Uniqueness of signature for simple curves

We propose a topological approach to the problem of determining a curve from its iterated integrals. In particular, we prove that a family of terms in the signature series of a two dimensional closed curve with finite p-variation, 1≤p<2, are in fact moments of its winding number. This relation allows us to prove that the signature series of a class of simple non-smooth curves uniquely determine the curves. This implies that outside a Chordal SLEκ null set, where 0<κ≤4, the signature series of curves uniquely determine the curves. Our calculations also enable us to express the Fourier transform of the n-point functions of SLE curves in terms of the expected signature of SLE curves. Although the techniques used in this article are deterministic, the results provide a platform for studying SLE curves through the signatures of their sample paths.

Fucoidan is a novel platelet agonist for the C-type lectin-like receptor 2 (CLEC-2)

Fucoidan, a sulfated polysaccharide from Fucus vesiculosus, decreases bleeding time and clotting time in hemophilia, possibly through inhibition of tissue factor pathway inhibitor. However, its effect on platelets and the receptor by which fucoidan induces cellular processes has not been elucidated. In this study, we demonstrate that fucoidan induces platelet activation in a concentration-dependent manner. Fucoidan-induced platelet activation was completely abolished by the pan-Src family kinase (SFK) inhibitor, PP2, or when Syk is inhibited. PP2 abolished phosphorylations of Syk and Phospholipase C-γ2. Fucoidan-induced platelet activation had a lag phase, which is reminiscent of platelet activation by collagen and CLEC-2 receptor agonists. Platelet activation by fucoidan was only slightly inhibited in FcRγ-chain null mice, indicating that fucoidan was not acting primarily through GPVI receptor. On the other hand, fucoidan-induced platelet activation was inhibited in platelet-specific CLEC-2 knock-out murine platelets revealing CLEC-2 as a physiological target of fucoidan. Thus, our data show fucoidan as a novel CLEC-2 receptor agonist that activates platelets through a SFK-dependent signaling pathway. Furthermore, the efficacy of fucoidan in hemophilia raises the possibility that decreased bleeding times could be achieved through activation of platelets.

Closed-loop feedback computation model of dynamical reputation based on the local trust evaluation in business-to-consumer e-commerce

Trust and reputation are important factors that influence the success of both traditional transactions in physical social networks and modern e-commerce in virtual Internet environments. It is difficult to define the concept of trust and quantify it because trust has both subjective and objective characteristics at the same time. A well-reported issue with reputation management system in business-to-consumer (BtoC) e-commerce is the “all good reputation” problem. In order to deal with the confusion, a new computational model of reputation is proposed in this paper. The ratings of each customer are set as basic trust score events. In addition, the time series of massive ratings are aggregated to formulate the sellers’ local temporal trust scores by Beta distribution. A logical model of trust and reputation is established based on the analysis of the dynamical relationship between trust and reputation. As for single goods with repeat transactions, an iterative mathematical model of trust and reputation is established with a closed-loop feedback mechanism. Numerical experiments on repeated transactions recorded over a period of 24 months are performed. The experimental results show that the proposed method plays guiding roles for both theoretical research into trust and reputation and the practical design of reputation systems in BtoC e-commerce.