The median function on graphs with bounded profiles

The median of a profile = (u1, . . . , uk ) of vertices of a graph G is the set of vertices x that minimize the sum of distances from x to the vertices of . It is shown that for profiles with diameter the median set can be computed within an isometric subgraph of G that contains a vertex x of and the r -ball around x, where r > 2 − 1 − 2 /| |. The median index of a graph and r -joins of graphs are introduced and it is shown that r -joins preserve the property of having a large median index. Consensus strategies are also briefly discussed on a graph with bounded profiles.

Axiomatic Characterization of the Antimedian Function on Paths and Hypercubes

An antimedian of a pro le = (x1; x2; : : : ; xk) of vertices of a graph G is a vertex maximizing the sum of the distances to the elements of the pro le. The antimedian function is de ned on the set of all pro les on G and has as output the set of antimedians of a pro le. It is a typical location function for nding a location for an obnoxious facility. The `converse' of the antimedian function is the median function, where the distance sum is minimized. The median function is well studied. For instance it has been characterized axiomatically by three simple axioms on median graphs. The median function behaves nicely on many classes of graphs. In contrast the antimedian function does not have a nice behavior on most classes. So a nice axiomatic characterization may not be expected. In this paper such a characterization is obtained for the two classes of graphs on which the antimedian is well-behaved: paths and hypercubes.

Confidence Bands for Isotonic Median Curves using Sign-Tests

Suppose that one observes independent random variables (X1, Y1), (X2, Y2), …, (Xn, Yn) in R2 with unknown distributions, except that Median(Yi | Xi = M(x) for some unknown isotonic function M. We describe an explicit algorithm for the computation of confidence bands for the median function M whose running time is of order O(n2). The bands rely on multiscale sign tests and are shown to have desirable asymptotic properties.

On the remoteness function in median graphs

A profile on a graph G is any nonempty multiset whose elements are vertices from G. The corresponding remoteness function associates to each vertex x 2 V.G/ the sum of distances from x to the vertices in the profile. Starting from some nice and useful properties of the remoteness function in hypercubes, the remoteness function is studied in arbitrary median graphs with respect to their isometric embeddings in hypercubes. In particular, a relation between the vertices in a median graph G whose remoteness function is maximum (antimedian set of G) with the antimedian set of the host hypercube is found. While for odd profiles the antimedian set is an independent set that lies in the strict boundary of a median graph, there exist median graphs in which special even profiles yield a constant remoteness function. We characterize such median graphs in two ways: as the graphs whose periphery transversal number is 2, and as the graphs with the geodetic number equal to 2. Finally, we present an algorithm that, given a graph G on n vertices and m edges, decides in O.mlog n/ time whether G is a median graph with geodetic number 2

Median graphs, the remoteness function, periphery transversals, and geodetic number two

A periphery transversal of a median graph G is introduced as a set of vertices that meets all the peripheral subgraphs of G. Using this concept, median graphs with geodetic number 2 are characterized in two ways. They are precisely the median graphs that contain a periphery transversal of order 2 as well as the median graphs for which there exists a profile such that the remoteness function is constant on G. Moreover, an algorithm is presented that decides in O(mlog n) time whether a given graph G with n vertices and m edges is a median graph with geodetic number 2. Several additional structural properties of the remoteness function on hypercubes and median graphs are obtained and some problems listed

Long-term Postoperative Atrophy Of Contralateral Hippocampus And Cognitive Function In Unilateral Refractory Mtle With Unilateral Hippocampal Sclerosis.

This study aimed to evaluate long-term atrophy in contralateral hippocampal volume after surgery for unilateral MTLE, as well as the cognitive outcome for patients submitted to either selective transsylvian amygdalohippocampectomy (SelAH) or anterior temporal lobe resection (ATL). We performed a longitudinal study of 47 patients with MRI signs of unilateral hippocampal sclerosis (23 patients with right-sided hippocampal sclerosis) who underwent surgical treatment for MTLE. They underwent preoperative/postoperative high-resolution MRI as well as neuropsychological assessment for memory and estimated IQ. To investigate possible changes in the contralateral hippocampus of patients, we included 28 controls who underwent two MRIs at long-term intervals. The volumetry using preoperative MRI showed significant hippocampal atrophy ipsilateral to the side of surgery when compared with controls (p<0.0001) but no differences in contralateral hippocampal volumes. The mean postoperative follow-up was 8.7 years (± 2.5 SD; median=8.0). Our patients were classified as Engel I (80%), Engel II (18.2%), and Engel III (1.8%). We observed a small but significant reduction in the contralateral hippocampus of patients but no volume changes in controls. Most of the patients presented small declines in both estimated IQ and memory, which were more pronounced in patients with left TLE and in those with persistent seizures. Different surgical approaches did not impose differences in seizure control or in cognitive outcome. We observed small declines in cognitive scores with most of these patients, which were worse in patients with left-sided resection and in those who continued to suffer from postoperative seizures. We also demonstrated that manual volumetry can reveal a reduction in volume in the contralateral hippocampus, although this change was mild and could not be detected by visual analysis. These new findings suggest that dynamic processes continue to act after the removal of the hippocampus, and further studies with larger groups may help in understanding the underlying mechanisms.

Effect of estradiol benzoate microinjection into the median raphe nucleus on contextual conditioning

Estrogen deficiency has been associated with stress, anxiety and depression. Estrogen receptors have been identified in the median raphe nucleus (MRN). This structure is the main source of serotonergic projections to the hippocampus, a forebrain area implicated in the regulation of defensive responses and in the resistance to chronic stress. There is reported evidence indicating that estrogen modulates 5-HT(1A) receptor function. In the MRN, somatodendritic 5-HT(1A) receptors control the activity of serotonergic neurones by negative feedback. The present study has evaluated the effect of intra-MRN injection of estradiol benzoate (EB, 600 or 1200 ng/0.2 mu l) on the performance of ovariectormized rats submitted to contextual conditioning. Additionally, the same treatment was given after intra-MRN injection of Way 100635 (100 ng/0.2 mu l). a 5-HT(1A) receptor antagonist. Both doses of EB decreased freezing and increased rearing, indicating an anxiolytic effect. Pretreatment with Way 100635 antagonized the anxiolytic effect of estradiol. On the basis of these results, it may be suggested that estrogens modulate anxiety by acting on 5-HT(1A) receptors localized in the MRN. (C) 2009 Elsevier B.V. All rights reserved.

Improvement in Insulin Sensitivity and B-Cell Function Following Ileal Interposition with Sleeve Gastrectomy in Type 2 Diabetic Patients: Potential Mechanisms

Bariatric surgery in morbidly obese type 2 diabetic (T2DM) patients is associated with high rates of diabetes remission. We investigated the mechanisms of the anti-diabetic effect of the laparoscopic ileal interposition with sleeve gastrectomy (LII-SG) in normal weight (NW), overweight (OW) and obese (OB) T2DM patients. Ninety-four patients (aged 54 +/- 8 years) with long-standing (median 10 years), treated diabetes (median HbA(1c) = 8.6%), who were NW (15), OW (64) or OB (15) based on BMI, underwent LII-SG. Insulin sensitivity and parameters of -cell function were measured from an Oral Glycaemic Tolerance Test pre- and post-operatively. At a median of 13.4 months post-operatively, weight loss averaged 9.4 +/- 1.3, 16.8 +/- 0.8 and 23.2 +/- 1.7 kg in NW, OW and OB subjects, respectively (p < 0.0001). Insulin sensitivity was fully restored (395 [108] vs 208 [99] ml min(-1) m(-2)), fasting insulin secretion rate decreased (68 [52] vs 146 [120] pmol min(-1) m(-2)) and total insulin output increased (52 [26] vs 39 [28] nmol m(-2), all p a parts per thousand currency signaEuro parts per thousand 0.001). -cell glucose sensitivity doubled (37 [33] vs 18 [24] mol min(-1) m(-2) mM(-1), p < 0.0001). The only parameter predicting remission of diabetes was a lower baseline insulin sensitivity (p = 0.005). LII-SG induced changes on T2DM by mechanisms in part distinct from weight loss, principally involving restoration of insulin sensitivity and improvement of -cell function.

Thyroid Function After Unilateral Total Lobectomy

Objective: To evaluate the incidence of postoperative hypothyroidism among patients who underwent unilateral total lobectomy and identify related factors. Design: Retrospective medical record analysis. Setting: Oncological center and private clinic. Patients: From March 1996 to July 2005, 228 euthyroid patients underwent unilateral total lobectomy for benign diseases; 168 had all the information required for inclusion in this study. Main Outcome Measures: Serum levels of thyrotropin and antithyroidal antibodies were assessed, as well as ultrasonographic evaluation of the remaining thyroid lobe and review of all histological specimens, with emphasis on lymphocytic infiltration. Hypothyroidism was defined as thyrotropin level greater than 5.5 mU/L. Results: Most patients were female (88%), with a median (range) age of 45 (16-72) years. Hypothyroidism occurred in 61 cases (32.8%), during a median follow-up period of 29 months (range, 6-108 months). Statistically related factors included higher preoperative thyrotropin levels (2.1 mU/L among hypothyroid patients vs 1.2 mU/L in euthyroid patients; P<.001), smaller thyroid remnant volume (3.9 mL vs; 6.0 mL, respectively; P = .003); right vs left lobectomy (P = .006), and higher thyroperoxidase antibody serum levels (P = .009). Conclusions: Postoperative hypothyroidism appeared in 32.8% of the cases in this series, especially among patients with elevated preoperative thyrotropin and postoperative thyroperoxidase antibody levels, after right lobectomy and when a smaller thyroid remnant was left. After confirmation with larger prospective series, these results may support the indication for early postoperative hormone supplementation in these instances.

Testicular Sertoli cell function in male systemic lupus erythematosus

Objective. To assess the testicular Sertoli cell function in male SLE patients. Methods. Thirty-four consecutive patients were prospectively selected to evaluate serum inhibin B. Clinical features, treatment, semen analysis, urological evaluation, testicular ultrasound, hormones and anti-sperm antibodies were determined. Results. Patients were subdivided into two groups: low serum inhibin B (Group 1, n = 8) and normal levels (Group 2, n 26). The median sperm concentration (P = 0.024), total sperm count (P = 0.023) and total motile sperm count (P = 0.025) were lower in Group 1. Inhibin B levels were positively correlated with sperm concentration (r = 0.343), total motile sperm count (r = 0.357), and negatively correlated with follicule-stimulating hormone (FSH) (r = 0.699) and luteinizing hormone (r = 0.397). The median serum inhibin B was lower in SLE patients treated with intravenous cyclophosphamide (IVCYC) compared with those without this therapy (P = 0.031). Further evaluation of the 26 SLE patients with normal inhibin B and FSH levels revealed that medians of inhibin B/FSH ratio were lower in SLE patients with oligozoospermia compared with normozoospermia (P = 0.004). This ratio was also lower in SLE patients treated with IVCYC than those without this therapy (P = 0.04). In contrast, inhibin B serum level alone did not discriminate the later group of patients (P = 0.12). Conclusions. This is the first study to identify a high frequency of testicular Sertoli cell dysfunction in male SLE associated with semen abnormalities. Further prospective studies are necessary to determine if inhibin levels and inhibin B/FSH ratio will be an earlier and useful marker of IVCYC toxicity in these patients.

The role of BPH, lower urinary tract symptoms, and PSA levels on erectile function of Brazilian men who undergo prostate cancer screening

Introduction. Lower urinary tract symptoms (LUTS) and erectile dysfunction (ED) are common problems in middle-aged and older men. Recently, epidemiologic studies have shown significant associations between severity of LUTS and male sexual dysfunction. Aim. We analyzed the role of prostate enlargement, LUTS, and prostate specific antigen (PSA) levels in the erectile function of Brazilian men who underwent prostate cancer (PCa) screening. Method. We analyzed data from 1,008 consecutive patients enrolled in a PCa screening program. Benign prostatic hyperplasia (BPH) was defined as a prostate weight greater than 30 g as defined by digital rectal examination. For statistical analysis, we used the chi-squared and analysis of variance tests. The odds ratios (OR) for correlation of ED with prostate volume LUTS and PSA were estimated using logistic regression models. Main Outcome Measure. The American Urological Association (AUA) symptom score for LUTS and the International Index of Erectile Function. Results. Mean patient age was 61.2 years (45-87) and median PSA value was 1.9 ng/mL. BPH was identified in 48.5% of patients. Mild, moderate, and severe LUTS were found in 52.3%, 30.9%, and 16.8% of cases, respectively. ED was classified as absent, mild, mild to moderate, moderate, and severe in 18.6%, 23.1%, 18.6%, 15.2%, and 24.5%, respectively. While only 5.4% of the patients with no ED presented severe LUTS, this finding was observed in 27.1% of patients with severe ED (P<0.001). Univariate logistic regression analysis demonstrated that age, prostate volume, AUA symptom score, and PSA levels were significant predictors of ED. However, when controlled for patient age, only LUTS remained as an independent predictor of ED. Conclusions. Controlling for patient age, LUTS are independent risk factors for the development of ED among Brazilian men who undergo PCa screening.

Pulmonary function testing in quadriplegic subjects

Study design: Cross-sectional study. Objective: Pulmonary functional capacity in 23 Brazilian quadriplegic subjects (ASIA A), aged 30 (9.5) years, weight 66 (10.75) kg, height 176 (7) cm, was investigated at 42 ( 64) months postinjury. Setting: University Hospital-UNICAMP, Campinas, Brazil. Method: Subjects performed forced vital capacity ( FVC) and maximal voluntary ventilation (MVV) tests while seated in their standard wheelchairs. Forced Expired Volume after 1 s (FEV1) and FVC/FEV1 ratio were calculated from these tests. Values obtained were compared to three prediction equations from the literature that are used specifically for spinal cord subjects and include different variables in their formulae, such as age, gender, height, postinjury time and injury level. Data are expressed as median (interquartile interval). Differences between values were demonstrated by median confidence interval with significance level set at a 0.05. Results: Obtained data were statistically different from prediction equation results, with FVC 3.11 ( 0.81), 4.46 (0.28), 4.16 (0.33), 4.26 (0.42); FEV1 2.77 (1.03), 3.67 (0.21), 3.66 (0.30), 3.45 (0.39) and MVV 92 (27), 154.2 (11.9), 156.6 (14),157.3 (16.8), where the first value is obtained experimentally and the second, third and fourth values correspond to predicted values. The results obtained from spirometry test in this study differed significantly from the results obtained when prediction equations were used. Conclusion: The use of prediction equations developed to estimate pulmonary function in wheelchair users significantly overestimates pulmonary function of quadriplegic individuals with complete lesions (ASIA group A), in comparison to measured values.

The Impact of Preexisting Myocardial Remodeling on Ventricular Function Early after Tetralogy of Fallot Repair

Background: Twenty-three patients (median age 23 months) who underwent Fallot`s tetralogy repair were investigated prospectively to detect a possible association between histopathologic myocardial remodeling and echocardiographic findings of systolic or diastolic ventricular dysfunction. Methods: Intraoperatively resected infundibular bands and subendocardial biopsy samples from the right ventricle (RV) and left ventricle were obtained for histopathologic evaluation. Tissue Doppler echocardiographic interrogation of the ventricles was performed before surgery and in the postoperative period. Results: Histopathologic data revealed hypertrophy of the RV cardiomyocytes and increased interstitial collagen in both ventricles. Mean values of RV isovolumic acceleration decreased significantly at the third evaluation compared with the preoperative values (P = .006). RV myocardial fibrosis greater than 8.3% was associated with a probability of altered E` of at least 0.7 (odds ratio = 2.31). Conclusion: Preoperative histologic myocardial remodeling influenced the postoperative RV function in this group of patients with late repair. Further studies are necessary to evaluate the myocardium in younger patients and to define its influence in the long-term follow-up. (J Am Soc Echocardiogr 2010;23:912-8.)

Effect on renal function of tenofovir co-administered with either efavirenz or boosted lopinavir or boosted atazanavir: the Swiss HIV Cohort Study

Reduced re'nal function has been reported with tenofovir disoproxil fumarate (TDF). It is not clear whether TDF co-administered with a boosted protease inhibitor (PI) leads to a greater decline in renal function than TDF co-administered with a non-nucleoside reverse transcriptase inhibitor (NNRTI).Methods: We selected ail antiretroviral therapy-naive patients in the Swiss HIV Cohort Study (SHCS) with calibrated or corrected serum creatinine measurements starting antiretroviral therapy with TDF and either efavirenz (EFV) or the ritonavir-boosted PIs, lopinavir (LPV/r) or atazanavir (ATV/r). As a measure of renal function, we used the Chronic Kidney Disease Epidemiology Collaboration (CKD-EPI) equation to estimate the glomerular filtration rate (eGFR). We calculated the difference in eGFR over time between two therapies using a marginal model for repeated measures. In weighted analyses, observations were weighted by the product of their point of treatment and censoring weights to adjust for differences both in the sort of patients starting each therapy and in the sort of patients remaining on each therapy over time.Results: By March 2011, 940 patients with at least one creatinine measurement on a first therapy with either TDF and EFV (n=484), TDF and LPVlr (n=269) or TDF and ATV/r (n=187) had been followed for a median of 1. 7, 1.2 and 1.3 years, respectively. Table 1 shows the difference in average estimated GFR (eGFR) over time since starting cART for two marginal models. The first model was not adjusted for potential confounders; the second mode! used weights to adjust for confounders. The results suggest a greater decline in renal function during the first 6 months if TDF is used with a PI rather than with an NNRTI, but no further difference between these therapies after the first 6 months. TDF and ATV/r may lead to a greater decline in the first 6 months than TDF and LPVlr.Conclusions: TDF co-administered with a boosted PI leads to a greater de cline in renal function over the first 6 months of therapy than TDF co-administered with an NNRTI; this decline may be worse with ATV/r than with LPV/r.

Long-term fluctuation of relative afferent pupillary defect in subjects with normal visual function.

PURPOSE: To determine whether the relative afferent pupillary defect (RAPD) remains constant over time in normal subjects. METHODS: Seventeen normal subjects were tested with infrared pupillography and automated perimetry in four sessions over 3 years. The changes in RAPD and visual field asymmetry between testing sessions were compared. RESULTS: The range of RAPD was 0.0 to 0.3 log unit, and the difference in the mean deviation between the eyes on automated static perimetry was 0 to 3 dB. Eight subjects repeatedly had an RAPD in the same eye. There was no correlation between the RAPD and the visual field asymmetry at the same visit. Changes in the magnitude of the RAPD between any two sessions were typically small (median, 0.08 log unit; 25th percentile, 0.04 log unit; 75th percentile, 0.15 log unit). CONCLUSIONS: Some normal subjects may show a persistent but small RAPD in the absence of detectable pathologic disease. Therefore, an isolated RAPD in the range of 0.3 log unit that is not associated with any other significant historical or clinical finding should probably be considered benign.