Lateral boundary contributions to wave-activity invariants and nonlinear stability theorems for balanced dynamics

The slow advective-timescale dynamics of the atmosphere and oceans is referred to as balanced dynamics. An extensive body of theory for disturbances to basic flows exists for the quasi-geostrophic (QG) model of balanced dynamics, based on wave-activity invariants and nonlinear stability theorems associated with exact symmetry-based conservation laws. In attempting to extend this theory to the semi-geostrophic (SG) model of balanced dynamics, Kushner & Shepherd discovered lateral boundary contributions to the SG wave-activity invariants which are not present in the QG theory, and which affect the stability theorems. However, because of technical difficulties associated with the SG model, the analysis of Kushner & Shepherd was not fully nonlinear. This paper examines the issue of lateral boundary contributions to wave-activity invariants for balanced dynamics in the context of Salmon's nearly geostrophic model of rotating shallow-water flow. Salmon's model has certain similarities with the SG model, but also has important differences that allow the present analysis to be carried to finite amplitude. In the process, the way in which constraints produce boundary contributions to wave-activity invariants, and additional conditions in the associated stability theorems, is clarified. It is shown that Salmon's model possesses two kinds of stability theorems: an analogue of Ripa's small-amplitude stability theorem for shallow-water flow, and a finite-amplitude analogue of Kushner & Shepherd's SG stability theorem in which the ‘subsonic’ condition of Ripa's theorem is replaced by a condition that the flow be cyclonic along lateral boundaries. As with the SG theorem, this last condition has a simple physical interpretation involving the coastal Kelvin waves that exist in both models. Salmon's model has recently emerged as an important prototype for constrained Hamiltonian balanced models. The extent to which the present analysis applies to this general class of models is discussed.

On Hamiltonian balanced dynamics and the slowest invariant manifold

The concept of a slowest invariant manifold is investigated for the five-component model of Lorenz under conservative dynamics. It is shown that Lorenz's model is a two-degree-of-freedom canonical Hamiltonian system, consisting of a nonlinear vorticity-triad oscillator coupled to a linear gravity wave oscillator, whose solutions consist of regular and chaotic orbits. When either the Rossby number or the rotational Froude number is small, there is a formal separation of timescales, and one can speak of fast and slow motion. In the same regime, the coupling is weak, and the Kolmogorov–Arnold-Moser theorem is shown to apply. The chaotic orbits are inherently unbalanced and are confined to regions sandwiched between invariant tori consisting of quasi-periodic regular orbits. The regular orbits generally contain free fast motion, but a slowest invariant manifold may be geometrically defined as the set of all slow cores of invariant tori (defined by zero fast action) that are smoothly related to such cores in the uncoupled system. This slowest invariant manifold is not global; in fact, its structure is fractal; but it is of nearly full measure in the limit of weak coupling. It is also nonlinearly stable. As the coupling increases, the slowest invariant manifold shrinks until it disappears altogether. The results clarify previous definitions of a slowest invariant manifold and highlight the ambiguity in the definition of “slowness.” An asymptotic procedure, analogous to standard initialization techniques, is found to yield nonzero free fast motion even when the core solutions contain none. A hierarchy of Hamiltonian balanced models preserving the symmetries in the original low-order model is formulated; these models are compared with classic balanced models, asymptotically initialized solutions of the full system and the slowest invariant manifold defined by the core solutions. The analysis suggests that for sufficiently small Rossby or rotational Froude numbers, a stable slowest invariant manifold can be defined for this system, which has zero free gravity wave activity, but it cannot be defined everywhere. The implications of the results for more complex systems are discussed.

Fine-grained multi-phase array designs

Hybrid multiprocessor architectures which combine re-configurable computing and multiprocessors on a chip are being proposed to transcend the performance of standard multi-core parallel systems. Both fine-grained and coarse-grained parallel algorithm implementations are feasible in such hybrid frameworks. A compositional strategy for designing fine-grained multi-phase regular processor arrays to target hybrid architectures is presented in this paper. The method is based on deriving component designs using classical regular array techniques and composing the components into a unified global design. Effective designs with phase-changes and data routing at run-time are characteristics of these designs. In order to describe the data transfer between phases, the concept of communication domain is introduced so that the producer–consumer relationship arising from multi-phase computation can be treated in a unified way as a data routing phase. This technique is applied to derive new designs of multi-phase regular arrays with different dataflow between phases of computation.

Balanced excitation and inhibition: Model based analysis of local field potentials

We have developed a model of the local field potential (LFP) based on the conservation of charge, the independence principle of ionic flows and the classical Hodgkin–Huxley (HH) type intracellular model of synaptic activity. Insights were gained through the simulation of the HH intracellular model on the nonlinear relationship between the balance of synaptic conductances and that of post-synaptic currents. The latter is dependent not only on the former, but also on the temporal lag between the excitatory and inhibitory conductances, as well as the strength of the afferent signal. The proposed LFP model provides a method for decomposing the LFP recordings near the soma of layer IV pyramidal neurons in the barrel cortex of anaesthetised rats into two highly correlated components with opposite polarity. The temporal dynamics and the proportional balance of the two components are comparable to the excitatory and inhibitory post-synaptic currents computed from the HH model. This suggests that the two components of the LFP reflect the underlying excitatory and inhibitory post-synaptic currents of the local neural population. We further used the model to decompose a sequence of evoked LFP responses under repetitive electrical stimulation (5 Hz) of the whisker pad. We found that as neural responses adapted, the excitatory and inhibitory components also adapted proportionately, while the temporal lag between the onsets of the two components increased during frequency adaptation. Our results demonstrated that the balance between neural excitation and inhibition can be investigated using extracellular recordings. Extension of the model to incorporate multiple compartments should allow more quantitative interpretations of surface Electroencephalography (EEG) recordings into components reflecting the excitatory, inhibitory and passive ionic current flows generated by local neural populations.

Nonlinear identification using orthogonal forward regression with nested optimal regularization

An efficient data based-modeling algorithm for nonlinear system identification is introduced for radial basis function (RBF) neural networks with the aim of maximizing generalization capability based on the concept of leave-one-out (LOO) cross validation. Each of the RBF kernels has its own kernel width parameter and the basic idea is to optimize the multiple pairs of regularization parameters and kernel widths, each of which is associated with a kernel, one at a time within the orthogonal forward regression (OFR) procedure. Thus, each OFR step consists of one model term selection based on the LOO mean square error (LOOMSE), followed by the optimization of the associated kernel width and regularization parameter, also based on the LOOMSE. Since like our previous state-of-the-art local regularization assisted orthogonal least squares (LROLS) algorithm, the same LOOMSE is adopted for model selection, our proposed new OFR algorithm is also capable of producing a very sparse RBF model with excellent generalization performance. Unlike our previous LROLS algorithm which requires an additional iterative loop to optimize the regularization parameters as well as an additional procedure to optimize the kernel width, the proposed new OFR algorithm optimizes both the kernel widths and regularization parameters within the single OFR procedure, and consequently the required computational complexity is dramatically reduced. Nonlinear system identification examples are included to demonstrate the effectiveness of this new approach in comparison to the well-known approaches of support vector machine and least absolute shrinkage and selection operator as well as the LROLS algorithm.

Missing steps in a staircase: a qualitative study of the perspectives of key stakeholders on the use of adaptive designs in confirmatory trials

Background Despite the promising benefits of adaptive designs (ADs), their routine use, especially in confirmatory trials, is lagging behind the prominence given to them in the statistical literature. Much of the previous research to understand barriers and potential facilitators to the use of ADs has been driven from a pharmaceutical drug development perspective, with little focus on trials in the public sector. In this paper, we explore key stakeholders’ experiences, perceptions and views on barriers and facilitators to the use of ADs in publicly funded confirmatory trials. Methods Semi-structured, in-depth interviews of key stakeholders in clinical trials research (CTU directors, funding board and panel members, statisticians, regulators, chief investigators, data monitoring committee members and health economists) were conducted through telephone or face-to-face sessions, predominantly in the UK. We purposively selected participants sequentially to optimise maximum variation in views and experiences. We employed the framework approach to analyse the qualitative data. Results We interviewed 27 participants. We found some of the perceived barriers to be: lack of knowledge and experience coupled with paucity of case studies, lack of applied training, degree of reluctance to use ADs, lack of bridge funding and time to support design work, lack of statistical expertise, some anxiety about the impact of early trial stopping on researchers’ employment contracts, lack of understanding of acceptable scope of ADs and when ADs are appropriate, and statistical and practical complexities. Reluctance to use ADs seemed to be influenced by: therapeutic area, unfamiliarity, concerns about their robustness in decision-making and acceptability of findings to change practice, perceived complexities and proposed type of AD, among others. Conclusions There are still considerable multifaceted, individual and organisational obstacles to be addressed to improve uptake, and successful implementation of ADs when appropriate. Nevertheless, inferred positive change in attitudes and receptiveness towards the appropriate use of ADs by public funders are supportive and are a stepping stone for the future utilisation of ADs by researchers.

Generic construction of monitors for floating point unit designs

This paper proposes a set of well defined steps to design functional verification monitors intended to verify Floating Point Units (FPU) described in HDL. The first step consists on defining the input and output domain coverage. Next, the corner cases are defined. Finally, an already verified reference model is used in order to test the correctness of the Device Under Verification (DUV). As a case study a monitor for an IEEE754-2008 compliant design is implemented. This monitor is built to be easily instantiated into verification frameworks such as OVM. Two different designs were verified reaching complete input coverage and successful compliant results.

Balanced Ocean-Data Assimilation near the Equator

The question is addressed whether using unbalanced updates in ocean-data assimilation schemes for seasonal forecasting systems can result in a relatively poor simulation of zonal currents. An assimilation scheme, where temperature observations are used for updating only the density field, is compared to a scheme where updates of density field and zonal velocities are related by geostrophic balance. This is done for an equatorial linear shallow-water model. It is found that equatorial zonal velocities can be detoriated if velocity is not updated in the assimilation procedure. Adding balanced updates to the zonal velocity is shown to be a simple remedy for the shallow-water model. Next, optimal interpolation (OI) schemes with balanced updates of the zonal velocity are implemented in two ocean general circulation models. First tests indicate a beneficial impact on equatorial upper-ocean zonal currents.

Cross-sector surveys assessing perceptions of key stakeholders towards barriers, concerns and facilitators to the appropriate use of adaptive designs in confirmatory trials

Background Appropriately conducted adaptive designs (ADs) offer many potential advantages over conventional trials. They make better use of accruing data, potentially saving time, trial participants, and limited resources compared to conventional, fixed sample size designs. However, one can argue that ADs are not implemented as often as they should be, particularly in publicly funded confirmatory trials. This study explored barriers, concerns, and potential facilitators to the appropriate use of ADs in confirmatory trials among key stakeholders. Methods We conducted three cross-sectional, online parallel surveys between November 2014 and January 2015. The surveys were based upon findings drawn from in-depth interviews of key research stakeholders, predominantly in the UK, and targeted Clinical Trials Units (CTUs), public funders, and private sector organisations. Response rates were as follows: 30(55 %) UK CTUs, 17(68 %) private sector, and 86(41 %) public funders. A Rating Scale Model was used to rank barriers and concerns in order of perceived importance for prioritisation. Results Top-ranked barriers included the lack of bridge funding accessible to UK CTUs to support the design of ADs, limited practical implementation knowledge, preference for traditional mainstream designs, difficulties in marketing ADs to key stakeholders, time constraints to support ADs relative to competing priorities, lack of applied training, and insufficient access to case studies of undertaken ADs to facilitate practical learning and successful implementation. Associated practical complexities and inadequate data management infrastructure to support ADs were reported as more pronounced in the private sector. For funders of public research, the inadequate description of the rationale, scope, and decision-making criteria to guide the planned AD in grant proposals by researchers were all viewed as major obstacles. Conclusions There are still persistent and important perceptions of individual and organisational obstacles hampering the use of ADs in confirmatory trials research. Stakeholder perceptions about barriers are largely consistent across sectors, with a few exceptions that reflect differences in organisations’ funding structures, experiences and characterisation of study interventions. Most barriers appear connected to a lack of practical implementation knowledge and applied training, and limited access to case studies to facilitate practical learning. Keywords: Adaptive designs; flexible designs; barriers; surveys; confirmatory trials; Phase 3; clinical trials; early stopping; interim analyses

Interim analyses and sequential designs in phase III studies

Recruitment of patients to a clinical trial usually occurs over a period of time, resulting in the steady accumulation of data throughout the trial's duration. Yet, according to traditional statistical methods, the sample size of the trial should be determined in advance, and data collected on all subjects before analysis proceeds. For ethical and economic reasons, the technique of sequential testing has been developed to enable the examination of data at a series of interim analyses. The aim is to stop recruitment to the study as soon as there is sufficient evidence to reach a firm conclusion. In this paper we present the advantages and disadvantages of conducting interim analyses in phase III clinical trials, together with the key steps to enable the successful implementation of sequential methods in this setting. Examples are given of completed trials, which have been carried out sequentially, and references to relevant literature and software are provided.

Nested diets: a novel pattern of individual-level resource use

Many generalist populations may actually be composed of relatively specialist individuals. This `individual specialization` may have important ecological and evolutionary implications. Although this phenomenon has been documented in more than one hundred taxa, it is still unclear how individuals within a population actually partition resources. Here we applied several methods based on network theory to investigate the intrapopulation patterns of resource use in the gracile mouse opossum Gracilinanus microtarsus. We found evidence of significant individual specialization in this species and that the diets of specialists are nested within the diets of generalists. This novel pattern is consistent with a recently proposed model of optimal foraging and implies strong asymmetry in the interactions among individuals of a population.

The nested assembly of individual-resource networks

P>1. Much of the current understanding of ecological systems is based on theory that does not explicitly take into account individual variation within natural populations. However, individuals may show substantial variation in resource use. This variation in turn may be translated into topological properties of networks that depict interactions among individuals and the food resources they consume (individual-resource networks). 2. Different models derived from optimal diet theory (ODT) predict highly distinct patterns of trophic interactions at the individual level that should translate into distinct network topologies. As a consequence, individual-resource networks can be useful tools in revealing the incidence of different patterns of resource use by individuals and suggesting their mechanistic basis. 3. In the present study, using data from several dietary studies, we assembled individual-resource networks of 10 vertebrate species, previously reported to show interindividual diet variation, and used a network-based approach to investigate their structure. 4. We found significant nestedness, but no modularity, in all empirical networks, indicating that (i) these populations are composed of both opportunistic and selective individuals and (ii) the diets of the latter are ordered as predictable subsets of the diets of the more opportunistic individuals. 5. Nested patterns are a common feature of species networks, and our results extend its generality to trophic interactions at the individual level. This pattern is consistent with a recently proposed ODT model, in which individuals show similar rank preferences but differ in their acceptance rate for alternative resources. Our findings therefore suggest a common mechanism underlying interindividual variation in resource use in disparate taxa.

Balanced polymorphism in bottlenecked populations: The case of the CCR5 5 ` cis-regulatory region in Amazonian Amerindians

The 5` cis-regulatory region of the CCR5 gene exhibits a strong signature of balancing selection in several human populations. Here we analyze the polymorphism of this region in Amerindians from Amazonia, who have a complex demographic history, including recent bottlenecks that are known to reduce genetic variability. Amerindians show high nucleotide diversity (pi = 0.27%) and significantly positive Tajima`s D, and carry haplotypes associated with weak and strong gene expression. To evaluate whether these signatures of balancing selection could be explained by demography, we perform neutrality tests based on empiric and simulated data. The observed Tajima`s D was higher than that of other world populations: higher than that found for 18 noncoding regions of South Amerindians, and higher than 99.6% of simulated genealogies, which assume nonequilibrium conditions. Moreover, comparing Amerindians and Asians, the Fst for CCR5 cis-regulatory region was unusually low, in relation to neutral markers. These findings indicate that, despite their complex demographic history, South Amerindians carry a detectable signature of selection on the CCR5 cis-regulatory region. (C) 2010 American Society for Histocompatibility and Immunogenetics. Published by Elsevier Inc. All rights reserved.