An efficiency upper bound for inverse covariance estimation

We derive an upper bound for the efficiency of estimating entries in the inverse covariance matrix of a high dimensional distribution. We show that in order to approximate an off-diagonal entry of the density matrix of a $d$-dimensional Gaussian random vector, one needs at least a number of samples proportional to $d$. Furthermore, we show that with $n \ll d$ samples, the hypothesis that two given coordinates are fully correlated, when all other coordinates are conditioned to be zero, cannot be told apart from the hypothesis that the two are uncorrelated.Comment: 7 Page

On Majorization for Matrices

In this paper, we give several results for majorized matrices by using continuous convex function and Green function. We obtain mean value theorems for majorized matrices and also give corresponding Cauchy means, as well as prove that these means are monotonic. We prove positive semi-definiteness of matrices generated by differences deduced from majorized matrices which implies exponential convexity and log-convexity of these differences and also obtain Lypunov's and Dresher's type inequalities for these differences

On an inverse to the Hölder inequality

An extension is given for the inverse to Hölder's inequality obtained recently by Zhuang

On matrix convexity of the Moore-Penrose inverse

Matrix convexity of the Moore-Penrose inverse was considered in the recent literature. Here we give some converse inequalities as well as further generalizations

Majorization Inequalities via Peano's Representation of Hermite's Polynomial

The Peano's representation of Hermite polynomial and new Green functions are used to construct the identities related to the generalization of majorization type inequalities in discrete as well as continuous case. $\check{C}$eby$\check{s}$ev functional is used to find the bounds for new generalized identities and to develop the Gr$\ddot{u}$ss and Ostrowski type inequalities. Further more, we present exponential convexity together with Cauchy means for linear functionals associated with the obtained inequalities and give some applications

Opial type L

This paper presents a class of Lp-type Opial inequalities for generalized fractional derivatives for integrable functions based on the results obtained earlier by the first author for continuous functions (1998). The novelty of our approach is the use of the index law for fractional derivatives in lieu of Taylor's formula, which enables us to relax restrictions on the orders of fractional derivatives

IL-33 Induces IL-9 Production in Human CD4+ T Cells and Basophils

IL-33, an IL-1 family member and ligand for the IL-1 receptor-related protein ST2, has been associated with induction of Th2 cytokines such as IL-4, IL-5, and IL-13. Here, we report that IL-33 can initiate IL-9 protein secretion in vitro in human CD4+ T cells and basophils isolated from peripheral blood. TGF-β has been described as a critical factor for IL-9 induction in Th2 cells; however, we found that TGF-β also induces co-production of IL-9 in purified, naïve (>99%) CD4+CD45RA+CD45RO−CD25− T cells differentiated towards a Th1 profile. Subsequently, it was demonstrated that TGF-β is important, although not an absolute requirement, for IL-9 production in CD4+ T cells. IL-9 production by purified (>95%) human basophils, cultured for 24 h with IL-3 or IL-33, was found, with a strong synergy between the two, likely to be explained by the IL-3 upregulated ST2 expression. Collectively, these data indicate that barrier functioning cells are important for the regulation of IL-9 production by immune cells in inflamed tissue

IL-33 Is Produced by Mast Cells and Regulates IgE-Dependent Inflammation

Background: IL-33 is a recently characterized IL-1 family cytokine and found to be expressed in inflammatory diseases, including severe asthma and inflammatory bowl disease. Recombinant IL-33 has been shown to enhance Th2-associated immune responses and potently increase mast cell proliferation and cytokine production. While IL-33 is constitutively expressed in endothelial and epithelial cells, where it may function as a transcriptional regulator, cellular sources of IL-33 and its role in inflammation remain unclear. Methodology/Principal Findings: Here, we identify mast cells as IL-33 producing cells. IgE/antigen activation of bone marrow-derived mast cells or a murine mast cell line (MC/9) significantly enhanced IL-33. Conversely, recombinant IL-33 directly activated mast cells to produce several cytokines including IL-4, IL-5 and IL-6 but not IL-33. We show that expression of IL-33 in response to IgE-activation required calcium and that ionomycin was sufficient to induce IL-33. In vivo, peritoneal mast cells expressed IL-33 and IL-33 levels were significantly lower within the skin of mast cell deficient mice, compared to littermate controls. Local activation of mast cells promotes edema, followed by the recruitment of inflammatory cells. We demonstrate using passive cutaneous anaphylaxis, a mast cell-dependent model, that deficiency in ST2 or antibody blockage of ST2 or IL-33 ablated the late phase inflammatory response but that the immediate phase response was unaffected. IL-33 levels in the skin were significantly elevated only during the late phase

Trefoil factor 2 rapidly induces interleukin 33 to promote type 2 immunity during allergic asthma and hookworm infection

The molecular mechanisms that drive mucosal T helper type 2 (T[subscript H]2) responses against parasitic helminths and allergens remain unclear. In this study, we demonstrate in mice that TFF2 (trefoil factor 2), an epithelial cell–derived repair molecule, is needed for the control of lung injury caused by the hookworm parasite Nippostrongylus brasiliensis and for type 2 immunity after infection. TFF2 is also necessary for the rapid production of IL-33, a T[subscript H]2-promoting cytokine, by lung epithelia, alveolar macrophages, and inflammatory dendritic cells in infected mice. TFF2 also increases the severity of allergic lung disease caused by house dust mite antigens or IL-13. Moreover, TFF2 messenger RNA expression is significantly increased in nasal mucosal brushings during asthma exacerbations in children. These experiments extend the biological functions of TFF2 from tissue repair to the initiation and maintenance of mucosal T[subscript H]2 responses