Level phase independence for GI/M/1-type Markov chains

GI/M/1-type Markov chains make up a class of two-dimensional Markov chains. One dimension is usually called the level, and the other is often called the phase. Transitions from states in level k are restricted to states in levels less than or equal to k+1. For given transition probabilities in the interior of the state space, we show that it is always possible to define the boundary transition probabilities in such a way that the level and phase are independent under the stationary distribution. We motivate our analysis by first considering the quasi-birth-and-death process special case in which transitions from any state are restricted to states in the same, or adjacent, levels.

A correspondence between product-form batch-movement queueing networks and single-movement networks

A number of recent papers have exhibited classes of queueing networks, with batches of customers served and routed through the network, which have generalised product-form equilibrium distributions. In this paper we look at these from a new viewpoint. In particular we show that, under standard assumptions, for a network to possess an equilibrium distribution that factorises into a product form over the nodes of the network for all possible transition rates, it is necessary and sufficient that it be equivalent to a suitably-defined single-movement network. We consider also the form of the state space for such networks.

A product-form ‘loss network' with a form of queueing

We show that a form of queueing can be introduced into the standard fixed-routing loss network model while retaining a product-form invariant measure.

Some new results on queueing networks with batch movement

Product-form equilibrium distributions in networks of queues in which customers move singly have been known since 1957, when Jackson derived some surprising independence results. A product-form equilibrium distribution has also recently been shown to be valid for certain queueing networks with batch arrivals, batch services and even correlated routing.

This paper derives the joint equilibrium distribution of states immediately before and after a batch of customers is released into the network. The results are valid for either discrete- or continuous-time queueing networks: previously obtained results can be seen as marginal distributions within a more general framework. A generalisation of the classical ‘arrival theorem' for continuous-time networks is given, which compares the equilibrium distribution as seen by arrivals to the time-averaged equilibrium distribution.

Braess's paradox in a loss network

Braess's paradox is said to occur in a network if the addition of an extra link leads to worse performance. It has been shown to occur in transportation networks (such as road networks) and also in queueing networks. Here, we show that it can occur in loss networks.

On the Dual Relationship Between Markov Chains of GI/M/1 and M/G/1 Type

In 1990, Ramaswami proved that, given a Markov renewal process of M/G/1 type, it is possible to construct a Markov renewal process of GI/M/1 type such that the matrix transforms G(z, s) for the M/G/1-type process and R(z, s) for the GI/M/1-type process satisfy a duality relationship. In his 1996 PhD thesis, Bright used time reversal arguments to show that it is possible to define a different dual for positive-recurrent and transient processes of M/G/1 type and GI/M/1 type. Here we compare the properties of the Ramaswami and Bright dual processes and show that the Bright dual has desirable properties that can be exploited in the design of algorithms for the analysis of Markov chains of GI/M/1 type and M/G/1 type.

State-dependent signalling in queueing networks

It has recently been shown that networks of queues with state-dependent movement of negative customers, and with state-independent triggering of customer movement have product-form equilibrium distributions. Triggers and negative customers are entities which, when arriving to a queue, force a single customer to be routed through the network or leave the network respectively. They are ‘signals' which affect/control network behaviour. The provision of state-dependent intensities introduces queues other than single-server queues into the network.

This paper considers networks with state-dependent intensities in which signals can be either a trigger or a batch of negative customers (the batch size being determined by an arbitrary probability distribution). It is shown that such networks still have a product-form equilibrium distribution. Natural methods for state space truncation and for the inclusion of multiple customer types in the network can be viewed as special cases of this state dependence. A further generalisation allows for the possibility of signals building up at nodes.

Discrete-time queueing networks with geometric release probabilities

This note is concerned with the continuing misconception that a discrete-time network of queues, with independent customer routing and the number of arrivals and services in a time interval following geometric and truncated geometric distributions respectively, has a product-form equilibrium distribution.

Connecting internally balanced quasi-reversible Markov processes

We provide a general framework for interconnecting a collection of quasi-reversible nodes in such a way that the resulting process exhibits a product-form invariant measure. The individual nodes can be quite general, although some degree of internal balance will be assumed. Any of the nodes may possess a feedback mechanism. Indeed, we pay particular attention to a class of feedback queues, characterized by the fact that their state description allows one to maintain a record of the order in which events occur. We also examine in some detail the problem of determining for which values of the arrival rates a node does exhibit quasi-reversibility.

Crystallization and morphology development in polyethylene–octakis(n-octadecyldimethylsiloxy)octasilsesquioxane nanocomposite blends

A detailed study of the crystallization kinetics and morphology development of a novel set of polyethylene–Q₈POSS blends.

Spinal pethidine for elective caesarean section

Pethidine (meperidine) is a unique member of the opioid family. In addition to its analgesic activity, it also has significant local anaesthetic activity. This property enables it to be used as the sole agent for spinal anaesthesia. We describe the successful use of intrathecal pethidine 1 mg/kg for an elective lower segment caesarean section in a patient presumed to be allergic to amide local anaesthetics. There were no significant adverse effects in either the mother or the newborn.

European Y-chromosomal lineages in Polynesians: a contrast to the population structure revealed by mtDNA

We have used Y-chromosomal polymorphisms to trace paternal lineages in Polynesians by use of samples previously typed for mtDNA variants. A genealogical approach utilizing hierarchical analysis of eight rare-event biallelic polymorphisms, seven microsatellite loci, and internal structural analysis of the hypervariable minisatellite, MSY1, has been used to define three major paternal-lineage clusters in Polynesians. Two of these clusters, both defined by novel MSY1 modular structures and representing 55% of the Polynesians studied, are also found in coastal Papua New Guinea. Reduced Polynesian diversity, relative to that in Melanesians, is illustrated by the presence of several examples of identical MSY1 codes and microsatellite haplotypes within these lineage clusters in Polynesians. The complete lack of Y chromosomes having the M4 base substitution in Polynesians, despite their prevalence (64%) in Melanesians, may also be a result of the multiple bottleneck events during the colonization of this region of the world. The origin of the M4 mutation has been dated by use of two independent methods based on microsatellite-haplotype and minisatellite-code diversity. Because of the wide confidence limits on the mutation rates of these loci, the M4 mutation cannot be conclusively dated relative to the colonization of Polynesia, 3,000 years ago. The other major lineage cluster found in Polynesians, defined by a base substitution at the 92R7 locus, represents 27% of the Polynesians studied and, most probably, originates in Europe. This is the first Y-chromosomal evidence of major European admixture with indigenous Polynesian populations and contrasts sharply with the picture given by mtDNA evidence.

Novel mutation processes in the evolution of a haploid minisatellite, MSY1: array homogenization without homogenization

The Y-specific locus MSY1 is the only known haploid minisatellite, and displays an extremely high degree of structural diversity which can be assayed by minisatellite variant repeat PCR (MVR-PCR). One group of alleles, in an African-specific class of Y chromosomes (haplogroup 8), behaves unusually in the conventional MVR-PCR assay, and sequencing demonstrates that this is because repeat units in these alleles contain an additional base substitution. We have designed a new MVR-PCR system to detect these novel variants, and show firstly that they are confined to the haplogroup 8 chromosomes, and secondly that the base substitution has spread through these arrays without the elimination of existing repeat variants. The sharing of a particular base substitution between otherwise distinct repeat types in these alleles represents evidence of a remarkable mutation process in their evolutionary history, in which the variant base must have been spread by a biased repair mechanism operating in very small patches within heteroduplexes.

Hypervariable digital DNA codes for human paternal lineages: MVR-PCR at the Y-specific minisatellite, MSY1 (DYF155S1)

We describe the first haploid minisatellite, the human Y chromosome-specific locus, MSY1. It consists of an array of 48-114 AT-rich 25 bp repeats of at least five different variant types. A minisatellite variant repeat PCR (MVR-PCR) system gives Y-specific DNA codes, with a virtual heterozygosity of 99.9%, making MSY1 by far the single most variable locus on the Y. African populations contain the most diverged MSY1 structures. MSY1 is the only Y-chromosomal system where the characteristics of large numbers of mutations can be studied in detail: it provides a uniquely powerful tool both for the investigation of mutation in a haploid system, and for the dating of paternal lineages.

On the Inverse of Erlang's Function

Erlang's function B(λ, C) gives the blocking probability that occurs when Poisson traffic of intensity λ is offered to a link consisting of C circuits. However, when dimensioning a telecommunications network, it is more convenient to use the inverse C(λ, B) of Erlang's function, which gives the number of circuits needed to carry Poisson traffic λ with blocking probability at most B. This paper derives simple bounds for C(λ, B). These bounds are close to each other and the upper bound provides an accurate linear approximation to C(λ, B) which is asymptotically exact in the limit as λ approaches infinity with B fixed

Iron bioavailability from diets consumed by different socioeconomic strata of the Venezuelan population

The iron bioavailability from three typical diets consumed by socioeconomic stratum IV (SES IV--working class) of the Venezuelan population was determined by the extrinsic label method. Although the iron content of the SES IV diets was about the same (250 mumol/d) as that of upper (SES I-III) and lower (SES V) socioeconomic strata diets, iron-replete subjects absorbed 43 and 61% more iron from the SES I-III diets than from the SES IV and V diets, respectively, and absorption from the main meal of the SES I-III diets was 100% greater. However, iron deficient subjects absorbed about the same amount of iron (45 mumol/d) from the SES IV diets as from the SES I-III diets. The SES I-III diets contained more iron absorption enhancers (ascorbic acid and meat protein) and less of the inhibitor phytate, than the SES IV and V diets. Iron absorption from the meals of four diets consumed at different times during the day was also measured. There was no significant difference in the percentage iron absorption from the same meals eaten in the morning after an overnight fast, and when eaten at the customary time of day.

Tight bounds on the sensitivity of generalised semi-Markov processes with a single generally distributed lifetime

There are some generalised semi-Markov processes (GSMP) which are insensitive, that is the value of some performance measures for the system depend only on the mean value of lifetimes and not on their actual distribution. In most cases this is not true and a performance measure can take on a number of values depending on the lifetime distributions. In this paper we present a method for finding tight bounds on the sensitivity of performance measures for the class of GSMPs with a single generally distributed lifetime. Using this method we can find upper and lower bounds for the value of a function of the stationary distribution as the distribution of the general lifetime ranges over a set of distributions with fixed mean. The method is applied to find bounds on the average queue length of the Engset queue and the time congestion in the GI/M/n/n queueing system.

The relationship between iron deficiency and anemia in Venezuelan children

The iron status of 3228 subjects from the nutrition survey Proyecto Venezuela was studied. The sample included children from 1 to 16 y of age grouped by age and sex. Values for three indicators of iron status were compared: hemoglobin concentration, serum ferritin concentration, and percentage saturation of serum transferrin. In all groups there was a strong overlap in the hemoglobin concentration distribution curves for non-iron-deficient and iron-deficient subjects classified as such according to the other two indexes. The prevalence of iron deficiency ranged from 35% in 1-3 y olds to 10% in adolescent males, the values being almost identical in the nonanemic group compared with the total population. In the different groups, 80-97% of the subjects with abnormal values of at least one of these two indexes were not anemic. The difficulties involved in establishing a state of iron deficiency according to these indexes are discussed.

Cloning and overexpression of Lactobacillus helveticus D-lactate dehydrogenase gene in Escherichia coli

NAD(+)-dependent D-lactate dehydrogenase from Lactobacillus helveticus was purified to apparent homogeneity, and the sequence of the first 36 amino acid residues determined. Using forward and reverse oligonucleotide primers, based on the N-terminal sequence and amino acid residues 220-215 of the Lactobacillus bulgaricus enzyme [Kochhar, S., Hunziker, P. E., Leong-Morgenthaler, P. & Hottinger, H. (1992) J. Biol. Chem. 267, 8499-8513], a 0.6-kbp DNA fragment was amplified from L. helveticus genomic DNA by the polymerase chain reaction. This amplified DNA fragment was used as a probe to identify two recombinant clones containing the D-lactate dehydrogenase gene. Both plasmids overexpressed D-lactate dehydrogenase (greater than 60% total soluble cell protein) and were stable in Escherichia coli, compared to plasmids carrying the L. bulgaricus and Lactobacillus plantarum genes. The entire nucleotide sequence of the L. helveticus D-lactate dehydrogenase gene was determined. The deduced amino acid sequence indicated a polypeptide consisting of 336 amino acid residues, which showed significant amino acid sequence similarity to the recently identified family of D-2-hydroxy-acid dehydrogenases [Kochhar, S., Hunziker, P. E., Leong-Morgenthaler, P. & Hottinger, H. (1992) Biochem. Biophys. Res. Commun. 184, 60-66]. The physicochemical and catalytic properties of recombinant D-lactate dehydrogenase were identical to those of the wild-type enzyme, e.g. alpha 2 dimeric subunit structure, isoelectric pH, Km and Kcat for pyruvate and other 2-oxo-acid substrates. The kinetic profiles of 2-oxo-acid substrates showed some marked differences from that of L-lactate dehydrogenase, suggesting different mechanisms for substrate binding and specificity.

Iron and transferrin uptake by phytohemagglutinin-stimulated human peripheral blood lymphocytes

Iron (Fe) and transferrin (TF) uptake by human peripheral blood lymphocytes stimulated in vitro with phytohemagglutinin was measured. Pulses of 59FeTF or 125I-TF were added to the cultures either at time 0 or 8 hr before the end of a 72-hr incubation. In time-course experiments, peak iron and transferrin uptake coincided with the peak of tritiated thymidine uptake taken as a measure of cellular activation. Iron, but not transferrin, was accumulated by the cells. Non-linear relationships existed between both iron and transferrin uptake and the degree of activation. Both rose markedly above basal levels only at a level of activation at least 50% of the maximum observed. The results suggest that although iron utilization is related to cellular activity, the uptake mechanism is only activated when an increased iron metabolism has exhausted internal stores.

Efficacy and safety of two oral solutions as maintenance therapy for acute diarrhea. A double-blind, randomized, multicenter trial

There is continuing uncertainty about the appropriate level of sodium in oral fluid therapy for children with acute gastroenteritis in developed countries. The present study was undertaken in order to assess whether an oral glucose/electrolyte solution designed for fluid replacement (Na+ concentration 75 mmol/l) and an oral glucose/electrolyte solution designed for maintenance of hydration (Na+ concentration 45 mmol/l) would be safe and effective in the treatment of acute childhood diarrhea in a developed country. Children aged 3-24 months (n = 54) with acute diarrhea and less than 5 percent dehydration were randomized to receive either maintenance (n = 27) or rehydration (n = 27) fluid. Outcome was assessed at 24 and 48 hours after entry to the study. Both solutions were found to be equally effective and safe. The fluid was refused by one child in each group. Analysis of efficacy showed that hydration status was maintained in all patients and 98 percent of children showed significant improvement in diarrheal status at 24 hours. We conclude that for well-nourished ambulatory children aged 3-24 months with acute diarrhea and minimal (less than 5%) or no dehydration, the use of an oral fluid containing 75 mmol/l of sodium is as safe and effective as the use of an oral fluid containing 45 mmol/l of sodium.

Daily physiological iron requirements in children

Median daily iron absorption was determined in iron-replete males and females between 2 and 19 years of age from the upper and lower socioeconomic strata of the Venezuelan population. A comparison was made with iron absorption of well-nourished children, on the basis of hematological and anthropometric reference values from the U.S. The median absorption level, which was calculated from the increase in total body iron due to growth and the daily losses through exfoliation and menstruation, was also used to estimate the requirements of 95% of the population. When the requirements were expressed in terms of body weight, no significant difference in iron absorption was observed between the three Venezuelan and one U.S. groups, ranging from about 30 to 38 micrograms/kg/day in both sexes between 4 and 16 years of age. However, when the requirements were expressed without division by the weight factor, the requirements of the better nourished groups were somewhat higher than those of the Venezuelan lower socioeconomic population with, in addition, a threefold variation over the 5 to 16 year age range. These findings suggest that the total iron requirements of children at a certain age may be most adequately expressed in terms of the optimal body weight for that age.

Lymphocyte activation, iron uptake and release by human mononuclear leukocytes in the presence of desferrioxamine

Desferrioxamine (DFO), an iron chelating drug, has been shown to inhibit the proliferative response of leukocytes to mitogen. In the present study we investigated the effect of DFO on different aspects of human mononuclear leukocyte (MNL) function in vitro. DFO, added at the beginning of the culture period, inhibited both tritiated thymidine and radioiron uptake by phytohemagglutinin-stimulated MNL and the degree of inhibition correlated with the degree of cellular activation, to the extent that in the absence of mitogen a significant stimulatory effect of DFO was observed, especially when iron supplement was present in the culture medium. However DFO was not found to inhibit iron uptake directly, and relatively low concentrations of iron as iron-transferrin totally reversed the inhibitory action of DFO on thymidine uptake. Although the release of iron from preloaded MNL in the presence of DFO was only 15% greater than the spontaneous release of control cultures, we conclude that the site of action of DFO is an intracellular iron pool, that increases in importance when the supply of iron to the cellular iron metabolism become limiting as in optimally activated MNL.

Physiological and non-physiological forms of iron affect differently proliferation and ferritin synthesis in human mononuclear cells in vitro

The effect of iron in different forms on the proliferative response to mitogen and ferritin content of human mononuclear leukocytes (MNL) was studied in vitro. Iron-loaded transferrin (FeTF) but not apotransferrin (apoTF) significantly enhanced the mitogenic response of MNL in serum-free culture. Removal of TF from serum markedly reduced its effectiveness as a serum supplement. This effect could be almost totally reversed when the serum was reconstituted with both iron and apoTF. Four forms of iron showed a stimulatory effect on ferritin synthesis in MNL in the increasing order: FeTF less than iron nitrilotriacetate less than iron citrate (molar ratio 1:20) less than iron citrate (1:1). The effect appeared to be correlated with their susceptibility to polymerization in aqueous solution. It is proposed that iron may a) enhance the mitogenic response of MNL, due probably to the physiological form of iron, FeTF, and b) stimulate ferritin synthesis, a protective reaction of the cell to toxic polymerized forms of the metal.

Does dress influence how parents first perceive house staff competence?

A random sample of parents of children admitted to the pediatric inpatient services of a university teaching hospital was studied using sets of paired photographs of house staff physicians wearing one of three typical outfits to assess the relationship between house staff physician dress and parents' perceptions of competence. The results indicated that parents were twice as likely to attribute competence to the physician wearing formal dress compared with the physician wearing an operating room outfit and four times more likely compared with the physician wearing an intern uniform. The likelihood of making assumptions of competence was significantly reduced in parents with a university education and in parents who had never previously had a child hospitalized. The gender of the physician had no effect on perceptions of competence.

The effect of cysteine-containing peptides released during meat digestion on iron absorption in humans

In order to investigate the constituents responsible for the enhancing effect of meat on intestinal iron absorption in humans, two different types of peptic digestion extracts were prepared from 100 g of beef, in which the thiol groups of the resulting peptides were either oxidized (CYS-), or left untreated (CYS+). The absorption of radioiron mixed with 250 g of maize was more than twofold greater when consumed along with the CYS+ extract than with the CYS- (p less than 0.05). It is suggested that the enhancing effect of meat on nonheme iron absorption is due to cysteine, and that cysteine-containing peptides, rather than the free amino acid, are responsible for this effect.

Presumed homozygous achondroplasia. A review and report of a further case

Presumptive homozygous achondroplasia (PHA) is a rare disorder. The clinical and detailed histological findings of the fifth case of this chondrodystrophy, studied in detail, are presented here. There is a severe disorder of the normal growth of the long bones, whose nature, however, is not well understood; it shows some resemblance to the pathological changes described in thanatophoric dysplasia which also presents many clinical similarities. The aspect of greatest interest, however, is the relation of PHA to the "classical" form of achondroplasia. Some investigators have maintained that in that disorder there are no significant qualitative, and at most some quantitative, alterations in the growth plate to be demonstrated by histologic examination, but have not explained the apparent abnormalities in the development of the bones and in the external phenotype, which appears to be a milder expression of that seen in PHA. In view of the genetic relationship and external phenotypic similarity one would also have expected in "classical" achondroplasia a milder form of the severe changes seen in PHA. Judging by some of the published reports this is not the case. Attention is drawn to this intriguing discrepancy.

Case--control study of counselling against neonatal circumcision

After two serious complications had alerted physicians to the potential risks of routine neonatal circumcision, the circumcision rate in a regional general hospital decreased significantly (p less than 0.001), from approximately 40% to 20%, settling at the level claimed to prevail when physicians oppose circumcision. Following this decrease 219 consecutive pregnancies resulting in male infants were prospectively studied in order to identify factors associated with insistence on circumcision. Factors significantly associated with circumcision were the existence of an older brother (p less than 0.001), especially if circumcised (p less than 0.001), and delivery of prenatal care by an obstetrician rather than a general practitioner (p less than 0.05). Factors significantly associated with no circumcision were the fact that this infant was the first male born in the family (p = 0.001), delivery of prenatal and infant care by the same general practitioner (p less than 0.05) and a maternal age of 20 years or less (p less than 0.02). The circumcision status of the father, the marital status of the mother, the mother's intention to breast-feed, attendance of a primigravida at prenatal classes, delivery of infant care by a pediatrician and socioeconomic status did not appear to influence whether circumcision was performed. These data may assist physicians in understanding the potential effectiveness and limitations of counselling against circumcision.

The spectrum of cardiac rate and rhythm in normal newborns

The distribution and variation of cardiac rate and rhythm in normal neonates has previously received little attention. This has made clinical assessment of dysrhythmia in newborns difficult. We therefore performed continuous 24-hour electrocardiography in 29 normal newborn subjects (age range, 1 to 6 days; mean, 3.5 days). The ECG tapes were then analysed in detail to define the normal range of cardiac rate, conduction intervals, and rhythm during waking and sleeping periods. Maximum sinus rate (awake) ranged from 150 to 222 beats per minute (mean, 192 +/- 16 [SD]), and minimum rate (awake) from 78 to 140 beats per minute (mean, 107 +/- 15). During sleep, the maximum rate ranged from 125 to 210 (mean, 168 +/- 23) and the minimum from 72 to 120 beats per minute (mean, 92 +/- 11). The maximum variation in rate for any individual during the 24-hour period ranged from 73 to 134 beats per minute (mean, 100 +/- 17). Sinus rhythm predominated with mild irregularity occurring episodically in 24 and moderate irregularity in 4 infants. An isolated atrial premature beat was present in 2 subjects, and an atrioventricular (AV) junctional escape rhythm occurred in one other after a sinus pause of 840 msec. Ventricular premature beats or AV conduction abnormalities were not observed. The corrected QT interval (QTc) ranged from 0.298 to 0.514 sec (mean, 0.390 +/- 0.026). The maximum variation in QTc over 24 hours ranged from 0.052 to 0.160 sec (mean, 0.097 +/- 0.028). We conclude that cardiac rhythm and conduction appear more stable in normal newborns than in older normal subjects and that bradycardia, conduction defects, and ventricular ectopy of the type recently reported in young normal adults seem to be more uncommon in the neonatal period.

A container for handling small specimens during preparation and examination in the scanning electron microscope (SEM)

The difficulties of handling small specimens of less than 1 mm3 are considerably reduced when the specimens are placed in a small container designed to be compatible with the dimensions of the preparatory instrumentation and of the microscope. The container described is unaffected by solvents used in the preparation of specimens for scanning electron microscopy.