The optimal graph partitioning problem

Summary In this paper we consider the problem of partitioning the set of nodes in a graph in at mostp classes, such that the sum of node weights in any class is not greater than the class capacityb, and such that the sum of edge weights, for edges connecting nodes in the same class, is maximal. This problem can be formulated as a MILP, which turns out to be completely symmetrical with respect to thep classes, and the gap between the relaxed LP solution and the optimal solution is the largest one possible. These two properties make it very difficult to solve even smaller problems. In this paper it is shown how it is possible to preassign certain nodes to certain classes, thus reducing both the symmetric nature of the formulation, the number of variables and constraints and the gap. It is also shown how the gap can be reduced even further by introducing combinatorial cuts. Computational results based on the two formulations of the problem and combinatorial cuts are presented.     

Contingent negative variation and cognitive performance in hypotension

The difference in attention and cognitive performance between 26 hypotensive (systolic blood pressure < 100 mmHg and diastolic blood pressure < 60 mmHg) and 22 normotensive female university students was assessed. Attention was examined with contingent negative variation (CNV) recorded using light and tone as S1 and S2. Cognitive performance was assessed by free recall of a list of words and two German tests of cognitive speed performance and sustained attention: Zahlen-Verbindungs-Test and d2. The hypotensive participants demonstrated a lower increase in negativity on the CNV. Moreover, in the free recall test, hypotensive individuals remembered fewer words, in comparison with normotensive subjects. Scores for hypotensive individuals on the Zahlen-Verbindungs-Test and d2 were also lower. No difference was found in reaction times to imperative stimuli (S2).     

Modeling the effects of hydroxypropylcellulose in acetaminophen tablet formulation

The objective of the research described here was to develop a set of predictive models that would be used to show the performance of hydroxypropylcellulose as a pharmaceutical tablet binder. A statistically designed set of experiments was used to relate tablet formulation to functionality. It was found that the binder level affected both hardness and dissolution time. Useful predictive models were generated for tablet hardness and dissolution time as a function of the binder or binder-drug ratio. The optimal formulation can be predicted from this study, and will depend upon the combination of desired hardness and the dissolution time for a particular drug.     

Amicrobial pustulosis of the folds. A cutaneous manifestation associated with connective tissue disease

Amicrobial pustulosis (AP) is a recently defined entity associated with connective tissue diseases. Few cases have appeared in the literature. We report a case of AP coexisting with a systemic lupus erythematosus-scleroderma overlap syndrome and marked photosensitivity. The patient presented prominent pustular skin lesions and a few discoid lupus ones. No significant differences in the inflammatory infiltrate were found between the two clinical variants. The infiltrate consisted mainly of CD4+ lymphocytes and many neutrophils. CD1a+ dendritic cells were few in both epidermis and dermis. AP introduces a potential source of diagnostic confusion, but increasing experience of this syndrome will improve the awareness and diagnostic potential among dermatologists.     

The kinetics of bioaccumulation of zinc, copper, lead and cadmium by oysters (Crassostrea iredalei and C. belcheri) under tropical field conditions

Cyanobacterial neurotoxins have been implicated in animal deaths resulting from drinking contaminated water. Anatoxin-a (AN) and homoanatoxin-a (HMAN) have previously been analysed using high-performance liquid chromatography (HPLC) with UV detection, but this procedure is insufficiently sensitive and is subject to interferences. A sensitive fluorimetric (FL) method for determining AN was recently developed using derivatisation with 4-fluoro-7-nitro-2,1,3-benzoxadiazole (NBD-F) and this has been applied to the simultaneous determination of AN, HMAN and their epoxy and dihydro degradation products. Microscale syntheses were used to prepare the dihydro and epoxy derivatives from AN and HMAN. These compounds were produced in high yields, as confirmed by electrospray MS and HPLC-FL of their benzoxadiazole derivatives. All six NBD derivatives were readily separated using isocratic reversed-phase HPLC. The recoveries of these compounds from spiked water samples, using weak cation-exchange (WCX) solid-phase extraction (SPE), were 83.2-84.9% at concentrations of 10 micrograms/l. The R.S.D. values were 1.7-3.9% (n = 8) and the limits of detection were better than 10 ng/l for all six compounds, illustrating the high sensitivity of the method. This methodology was successfully applied to the analysis toxin degradation products in natural samples. Dihydroanatoxin-a (0.8 mg/g) was isolated from a benthic Oscillatoria bloom from Caragh Lake, Ireland, and was found to contain two isomers but their ratio was different from that found in the synthetic material.     

A formula for thermal stability (Tm) prediction of PNA/DNA duplexes

An empirical formula for thermal stability (T m) prediction of PNA/DNA duplexes has been derived. The model is based on the T m as calculated for the corresponding DNA/DNA duplex employing a nearest neighbour approach, by including terms for the pyrimidine content and length of the PNA to take into account the increased thermostability of PNA/DNA hybrids and the asymmetry of the PNA-DNA heteroduplex. The predictive power of the T m prediction formula was challenged with an independent data set not used for model building. The T m of >90% of the sequences was predicted within 5 K; 98% of the predicted T ms differ by not more than 10 K from the experimentally determined T m.     

Reduced beta-adrenergic sensitivity in patients with type 1 diabetes and hypoglycemia unawareness

OBJECTIVE: We tested the hypothesis that impaired tissue sensitivity to catecholamines contributes to hypoglycemia unawareness in subjects with type 1 diabetes. RESEARCH DESIGN AND METHODS: A total of 21 subjects with type 1 diabetes underwent a standardized insulin infusion protocol to produce a stepwise decrease in plasma glucose to 45-min plateaus of 4.3, 3.6, 3.0, and 2.3 mmol/l. Glycemic thresholds, maximum responses for adrenergic and neuroglycopenic symptoms, and counterregulatory hormones were determined. Patients were classified as hypoglycemia unaware if the initiation of adrenergic symptoms occurred at a plasma glucose level 2 SD below that of nondiabetic volunteers. beta-Adrenergic sensitivity was measured as the dose of isoproterenol required to produce an increment in heart rate of 25 beats per minute above baseline (I25) in resting subjects. RESULTS: Subjects with type 1 diabetes and hypoglycemia unawareness experienced the onset of adrenergic symptoms at a lower plasma glucose level than did those with awareness (2.5+/-0.1 vs. 3.7+/-0.1 mmol/l, P < 0.001), whereas neuroglycopenic symptoms occurred at similar glucose levels (2.7+/-0.2 vs. 2.8+/- 0.1 mmol/l). The plasma glucose levels for counterregulatory hormone secretion (epinephrine 2.9+/-0.2 vs. 4.1+/-0.2 mmol/l; norepinephrine 2.7+/-0.1 vs. 3.2+/-0.2 mmol/l; cortisol 2.5+/-0.2 vs. 3.3+/-0.2 mmol/l, P < 0.01) were also lower in subjects with unawareness. The maximal epinephrine (1,954+/-486 vs. 5,332+/- 1,059 pmol/l, P < 0.01), norepinephrine (0.73 +/- 0.14 vs. 1.47+/-0.21 nmol/l, P = 0.04), and cortisol (276+/-110 vs. 579+/-83 nmol/l, P < 0.01) responses were reduced in the unaware group. I25 was greater in unaware subjects than in subjects without unawareness (1.5+/-0.3 vs. 0.8+/-0.2 microg), where I25 was not different from that of controls (0.8 +/-0.2 microg). CONCLUSIONS: We conclude that subjects with type 1 diabetes and hypoglycemia unawareness have reduced beta-adrenergic sensitivity, which may contribute to their impaired adrenergic warning symptoms during hypoglycemia.