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.

Path integrals for continuous-time Markov chains

This note presents a method of evaluating the distribution of a path integral for Markov chains on a countable state space.

A real-time PCR assay for the detection of Neisseria gonorrhoeae by LightCycler

The detection of Neisseria gonorrhoeae by the polymerase chain reaction (PCR) is now recognized as a sensitive and specific method of diagnosing infection by the organism. In this Study 152 urine specimens were examined for N. gonorrhoeae by a real-time PCR method using the LightCycler platform and results were compared to an in-house PCR assay using an ELISA-based detection method. N. gonorrhoeae DNA was detected in 29 (19%) specimens by LightCycler PCR (LC-PCR) and in 31 (20%) specimens by the in house PCR method. The LightCycler assay proved to be specific and 94% sensitive when compared to the in house PCR method. These features combined with the rapid turn-around time for results makes the LC-PCR particularly suitable for the detection of N. gonorrhoeae in a routine clinical laboratory. (C) 2002 Elsevier Science Inc. All rights reserved.

Reasoning about real-time repetitions: terminating and nonterminating

It is common for a real-time system to contain a nonterminating process monitoring an input and controlling an output. Hence, a real-time program development method needs to support nonterminating repetitions. In this paper we develop a general proof rule for reasoning about possibly nonterminating repetitions. The rule makes use of a Floyd-Hoare-style loop invariant that is maintained by each iteration of the repetition, a Jones-style relation between the pre- and post-states on each iteration, and a deadline specifying an upper bound on the starting time of each iteration. The general rule is proved correct with respect to a predicative semantics. In the case of a terminating repetition the rule reduces to the standard rule extended to handle real time. Other special cases include repetitions whose bodies are guaranteed to terminate, nonterminating repetitions with the constant true as a guard, and repetitions whose termination is guaranteed by the inclusion of a fixed deadline. (C) 2002 Elsevier Science B.V. All rights reserved.

Saving, productivity and national income: a discrete-time geometric framework

This paper proposes an alternative geometric framework for analysing the inter-relationship between domestic saving, productivity and income determination in discrete time. The framework provides a means of understanding how low saving economies like the United States sustained high growth rates in the 1990s whereas high saving Japan did not. It also illustrates how the causality between saving and economic activity runs both ways and that discrete changes in national output and income depend on both current and previous accumulation behaviour. The open economy analogue reveals how international capital movements can create external account imbalances that enhance income growth for both borrower and lender economies. (C) 2002 Elsevier Science B.V. All rights reserved.

Integrals for continuous-time Markov chains

This paper presents a method of evaluating the expected value of a path integral for a general Markov chain on a countable state space. We illustrate the method with reference to several models, including birth-death processes and the birth, death and catastrophe process. (C) 2002 Elsevier Science Inc. All rights reserved.

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.

Adaptive multiscale principal components analysis for online monitoring of wastewater treatment

Fault detection and isolation (FDI) are important steps in the monitoring and supervision of industrial processes. Biological wastewater treatment (WWT) plants are difficult to model, and hence to monitor, because of the complexity of the biological reactions and because plant influent and disturbances are highly variable and/or unmeasured. Multivariate statistical models have been developed for a wide variety of situations over the past few decades, proving successful in many applications. In this paper we develop a new monitoring algorithm based on Principal Components Analysis (PCA). It can be seen equivalently as making Multiscale PCA (MSPCA) adaptive, or as a multiscale decomposition of adaptive PCA. Adaptive Multiscale PCA (AdMSPCA) exploits the changing multivariate relationships between variables at different time-scales. Adaptation of scale PCA models over time permits them to follow the evolution of the process, inputs or disturbances. Performance of AdMSPCA and adaptive PCA on a real WWT data set is compared and contrasted. The most significant difference observed was the ability of AdMSPCA to adapt to a much wider range of changes. This was mainly due to the flexibility afforded by allowing each scale model to adapt whenever it did not signal an abnormal event at that scale. Relative detection speeds were examined only summarily, but seemed to depend on the characteristics of the faults/disturbances. The results of the algorithms were similar for sudden changes, but AdMSPCA appeared more sensitive to slower changes.

Alterations in Plasmodium falciparum genotypes during sequential infections suggest the presence of strain specific immunity

Many of the asexual stage Plasmodium falciparum proteins that are the targets of host protective responses are markedly polymorphic. The full repertoire of diversity is not defined for any antigen. Most studies have focused on the genes encoding merozoite surface proteins 1 and 2 (MSP1, MSP2). We explored the extent of diversity of some of the less studied merozoite surface antigens and analyzed the degree of complexity of malaria field isolates by deriving nucleotide sequences of several antigens. We have determined the genotype of apical membrane antigen 1 (AMA1) in a group of 30 field samples, collected over 29 months, from individuals living in an area of intense malaria transmission in Irian Jaya, identifying 14 different alleles. AMA1 genotyping was combined with previously determined MSP2 typing. AMA1 had the greatest power in distinguishing between isolates but methodological problems, especially when mixed infections are present, suggest it is not an ideal typing target. MSP1, MSP3, and glutamate-rich protein genotypes were also determined from a smaller group of samples, and all results were combined to derive an extended antigenic haplotype. Within this subset of 10 patients, nine different genotypes could be discerned; however, five patients were all infected with the same strain. This strain was present in individuals from two separate villages and was still present 12 months later. This strain was predominant at the first time point but had disappeared at the fourth time point. This significant change in malaria genotypes could be due to strain-specific immunity developing in this population.

Cash, customers, and care: The experience and meaning of differential payment for high care places in aged care facilities

The introduction of new asset/income tested charges for high care residents was the 1997-98 Commonwealth government policy response to concerns about financing residential aged care. This in-depth study of residents, families, staff and managers in three aged care facilities explores issues of equity, access and empowerment arising when some residents pay more for the same level of care and amenity. The study reports little evidence of financial contributions affecting access to high care places and the delivery of care, the potential for differential access to amenities such as single rooms linked to the extra payments, and no evidence of a sense of empowerment linked to payment of the new charges. The complexity of current financial arrangements, access to appropriate financial advice at the time of entry, and the potential for an informal two tier system in relation to the allocation Of amenities are identified as developing policy issues.

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.

Anticipation of a non-aversive reaction time task facilitates the blink startle reflex

The conditions under which blink startle facilitation can be found in anticipation of a reaction time task were investigated to resolve inconsistent findings across previous studies. Four groups of participants (n = 64) were presented with two visual stimuli, one predicting a reaction time task (S+) and the second presented alone (S-). Participants were asked to make a speeded response to the offset of the S+ (S1 paradigm) or were asked to respond to a tactile stimulus presented at the offset of the S+ (S1-S2 paradigm). Half of the participants in each paradigm condition received performance feedback. Overall, blink latency shortening and magnitude facilitation were larger during S+ than during S-. More detailed analyses, however, found these differences to be reliable only in the Feedback conditions. Ratings of S+ pleasantness did not change across the experiment. Electrodermal responses to S+ were larger than to S- in all groups with differential electrodermal responding emerging earlier in the S1 paradigm. Taken together, the data support the notion that startle facilitation can occur during non-aversive Pavlovian conditioning. (C) 2002 Elsevier Science B.V. All rights reserved.