Generalized Cauchy means

Given two means M and N, the operator MM,NMM,N assigning to a given mean μ the mean MM,N(μ)(x,y)=M(μ(x,N(x,y)),μ(N(x,y),y)) was defined in Berrone and Moro (Aequationes Math 60:1–14, 2000) in connection with Cauchy means: the Cauchy mean generated by the pair f, g of continuous and strictly monotonic functions is the unique solution μ to the fixed point equation MA(f),A(g)(μ)=μ, where A(f) and A(g) are the quasiarithmetic means respectively generated by f and g. In this article, the operator MM,NMM,N is studied under less restrictive conditions and a general fixed point theorem is derived from an explicit formula for the iterates MnM,NMM,Nn . The concept of class of generalized Cauchy means associated to a given family of mixing pairs of means is introduced and some distinguished families of pairs are presented. The question of equality in these classes of means remains a challenging open problem.Fil: Berrone, Lucio Renato. Universidad Nacional de Rosario. Facultad de Ciencias Exactas, Ingeniería y Agrimensura; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentin

New generalized fuzzy metrics and fixed point theorem in fuzzy metric space

In this paper, in fuzzy metric spaces (in the sense of Kramosil and Michalek (Kibernetika 11:336-344, 1957)) we introduce the concept of a generalized fuzzy metric which is the extension of a fuzzy metric. First, inspired by the ideas of Grabiec (Fuzzy Sets Syst. 125:385-389, 1989), we define a new G-contraction of Banach type with respect to this generalized fuzzy metric, which is a generalization of the contraction of Banach type (introduced by M Grabiec). Next, inspired by the ideas of Gregori and Sapena (Fuzzy Sets Syst. 125:245-252, 2002), we define a new GV-contraction of Banach type with respect to this generalized fuzzy metric, which is a generalization of the contraction of Banach type (introduced by V Gregori and A Sapena). Moreover, we provide the condition guaranteeing the existence of a fixed point for these single-valued contractions. Next, we show that the generalized pseudodistance J:X×X→[0,∞) (introduced by Włodarczyk and Plebaniak (Appl. Math. Lett. 24:325-328, 2011)) may generate some generalized fuzzy metric NJ on X. The paper includes also the comparison of our results with those existing in the literature

Translation Representations and Scattering By Two Intervals

Studying unitary one-parameter groups in Hilbert space (U(t),H), we show that a model for obstacle scattering can be built, up to unitary equivalence, with the use of translation representations for L2-functions in the complement of two finite and disjoint intervals. The model encompasses a family of systems (U (t), H). For each, we obtain a detailed spectral representation, and we compute the scattering operator, and scattering matrix. We illustrate our results in the Lax-Phillips model where (U (t), H) represents an acoustic wave equation in an exterior domain; and in quantum tunneling for dynamics of quantum states

Means and covariance functions for geostatistical compositional data: an axiomatic approach

This work focuses on the characterization of the central tendency of a sample of compositional data. It provides new results about theoretical properties of means and covariance functions for compositional data, with an axiomatic perspective. Original results that shed new light on the geostatistical modeling of compositional data are presented. As a first result, it is shown that the weighted arithmetic mean is the only central tendency characteristic satisfying a small set of axioms, namely continuity, reflexivity and marginal stability. Moreover, this set of axioms also implies that the weights must be identical for all parts of the composition. This result has deep consequences on the spatial multivariate covariance modeling of compositional data. In a geostatistical setting, it is shown as a second result that the proportional model of covariance functions (i.e., the product of a covariance matrix and a single correlation function) is the only model that provides identical kriging weights for all components of the compositional data. As a consequence of these two results, the proportional model of covariance function is the only covariance model compatible with reflexivity and marginal stability

Effect of prior neuromuscular electrical stimulation of vastus lateralis on the fatigue induced by a sustained voluntary knee extension in men.

The purpose of this study was to investigate the effect of vastus lateralis (VL) selective fatigue induced by neuromuscular electrical stimulation (NMES) on knee extensor electromyographic (EMG) activity during a sustained submaximal isometric contraction. Thirteen healthy men (28 ± 5 years) completed two experimental sessions in which either the VL was pre-fatigued for 17 min (NMES session) or no intervention was performed (control session, CTRL). Subsequently, participants were asked to sustain an isometric knee extension at 20 % of maximal voluntary contraction (MVC) torque until task failure. VL M-wave amplitude was reduced (-34 ± 26 %, P = 0.008) following the NMES intervention, while MVC torque was reduced by 26 ± 10 %. The time to task failure was 23 ± 10 % shorter (P = 0.002) in NMES (186 ± 75 s) than in CTRL (251 ± 128 s). EMG activity measured during the sustained contraction was higher for vastus medialis and rectus femoris muscles in NMES compared to CTRL (P < 0.001), but was comparable for VL (P > 0.05). The extent and origin of neuromuscular fatigue at task failure measured through MVCs combined with electrically-evoked contractions did not differ between NMES and CTRL. Compensatory activity from synergist muscles occurred in response to a pre-fatigue intervention, which reduced the time to task failure of a sustained submaximal contraction but did not affect the extent and origin of neuromuscular fatigue

Tumour-draining axillary lymph nodes in patients with large and locally advanced breast cancers undergoing neoadjuvant chemotherapy (NAC): the crucial contribution of immune cells (effector, regulatory) and cytokines (TH1, TH2) to immune-mediated tumour cell death induced by NAC

Background The tumour microenvironment consists of malignant cells, stroma and immune cells. In women with large and locally advanced breast cancers (LLABCs) undergoing neoadjuvant chemotherapy (NAC), tumour-infiltrating lymphocytes (TILs), various subsets (effector, regulatory) and cytokines in the primary tumour play a key role in the induction of tumour cell death and a pathological complete response (pCR) with NAC. Their contribution to a pCR in nodal metastases, however, is poorly studied and was investigated. Methods Axillary lymph nodes (ALNs) (24 with and 9 without metastases) from women with LLABCs undergoing NAC were immunohistochemically assessed for TILs, T effector and regulatory cell subsets, NK cells and cytokine expression using labelled antibodies, employing established semi-quantitative methods. IBM SPSS statistical package (21v) was used. Non-parametric (paired and unpaired) statistical analyses were performed. Univariate and multivariate regression analyses were carried out to establish the prediction of a pCR and Spearman’s Correlation Coefficient was used to determine the correlation of immune cell infiltrates in ALN metastatic and primary breast tumours. Results In ALN metastases high levels of TILs, CD4+ and CD8+ T and CD56+ NK cells were significantly associated with pCRs.. Significantly higher levels of Tregs (FOXP3+, CTLA-4+) and CD56+ NK cells were documented in ALN metastases than in the corresponding primary breast tumours. CD8+ T and CD56+ NK cells showed a positive correlation between metastatic and primary tumours. A high % CD8+ and low % FOXP3+ T cells and high CD8+: FOXP3+ ratio in metastatic ALNs (tumour-free para-cortex) were associated with pCRs. Metastatic ALNs expressed high IL-10, low IL-2 and IFN-ϒ. Conclusions Our study has provided new data characterising the possible contribution of T effector and regulatory cells and NK cells and T helper1 and 2 cytokines to tumour cell death associated with NAC in ALNs

Loureirin B, an essential component of Sanguis Draxonis, inhibits Kv1.3 channel and suppresses cytokine release from Jurkat T cells

Sanguis draxonis (SD), also known as “Dragon’s Blood”, is a traditional herb medicine that has been used to treat a variety of complications with unknown mechanisms. Recent studies show that SD displays immunosuppressive activities and improves symptoms of type I diabetes in animal models. However, the mechanisms underlying SD’s immunosuppressive actions are not completely understood. The voltage-gated Kv1.3 channel plays a critical role in the pathogenesis of autoimmune diseases by regulating the functions of both T cells and B cells. Here we investigated the effect of SD and one of its active components loureirin B (LrB) on Kv1.3. Both SD and LrB inhibited Kv1.3-mediated currents, produced a membrane depolarization, and reduced Ca(2+) influx in Jurkat T cells. In addition, application of LrB inhibited phytohemagglutinin (PHA)-induced IL-2 release from activated Jurkat T cells. Furthermore, point mutations in the selective filter region significantly reduced the inhibitory effect of LrB on Kv1.3. The results of these experiments provide evidence that LrB is a channel blocker of Kv1.3 by interacting with amino acid residues in its selective filter region. Direct inhibition of Kv1.3 in T cells by SD and LrB might be the cellular and molecular basis of SD-mediated immunosuppression

Loss of estrogen receptor beta expression correlates with shorter overall survival and lack of clinical response to chemotherapy in ovarian cancer patients

Background: Estrogen receptor beta (ERβ) belongs to a large family of nuclear receptors. Recent studies have suggested that ERβ in contrast to ERα might act as a tumour suppressor in ovarian cancer (OVCA). Materials and Methods: Expression of ERβ was detected by immunocytochemistry in 11 OVCA cell lines and by immunohistochemistry in 43 (41 FIGO stage III) OVCA specimens prepared before chemotherapy and 30 specimens from the same group after chemotherapy. Cisplatin sensitivity in the 11 cell lines was also analysed. Results: No significant correlations between cisplatin-sensitivity and expression of ERβ was found in the cell lines. In the cases which responded well to chemotherapy (complete response) ERβ expression at preliminary laparotomy (PL) was significantly higher (p=0.0004) than in those with progressive disease. Kaplan-Meier analysis revealed that the patients with higher ERβ expression (>30% of cells) at PL had an increased overall survival time and progression-free time (p=0.00161 and p=0.03255, respectively) than the patients with lower ERβ espression. Significantly shorter overall survival time characterized the cases with lower immunoreactivity score of ERβ expression at secondary cytoreduction (SCR) (p=0.00346). Conclusion: The loss of ERβ expression in ovarian tumours may be a feature of malignant transformation