The laplacian of a graph as a density matrix: a basic combinatorial approach to separability of mixed states

We study entanglement properties of mixed density matrices obtained from combinatorial Laplacians. This is done by introducing the notion of the density matrix of a graph. We characterize the graphs with pure density matrices and show that the density matrix of a graph can be always written as a uniform mixture of pure density matrices of graphs. We consider the von Neumann entropy of these matrices and we characterize the graphs for which the minimum and maximum values are attained. We then discuss the problem of separability by pointing out that separability of density matrices of graphs does not always depend on the labelling of the vertices. We consider graphs with a tensor product structure and simple cases for which combinatorial properties are linked to the entanglement of the state. We calculate the concurrence of all graph on four vertices representing entangled states. It turns out that for some of these graphs the value of the concurrence is exactly fractional.Comment: 20 pages, 11 figure

The rna-binding ubiquitin ligase mex3a affects glioblastoma tumorigenesis by inducing ubiquitylation and degradation of rig-i

Glioblastoma multiforme (GB) is the most malignant primary brain tumor in humans, with an overall survival of approximatively 15 months. The molecular heterogeneity of GB, as well as its rapid progression, invasiveness and the occurrence of drug-resistant cancer stem cells, limits the efficacy of the current treatments. In order to develop an innovative therapeutic strategy, it is mandatory to identify and characterize new molecular players responsible for the GB malignant phenotype. In this study, the RNA-binding ubiquitin ligase MEX3A was selected from a gene expression analysis performed on publicly available datasets, to assess its biological and still-unknown activity in GB tumorigenesis. We find that MEX3A is strongly up-regulated in GB specimens, and this correlates with very low protein levels of RIG-I, a tumor suppressor involved in differentiation, apoptosis and innate immune response. We demonstrate that MEX3A binds RIG-I and induces its ubiquitylation and proteasome-dependent degradation. Further, the genetic depletion of MEX3A leads to an increase of RIG-I protein levels and results in the suppression of GB cell growth. Our findings unveil a novel molecular mechanism involved in GB tumorigenesis and suggest MEX3A and RIG-I as promising therapeutic targets in GB

On moments of the integrated exponential Brownian motion

We present new exact expressions for a class of moments for the geometric Brownian motion, in terms of determinants, obtained using a recurrence relation and combinatorial arguments for the case of a Ito's Wiener process. We then apply the obtained exact formulas to computing averages of the solution of the logistic stochastic differential equation via a series expansion, and compare the results to the solution obtained via Monte Carlo

Pretty good state transfer in qubit chains-The Heisenberg Hamiltonian

Pretty good state transfer in networks of qubits occurs when a continuous-time quantum walk allows the transmission of a qubit state from one node of the network to another, with fidelity arbitrarily close to 1. We prove that in a Heisenberg chain with n qubits, there is pretty good state transfer between the nodes at the jth and (n − j + 1)th positions if n is a power of 2. Moreover, this condition is also necessary for j = 1. We obtain this result by applying a theorem due to Kronecker about Diophantine approximations, together with techniques from algebraic graph theory

Dynamic response of masonry arch with geometrical irregularities subjected to a pulse-type ground motion

Ancient masonry structures often rely on the masonry arch as a load bearing element. The understanding of its response under seismic actions is a first fundamental step towards the comprehension of the behaviour of more complex structures. It is well known that the stability of masonry arches is primarily related to the geometry. The safety assessment under seismic actions is usually carried out by considering known deterministic geometrical parameters, such as thickness, rise and span, and the voussoirs are assumed with equal dimensions. However, many factors, like defects or irregularities in the shape of the voussoirs and imprecise construction, produce variations of the geometry with respect to the nominal one and, as a consequence, may effect the ability of the arch to resist seismic actions. In this paper, the effect of geometrical irregularities on the dynamic response of circular masonry arches is considered. Irregular geometries are obtained through a random generation of the key geometrical parameters, and the effect of these irregularities is quantified by analysing the dynamic response to ground motion. The masonry arch is modelled as a four-link mechanism, i.e. a system made of three rigid blocks hinged at their ends. The position of the hinges at the instant of activation of the motion is determined through limit analysis. Lagrange’s equations of motion have been written for the generated irregular geometries and solved through numerical integration. The results are summarised by a fragility surface that quantify the extent to which geometrical uncertainties can alter the dynamic response of the masonry arch and increase its seismic vulnerability

effect of geometric irregularities on the dynamic response of masonry arches

Abstract In this paper, the effect of geometric irregularities on the dynamic response of circular masonry arches is considered. Irregular geometries are obtained through a random generation of the key geometric parameters, and the effect of these irregularities is shown by modelling the dynamic response to ground motion. The masonry arch is modelled as a four-link mechanism, i.e., a system made of three rigid blocks hinged at their ends, where the position of the hinges at the instant of activation of the motion is determined through limit analysis. Lagrange's non-linear equations of motion have been solved through numerical integration. The results show that geometrical uncertainties produce an alteration of the mechanical features of the rigid blocks which may reduce the seismic capacity

Matrix permanent and quantum entanglement of permutation invariant states

We point out that a geometric measure of quantum entanglement is related to the matrix permanent when restricted to permutation invariant states. This connection allows us to interpret the permanent as an angle between vectors. By employing a recently introduced permanent inequality by Carlen, Loss and Lieb, we can prove explicit formulas of the geometric measure for permutation invariant basis states in a simple way.Comment: 10 page

Some families of density matrices for which separability is easily tested

We reconsider density matrices of graphs as defined in [quant-ph/0406165]. The density matrix of a graph is the combinatorial laplacian of the graph normalized to have unit trace. We describe a simple combinatorial condition (the "degree condition") to test separability of density matrices of graphs. The condition is directly related to the PPT-criterion. We prove that the degree condition is necessary for separability and we conjecture that it is also sufficient. We prove special cases of the conjecture involving nearest point graphs and perfect matchings. We observe that the degree condition appears to have value beyond density matrices of graphs. In fact, we point out that circulant density matrices and other matrices constructed from groups always satisfy the condition and indeed are separable with respect to any split. The paper isolates a number of problems and delineates further generalizations.Comment: 14 pages, 4 figure