A Geometrical Interpretation to Define Contradiction Degrees between Two Fuzzy Sets

For inference purposes in both classical and fuzzy logic, neither the information itself should be contradictory, nor should any of the items of available information contradict each other. In order to avoid these troubles in fuzzy logic, a study about contradiction was initiated by Trillas et al. in [5] and [6]. They introduced the concepts of both self-contradictory fuzzy set and contradiction between two fuzzy sets. Moreover, the need to study not only contradiction but also the degree of such contradiction is pointed out in [1] and [2], suggesting some measures for this purpose. Nevertheless, contradiction could have been measured in some other way. This paper focuses on the study of contradiction between two fuzzy sets dealing with the problem from a geometrical point of view that allow us to find out new ways to measure the contradiction degree. To do this, the two fuzzy sets are interpreted as a subset of the unit square, and the so called contradiction region is determined. Specially we tackle the case in which both sets represent a curve in [0,1]2. This new geometrical approach allows us to obtain different functions to measure contradiction throughout distances. Moreover, some properties of these contradiction measure functions are established and, in some particular case, the relations among these different functions are obtained.

Quantum phases of dimerized and frustrated Heisenberg spin chains with s=1/2, 1 and 3/2: an entanglement entropy and fidelity study

We study here different regions in phase diagrams of the spin-1/2, spin-1 and spin-3/2 one-dimensional antiferromagnetic Heisenberg systems with frustration (next-nearest-neighbor interaction J(2)) and dimerization (delta). In particular, we analyze the behaviors of the bipartite entanglement entropy and fidelity at the gapless to gapped phase transitions and across the lines separating different phases in the J(2)-delta plane. All the calculations in this work are based on numerical exact diagonalizations of finite systems.

SYNTHESIS AND STRUCTURE CHARACTERIZATION OF LANTHANUM [2,2,2]CRYPTATES, [LACL[2,2,2](H2O)]CL-2-CENTER-DOT-H2O AND [LA(CF3SO3)[2,2,2]1(DMF)](CF3SO3)(2)

Two lanthanum(III) [2,2,2]cryptates, [LaCl[2,2,2](H2O)]Cl-2.H2O (1) and [La(CF3SO3)[2,2,2](DMF)] (CF3SO3)(2) (2) have been prepared by the reaction of LaCl3 and La(CF3SO3)(3) with [2,2,2]cryptand, respectively and their crystal structures have been determ

Low-level Laser Therapy Improves Skeletal Muscle Performance, Decreases Skeletal Muscle Damage and Modulates mRNA Expression of COX-1 and COX-2 in a Dose-dependent Manner

We tested if modulation in mRNA expression of cyclooxygenase isoforms (COX-1 and COX-2) can be related to protective effects of phototherapy in skeletal muscle. Thirty male Wistar rats were divided into five groups receiving either one of four laser doses (0.1, 0.3, 1.0 and 3.0 J) or a no-treatment control group. Laser irradiation (904 nm, 15 mW average power) was performed immediately before the first contraction for treated groups. Electrical stimulation was used to induce six tetanic tibial anterior muscle contractions. Immediately after sixth contraction, blood samples were collected to evaluate creatine kinase activity and muscles were dissected and frozen in liquid nitrogen to evaluate mRNA expression of COX-1 and COX-2. The 1.0 and 3.0 J groups showed significant enhancement (P < 0.01) in total work performed in six tetanic contractions compared with control group. All laser groups, except the 3.0 J group, presented significantly lower post-exercise CK activity than control group. Additionally, 1.0 J group showed increased COX-1 and decreased COX-2 mRNA expression compared with control group and 0.1, 0.3 and 3.0 J laser groups (P < 0.01). We conclude that pre-exercise infrared laser irradiation with dose of 1.0 J enhances skeletal muscle performance and decreases post-exercise skeletal muscle damage and inflammation.

Photodissociation dynamics of tert-butylnitrite following excitation to the S(1) and S(2) states. A study by velocity-map ion-imaging and 3D-REMPI spectroscopy

Excitation of tert-butylnitrite into the first and second UV absorption bands leads to efficient dissociation into the fragment radicals NO and tert-butoxy in their electronic ground states (2)Π and (2)E, respectively. Velocity distributions and angular anisotropies for the NO fragment in several hundred rotational and vibrational quantum states were obtained by velocity-map imaging and the recently developed 3D-REMPI method. Excitation into the well resolved vibronic progression bands (k = 0, 1, 2) of the NO stretch mode in the S(1) ← S(0) transition produces NO fragments mostly in the vibrational state with v = k, with smaller fractions in v = k - 1 and v = k - 2. It is concluded that dissociation occurs on the purely repulsive PES of S(1) without barrier. All velocity distributions from photolysis via the S(1)(nπ*) state are monomodal and show high negative anisotropy (β ≈ -1). The rotational distributions peak near j = 30.5 irrespective of the vibronic state S(1)(k) excited and the vibrational state v of the NO fragment. On average 46% of the excess energy is converted to kinetic energy, 23% and 31% remain as internal energy in the NO fragment and the t-BuO radical, respectively. Photolysis via excitation into the S(2) ← S(0) transition at 227 nm yields NO fragments with about equal populations in v = 0 and v = 1. The rotational distributions have a single maximum near j = 59.5. The velocity distributions are monomodal with positive anisotropy β ≈ 0.8. The average fractions of the excess energy distributed into translation, internal energy of NO, and internal energy of t-BuO are 39%, 23%, and 38%, respectively. In all cases ∼8500 cm(-1) of energy remain in the internal degrees of freedom of the t-BuO fragment. This is mostly assigned to rotational energy. An ab initio calculation of the dynamic reaction path shows that not only the NO fragment but also the t-BuO fragment gain large angular momentum during dissociation on the purely repulsive potential energy surface of S(2).

Differential regulation of beta 1 and beta 2 integrin avidity by chemoattractants in eosinophils.

The CC chemokines regulated on activation normal T expressed and secreted (RANTES) and monocyte chemotactic protein 3 (MCP-3), and the anaphylatoxin C5a, induce activation, degranulation, chemotaxis, and transendothelial migration of eosinophils. Adhesion assays on purified ligands showed differential regulation of beta 1 and beta 2 integrin avidity in eosinophils. Adhesiveness of VLA-4 (alpha 4 beta 1, CD29/CD49d) for vascular cell adhesion molecule 1 or fibronectin was rapidly increased but subsequently reduced by RANTES, MCP-3, or C5a. The deactivation of VLA-4 lead to cell detachment, whereas phorbol 12-myristate 13-acetate induced sustained activation of VLA-4. In contrast, chemoattractants stimulated a prolonged increase in the adhesiveness of Mac-1 (alpha M beta 2, CD11b/CD18) for intercellular adhesion molecule 1. Inhibition by pertussis toxin confirmed signaling via G protein-coupled receptors. Chemoattractants induced transient, while phorbol 12-myristate 13-acetate induced sustained actin polymerization. Disruption of actin filaments by cytochalasins inhibited increases in avidity of VLA-4 but not of Mac-1. Chemoattractants did not upregulate a Mn2+-inducible beta 1 neoepitope defined by the mAb 9EG7, but induced prolonged expression of a Mac-1 activation epitope recognized by the mAb CBRM1/5. This mAb inhibited chemoattractant-stimulated adhesion of eosinophils to intercellular adhesion molecule 1. Thus, regulation of VLA-4 was dependent on the actin cytoskeleton, whereas conformational changes appeared to be crucial for activation of Mac-1. To our knowledge, this is the first demonstration that physiological agonists, such as chemoattractants, can differentially regulate the avidity of a beta 1 and a beta 2 integrin expressed on the same leukocyte.

The N-terminal region (A/B) of rat thyroid hormone receptors alpha 1, beta 1, but not beta 2 contains a strong thyroid hormone-dependent transactivation function.

In this study we have investigated the role of the N-terminal region of thyroid hormone receptors (TRs) in thyroid hormone (TH)-dependent transactivation of a thymidine kinase promoter containing TH response elements composed either of a direct repeat or an inverted palindrome. Comparison of rat TR beta 1 with TR beta 2 provides an excellent model since they share identical sequences except for their N termini. Our results show that TR beta 2 is an inefficient TH-dependent transcriptional activator. The degree of transactivation corresponds to that observed for the mutant TR delta N beta 1/2, which contains only those sequences common to TR beta 1 and TR beta 2. Thus, TH-dependent activation appears to be associated with two separate domains. The more important region, however, is embedded in the N-terminal domain. Furthermore, the transactivating property of TR alpha 1 was also localized to the N-terminal domain between amino acids 19 and 30. Using a coimmunoprecipitation assay, we show that the differential interaction of the N terminus of TR beta 1 and TR beta 2 with transcription factor IIB correlates with the TR beta 1 activation function. Hence, our results underscore the importance of the N-terminal region of TRs in TH-dependent transactivation and suggest that a transactivating signal is transmitted to the general transcriptional machinery via a direct interaction of the receptor N-terminal region with transcription factor IIB.

Fuzzy sets: Abstraction Axiom, Statistical Interpretation, Observations of Fuzzy Sets

The issues relating fuzzy sets definition are under consideration including the analogue for separation axiom, statistical interpretation and membership function representation by the conditional Probabilities.

QTc interval and resting heart rate as long-term predictors of mortality in type 1 and type 2 diabetes mellitus: a 23-year follow-up

We evaluated the association of QT interval corrected for heart rate (QT(c)) and resting heart rate (rHR) with mortality (all-causes, cardiovascular, cardiac, and ischaemic heart disease) in subjects with type 1 and type 2 diabetes.

Association of soluble tumor necrosis factor receptors 1 and 2 with nephropathy, cardiovascular events, and total mortality in type 2 diabetes

AIMS/HYPOTHESIS: Soluble tumor necrosis factor receptors 1 and 2 (sTNFR1 and sTNFR2) contribute to experimental diabetic kidney disease, a condition with substantially increased cardiovascular risk when present in patients. Therefore, we aimed to explore the levels of sTNFRs, and their association with prevalent kidney disease, incident cardiovascular disease, and risk of mortality independently of baseline kidney function and microalbuminuria in a cohort of patients with type 2 diabetes. In pre-defined secondary analyses we also investigated whether the sTNFRs predict adverse outcome in the absence of diabetic kidney disease. METHODS: The CARDIPP study, a cohort study of 607 diabetes patients [mean age 61 years, 44 % women, 45 cardiovascular events (fatal/non-fatal myocardial infarction or stroke) and 44 deaths during follow-up (mean 7.6 years)] was used. RESULTS: Higher sTNFR1 and sTNFR2 were associated with higher odds of prevalent kidney disease [odd ratio (OR) per standard deviation (SD) increase 1.60, 95 % confidence interval (CI) 1.32-1.93, p < 0.001 and OR 1.54, 95 % CI 1.21-1.97, p = 0.001, respectively]. In Cox regression models adjusting for age, sex, glomerular filtration rate and urinary albumin/creatinine ratio, higher sTNFR1 and sTNFR2 predicted incident cardiovascular events [hazard ratio (HR) per SD increase, 1.66, 95 % CI 1.29-2.174, p < 0.001 and HR 1.47, 95 % CI 1.13-1.91, p = 0.004, respectively]. Results were similar in separate models with adjustments for inflammatory markers, HbA1c, or established cardiovascular risk factors, or when participants with diabetic kidney disease at baseline were excluded (p < 0.01 for all). Both sTNFRs were associated with mortality. CONCLUSIONS/INTERPRETATIONS: Higher circulating sTNFR1 and sTNFR2 are associated with diabetic kidney disease, and predicts incident cardiovascular disease and mortality independently of microalbuminuria and kidney function, even in those without kidney disease. Our findings support the clinical utility of sTNFRs as prognostic markers in type 2 diabetes.

Approximation of centroid end-points and switch points for replacing type reduction algorithms

Despite several years of research, type reduction (TR) operation in interval type-2 fuzzy logic system (IT2FLS) cannot perform as fast as a type-1 defuzzifier. In particular, widely used Karnik-Mendel (KM) TR algorithm is computationally much more demanding than alternative TR approaches. In this work, a data driven framework is proposed to quickly, yet accurately, estimate the output of the KM TR algorithm using simple regression models. Comprehensive simulation performed in this study shows that the centroid end-points of KM algorithm can be approximated with a mean absolute percentage error as low as 0.4%. Also, switch point prediction accuracy can be as high as 100%. In conjunction with the fact that simple regression model can be trained with data generated using exhaustive defuzzification method, this work shows the potential of proposed method to provide highly accurate, yet extremely fast, TR approximation method. Speed of the proposed method should theoretically outperform all available TR methods while keeping the uncertainty information intact in the process.

Identifying common and specific microRNAs expressed in peripheral blood mononuclear cell of type 1, type 2, and gestational diabetes mellitus patients

Abstract Background Regardless the regulatory function of microRNAs (miRNA), their differential expression pattern has been used to define miRNA signatures and to disclose disease biomarkers. To address the question of whether patients presenting the different types of diabetes mellitus could be distinguished on the basis of their miRNA and mRNA expression profiling, we obtained peripheral blood mononuclear cell (PBMC) RNAs from 7 type 1 (T1D), 7 type 2 (T2D), and 6 gestational diabetes (GDM) patients, which were hybridized to Agilent miRNA and mRNA microarrays. Data quantification and quality control were obtained using the Feature Extraction software, and data distribution was normalized using quantile function implemented in the Aroma light package. Differentially expressed miRNAs/mRNAs were identified using Rank products, comparing T1DxGDM, T2DxGDM and T1DxT2D. Hierarchical clustering was performed using the average linkage criterion with Pearson uncentered distance as metrics. Results The use of the same microarrays platform permitted the identification of sets of shared or specific miRNAs/mRNA interaction for each type of diabetes. Nine miRNAs (hsa-miR-126, hsa-miR-1307, hsa-miR-142-3p, hsa-miR-142-5p, hsa-miR-144, hsa-miR-199a-5p, hsa-miR-27a, hsa-miR-29b, and hsa-miR-342-3p) were shared among T1D, T2D and GDM, and additional specific miRNAs were identified for T1D (20 miRNAs), T2D (14) and GDM (19) patients. ROC curves allowed the identification of specific and relevant (greater AUC values) miRNAs for each type of diabetes, including: i) hsa-miR-1274a, hsa-miR-1274b and hsa-let-7f for T1D; ii) hsa-miR-222, hsa-miR-30e and hsa-miR-140-3p for T2D, and iii) hsa-miR-181a and hsa-miR-1268 for GDM. Many of these miRNAs targeted mRNAs associated with diabetes pathogenesis. Conclusions These results indicate that PBMC can be used as reporter cells to characterize the miRNA expression profiling disclosed by the different diabetes mellitus manifestations. Shared miRNAs may characterize diabetes as a metabolic and inflammatory disorder, whereas specific miRNAs may represent biological markers for each type of diabetes, deserving further attention.

Tyrosine phosphorylation mediates ConA-induced membrane type 1-matrix metalloproteinase expression and matrix metalloproteinase-2 activation in MDA-MB-231 human breast carcinoma cells

ConA-induced cell surface activation of pro-matrix metalloproteinase-2 (pro-MMP-2) by MDA-MB-231 human breast cancer cells is apparently mediated by up-regulation of membrane type 1 MMP (MT1-MMP) through transcriptional and posttranscriptional mechanisms. Here, we have explored the respective roles of cell surface clustering and protein tyrosine phosphorylation in the ConA- induction effects. Treatment with succinyl-ConA, a variant lacking significant clusterability, partially stimulated MT1-MMP mRNA and protein levels but did not induce MMP-2 activation, suggesting that clustering contributes to the transcriptional regulation by ConA but appears to be critical for the nontranscriptional component. We further found that genistein, an inhibitor of tyrosine phosphorylation, blocked ConA-induced pro-MMP-2 activation and ConA-induced MT1-MMP mRNA level in a dose-dependent manner, implicating tyrosine phosphorylation in the transcriptional aspect. This was confirmed by the dose-dependent promotion of pro-MMP-2 activation by sodium orthovanadate in the presence of suboptimal concentrations of ConA (7.5 μg/ml), with optimal effects seen at 25 μg/g orthovanadate. Genistein did not inhibit the ConA potentiation of MMP-2 activation in MCF-7 cells, in which transfected MT1-MMP is driven by a heterologous promoter, supporting the major implication of phosphotyrosine in the transcriptional component of ConA regulation. These data describe a major signaling event upstream of MT1- MMP induction by ConA and set the stage for further analysis of the nontranscriptional component.

Implication of collagen type I-induced membrane-type 1-matrix metalloproteinase expression and matrix metalloproteinase-2 activation in the metastatic progression of breast carcinoma

We have previously demonstrated that fibroblasts and invasive human breast carcinoma (HBC) cells specifically activate matrix metalloproteinase- 2 (MMP-2) when cultured on 3-dimensional gels of type I collagen but not a range of other substrates. We show here the constitutive expression of membrane-type 1 (MT1)-MMP in both fibroblasts, and invasive HBC cell lines, that have fibroblastic attributes presumably acquired through an epithelial- to-mesenchymal transition (EMT). Treatment with collagen type I increased the steady-state MT1-MMP mRNA levels in these cells but did not induce either MT1-MMP expression or MMP-2 activation in noninvasive breast carcinoma cell lines, which retain epithelial features. Basal MT3-MMP mRNA expression had a pattern similar to that of MT1-MMP but was not up-regulated by collagen. MT4- MMP mRNA was seen in both invasive and noninvasive HBC cell lines and was also not collagen-regulated, and MT2-MMP mRNA was not detected in any of the HBC cell lines tested. These data support a role for MT1-MMP in the collagen- induced MMP-2-activation seen in these cells. In situ hybridization analysis of archival breast cancer specimens revealed a close parallel in expression of both collagen type I and MT1-MMP mRNA in peritumoral fibroblasts, which was correlated with aggressiveness of the lesion. Relatively high levels of expression of both mRNA species were seen in fibroblasts close to invasive tumor nests and, although only focally, in certain areas close to preinvasive tumors. These foci may represent hot spots for local degradation and invasive progression. Collectively, these results implicate MT1-MMP in collagen- stimulated MMP-2 activation and suggest that this mechanism may be employed in vivo by both tumor-associated fibroblasts and EMT-derived carcinoma cells to facilitate increased invasion and/or metastasis.

Anthropometric measures of obesity-their association with type 2 diabetes and hypertension across ethnic groups

Clinical trials have shown that weight reduction with lifestyles can delay or prevent diabetes and reduce blood pressure. An appropriate definition of obesity using anthropometric measures is useful in predicting diabetes and hypertension at the population level. However, there is debate on which of the measures of obesity is best or most strongly associated with diabetes and hypertension and on what are the optimal cut-off values for body mass index (BMI) and waist circumference (WC) in this regard. The aims of the study were 1) to compare the strength of the association for undiagnosed or newly diagnosed diabetes (or hypertension) with anthropometric measures of obesity in people of Asian origin, 2) to detect ethnic differences in the association of undiagnosed diabetes with obesity, 3) to identify ethnic- and sex-specific change point values of BMI and WC for changes in the prevalence of diabetes and 4) to evaluate the ethnic-specific WC cutoff values proposed by the International Diabetes Federation (IDF) in 2005 for central obesity. The study population comprised 28 435 men and 35 198 women, ≥ 25 years of age, from 39 cohorts participating in the DECODA and DECODE studies, including 5 Asian Indian (n = 13 537), 3 Mauritian Indian (n = 4505) and Mauritian Creole (n = 1075), 8 Chinese (n =10 801), 1 Filipino (n = 3841), 7 Japanese (n = 7934), 1 Mongolian (n = 1991), and 14 European (n = 20 979) studies. The prevalence of diabetes, hypertension and central obesity was estimated, using descriptive statistics, and the differences were determined with the χ2 test. The odds ratios (ORs) or  coefficients (from the logistic model) and hazard ratios (HRs, from the Cox model to interval censored data) for BMI, WC, waist-to-hip ratio (WHR), and waist-to-stature ratio (WSR) were estimated for diabetes and hypertension. The differences between BMI and WC, WHR or WSR were compared, applying paired homogeneity tests (Wald statistics with 1 df). Hierarchical three-level Bayesian change point analysis, adjusting for age, was applied to identify the most likely cut-off/change point values for BMI and WC in association with previously undiagnosed diabetes. The ORs for diabetes in men (women) with BMI, WC, WHR and WSR were 1.52 (1.59), 1.54 (1.70), 1.53 (1.50) and 1.62 (1.70), respectively and the corresponding ORs for hypertension were 1.68 (1.55), 1.66 (1.51), 1.45 (1.28) and 1.63 (1.50). For diabetes the OR for BMI did not differ from that for WC or WHR, but was lower than that for WSR (p = 0.001) in men while in women the ORs were higher for WC and WSR than for BMI (both p < 0.05). Hypertension was more strongly associated with BMI than with WHR in men (p < 0.001) and most strongly with BMI than with WHR (p < 0.001), WSR (p < 0.01) and WC (p < 0.05) in women. The HRs for incidence of diabetes and hypertension did not differ between BMI and the other three central obesity measures in Mauritian Indians and Mauritian Creoles during follow-ups of 5, 6 and 11 years. The prevalence of diabetes was highest in Asian Indians, lowest in Europeans and intermediate in others, given the same BMI or WC category. The  coefficients for diabetes in BMI (kg/m2) were (men/women): 0.34/0.28, 0.41/0.43, 0.42/0.61, 0.36/0.59 and 0.33/0.49 for Asian Indian, Chinese, Japanese, Mauritian Indian and European (overall homogeneity test: p > 0.05 in men and p < 0.001 in women). Similar results were obtained in WC (cm). Asian Indian women had lower  coefficients than women of other ethnicities. The change points for BMI were 29.5, 25.6, 24.0, 24.0 and 21.5 in men and 29.4, 25.2, 24.9, 25.3 and 22.5 (kg/m2) in women of European, Chinese, Mauritian Indian, Japanese, and Asian Indian descent. The change points for WC were 100, 85, 79 and 82 cm in men and 91, 82, 82 and 76 cm in women of European, Chinese, Mauritian Indian, and Asian Indian. The prevalence of central obesity using the 2005 IDF definition was higher in Japanese men but lower in Japanese women than in their Asian counterparts. The prevalence of central obesity was 52 times higher in Japanese men but 0.8 times lower in Japanese women compared to the National Cholesterol Education Programme definition. The findings suggest that both BMI and WC predicted diabetes and hypertension equally well in all ethnic groups. At the same BMI or WC level, the prevalence of diabetes was highest in Asian Indians, lowest in Europeans and intermediate in others. Ethnic- and sex-specific change points of BMI and WC should be considered in setting diagnostic criteria for obesity to detect undiagnosed or newly diagnosed diabetes.