Products of Generalized Stochastic Sarymsakov Matrices

In the set of stochastic, indecomposable, aperiodic (SIA) matrices, the class of stochastic Sarymsakov matrices is the largest known subset (i) that is closed under matrix multiplication and (ii) the infinitely long left-product of the elements from a compact subset converges to a rank-one matrix. In this paper, we show that a larger subset with these two properties can be derived by generalizing the standard definition for Sarymsakov matrices. The generalization is achieved either by introducing an "SIA index", whose value is one for Sarymsakov matrices, and then looking at those stochastic matrices with larger SIA indices, or by considering matrices that are not even SIA. Besides constructing a larger set, we give sufficient conditions for generalized Sarymsakov matrices so that their products converge to rank-one matrices. The new insight gained through studying generalized Sarymsakov matrices and their products has led to a new understanding of the existing results on consensus algorithms and will be helpful for the design of network coordination algorithms

Tree formation with physical layer security considerations in wireless multi-hop networks

Physical layer security has emerged as a promising technique that complements existing cryptographic approaches and enables the securing of wireless transmissions against eavesdropping. In this paper, the impact of optimizing physical layer security metrics on the architecture and interactions of the nodes in multi-hop wireless networks is studied. In particular, a game-theoretic framework is proposed using which a number of nodes interact and choose their optimal and secure communication paths in the uplink of a wireless multi-hop network, in the presence of eavesdroppers. To this end, a tree formation game is formulated in which the players are the wireless nodes that seek to form a network graph among themselves while optimizing their multi-hop secrecy rates or the path qualification probabilities, depending on their knowledge of the eavesdroppers' channels. To solve this game, a distributed tree formation algorithm is proposed and is shown to converge to a stable Nash network. Simulation results show that the proposed approach yields significant performance gains in terms of both the average bottleneck secrecy rate per node and the average path qualification probability per node, relative to classical best-channel algorithms and the single-hop star network. The results also assess the properties and characteristics of the resulting Nash networks.This work was supported in part by the Australian Research Council's Discovery Projects funding scheme (project no. DP110102548), and in part by an AFOSR MURI Grant (FA9550-10-1-0573)

Group Chase and Escape

We describe here a new concept of one group chasing another, called "group chase and escape", by presenting a simple model. We will show that even a simple model can demonstrate rather rich and complex behavior. In particular, there are cases in which an optimal number of chasers exists for a given number of escapees (or targets) to minimize the cost of catching all targets. We have also found an indication of self-organized spatial structures formed by both groups.Comment: 13 pages, 12 figures, accepted and to appear in New Journal of Physic

Inhibition of weak-affinity epitope-IgE interactions prevents mast cell degranulation

Development of specific inhibitors of allergy has had limited success, in part, owing to a lack of experimental models that reflect the complexity of allergen-IgE interactions. We designed a heterotetravalent allergen (HtTA) system, which reflects epitope heterogeneity, polyclonal response and number of immunodominant epitopes observed in natural allergens, thereby providing a physiologically relevant experimental model to study mast cell degranulation. The HtTA design revealed the importance of weak-affinity epitopes in allergy, particularly when presented with high-affinity epitopes. The effect of selective inhibition of weak-affinity epitope-IgE interactions was investigated with heterobivalent inhibitors (HBIs) designed to simultaneously target the antigen- and nucleotide-binding sites on the IgE Fab. HBI demonstrated enhanced avidity for the target IgE and was a potent inhibitor of degranulation in vitro and in vivo. These results demonstrate that partial inhibition of allergen-IgE interactions was sufficient to prevent mast cell degranulation, thus establishing the therapeutic potential of the HBI design

Force Constants of Cu Crystals from Diffuse Neutron Scattering Measurement

Diffuse neutron scattering measurement on Cu crystals was performed at 10 K and 300 K. Oscillatory forms were observed in the diffuse scattering intensities. The observed diffuse scattering intensities are analyzed by including the correlation effects among thermal displacements of atoms in the theory. Using the values of correlation effects among neighboring atoms and the values of Debye-Waller temperature parameter, force constants among first, second and third nearest neighboring atoms have been evaluated. The result of correlation effects in Cu crystals are compared to that of ionic crystal and semiconductor. The relation between correlation effects and the inter-atomic distance is not depending much on the crystal binding types. Received: 12 October 2010; Revised: 22 October 2010; Accepted: 16 December 201

Bioassay-guided isolation of antioxidants and ?-Glucosidase inhibitors from the root of cassia sieberiana D.C. (fabaceae)

Bioassay-guided isolation was used to investigate the antioxidants and α-glucosidase inhibitors from extract of root of Cassia sieberiana. The ethyl acetate fraction demonstrated strong free radical scavenging (DPPH and ABTS+) and potent α-glucosidase inhibition. The subsequent fractionation and purification of the ethyl acetate fraction using silica gel chromatography and Sephadex LH-20, yielded; islandicin (1), chrysophanol (2), physcion (3), emodin (4), quercetin (5), kaempferol (6), dihydrokaempferol (7), and piceatannol (8). Quercetin (5) showed the most active antioxidant activity with IC50 values of 1.58 mM and 1.30 mM against DPPH and ABTS+ radicals, followed by piceatannol (8) with IC50 values of 3.96 mM and 3.28 mM, which is better than the standard BHT (with IC50 value 8.93 mM) and trolox (with IC50 value 8.25 mM), for DPPH and ABTS+ radicals scavenging activities, respectively. For the α-glucosidase inhibitory assay, quercetin (5) and piceatannol (8) showed higher potency against α-glucosidase with IC50 values of 5.73 μM and 7.37 μM respectively, than standard quercetin with IC50 value of 9.20 μM and acarbose with IC50 value of 14.12 μM. This study presents the first report on the α-glucosidase inhibitors from root of C. sieberiana and all the compounds are isolated from this source for the first time