Medians and means in Finsler geometry

We investigate existence and uniqueness of p-means ep and the median e1 of a probability measure μ on a Finsler manifold, in relation with the convexity of the support of μ. We prove that ep is the limit point of a continuous time gradient flow. Under some additional condition which is always satisfied for p≥2, a discretization of this path converges to ep. This provides an algorithm for determining the Finsler center points.

Uterine contraction induced by Tanzanian plants used to induce abortion

ETHNOPHARMACOLOGICAL RELEVANCE

Women in Tanzania use plants to induce abortion. It is not known whether the plants have an effect.

AIMS OF STUDY

Collect data on plant use in relation to induced abortion and test the effect of plant extracts on uterine contraction.

MATERIALS AND METHODS

During interviews with traditional birth attendants and nurses, plants were identified. Cumulative doses of plant extracts were added to rat uterine tissue in an organ bath, and the force and frequency of contractions recorded. Acetylcholine was used as positive control.

RESULTS

21 plant species were tested for effect on uterine contraction. 11 species increased the force of contraction, and 12 species the frequency of contractions. The strongest contractions comparable to the maximum response obtained with acetylcholine were obtained with extracts of Bidens pilosa, Commelina africana, Desmodium barbatum, Manihot esculenta, Ocimum suave, Oldenlandia corymbosa and Sphaerogyne latifolia. 7 species increased both the force and frequency of contractions.

CONCLUSION

Several of the plant species induced strong and frequent contractions of the uterus, and can be used to induce an abortion.

Probe depth matters in dermal microdialysis sampling of benzoic acid after topical application: an ex vivo study in human skin

Microdialysis (MD) in the skin - dermal microdialysis (DMD) - is a unique technique for sampling of topically as well as systemically administered drugs at the site of action, e.g. sampling of dermatological drug concentrations in the dermis. Debate has concerned the existence of a correlation between the depth of the sampling device - the probe - in the dermis and the amount of drug sampled following topical drug administration. This study evaluates the relation between probe depth and drug sampling using dermal DMD sampling ex vivo in human skin. We used superficial (<1 mm), intermediate (1-2 mm) and deep (>2 mm) positioning of the linear MD probe in the dermis of human abdominal skin, followed by topical application of 4 mg/ml of benzoic acid (BA) in skin chambers overlying the probes. Dialysate was sampled every hour for 12 h and analysed for BA content by high-performance liquid chromatography. Probe depth was measured by 20-MHz ultrasound scanning. The area under the time-versus-concentration curve (AUC) describes the drug exposure in the tissue during the experiment and is a relevant parameter to compare for the 3 dermal probe depths investigated. The AUC(0-12) were: superficial probes: 3,335 ± 1,094 μg·h/ml (mean ± SD); intermediate probes: 2,178 ± 1,068 μg·h/ml, and deep probes: 1,159 ± 306 μg·h/ml. AUC(0-12) sampled by the superficial probes was significantly higher than that of samples from the intermediate and deeply positioned probes (p value <0.05). There was a significant inverse correlation between probe depth and AUC(0-12) sampled by the same probe (p value <0.001, r(2) value = 0.5). The mean extrapolated lag-times (±SD) for the superficial probes were 0.8 ± 0.1 h, for the intermediate probes 1.7 ± 0.5 h, and for the deep probes 2.7 ± 0.5 h, which were all significantly different from each other (p value <0.05). In conclusion, this paper demonstrates that there is an inverse relationship between the depth of the probe in the dermis and the amount of drug sampled following topical penetration ex vivo. The result is of relevance to the in vivo situation, and it can be predicted that the differences in sampling at different probe depths will have a more significant impact in the beginning of a study or in studies of short duration. Based on this study it can be recommended that studies of topical drug penetration using DMD sampling should include measurements of probe depth and that efforts should be made to minimize probe depth variability.

Total Bregman divergence and its applications to DTI analysis

Divergence measures provide a means to measure the pairwise dissimilarity between "objects," e.g., vectors and probability density functions (pdfs). Kullback-Leibler (KL) divergence and the square loss (SL) function are two examples of commonly used dissimilarity measures which along with others belong to the family of Bregman divergences (BD). In this paper, we present a novel divergence dubbed the Total Bregman divergence (TBD), which is intrinsically robust to outliers, a very desirable property in many applications. Further, we derive the TBD center, called the t-center (using the l(1)-norm), for a population of positive definite matrices in closed form and show that it is invariant to transformation from the special linear group. This t-center, which is also robust to outliers, is then used in tensor interpolation as well as in an active contour based piecewise constant segmentation of a diffusion tensor magnetic resonance image (DT-MRI). Additionally, we derive the piecewise smooth active contour model for segmentation of DT-MRI using the TBD and present several comparative results on real data.

Total Bregman Divergence and its Applications to Shape Retrieval

Shape database search is ubiquitous in the world of biometric systems, CAD systems etc. Shape data in these domains is experiencing an explosive growth and usually requires search of whole shape databases to retrieve the best matches with accuracy and efficiency for a variety of tasks. In this paper, we present a novel divergence measure between any two given points in [Formula: see text] or two distribution functions. This divergence measures the orthogonal distance between the tangent to the convex function (used in the definition of the divergence) at one of its input arguments and its second argument. This is in contrast to the ordinate distance taken in the usual definition of the Bregman class of divergences [4]. We use this orthogonal distance to redefine the Bregman class of divergences and develop a new theory for estimating the center of a set of vectors as well as probability distribution functions. The new class of divergences are dubbed the total Bregman divergence (TBD). We present the l1-norm based TBD center that is dubbed the t-center which is then used as a cluster center of a class of shapes The t-center is weighted mean and this weight is small for noise and outliers. We present a shape retrieval scheme using TBD and the t-center for representing the classes of shapes from the MPEG-7 database and compare the results with other state-of-the-art methods in literature.

Bregman divergences and surrogates for learning

Bartlett et al. (2006) recently proved that a ground condition for surrogates, classification calibration, ties up their consistent minimization to that of the classification risk, and left as an important problem the algorithmic questions about their minimization. In this paper, we address this problem for a wide set which lies at the intersection of classification calibrated surrogates and those of Murata et al. (2004). This set coincides with those satisfying three common assumptions about surrogates. Equivalent expressions for the members-sometimes well known-follow for convex and concave surrogates, frequently used in the induction of linear separators and decision trees. Most notably, they share remarkable algorithmic features: for each of these two types of classifiers, we give a minimization algorithm provably converging to the minimum of any such surrogate. While seemingly different, we show that these algorithms are offshoots of the same "master" algorithm. This provides a new and broad unified account of different popular algorithms, including additive regression with the squared loss, the logistic loss, and the top-down induction performed in CART, C4.5. Moreover, we show that the induction enjoys the most popular boosting features, regardless of the surrogate. Experiments are provided on 40 readily available domains.

Converting enzyme inhibition in mild and moderate essential hypertension. I. Acute effects on blood pressure, the renin-angiotensin system and blood bradykinin after a single dose of captopril

The acute effects of 25 mg captopril on blood pressure, heart rate, components of the renin-angiotensin system and blood concentration of bradykinin were followed in a single-blind placebo study of untreated (group A, n = 15) and thiazide-treated (group B, n = 13) patients with mild or moderate essential hypertension. A drug-related fall in blood pressure was seen in both groups. The blood pressure reduction was more marked in group B than in group A. Heart rate remained unchanged. Plasma concentrations of angiotensin II decreased significantly with concurrent increases in plasma concentrations of renin and angiotensin I, indicating the in vivo inhibition of converting enzyme. Blood concentrations of bradykinin showed no systemic changes. The magnitude of blood pressure reduction was correlated both with the pretreatment levels and the concurrent decreases in plasma angiotensin II. Inhibition of angiotensin II formation can explain a large part of the acute hypotensive pharmacological action of captopril. Other vasoactive systems may be involved. The kallikrein-kinin system does not appear to participate as indicated by the unchanged concentrations of kinin in blood.

Papillary muscle rupture as a first event in acute myocardial infarction

Cardiogenic shock caused by papillary muscle rupture in acute myocardial infarction is potentially reversible by surgical treatment. A case of inferior myocardial infarction in a 56-year-old previously healthy man is reported, in which the first event was papillary muscle rupture. The patient was in shock and had a mitral insufficiency murmur. The diagnosis was made by echocardiography and ventriculography. A St. Jude valve was implanted, and the patient was discharged in good health. It is suggested that routine echocardiography be carried out on patients with sudden cardiogenic shock, when a mitral murmur is present.

Converting enzyme inhibition in mild and moderate essential hypertension. II

In 24 patients with mild/moderate essential hypertension, we studied the effects of captopril with/without hydrochlorothiazide (Htz) on blood pressure, the renin-angiotensin system, blood bradykinin concentration (BBK), plasma volume, exchangeable sodium and glomerular filtration. Daily captopril doses of 75 and 150 mg were equally effective in reducing the blood pressure. Addition of Htz caused further blood pressure reductions. Nineteen patients attained a diastolic blood pressure less than or equal to 90 mmHg. Angiotensin converting enzyme inhibition with captopril led to a fall in plasma concentrations of angiotensin II (PAII) and renin substrate, and an increase in plasma concentrations of renin and angiotensin I. Patients starting with Htz had a higher PAII and subsequently a larger fall in blood pressure on captopril than untreated patients. BBK remained unchanged, indicating that the hypotensive action of captopril does not involve an accumulation of circulating kinin. Body fluid volumes and renal function were not affected by the various treatment regimens.

Study rationale and design of the CIMT trial: the Copenhagen Insulin and Metformin Therapy trial

BACKGROUND

Patients with type 2 diabetes (T2DM) have an increased mortality rate primarily because of macrovascular disease. Where T2DM patients cannot be managed sufficiently through diet, exercise and peroral antidiabetic drugs, that is when haemoglobin A1c (HbA1c) is above 7.0%, it is yet unknown whether a combination of metformin and insulin analogues is superior to insulin analogues alone. Nor is it known which insulin analogue regimen is the optimal.

OBJECTIVE

The primary objective of this trial is to evaluate the effect of an 18-month treatment with metformin vs. placebo in combination with one of three insulin analogue regimens, the primary outcome measure being carotid intima-media thickness (CIMT) in T2DM patients.

DESIGN

A randomized, stratified, multicentre trial having a 2 x 3 factorial design. The metformin part is double masked and placebo controlled. The insulin treatment is open. The intervention period is 18 months.

PATIENT POPULATION

Nine hundred and fifty patients with T2DM and HbA1c > or = 7.5% on treatment with oral hypoglycaemic agents or on insulin treatment and deemed able, by the investigator, to manage once-daily insulin therapy with a long-acting insulin analogue.

RANDOMIZATION

Central randomization stratified for age (above 65 years), previous insulin treatment and treatment centre.

INTERVENTIONS

Metformin 1 g x two times daily vs. placebo (approximately 475 patients vs. 475 patients) in combination with insulin detemir before bedtime (approximately 315 patients) or biphasic insulin aspart 30 before dinner with the possibility to increase to two or three injections daily (approximately 315 patients) or insulin aspart before the main meals (three times daily) and insulin detemir before bedtime (approximately 315 patients). Intervention follows a treat-to-target principle in all six arms aiming for an HbA1c < or = 7.0%.

OUTCOME MEASURES

Primary outcome measure is the change in CIMT from baseline to 18 months. Secondary outcome measures comprises the composite outcome of death, acute myocardial infarction, stroke or amputation assessed by an adjudication committee blinded to intervention, other cardiovascular clinical outcomes, average postprandial glucose increment from 0 to 18 months, hypoglycaemia and any inadvertent medical episodes. In addition, change in plaque formation in the carotids, HbA1c, cardiovascular biomarkers, body composition, progression of microvascular complications and quality of life will be assessed as tertiary outcome measures. TIME SCHEDULE: Patient enrolment started May 2008. Follow-up is expected to finish in March 2011.

CONCLUSION

CIMT is designed to provide evidence as to whether metformin is advantageous even during insulin treatment and to provide evidence regarding which insulin analogue regimen is most advantageous with regard to cardiovascular disease.

G-protein coupled receptor signaling architecture of mammalian immune cells

A series of recent studies on large-scale networks of signaling and metabolic systems revealed that a certain network structure often called “bow-tie network” are observed. In signaling systems, bow-tie network takes a form with diverse and redundant inputs and outputs connected via a small numbers of core molecules. While arguments have been made that such network architecture enhances robustness and evolvability of biological systems, its functional role at a cellular level remains obscure. A hypothesis was proposed that such a network function as a stimuli-reaction classifier where dynamics of core molecules dictate downstream transcriptional activities, hence physiological responses against stimuli. In this study, we examined whether such hypothesis can be verified using experimental data from Alliance for Cellular Signaling (AfCS) that comprehensively measured GPCR related ligands response for B-cell and macrophage. In a GPCR signaling system, cAMP and Ca²⁺ act as core molecules. Stimuli-response for 32 ligands to B-Cells and 23 ligands to macrophages has been measured. We found that ligands with correlated changes of cAMP and Ca²⁺ tend to cluster closely together within the hyperspaces of both cell types and they induced genes involved in the same cellular processes. It was found that ligands inducing cAMP synthesis activate genes involved in cell growth and proliferation; cAMP and Ca²⁺ molecules that increased together form a feedback loop and induce immune cells to migrate and adhere together. In contrast, ligands without a core molecules response are scattered throughout the hyperspace and do not share clusters. G-protein coupling receptors together with immune response specific receptors were found in cAMP and Ca²⁺ activated clusters. Analyses have been done on the original software applicable for discovering ‘bow-tie’ network architectures within the complex network of intracellular signaling where ab initio clustering has been implemented as well. Groups of potential transcription factors for each specific group of genes were found to be partly conserved across B-Cell and macrophage. A series of findings support the hypothesis.

Linking exposure to polychlorinated biphenyls with fatty fish consumption and reduced fetal growth among Danish pregnant women: a cause for concern?

In a selected group of women from the Danish National Birth Cohort, the authors investigated the association between intake of fatty fish and plasma concentrations of polychlorinated biphenyls (PCBs) on the one hand and the association between maternal PCB concentrations and fetal growth on the other. Of 70,183 women who filled in a food frequency questionnaire during 1996-2002, 100 nulliparous women aged 25-35 years with normal prepregnancy body mass index were selected according to their intake of fatty fish (low (0 meals/month, n = 34), medium (1-3 meals/month, n = 33), or high (> or = meals/month, n = 33)). Women with a high intake of fatty fish had 50% (95% confidence interval (CI): 31, 72) higher plasma PCB concentrations than women with low intake. Maternal plasma PCB concentrations were inversely associated with birth weight and placental weight. The adjusted mean difference between the 75th and 25th PCB percentiles was -155 g (95% CI: -291, -19) for birth weight and -81 g (95% CI: -135, -26) for placental weight. These results support previous findings from this cohort, where fatty fish intake was inversely associated with fetal growth. Dietary recommendations often encourage weekly consumption of fatty fish. These results suggest that potential exposure to PCBs should be carefully considered before recommending such intakes among women of childbearing age.

On weighting clustering

Recent papers and patents in iterative unsupervised learning have emphasized a new trend in clustering. It basically consists of penalizing solutions via weights on the instance points, somehow making clustering move toward the hardest points to cluster. The motivations come principally from an analogy with powerful supervised classification methods known as boosting algorithms. However, interest in this analogy has so far been mainly borne out from experimental studies only. This paper is, to the best of our knowledge, the first attempt at its formalization. More precisely, we handle clustering as a constrained minimization of a Bregman divergence. Weight modifications rely on the local variations of the expected complete log-likelihoods. Theoretical results show benefits resembling those of boosting algorithms and bring modified (weighted) versions of clustering algorithms such as k-means, fuzzy c-means, Expectation Maximization (EM), and k-harmonic means. Experiments are provided for all these algorithms, with a readily available code. They display the advantages that subtle data reweighting may bring to clustering.