Obtainable Sizes of Topologies on Finite Sets

We study the smallest possible number of points in a topological space having k open sets. Equivalently, this is the smallest possible number of elements in a poset having k order ideals. Using efficient algorithms for constructing a topology with a prescribed size, we show that this number has a logarithmic upper bound. We deduce that there exists a topology on n points having k open sets, for all k in an interval which is exponentially large in n. The construction algorithms can be modified to produce topologies where the smallest neighborhood of each point has a minimal size, and we give a range of obtainable sizes for such topologies.Comment: Final version, to appear in Journal of Combinatorial Theory, Series

The Progression of β-amyloid Deposition in the Frontal Cortex of the Aged Canine

Brains from 41 aged canines (≥10 years of age) were examined immunohistochemically to characterize the laminar distribution and age-related progression of β-amyloid (Aβ) in frontal cortex. We classified the Aβ patterns into four distinct types. Type I was characterized by small, faint deposits of Aβ in deep cortical layers. Type II consisted of diffuse deposits of Aβ mainly in layers V and VI. Type III had both dense plaques in superficial layers, and diffuse deposits in deep layers. Finally, Type IV had solely dense plaques throughout all layers of cortex. We compared the Aβ distribution pattern between the Old canines (10–15 years, n=22) and the Very Old canines (\u3e15 years, n=19). The Old group primarily had negative staining, or Type I and Type II patterns of amyloid deposition (73%). Conversely, the Very Old group had predominantly Types II, III and IV deposits (89.5%), a difference that was significant (Pβ deposition in canine frontal cortex is a progressive age-related process beginning with diffuse deposits in the deep cortical layers followed by the development of deposits in outer layers. In support of this hypothesis, the deeper layer diffuse plaques in the Very Old group of dogs also contain the largest proportion of β-amyloid with an isomerized aspartic acid residue at position 7, indicating that these deposits had been present for some time. We also observed fiber-like Aβ immunoreactivity within regions of diffuse Aβ deposits. These fibers appeared to be degenerating neurites, which were negative for hyperphosphorylated tau. Therefore, these fibers may represent a very early form of neuritic change that precede tau hyperphosphorylation or develop by an alternative pathway

Differential Indicators of Diabetes-Induced Oxidative Stress in New Zealand White Rabbits: Role of Dietary Vitamin E Supplementation

Determination of reliable bioindicators of diabetes-induced oxidative stress and the role of dietary vitamin E supplementation were investigated. Blood (plasma) chemistries, lipid peroxidation (LPO), and antioxidant enzyme activities were measured over 12 weeks in New Zealand White rabbits (control, diabetic, and diabetic + vitamin E). Cholesterol and triglyceride levels did not correlate with diabetic state. PlasmaLPOwas influenced by diabetes and positively correlated with glucose concentration only, not cholesterol or triglycerides. Liver glutathione peroxidase (GPX) activity negatively correlated with glucose and triglyceride levels. Plasma and erythrocyte GPX activities positively correlated with glucose, cholesterol, and triglyceride concentrations. Liver superoxide dismutase activity positively correlated with glucose and cholesterol concentration. Vitamin E reduced plasma LPO, but did not affect the diabetic state. Thus, plasmaLPOwas the most reliable indicator of diabetes-induced oxidative stress. Antioxidant enzyme activities and types of reactive oxygen species generated were tissue dependent. Diabetes-induced oxidative stress is diminished by vitamin E supplementation

The Prevalence and Volumetry of Pituitary Cysts in Children with Growth Hormone Deficiency and Idiopathic Short Stature

Background Pituitary cysts have been speculated to cause endocrinopathies. We sought to describe the prevalence and volumetry of pituitary cysts in patients with growth hormone deficiency (GHD) and idiopathic short stature (ISS). Methods Six hundred and eighteen children evaluated for growth failure at the Division of Pediatric Endocrinology at New York Medical College between the years 2002 and 2012, who underwent GH stimulation testing and had a brain magnetic resonance imaging (MRI) prior to initiating GH treatment were randomly selected to be a part of this study. High resolution MRI was used to evaluate the pituitary gland for size and the presence of a cyst. Cyst prevalence, cyst volume and percentage of the gland occupied by the cyst (POGO) were documented. Results Fifty-six patients had a cyst, giving an overall prevalence of 9.1%. The prevalence of cysts in GHD patients compared to ISS patients was not significant (13.5% vs. 5.7%, p=0.46). Mean cyst volume was greater in GHD patients than ISS patients (62.0 mm3 vs. 29.4 mm3, p=0.01). POGO for GHD patients was significantly greater (p=0.003) than for ISS patients (15.3%+/-12.8 vs. 7.1%+/-8.0). Observers were blinded to patient groups. Conclusions GHD patients had a significantly greater volume and POGO compared to ISS patients. This raises the question of whether cysts are implicated in the pathology of growth failure

Absence of HIV-1 Evolution in the Gut-Associated Lymphoid Tissue from Patients on Combination Antiviral Therapy Initiated during Primary Infection

Mucosal mononuclear (MMC) CCR5+CD4+ T cells of the gastrointestinal (GI) tract are selectively infected and depleted during acute HIV-1 infection. Despite early initiation of combination antiretroviral therapy (cART), gut-associated lymphoid tissue (GALT) CD4+ T cell depletion and activation persist in the majority of HIV-1 positive individuals studied. This may result from ongoing HIV-1 replication and T-cell activation despite effective cART. We hypothesized that ongoing viral replication in the GI tract during cART would result in measurable viral evolution, with divergent populations emerging over time. Subjects treated during early HIV-1 infection underwent phlebotomy and flexible sigmoidoscopy with biopsies prior to and 15–24 months post initiation of cART. At the 2nd biopsy, three GALT phenotypes were noted, characterized by high, intermediate and low levels of immune activation. A representative case from each phenotype was analyzed. Each subject had plasma HIV-1 RNA levels <50 copies/ml at 2nd GI biopsy and CD4+ T cell reconstitution in the peripheral blood. Single genome amplification of full-length HIV-1 envelope was performed for each subject pre- and post-initiation of cART in GALT and PBMC. A total of 280 confirmed single genome sequences (SGS) were analyzed for experimental cases. For each subject, maximum likelihood phylogenetic trees derived from molecular sequence data showed no evidence of evolved forms in the GALT over the study period. During treatment, HIV-1 envelope diversity in GALT-derived SGS did not increase and post-treatment GALT-derived SGS showed no substantial genetic divergence from pre-treatment sequences within transmitted groups. Similar results were obtained from PBMC-derived SGS. Our results reveal that initiation of cART during acute/early HIV-1 infection can result in the interruption of measurable viral evolution in the GALT, suggesting the absence of de-novo rounds of HIV-1 replication in this compartment during suppressive cART

Association of Stromal Tumor-Infiltrating Lymphocytes With Recurrence-Free Survival in the N9831 Adjuvant Trial in Patients With Early-Stage HER2-Positive Breast Cancer

Importance The presence of tumor-infiltrating lymphocytes at diagnosis is reported to be prognostic in triple-negative breast cancer. Objective To evaluate the association of stromal tumor-infiltrating lymphocytes (STILs) with recurrence-free survival (RFS) in women with human epidermal growth factor receptor 2 (HER2)–positive breast cancer treated with chemotherapy or chemotherapy plus trastuzumab in the N9831 trial. Design, Setting, and Participants Hematoxylin-eosin–stained tumor slides from patients with early-stage HER2-positive breast cancer in 2 of the 3 arms of the N9831 trial were assessed for STILs at an academic medical center. The amounts of STILs were quantitated in deciles, and a level of at least 60% STILs was used for the prespecified categorical cutoff. The association between STILs and RFS was evaluated with Cox models. Exposure Standard chemotherapy consisting of doxorubicin-cyclophosphamide followed by weekly paclitaxel (arm A) or doxorubicin-cyclophosphamide followed by weekly paclitaxel plus trastuzumab followed by trastuzumab alone (arm C). Main Outcomes and Measures Stromal tumor-infiltrating lymphocytes and their association with RFS. Results A total of 489 patients from arm A and 456 patients from arm C were assessed with a median (range) follow-up of 4.4 (0-13.6) years. The 10-year Kaplan-Meier estimates for RFS in arm A were 90.9% and 64.5% for patients with high and low levels of STILs, respectively (hazard ratio [HR], 0.23 [95% CI, 0.07-0.73]; P = .01). The 10-year estimates for RFS in arm C were 80.0% and 80.1% for patients with high and low levels of STILs, respectively (HR, 1.26 [95% CI, 0.50-3.17]; P = .63). The test for interaction between trastuzumab treatment and STIL status was statistically significant (P = .03). In a multivariable analysis, STIL status remained significantly associated with RFS in arm A and not significantly associated in arm C (HR, 1.01 [95% CI, 0.89-1.15]; interaction P = .04). Conclusions and Relevance This analysis of participants in the N9831 trial found that the presence of STILs was prognostically associated with RFS in patients treated with chemotherapy alone but not in patients treated with chemotherapy plus trastuzumab. High levels of STILs were associated with lack of trastuzumab therapy benefit, in contrast to a previously reported association between increased levels of STILs and increased trastuzumab benefit in HER2-positive patients