The Kemeny Constant For Finite Homogeneous Ergodic Markov Chains

A quantity known as the Kemeny constant, which is used to measure the expected number of links that a surfer on the World Wide Web, located on a random web page, needs to follow before reaching his/her desired location, coincides with the more well known notion of the expected time to mixing, i.e., to reaching stationarity of an ergodic Markov chain. In this paper we present a new formula for the Kemeny constant and we develop several perturbation results for the constant, including conditions under which it is a convex function. Finally, for chains whose transition matrix has a certain directed graph structure we show that the Kemeny constant is dependent only on the common length of the cycles and the total number of vertices and not on the specific transition probabilities of the chain

NanoBiT System and Hydrofurimazine for Optimized Detection of Viral Infection in Mice-A Novel in Vivo Imaging Platform.

Reporter genes are used to visualize intracellular biological phenomena, including viral infection. Here we demonstrate bioluminescent imaging of viral infection using the NanoBiT system in combination with intraperitoneal injection of a furimazine analogue, hydrofurimazine. This recently developed substrate has enhanced aqueous solubility allowing delivery of higher doses for in vivo imaging. The small high-affinity peptide tag (HiBiT), which is only 11 amino-acids in length, was engineered into a clinically used oncolytic adenovirus, and the complementary large protein (LgBiT) was constitutively expressed in tumor cells. Infection of the LgBiT expressing cells with the HiBiT oncolytic virus will reconstitute NanoLuc in the cytosol of the cell, providing strong bioluminescence upon treatment with substrate. This new bioluminescent system served as an early stage quantitative viral transduction reporter in vitro and also in vivo in mice, for longitudinal monitoring of oncolytic viral persistence in infected tumor cells. This platform provides novel opportunities for studying the biology of viruses in animal models

Petrogenesis and Ni-Cu sulphide potential of mafic-ultramafic rocks in the Mesoproterozoic Fraser Zone within the Albany-Fraser Orogen, Western Australia

The Albany Fraser Orogen is located along the southern and southeastern margins of the Archean Yilgarn Craton. The orogen formed during reworking of the Yilgarn Craton, along with variable additions of juvenile mantle material, from at least 1810 Ma to 1140 Ma. The Fraser Zone is a 425 km long and 50 km wide geophysically distinct belt near the northwestern edge of the orogen, hosting abundant sills of predominantly metagabbroic non-cumulate rocks, but including larger cumulate bodies, all emplaced at c. 1300 Ma. The gabbroic rocks are interpreted to have crystallised from a basaltic magma that had ∼8.8% MgO, 185 ppm Ni, 51 ppm Cu, and extremely low contents of platinum-group elements (PGE, <1 ppb). Levels of high field-strength elements (HFSE) in the least enriched rocks indicate that the magma was derived from a mantle source more depleted than a MORB source. Isotope and trace element systematics suggest that the magma was contaminated (εNd 0 to −2 throughout, La/Nb around 3) with small (<10%) amounts of crust before and during ascent and emplacement. Larger bodies of cumulate rocks show evidence for additional contamination, at the emplacement level, with country-rock metasedimentary rocks or their anatectic melts. The area has been the focus of considerable exploration for Ni–Cu sulphides following the discovery of the Nova deposit in 2012 in an intrusion consisting of olivine gabbronoritic, noritic and peridotitic cumulates, interlayered with metasedimentary rocks belonging to the Snowys Dam Formation of the Arid Basin. Disseminated sulphides from a drillcore intersecting the structurally upper portion of the intrusion, above the main ore zone, have tenors of ∼3–6.3% Ni, 1.8–6% Cu and mostly <500 ppb PGE, suggesting derivation from magma with the same composition as the regional Fraser Zone metagabbroic sills, at R factors of ∼1500. However, the Nova rocks tend to have higher εSr (38–52) and more variable δ34S (−2 to +4) than the regional metagabbros (εSr 17–32, δ34S around 0), consistent with the geochemical evidence for enhanced crustal assimilation of the metasedimentary country-rock in a relatively large magma staging chamber from which pulses of sulphide bearing, crystal-charged magmas were emplaced at slightly different crustal levels. Preliminary investigations suggest that the critical factors determining whether or not Fraser Zone mafic magmas are mineralised probably relate to local geodynamic conditions that allow large magma chambers to endure long enough to sequester country-rock sulphur

The Kemeny Constant For Finite Homogeneous Ergodic Markov Chains

A quantity known as the Kemeny constant, which is used to measure the expected number of links that a surfer on the World Wide Web, located on a random web page, needs to follow before reaching his/her desired location, coincides with the more well known notion of the expected time to mixing, i.e., to reaching stationarity of an ergodic Markov chain. In this paper we present a new formula for the Kemeny constant and we develop several perturbation results for the constant, including conditions under which it is a convex function. Finally, for chains whose transition matrix has a certain directed graph structure we show that the Kemeny constant is dependent only on the common length of the cycles and the total number of vertices and not on the specific transition probabilities of the chain

The Kemeny Constant For Finite Homogeneous Ergodic Markov Chains

A quantity known as the Kemeny constant, which is used to measure the expected number of links that a surfer on the World Wide Web, located on a random web page, needs to follow before reaching his/her desired location, coincides with the more well known notion of the expected time to mixing, i.e., to reaching stationarity of an ergodic Markov chain. In this paper we present a new formula for the Kemeny constant and we develop several perturbation results for the constant, including conditions under which it is a convex function. Finally, for chains whose transition matrix has a certain directed graph structure we show that the Kemeny constant is dependent only on the common length of the cycles and the total number of vertices and not on the specific transition probabilities of the chain

Algebraic multiplicity of the eigenvalues of a tournament matrix

AbstractLet Tn denote the set of irreducible n × n tournament matrices. Here are our main results: (1) For all n ⩾ 3, every matrix in Tn has at least three distinct eigenvalues; such a matrix has exactly three distinct eigenvalues if and only if it is a Hadamard tournament matrix. (2) For all n ⩾ 3 there is a matrix in Tn having n distinct eigenvalues. (3) If αn denotes the maximum algebraic multiplicity of 0 as an eigenvalue of the matrices in Tn, then ⌊n2⌋ − 2 ⩽ αn ⩽ n − 6 for all n ⩾ 8. Each algebraic multiplicity m with 1 ⩽ m ⩽ ⌊n2⌋; − 2 is achieved for the eigenvalue 0 by some matrix in Tn for every n⩾6. (4) If πn is the minimum Perron value (i.e. spectral radius) of all matrices in Tn, then 2 < πn < 2.5 for all n⩾8