Determining when the absolute state complexity of a Hermitian code achieves its DLP bound

Let g be the genus of the Hermitian function field H/F(q)2 and let C-L(D,mQ(infinity)) be a typical Hermitian code of length n. In [Des. Codes Cryptogr., to appear], we determined the dimension/length profile (DLP) lower bound on the state complexity of C-L(D,mQ(infinity)). Here we determine when this lower bound is tight and when it is not. For m less than or equal to n-2/2 or m greater than or equal to n-2/2 + 2g, the DLP lower bounds reach Wolf's upper bound on state complexity and thus are trivially tight. We begin by showing that for about half of the remaining values of m the DLP bounds cannot be tight. In these cases, we give a lower bound on the absolute state complexity of C-L(D,mQ(infinity)), which improves the DLP lower bound. Next we give a good coordinate order for C-L(D,mQ(infinity)). With this good order, the state complexity of C-L(D,mQ(infinity)) achieves its DLP bound (whenever this is possible). This coordinate order also provides an upper bound on the absolute state complexity of C-L(D,mQ(infinity)) (for those values of m for which the DLP bounds cannot be tight). Our bounds on absolute state complexity do not meet for some of these values of m, and this leaves open the question whether our coordinate order is best possible in these cases. A straightforward application of these results is that if C-L(D,mQ(infinity)) is self-dual, then its state complexity (with respect to the lexicographic coordinate order) achieves its DLP bound of n /2 - q(2)/4, and, in particular, so does its absolute state complexity.

Lower Bounds on the State Complexity of Geometric Goppa Codes

We reinterpret the state space dimension equations for geometric Goppa codes. An easy consequence is that if deg G less than or equal to n-2/2 or deg G greater than or equal to n-2/2 + 2g then the state complexity of C-L(D, G) is equal to the Wolf bound. For deg G is an element of [n-1/2, n-3/2 + 2g], we use Clifford's theorem to give a simple lower bound on the state complexity of C-L(D, G). We then derive two further lower bounds on the state space dimensions of C-L(D, G) in terms of the gonality sequence of F/F-q. (The gonality sequence is known for many of the function fields of interest for defining geometric Goppa codes.) One of the gonality bounds uses previous results on the generalised weight hierarchy of C-L(D, G) and one follows in a straightforward way from first principles; often they are equal. For Hermitian codes both gonality bounds are equal to the DLP lower bound on state space dimensions. We conclude by using these results to calculate the DLP lower bound on state complexity for Hermitian codes.

Pro re nata medication for psychoses: the knowledge and beliefs of doctors and nurses

Objective: To examine the knowledge and beliefs of doctors and nurses in inpatient psychiatric units about pro re nata (PRN) (as needed) medications for psychotic disorders. Methods: Medical (n = 44) and nursing (n = 80) staff in two metropolitan public hospital units completed a structured questionnaire about their use of PRN psychotropic medications on one occasion during the four months from March-June 1999. Results: Nurses selected more indications for PRN antipsychotics than doctors (3.49 vs 2.72, p < 0.05), whereas doctors selected more indications for PRN benzodiazepines (3.77 vs 3.19, p < 0.05). The groups did not differ in the number of selected indications for using anticholinergics. For agitation, the majority of nurses viewed both benzodiazepines (56%) and antipsychotics (86%) as effective, with 60% preferring an antipsychotic. For the acute control of psychotic symptoms, 99% of nurses believed antipsychotics were effective and 58% benzodiazepines, with 87% preferring an antipsychotic. A large majority of doctors viewed both PRN benzodiazepines, 94% ,and antipsychotics, 81%, as effective for agitation, and 55% preferred to use a benzodiazepine. For psychotic symptoms, 80% believed PRN antipsychotics were effective, but only 32% viewed benzodiazepines as effective, and 64% preferred to use an antipsychotic. Nursing staff identified more non-pharmacological techniques for managing both agitation and psychotic symptoms and reported using these more often than doctors. Junior staff, both nursing and medical, had less knowledge of non-pharmacological alternatives to PRN medication than senior staff. Conclusions: Disparities existed between doctors and nurses views on the indications for PRN medication in the acute management of psychoses, thus it is important for doctors to specify indications when writing PRN prescriptions. Despite evidence for the safety and effectiveness of benzodiazepines, there was widespread reluctance to use them as PRN medication in acute psychoses. Beliefs of some staff about PRN medications were at odds with the known properties of these medicines. Educational interventions for both nurses and doctors are required to achieve best practice in PRN medication.

Pro re nata medication for psychoses: an audit of practice in two metropolitan hospitals

Objective: To examine the use of pro re nata (PRN) (as needed) medication in hospitalized patients with psychotic disorders. Methods: Retrospective chart reviews were conducted at two large public psychiatry units situated in inner city general hospitals. Pro re nata medication prescription, administration and outcomes were examined during inpatient episodes of care for 184 consecutive admissions of patients diagnosed with a psychotic disorder. Patient demographics, diagnoses, and regularly prescribed medication were also recorded. All admissions were drawn from a three-month period from December 1998-February 1999. Results: The most prevalent diagnoses were schizophrenia related disorders (n = 111) and mania (n = 34). Substance use disorders (n = 49) were the most common comorbid dis-orders. Pro re nata medication was administered during the acute phase of 82% of admissions. Drugs prescribed Pro re nata were mostly typical antipsychotics, benzodiazepines and/or anti-cholinergics. Coprescription of typical antipsychotics PRN with regularly scheduled atypical antipsychotics was common (64%). Pro re nata medications accounted for 31% of the total antipsychotic dose and 28% of the total anxiolytic dose administered during acute treatment. Higher daily doses of PRN medication were given to manic patients, males, younger patients and those with substance use disorders. Pro re nata prescriptions usually specified a maximum daily dose (87%) but rarely gave indications for use (6%). Adminis-tration records frequently lacked a specified reason for use (48%) or a notation of outcome (64%). Unit staff noted medication-related morbidity in 37% of patients receiving PRN medication, compared to 3% of patients receiving only regularly scheduled medication. Extrapyramidal symptoms (EPS) were most frequently associated with administration of PRN haloperidol (Relative Risk vs other PRN medications = 5.61, 95% CI = 2.36-13.73). Conclusions: Pro re nata medications comprised a significant part of the treatment which psychotic patients received. The common practice of coprescribing PRN typical antipsychotics with scheduled atypical antipsychotics is potentially problematical since administration of PRN medication is associated with significant medication related morbidity. Preferential use of benzodiazepines as PRN agents may minimize this morbidity and foster subsequent compliance with regularly prescribed antipsychotics.

Local complexity of Delone sets and crystallinity

This paper characterizes when a Delone set X in R-n is an ideal crystal in terms of restrictions on the number of its local patches of a given size or on the heterogeneity of their distribution. For a Delone set X, let N-X (T) count the number of translation-inequivalent patches of radius T in X and let M-X (T) be the minimum radius such that every closed ball of radius M-X(T) contains the center of a patch of every one of these kinds. We show that for each of these functions there is a gap in the spectrum of possible growth rates between being bounded and having linear growth, and that having sufficiently slow linear growth is equivalent to X being an ideal crystal. Explicitly, for N-X (T), if R is the covering radius of X then either N-X (T) is bounded or N-X (T) greater than or equal to T/2R for all T > 0. The constant 1/2R in this bound is best possible in all dimensions. For M-X(T), either M-X(T) is bounded or M-X(T) greater than or equal to T/3 for all T > 0. Examples show that the constant 1/3 in this bound cannot be replaced by any number exceeding 1/2. We also show that every aperiodic Delone set X has M-X(T) greater than or equal to c(n)T for all T > 0, for a certain constant c(n) which depends on the dimension n of X and is > 1/3 when n > 1.

Young children's performance on the balance scale: The influence of relational complexity

Three experiments investigated the effect of complexity on children's understanding of a beam balance. In nonconflict problems, weights or distances varied, while the other was held constant. In conflict items, both weight and distance varied, and items were of three kinds: weight dominant, distance dominant, or balance (in which neither was dominant). In Experiment 1, 2-year-old children succeeded on nonconflict-weight and nonconflict-distance problems. This result was replicated in Experiment 2, but performance on conflict items did not exceed chance. In Experiment 3, 3- and 4-year-olds succeeded on all except conflict balance problems, while 5- and 6-year-olds succeeded on all problem types. The results were interpreted in terms of relational complexity theory. Children aged 2 to 4 years succeeded on problems that entailed binary relations, but 5- and 6-year-olds also succeeded on problems that entailed ternary relations. Ternary relations tasks from other domains-transitivity and class inclusion-accounted for 93% of the age-related variance in balance scale scores. (C) 2002 Elsevier Science (USA).

A cognitive complexity metric applied to cognitive development

Two experiments tested predictions from a theory in which processing load depends on relational complexity (RC), the number of variables related in a single decision. Tasks from six domains (transitivity, hierarchical classification, class inclusion, cardinality, relative-clause sentence comprehension, and hypothesis testing) were administered to children aged 3-8 years. Complexity analyses indicated that the domains entailed ternary relations (three variables). Simpler binary-relation (two variables) items were included for each domain. Thus RC was manipulated with other factors tightly controlled. Results indicated that (i) ternary-relation items were more difficult than comparable binary-relation items, (ii) the RC manipulation was sensitive to age-related changes, (iii) ternary relations were processed at a median age of 5 years, (iv) cross-task correlations were positive, with all tasks loading on a single factor (RC), (v) RC factor scores accounted for 80% (88%) of age-related variance in fluid intelligence (compositionality of sets), (vi) binary- and ternary-relation items formed separate complexity classes, and (vii) the RC approach to defining cognitive complexity is applicable to different content domains. (C) 2002 Elsevier Science (USA). All rights reserved.

Development of a quality use of medicines coding system to rate clinical pharmacists' medication review recommendations

Objective: To develop a 'quality use of medicines' coding system for the assessment of pharmacists' medication reviews and to apply it to an appropriate cohort. Method: A 'quality use of medicines' coding system was developed based on findings in the literature. These codes were then applied to 216 (111 intervention, 105 control) veterans' medication profiles by an independent clinical pharmacist who was supported by a clinical pharmacologist with the aim to assess the appropriateness of pharmacy interventions. The profiles were provided for veterans participating in a randomised, controlled trial in private hospitals evaluating the effect of medication review and discharge counselling. The reliability of the coding was tested by two independent clinical pharmacists in a random sample of 23 veterans from the study population. Main outcome measure: Interrater reliability was assessed by applying Cohen's kappa score on aggregated codes. Results: The coding system based on the literature consisted of 19 codes. The results from the three clinical pharmacists suggested that the original coding system had two major problems: (a) a lack of discrimination for certain recommendations e. g. adverse drug reactions, toxicity and mortality may be seen as variations in degree of a single effect and (b) certain codes e. g. essential therapy were in low prevalence. The interrater reliability for an aggregation of all codes into positive, negative and clinically non-significant codes ranged from 0.49-0.58 (good to fair). The interrater reliability increased to 0.72-0.79 (excellent) when all negative codes were excluded. Analysis of the sample of 216 profiles showed that the most prevalent recommendations from the clinical pharmacists were a positive impact in reducing adverse responses (31.9%), an improvement in good clinical pharmacy practice (25.5%) and a positive impact in reducing drug toxicity (11.1%). Most medications were assigned the clinically non-significant code (96.6%). In fact, the interventions led to a statistically significant difference in pharmacist recommendations in the categories; adverse response, toxicity and good clinical pharmacy practice measured by the quality use of medicine coding system. Conclusion: It was possible to use the quality use of medicine coding system to rate the quality and potential health impact of pharmacists' medication reviews, and the system did pick up differences between intervention and control patients. The interrater reliability for the summarised coding system was fair, but a larger sample of medication regimens is needed to assess the non-summarised quality use of medicines coding system.

Independent contribution of plaque complexity to myocardial ischemia during Dobutamine stress echocardiography

The influence of complex plaque morphology on the extent of demand-induced ischemia in unselected patients is not well defined. We sought to investigate the functional significance of lesion morphology in patients who underwent coronary angiography and dobutamine stress echocardiography (DSE).,Angiography and DSE were performed within a 6-month period (mean 1 +/- 1 month) in 196 patients. Angiographic assessments involved quantification of stenosis severity, assessment of the extent of jeopardized myocardium, and categorization of plaque morphology according to the Ambrose classification. DSE was interpreted by separate investigators with respect to wall motion score index (WMSI) and number of coronary territories involved. A general linear model was constructed to assess,the independent contribution of patient characteristics and angiographic and DSE results with respect to extent of ischemic myocardium. Complex lesion morphology was seen in 62 patients (32%). Patients with complex lesions were more likely to have had prior myocardial infarction (p < 0.001) and be current smokers (p = 0.03). During angiography, they exhibited a trend toward a greater number of diseased vessels, had a greater coronary jeopardy score (p < 0.001) and more frequent collateral flow (p = 0.03). During echocardiography, patients had a higher stress WMSI (p < 0.001) and were more likely to show ischemia in all 3 arterial territories (p < 0.01). On multivariate regression, the coronary artery jeopardy score and the presence of complex plaque morphology were independent predictors of the extent of ischemic myocardium (R 2 = 34%, p < 0.001). Thus, patients with complex plaque morphology are older, more likely to smoke, and more likely to have had prior myocardial. infarction. They exhibit more extensive disease with higher coronary jeopardy scores and a higher resting and peak stress WMSI. Despite these differences, complex plaque morphology remains an independent predictor of the extent of ischemia during stress. (C) 2003 by Excerpta Medica, Inc.