Stability of solutions of linear difference equations with periodic coefficients

This paper represents the last technical contribution of Professor Patrick Parks before his untimely death in February 1995. The remaining authors of the paper, which was subsequently completed, wish to dedicate the article to Patrick. A frequency criterion for the stability of solutions of linear difference equations with periodic coefficients is established. The stability criterion is based on a consideration of the behaviour of a frequency hodograph with respect to the origin of coordinates in the complex plane. The formulation of this criterion does not depend on the order of the difference equation.

The representation of fathers by children of depressed mothers: refining the meaning of parentification in high-risk samples

Background: Children’s representations of mothers in doll-play are associated with child adjustment. Despite the importance of fathers for children’s adjustment, especially in the context of maternal psychopathology, few studies have considered children’s representations of their fathers. Method: We examined the portrayal of fathers by 5-year-old children of depressed (N = 55) and non-depressed (N = 39) mothers in a doll-play procedure concerning family experience. Results: Children gave equal prominence in their play to mothers and fathers. Representations of fathers were unrelated to maternal mood, but were associated with parental conflict. Representations of child care for the father that was unreciprocated predicted poor child adjustment in school, but only in children exposed to maternal postnatal depression. Conclusions: It may be clinically useful to consider children’s distinctive representations of their mother and father; but the concept of parentification in relation to risk and resilience effects requires refinement.

Cumulant-based deconvolution and identification: several new families of linear equations

This paper presents several new families of cumulant-based linear equations with respect to the inverse filter coefficients for deconvolution (equalisation) and identification of nonminimum phase systems. Based on noncausal autoregressive (AR) modeling of the output signals and three theorems, these equations are derived for the cases of 2nd-, 3rd and 4th-order cumulants, respectively, and can be expressed as identical or similar forms. The algorithms constructed from these equations are simpler in form, but can offer more accurate results than the existing methods. Since the inverse filter coefficients are simply the solution of a set of linear equations, their uniqueness can normally be guaranteed. Simulations are presented for the cases of skewed series, unskewed continuous series and unskewed discrete series. The results of these simulations confirm the feasibility and efficiency of the algorithms.

Structure adaptation of linear MMSE adaptive filters

The tap-length, or the number of the taps, is an important structural parameter of the linear MMSE adaptive filter. Although the optimum tap-length that balances performance and complexity varies with scenarios, most current adaptive filters fix the tap-length at some compromise value, making them inefficient to implement especially in time-varying scenarios. A novel gradient search based variable tap-length algorithm is proposed, using the concept of the pseudo-fractional tap-length, and it is shown that the new algorithm can converge to the optimum tap-length in the mean. Results of computer simulations are also provided to verify the analysis.

Maternal affective disorder and children’s representation of their families

Children’s perceptions of family relationship are related to their later emotional and social adjustment. This is of particular relevance in the context of family stressors such as maternal affective disorder. This study investigated the effects of maternal postnatal depression and anxiety on children’s family representations. In our sample of postnatally depressed mothers we also explored marital conflict as mediator between maternal psychopathology and children’s representations. Family drawings of 235 4–5 year-old children (93 control, 53 depressed and 89 anxious) were examined. When compared to controls, children of depressed, but not of anxious mothers, were more likely to draw themselves as less prominent than other family members and to represent a dysfunctional family, less likely to represent themselves with a happy face and showed a greater tendency of drawing bizarre pictures. Marital conflict mediated the association between maternal depression and dysfunctionality in drawings.

Discrete time representation of continuous time ARMA processes

This paper derives exact discrete time representations for data generated by a continuous time autoregressive moving average (ARMA) system with mixed stock and flow data. The representations for systems comprised entirely of stocks or of flows are also given. In each case the discrete time representations are shown to be of ARMA form, the orders depending on those of the continuous time system. Three examples and applications are also provided, two of which concern the stationary ARMA(2, 1) model with stock variables (with applications to sunspot data and a short-term interest rate) and one concerning the nonstationary ARMA(2, 1) model with a flow variable (with an application to U.S. nondurable consumers’ expenditure). In all three examples the presence of an MA(1) component in the continuous time system has a dramatic impact on eradicating unaccounted-for serial correlation that is present in the discrete time version of the ARMA(2, 0) specification, even though the form of the discrete time model is ARMA(2, 1) for both models.

Towards an improved and more flexible representation of water stress in coupled photosynthesis–stomatal conductance models

Coupled photosynthesis–stomatal conductance (A–gs) models are commonly used in ecosystem models to represent the exchange rate of CO2 and H2O between vegetation and the atmosphere. The ways these models account for water stress differ greatly among modelling schemes. This study provides insight into the impact of contrasting model configurations of water stress on the simulated leaf-level values of net photosynthesis (A), stomatal conductance (gs), the functional relationship among them and their ratio, the intrinsic water use efficiency (A/gs), as soil dries. A simple, yet versatile, normalized soil moisture dependent function was used to account for the effects of water stress on gs, on mesophyll conductance (gm) and on the biochemical capacity. Model output was compared to leaf-level values obtained from the literature. The sensitivity analyses emphasized the necessity to combine both stomatal and non-stomatal limitations of A in coupled A–gs models to accurately capture the observed functional relationships A vs. gs and A/gsvs. gs in response to drought. Accounting for water stress in coupled A–gs models by imposing either stomatal or biochemical limitations of A, as commonly practiced in most ecosystem models, failed to reproduce the observed functional relationship between key leaf gas exchange attributes. A quantitative limitation analysis revealed that the general pattern of C3 photosynthetic response to water stress may be well represented in coupled A–gs models by imposing the highest limitation strength to gm, then to gs and finally to the biochemical capacity.

In vitro fermentation of linear and alpha-1,2-branched dextrans by the human fecal microbiota

The role of structure and molecular weight in fermentation selectivity in linear α-1,6 dextrans and dextrans with α-1,2 branching was investigated. Fermentation by gut bacteria was determined in anaerobic, pH-controlled fecal batch cultures after 36 h. Inulin (1%, wt/vol), which is a known prebiotic, was used as a control. Samples were obtained at 0, 10, 24, and 36 h of fermentation for bacterial enumeration by fluorescent in situ hybridization and short-chain fatty acid analyses. The gas production of the substrate fermentation was investigated in non-pH-controlled, fecal batch culture tubes after 36 h. Linear and branched 1-kDa dextrans produced significant increases in Bifidobacterium populations. The degree of α-1,2 branching did not influence the Bifidobacterium populations; however, α-1,2 branching increased the dietary fiber content, implying a decrease in digestibility. Other measured bacteria were unaffected by the test substrates except for the Bacteroides-Prevotella group, the growth levels of which were increased on inulin and 6- and 70-kDa dextrans, and the Faecalibacterium prausnitzii group, the growth levels of which were decreased on inulin and 1-kDa dextrans. A considerable increase in short-chain fatty acid concentration was measured following the fermentation of all dextrans and inulin. Gas production rates were similar among all dextrans tested but were significantly slower than that for inulin. The linear 1-kDa dextran produced lower total gas and shorter time to attain maximal gas production compared to those of the 70-kDa dextran (branched) and inulin. These findings indicate that dextrans induce a selective effect on the gut flora, short-chain fatty acids, and gas production depending on their length.

The representation of highly pathogenic avian influenza in the Chinese media

In the early 2000s the threat of Highly Pathogenic Avian Influenza captured the attention of the world's media. While China is often considered the epicentre of the panzootic, few studies have explored coverage of this variant of avian flu in China. To address this issue, the authors examined the portrayal of Highly Pathogenic Avian Influenza across four Chinese newspapers at the local and national level. A textual analysis was performed on 160 articles across an eight-year period from 2001–2008. The study approach drew from Critical Discourse Analysis and Social Representation Theory. The headline analysis showed the extent that risk of the disease was subverted by the depiction of a strong and efficient ‘China’ that was a global leader in the fight against the disease. Ideological referents were called upon to stress teamwork in confronting the crisis. The diachronic analysis illustrated how the relationship between commercial interests, science and public health risks played out within the Chinese media.

Superensembles of linear viscoelastic models of polymer melts

The idea of incorporating multiple models of linear rheology into a superensemble, to forge a consensus forecast from the individual model predictions, is investigated. The relative importance of the individual models in the so-called multimodel superensemble (MMSE) was inferred by evaluating their performance on a set of experimental training data, via nonlinear regression. The predictive ability of the MMSE model was tested by comparing its predictions on test data that were similar (in-sample) and dissimilar (out-of-sample) to the training data used in the calibration. For the in-sample forecasts, we found that the MMSE model easily outperformed the best constituent model. The presence of good individual models greatly enhanced the MMSE forecast, while the presence of some bad models in the superensemble also improved the MMSE forecast modestly. While the performance of the MMSE model on the out-of-sample training data was not as spectacular, it demonstrated the robustness of this approach.

A note on the Fredholm properties of Toeplitz operators on weighted Bergman spaces with matrix-valued symbols

We characterize the essential spectra of Toeplitz operators Ta on weighted Bergman spaces with matrix-valued symbols; in particular we deal with two classes of symbols, the Douglas algebra C+H∞ and the Zhu class Q := L∞ ∩VMO∂ . In addition, for symbols in C+H∞ , we derive a formula for the index of Ta in terms of its symbol a in the scalar-valued case, while in the matrix-valued case we indicate that the standard reduction to the scalar-valued case fails to work analogously to the Hardy space case. Mathematics subject classification (2010): 47B35,

The contribution of primary and secondary somatosensory cortices to the representation of body parts and body sides: an fMRI adaptation study

Although the somatosensory homunculus is a classically used description of the way somatosensory inputs are processed in the brain, the actual contributions of primary (SI) and secondary (SII) somatosensory cortices to the spatial coding of touch remain poorly understood. We studied adaptation of the fMRI BOLD response in the somatosensory cortex by delivering pairs of vibrotactile stimuli to the finger tips of the index and middle fingers. The first stimulus (adaptor) was delivered either to the index or to the middle finger of the right or left hand, whereas the second stimulus (test) was always administered to the left index finger. The overall BOLD response evoked by the stimulation was primarily contralateral in SI and was more bilateral in SII. However, our fMRI adaptation approach also revealed that both somatosensory cortices were sensitive to ipsilateral as well as to contralateral inputs. SI and SII adapted more after subsequent stimulation of homologous as compared with nonhomologous fingers, showing a distinction between different fingers. Most importantly, for both somatosensory cortices, this finger-specific adaptation occurred irrespective of whether the tactile stimulus was delivered to the same or to different hands. This result implies integration of contralateral and ipsilateral somatosensory inputs in SI as well as in SII. Our findings suggest that SI is more than a simple relay for sensory information and that both SI and SII contribute to the spatial coding of touch by discriminating between body parts (fingers) and by integrating the somatosensory input from the two sides of the body (hands).

Understanding advances in the simulation of intraseasonal variability in the ECMWF model. Part I: the representation of the MJO

As a major mode of intraseasonal variability, which interacts with weather and climate systems on a near-global scale, the Madden – Julian Oscillation (MJO) is a crucial source of predictability for numerical weather prediction (NWP) models. Despite its global significance and comprehensive investigation, improvements in the representation of the MJO in an NWP context remain elusive. However, recent modifications to the model physics in the ECMWF model led to advances in the representation of atmospheric variability and the unprecedented propagation of the MJO signal through the entire integration period. In light of these recent advances, a set of hindcast experiments have been designed to assess the sensitivity of MJO simulation to the formulation of convection. Through the application of established MJO diagnostics, it is shown that the improvements in the representation of the MJO can be directly attributed to the modified convective parametrization. Furthermore, the improvements are attributed to the move from a moisture-convergent- to a relative-humidity-dependent formulation for organized deep entrainment. It is concluded that, in order to understand the physical mechanisms through which a relative-humidity-dependent formulation for entrainment led to an improved simulation of the MJO, a more process-based approach should be taken. T he application of process-based diagnostics t o t he hindcast experiments presented here will be the focus of Part II of this study.