wobbegong sharks (Orectolobidae) and angel sharks (Squatinidae) represent two distantly related families that have independently evolved a similar dorso-ventrally compressed body form to complement their benthic ambush feeding strategy. Consequently, these groups represent useful models in which to investigate the specific morphological and physiological adaptations that are driven by the adoption of a benthic lifestyle. In this study, we compared the distribution and abundance of electrosensory pores in the spotted wobbegong shark (Orectolobus maculatus) with the Australian angel shark (Squatina australis) to determine whether both species display a similar pattern of clustering of sub-dermal electroreceptors and to further understand the functional importance of electroreception in the feeding behaviour of these benthic sharks. Orectolobus maculatus has a more complex electrosensory system than S. australis, with a higher abundance of pores and an additional cluster of electroreceptors positioned in the snout (the superficial ophthalmic cluster). Interestingly, both species possess a cluster of pores (the hyoid cluster, positioned slightly posterior to the first gill slit) more commonly found in rays, but which may be present in all benthic elasmobranchs to assist in the detection of approaching predators.

Optimization of gasket thickness in a Bridgman anvil system

The effect of gasket thickness on the pressure in the Bridgman anvil system has been studied experimentally. The existence of the optimum thickness from the experimental data has been interpreted in a theoretical model of stress distribution in an anvil system. Review of Scientific Instruments is copyrighted by The American Institute of Physics.

Single network adaptive critic design for power system stabilisers

The recently developed single network adaptive critic (SNAC) design has been used in this study to design a power system stabiliser (PSS) for enhancing the small-signal stability of power systems over a wide range of operating conditions. PSS design is formulated as a discrete non-linear quadratic regulator problem. SNAC is then used to solve the resulting discrete-time optimal control problem. SNAC uses only a single critic neural network instead of the action-critic dual network architecture of typical adaptive critic designs. SNAC eliminates the iterative training loops between the action and critic networks and greatly simplifies the training procedure. The performance of the proposed PSS has been tested on a single machine infinite bus test system for various system and loading conditions. The proposed stabiliser, which is relatively easier to synthesise, consistently outperformed stabilisers based on conventional lead-lag and linear quadratic regulator designs.

Projecting future expansion of invasive species: Comparing and improving methodologies for species distribution modeling

Modeling the distributions of species, especially of invasive species in non-native ranges, involves multiple challenges. Here, we developed some novel approaches to species distribution modeling aimed at reducing the influences of such challenges and improving the realism of projections. We estimated species-environment relationships with four modeling methods run with multiple scenarios of (1) sources of occurrences and geographically isolated background ranges for absences, (2) approaches to drawing background (absence) points, and (3) alternate sets of predictor variables. We further tested various quantitative metrics of model evaluation against biological insight. Model projections were very sensitive to the choice of training dataset. Model accuracy was much improved by using a global dataset for model training, rather than restricting data input to the species’ native range. AUC score was a poor metric for model evaluation and, if used alone, was not a useful criterion for assessing model performance. Projections away from the sampled space (i.e. into areas of potential future invasion) were very different depending on the modeling methods used, raising questions about the reliability of ensemble projections. Generalized linear models gave very unrealistic projections far away from the training region. Models that efficiently fit the dominant pattern, but exclude highly local patterns in the dataset and capture interactions as they appear in data (e.g. boosted regression trees), improved generalization of the models. Biological knowledge of the species and its distribution was important in refining choices about the best set of projections. A post-hoc test conducted on a new Partenium dataset from Nepal validated excellent predictive performance of our “best” model. We showed that vast stretches of currently uninvaded geographic areas on multiple continents harbor highly suitable habitats for Parthenium hysterophorus L. (Asteraceae; parthenium). However, discrepancies between model predictions and parthenium invasion in Australia indicate successful management for this globally significant weed. This article is protected by copyright. All rights reserved.

Projecting future expansion of invasive species: Comparing and improving methodologies for species distribution modeling

Modeling the distributions of species, especially of invasive species in non-native ranges, involves multiple challenges. Here, we developed some novel approaches to species distribution modeling aimed at reducing the influences of such challenges and improving the realism of projections. We estimated species-environment relationships with four modeling methods run with multiple scenarios of (1) sources of occurrences and geographically isolated background ranges for absences, (2) approaches to drawing background (absence) points, and (3) alternate sets of predictor variables. We further tested various quantitative metrics of model evaluation against biological insight. Model projections were very sensitive to the choice of training dataset. Model accuracy was much improved by using a global dataset for model training, rather than restricting data input to the species’ native range. AUC score was a poor metric for model evaluation and, if used alone, was not a useful criterion for assessing model performance. Projections away from the sampled space (i.e. into areas of potential future invasion) were very different depending on the modeling methods used, raising questions about the reliability of ensemble projections. Generalized linear models gave very unrealistic projections far away from the training region. Models that efficiently fit the dominant pattern, but exclude highly local patterns in the dataset and capture interactions as they appear in data (e.g. boosted regression trees), improved generalization of the models. Biological knowledge of the species and its distribution was important in refining choices about the best set of projections. A post-hoc test conducted on a new Partenium dataset from Nepal validated excellent predictive performance of our “best” model. We showed that vast stretches of currently uninvaded geographic areas on multiple continents harbor highly suitable habitats for Parthenium hysterophorus L. (Asteraceae; parthenium). However, discrepancies between model predictions and parthenium invasion in Australia indicate successful management for this globally significant weed. This article is protected by copyright. All rights reserved.