On Ideal Secret-Sharing Schemes for kk-homogeneous access structures

A $k$-uniform hypergraph is a hypergraph where each $k$-hyperedge has exactly $k$ vertices. A $k$-homogeneous access structure is represented by a $k$-uniform hypergraph $\mathcal{H}$, in which the participants correspond to the vertices of hypergraph $\mathcal{H}$. A set of vertices can reconstruct the secret value from their shares if they are connected by a $k$-hyperedge, while a set of non-adjacent vertices does not obtain any information about the secret. One parameter for measuring the efficiency of a secret sharing scheme is the information rate, defined as the ratio between the length of the secret and the maximum length of the shares given to the participants. Secret sharing schemes with an information rate equal to one are called ideal secret sharing schemes. An access structure is considered ideal if an ideal secret sharing scheme can realize it. Characterizing ideal access structures is one of the important problems in secret sharing schemes. The characterization of ideal access structures has been studied by many authors~\cite{BD, CT,JZB, FP1,FP2,DS1,TD}. In this paper, we characterize ideal $k$-homogeneous access structures using the independent sequence method. In particular, we prove that the reduced access structure of $\Gamma$ is an $(k, n)$-threshold access structure when the optimal information rate of $\Gamma$ is larger than $\frac{k-1}{k}$, where $\Gamma$ is a $k$-homogeneous access structure satisfying specific criteria.Comment: 19 page

Variation in and assessment of inferior alveolar nerve block landmarks in children and adolescents

OBJECTIVES: In earlier work (Lambert et al., 2017) we demonstrated the efficacy of new landmarks for inferior alveolar nerve (IAN) block injections. While the latter study focused on adult morphology, the landmarks were shown to be effective in cases where the M3/3 were present but unerupted. Based on these result a question arose as to their applicability of the landmarks to children and adolescents, given the known changes in mandibular foramen position during growth. Here we quantify the position of the mandibular foramen relative to standard landmarks during growth and assess the new landmarks applicability for IAN injections in pre-adolescents

Analysis of Black Widow’s scaffolding fibers

Spider silk is characterized to be incredibly strong and versatile, making it a valuable resource for manufacturing synthetic fibers for industrial applications. The objective of this study is to analyze the scaffolding fibers of Lactrodectus hesperus, a cobweaver, which creates asymmetrical three-dimensional web. To date, scaffolding silk has been shown to contain two structural silk proteins, Major Ampullate Spidroin 1 (MaSp1) and Major Ampullate Spidroin 2 (MaSp2). We hypothesize that scaffolding silk contains other novel proteins that have yet to be identified. In order to explore the potential of novel proteins assembled into scaffolding fibers, we collected threads from female black widow spiders, dissolved the fibers in a protein denaturant, alkylated the side chain cysteine residues, and then digested the protein mixture with trypsin. Tryptic peptides were separated using nano high performance liquid chromatography (nanoHPLC) and then subject to MS and MS/MS analysis using an Orbitrap Fusion mass spectrometer. Analysis of the scaffolding threads revealed the presence of several new proteins in scaffolding fibers

Needle position in relation to the occlusal and coronoid notch planes and anesthesia in children and juveniles

Earlier (Lambert et al., 2017) we demonstrated the efficacy of new inferior alveolar nerve (IAN) block landmarks in adolescents-adults and their validity in infants-juveniles (Soi et al, 2018). We present a refined assessment of distances and injection pathways to better assess these landmarks

Needle position in relation to the occlusal and coronoid notch planes and anesthesia in children and juveniles

Earlier (Lambert et al., 2017) we demonstrated the efficacy of new inferior alveolar nerve (IAN) block landmarks in adolescents-adults and their validity in infants-juveniles (Soi et al, 2018). We present a refined assessment of distances and injection pathways to better assess these landmarks

Variation in and assessment of inferior alveolar nerve block landmarks in children and adolescents

OBJECTIVES: In earlier work (Lambert et al., 2017) we demonstrated the efficacy of new landmarks for inferior alveolar nerve (IAN) block injections. While the latter study focused on adult morphology, the landmarks were shown to be effective in cases where the M3/3 were present but unerupted. Based on these result a question arose as to their applicability of the landmarks to children and adolescents, given the known changes in mandibular foramen position during growth. Here we quantify the position of the mandibular foramen relative to standard landmarks during growth and assess the new landmarks applicability for IAN injections in pre-adolescents

Relating domain size distribution to line tension and molecular dipole density in model cytoplasmic myelin lipid monolayers

We fit the size distribution of liquid-ordered (Lo) domains measured from fluorescence images of model cytoplasmic myelin monolayers with an equilibrium thermodynamic expression that includes the competing effects of line tension, λ, dipole density difference, Δm, and the mixing entropy. From these fits, we extract the line tension, λ, and dipole density difference, Δm, between the Lo and liquid-disordered (Ld) phases. Both λ and Δm decrease with increasing surface pressure, Graphic, although λ/Δm2 remains roughly constant as the monolayer approaches the miscibility surface pressure. As a result, the mean domain size changed little with surface pressure, although the polydispersity increased significantly. The most probable domain radius was significantly smaller than that predicted by the energy alone, showing that the mixing entropy promotes a greater number of smaller domains. Our results also explain why domain shapes are stable; at equilibrium, only a small fraction of the domains are large enough to undergo theoretically predicted shape fluctuations. Monolayers based on the composition of myelin from animals with experimental allergic encephalomyelitis had slightly lower values of λ and Δm, and a higher area fraction of domains, than control monolayers at all Graphic. While it is premature to generalize these results to myelin bilayers, our results show that the domain distribution in myelin may be an equilibrium effect and that subtle changes in surface pressure and composition can alter the distribution of material in the monolayer, which will likely also alter the interactions between monolayers important to the adhesion of the myelin sheath.National Institutes of Health (U.S.) (Grant GM076709)National Institutes of Health (U.S.) (Grant HL051177

Adsorption mechanism of myelin basic protein on model substrates and its bridging interaction between the two surfaces

Myelin basic protein (MBP) is an intrinsically disordered (unstructured) protein known to play an important role in the stability of myelin's multilamellar membrane structure in the central nervous system. The adsorption of MBP and its capacity to interact with and bridge solid substrates has been studied using a surface forces apparatus (SFA) and a quartz crystal microbalance with dissipation (QCM-D). Adsorption experiments show that MBP molecules adsorb to the surfaces in a swollen state before undergoing a conformational change into a more compact structure with a thickness of similar to 3 nm. Moreover, this compact structure is able to interact with nearby mica surfaces to form adhesive bridges. The measured adhesion force (energy) between two bridged surfaces is 1.0 +/- 0.1 mN/m, (E-ad = 0.21 +/- 0.02 mJ/m(2)), which is slightly smaller than our previously reported adhesion force of 1.7 mN/m (E-ad = 0.36 mJ/m(2)) for MBP adsorbed on two supported lipid bilayers (Lee et al., Proc. Natl. Acad. Sci. U.S.A. 2014, 111, E768-E775). The saturated surface concentration of compact MBP on a single SiO2 surface reaches a stable value of 310 +/- 10 ng/cm(2) regardless of the bulk MBP concentration. A kinetic three-step adsorption model was developed that accurately fits the adsorption data. The developed model is a general model, not limited to intrinsically disordered proteins, that can be extended to the adsorption of various chemical compounds that undergo chemical reactions and/or conformational changes upon adsorbing to surfaces. Taken together with our previously published data (Lee et al., Proc. Natl. Acad. Sci. U.S.A. 2014, 111, E768-E775), the present results confirm that conformational changes of MBP upon adsorption are a key for strong adhesion, and that such conformational changes are strongly dependent on the nature of the surfaces.close1