Optimal 5-step nilpotent quadratic algebras

By the Golod–Shafarevich theorem, an associative algebra $R$ given by $n$ generators and $<n^2/3$ homogeneous quadratic relations is not 5-step nilpotent. We prove that this estimate is optimal. Namely, we show that for every positive integer $n$, there is an algebra $R$ given by $n$ generators and $\lceil n^2/3\rceil$ homogeneous quadratic relations such that $R$ is 5-step nilpotent.

The Experience and Practice of Approved Social Workers in Northern Ireland

This article reports on the first extensive survey of Approved Social Worker (ASW) activity under the Mental Health (Northern Ireland) Order 1986. The integrated health and social services organizational structure, the adverse effects on individual mental health of the legacy of thirty years of civil conflict and the move from hospital to community care are significant features which have influenced the delivery of mental health social work services locally. The practice and experience of ASWs was surveyed by postal questionnaire and user and carer experience of compulsory hospital admission was investigated by a series of focus groups. The study revealed that two&hyphen;thirds of ASWs had experience of acting as an applicant in compulsory hospital admission during the past two years. Nearly half (42 per cent) of these ASWs had reported experience of between one and five admissions and one&hyphen;tenth had completed over twenty admissions in the two&hyphen;year period. In only a small minority of cases did joint face&hyphen;to&hyphen;face assessment with the General Practitioner (doctor) take place; nearly half of ASWs reported difficulties in obtaining transport; and only one&hyphen;fifth of ASWs had experience of acting as a second approved social worker. Half of ASWs reported experience of guardianship, either as applicant or in making the recommendation. Both service users and carers reported a lack of understanding about the role of the ASW and complained about the lack of alternative resources that ASWs could use to prevent hospital admissions. These findings are discussed and a number of recommendations are proposed for improvements to approved social worker practice.

Nonapical and Cytoplasmic Expression of Interleukin-8, CXCR1, and CXCR2 Correlates with Cell Proliferation and Microvessel Density in Prostate Cancer

Purpose: We characterized interleukin-8 (IL-8) and IL-8 receptor expression (CXCR1 and CXCR2) in prostate cancer to address their significance to this disease. Experimental Design: Immunohistochemistry was conducted on 40 cases of human prostate biopsy containing histologically normal and neoplastic tissue, excised from patients with locally confined or invasive androgen-dependent prostate cancer, and 10 cases of transurethral resection of the prostate material from patients with androgen-independent disease. Results: Weak to moderate IL-8 expression was strictly localized to the apical membrane of normal prostate epithelium. In contrast, membranous expression of IL-8, CXCR1, and CXCR2 was nonapical in cancer cells of Gleason pattern 3 and 4, whereas circumferential expression was present in Gleason pattern 5 and androgen-independent prostate cancer. Each of IL-8, CXCR1, and CXCR2 were also increasingly localized to the cytoplasm of cancer cells in correlation with advancing stage of disease. Cytoplasmic expression (but not apical membrane expression) of IL-8 in Gleason pattern 3 and 4 cancer correlated with Ki-67 expression (R = 0.79; P <0.001), cyclin D1 expression (R = 0.79; P <0.001), and microvessel density (R = 0.81; P <0.001). In vitro studies on androgen-independent PC3 cells confirmed the mitogenic activity of IL-8, increasing the rate of cell proliferation through activation of both CXCR1 and CXCR2 receptors. Conclusions: We propose that the concurrent increase in IL-8 and IL-8 receptor expression in human prostate cancer induces autocrine signaling that may be functionally significant in initiating and promoting the progression of prostate cancer by underpinning cell proliferation and angiogenesis.

Effects of roziglitazone and interactions with growth-regulating factors in ventricular cell hypertrophy

Chronic administration of thiazolidinediones might predispose to cardiac hypertrophy. The aim was to investigate direct effects of rosiglitazone in rat ventricular cardiomyocytes maintained in vitro (24 h). Rosiglitazone (=10-5 M) did not increase protein synthesis and produced small inconsistent increases in cellular protein. In the presence of serum (10% v/v), but not insulin-like growth factor (IGF-1, 10-8 M) or insulin (1 U/ml), an interaction with rosiglitazone to stimulate protein synthesis was observed. The hypertrophic responses to noradrenaline (5×10-6 M), PMA (10-7 M) and ET-1 (10-7 M) were not attenuated by rosiglitazone. Rosiglitazone (10-7 M) did not influence protein synthesis in response to insulin (1 U/ml) and elevated glucose (2.5×10-2 M) alone or in combination, but attenuated the increase in protein mass observed in response to elevated glucose alone. In re-differentiated cardiomyocytes, a model of established hypertrophy, rosiglitazone (10-8 M–10-6 M) increased protein synthesis. Together, these data indicate that rosiglitazone does not initiate cardiomyocyte hypertrophy directly in vitro. However, during chronic administration, the interaction of rosiglitazone with locally-derived growth-regulating factors may make a modest contribution to cardiac remodelling and influence the extent of compensatory hypertrophy of the compromised rat heart.

Isotopic composition of tropospheric and soil N2O from successive depths of agricultural plots with contrasting crops and nitrogen amendments

Agricultural soils are the dominant contributor to increases in atmospheric nitrous oxide (N2O). Few studies have investigated the natural N and O isotopic composition of soil N2O. We collected soil gas samples using horizontal sampling tubes installed at successive depths under five contrasting agricultural crops (e.g., unamended alfalfa, fertilized cereal), and tropospheric air samples. Mean d 15N and d 18O values of soil N2O ranged from -28.0 to +8.9‰, and from +29.0 to +53.6‰. The mean d 15N and d 18O values of tropospheric N2O were +4.6 ± 0.7‰ and +48.3 ± 0.2‰, respectively. In general, d values were lowest at depth, they were negatively correlated to soil [N2O], and d 15N was positively correlated to d 18O for every treatment on all sampling dates. N2O from the different agricultural treatments had distinct d 15N and d 18O values that varied among sampling dates. Fertilized treatments had soil N2O with low d values, but the unamended alfalfa yielded N2O with the lowest d values. Diffusion was not the predominant process controlling N2O concentration profiles. Based on isotopic and concentration data, it appears that soil N2O was consumed, as it moved from deeper to shallower soil layers. To better assess the main process(es) controlling N2O within a soil profile, we propose a conceptual model that integrates data on net N2O production or consumption and isotopic data. The direct local impact of agricultural N2O on the isotopic composition of tropospheric N2O was recorded by a shift toward lower d values of locally measured tropospheric N2O on a day with very high soil N2O emissions.

Completeness of certain function spaces

We give an example of a complete locally convex m-topology on the algebra of infinite differentiable functions on [0, 1] which is strictly coarser than the natural Frechet-topology but finer than the topology of pointwise convergence. A similar construction works on the algebra of continuous functions on [0, 1]. Using this examples we can separate different notions of diffotopy and homotopy.

On weak and strong Peano theorems

We say that the Peano theorem holds for a topological vector space $E$ if, for any continuous mapping $f : {\Bbb R}\times E \to E$ and any $(t(0), x(0))$ is an element of ${\Bbb R}\times E$, the Cauchy problem $\dot x(t) = f(t,x(t))$, $x(t(0)) = x(0)$, has a solution in some neighborhood of $t(0)$. We say that the weak version of Peano theorem holds for $E$ if, for any continuous map $f : {\Bbb R}\times E \to E$, the equation $\dot x(t) = f (t, x(t))$ has a solution on some interval. We construct an example (answering a question posed by S. G. Lobanov) of a Hausdorff locally convex topological vector space E for which the weak version of Peano theorem holds and the Peano theorem fails to hold. We also construct a Hausdorff locally convex topological vector space E for which the Peano theorem holds and any barrel in E is neither compact nor sequentially compact.

Gateaux complex differentiability and continuity

As is known, there are everywhere discontinuous infinitely Frechet differentiable functions on the real locally convex spaces D(R) and V(R) of finitely supported infinitely differentiable functions and, respectively, of generalized functions. In this paper the relationship between the complex differentiability and continuity of a function on a complex locally convex space is considered. We describe a class of complex locally convex spaces, which includes the complex space V(R), such that every Gateaux complex-differentiable function on a space of this class is continuous. We also describe another class of locally convex spaces, which includes the complex space D(R), such that on every space of this class there is an everywhere discontinuous infinitely Frechet complex-differentiable function whose derivatives are continuous.

On linear extension operators

We construct a countable-dimensional Hausdorff locally convex topological vector space $E$ and a stratifiable closed linear subspace $F$ subset of $E$ such that any linear extension operator from $C_b(F)$ to $C_b(E)$ is unbounded (here $C_b(X)$ stands for the Banach space of continuous bounded real-valued functions on $X$).

Genetic algorithms for local controller network construction

Local Controller Networks (LCNs) provide nonlinear control by interpolating between a set of locally valid, subcontrollers covering the operating range of the plant. Constructing such networks typically requires knowledge of valid local models. This paper describes a new genetic learning approach to the construction of LCNs directly from the dynamic equations of the plant, or from modelling data. The advantage is that a priori knowledge about valid local models is not needed. In addition to allowing simultaneous optimisation of both the controller and validation function parameters, the approach aids transparency by ensuring that each local controller acts independently of the rest at its operating point. It thus is valuable for simultaneous design of the LCNs and identification of the operating regimes of an unknown plant. Application results from a highly nonlinear pH neutralisation process and its associated neural network representation are utilised to illustrate these issues.

Comparison of two construction algorithms for local model networks

The divide-and-conquer approach of local model (LM) networks is a common engineering approach to the identification of a complex nonlinear dynamical system. The global representation is obtained from the weighted sum of locally valid, simpler sub-models defined over small regions of the operating space. Constructing such networks requires the determination of appropriate partitioning and the parameters of the LMs. This paper focuses on the structural aspect of LM networks. It compares the computational requirements and performances of the Johansen and Foss (J&F) and LOLIMOT tree-construction algorithms. Several useful and important modifications to each algorithm are proposed. The modelling performances are evaluated using real data from a pilot plant of a pH neutralization process. Results show that while J&F achieves a more accurate nonlinear representation of the pH process, LOLIMOT requires significantly less computational effort.

Robust fuzzy Gustafson-Kessel clustering for nonlinear system identification

This paper deals with Takagi-Sugeno (TS) fuzzy model identification of nonlinear systems using fuzzy clustering. In particular, an extended fuzzy Gustafson-Kessel (EGK) clustering algorithm, using robust competitive agglomeration (RCA), is developed for automatically constructing a TS fuzzy model from system input-output data. The EGK algorithm can automatically determine the 'optimal' number of clusters from the training data set. It is shown that the EGK approach is relatively insensitive to initialization and is less susceptible to local minima, a benefit derived from its agglomerate property. This issue is often overlooked in the current literature on nonlinear identification using conventional fuzzy clustering. Furthermore, the robust statistical concepts underlying the EGK algorithm help to alleviate the difficulty of cluster identification in the construction of a TS fuzzy model from noisy training data. A new hybrid identification strategy is then formulated, which combines the EGK algorithm with a locally weighted, least-squares method for the estimation of local sub-model parameters. The efficacy of this new approach is demonstrated through function approximation examples and also by application to the identification of an automatic voltage regulation (AVR) loop for a simulated 3 kVA laboratory micro-machine system.

Coastline configuration as a determinant of structure in larval assemblages

The richness and turnover of coastal larval pools set upper limits for biodiversity in coastal systems. For particular local systems, such as embayments, the characteristics of the local larval pool are determined by the relative contributions of locally produced and external larvae. The balance between these sources partially reflects the extent of tidal exchange and is hence related to system size and flushing time. Larvae of benthic marine invertebrates were sampled from 8 bays along the Irish coast to investigate the effect of coastline configuration on the characteristics of the larval pool. Flushing time explained 34.5% of the variability in species richness from a series of daily samples. Many of the potentially relevant environmental variables are correlated, limiting the potential for individual variables to be examined in isolation. We therefore used a principal components analysis to describe the major patterns in environmental variability across bays. The second principal component separated bays along a gradient of increasing depth, salinity, tidal range and flushing time. Scores along this component were generally better predictors of the larval pool than single variables, explaining as much as 61.2% of the variation in species richness, diversity and similarity between dates. Deeper bays, with more saline water and longer flushing times, tended to have richer and more diverse larval pools, with a greater consistency in species composition between sample dates. No relationship was found between environmental variables and larval abundance. Our results suggest that flushing time, particularly when in combination with topographic variables, chlorophyll, tidal range and salinity, may be a useful predictor for the richness and turnover of local larval pools.

Effects of environment and an introduced invertebrate species on the structure of benthic macroinvertebrate species at the catchment level

Biotic interactions such as predation and competition can influence aquatic communities at small spatial scales, but they are expected to be overridden by environmental factors at large scales. The continuing threat to freshwater biodiversity of biological invasions indicates that biotic factors do, however, have important structuring roles. In Irish rivers, the native amphipod Gammarus duebeni celticus has become locally extinct, ostensibly through differential predation by the more aggressive and introduced G. pulex. This mechanism explains impacts of G. pulex at within-river spatial scales on native macroinvertebrate community diversity, including declines in ephemeropterans, plecopterans, dipterans and oligochaetes. To determine if these patterns are predictable at larger spatial scales, we assessed patterns in native macroinvertebrate communities across river sites of the Erne catchment in 1998 and 1999, in conjunction with the distribution of G. pulex and G. d. celticus. In both years, G. pulex dominated invaded sites, whereas G. d. celticus occurred at low abundance in uninvaded sites. In both years, invaded sites had lower diversity and fewer pollution sensitive invertebrate species than un-invaded sites. Community ordination in 1998 showed that invaded sites had higher conductivity, smaller substrate particle size and comprised a lower proportion of pollution sensitive taxa including Ephemeroptera and Plecoptera. In contrast, in 1999, conductivity was the only variable explaining site ordination along axis 1, but was unable to separate sites with respect to invasion status. A second explanatory axis separated sites with respect to invasion status, with invaded sites having fewer taxa, including lower abundance of ephemeropterans, dipterans and plecopterans. Laboratory experiments examined the potential role of differential predation between the two Gammarus species in explaining these taxon specific patterns in the field. Survival of the ephemeropterans, Ephemerella ignita and Ecdyonurus venosus and the isopod, Asellus aquaticus, was lower when interacting with G. pulex than with G. d. celticus. This study indicates that G. putex may alter invertebrate community structure at scales beyond those detected within individual rivers. However, effects may be influenced by gradients in physico-chemistry, which may be temporal or depend on catchment characteristics. Invasions by amphipods have increased globally, thus comprehensive assessments of their impacts and of other aquatic invaders, may only be apparent when studies are conducted at a range of spatio-temporal scales.