Text Snippets to Corroborate Medical Relations: An Unsupervised Approach using a Knowledge Graph and Embeddings.

Knowledge graphs have been shown to significantly improve search results. Usually populated by subject matter experts, relations therein need to keep up to date with medical literature in order for search to remain relevant. Dynamically identifying text snippets in literature that confirm or deny knowledge graph triples is increasingly becoming the differentiator between trusted and untrusted medical decision support systems. This work describes our approach to mapping triples to medical text. A medical knowledge graph is used as a source of triples that are used to find matching sentences in reference text. Our unsupervised approach uses phrase embeddings and cosine similarity measures, and boosts candidate text snippets when certain key concepts exist. Using this approach, we can accurately map semantic relations within the medical knowledge graph to text snippets with a precision of 61.4% and recall of 86.3%. This method will be used to develop a novel application in the future to retrieve medical relations and corroborating snippets from medical text given a user query.

Excitation spectrum and staggering transformations in lattice quantum models.

We consider the energy-momentum excitation spectrum of diverse lattice Hamiltonian operators: the generator of the Markov semigroup of Ginzburg-Landau models with Langevin stochastic dynamics, the Hamiltonian of a scalar quantum field theory, and the Hamiltonian associated with the transfer matrix of a classical ferromagnetic spin system at high temperature. The low-lying spectrum consists of a one-particle state and a two-particle band. The two-particle spectrum is determined using a lattice version of the Bethe-Salpeter equation. In addition to the two-particle band, depending on the lattice dimension and on the attractive or repulsive character of the interaction between the particles of the system, there is, respectively, a bound state below or above the two-particle band. We show how the existence or nonexistence of these bound states can be understood in terms of a nonrelativistic single-particle lattice Schrödinger Hamiltonian with a delta potential. A staggering transformation relates the spectra of the attractive and the repulsive cases.

Energy-momentum spectrum of some two-particle lattice Schrödinger Hamiltonians.

We determine the excitation spectrum of some one and two-particle Z(d) lattice Schrödinger Hamiltonians. They occur as approximate Hamiltonians for the low-lying energy-momentum spectrum of diverse infinite lattice nonlinear quantum systems. A unitary staggering transformation relates the low-energy-momentum spectrum to the high-energy-momentum spectrum of the transformed operators. A feature for the one-particle repulsive delta function Hamiltonian is that, in addition to the continuous band spectrum, there is a bound state above the band, and the repulsive case spectrum and scattering can be obtained from the attractive potential case by staggering. For the two-particle pair potential Hamiltonian, there are commuting self-adjoint energy-momentum operators, and we determine the joint spectrum. For the case of a lambda delta pair potential, and equal particle masses, for arbitrarily small /lambda/, lambda < 0, and d >or = 3, there is no bound state for small system momentum, but a bound state exists below the band if the momentum is large. We find that the binding energy is an increasing function of the system momentum. The existence of this bound state is in contrast with the continuum case, where the Birman-Schwinger bound excludes negative-energy bound states for small couplings; this bound state is absent if the two masses are different. Other spectral results are also obtained for the large coupling case. An eigenfunction expansion that uses products of plane waves in the sum and difference coordinates is used to obtain the spectral results.

Interband spectrum of weakly coupled stochastic lattice Ginzburg-Landau models.

We analyze the excitation spectrum of the generator associated with the relaxation rate to equilibrium in weakly coupled stochastic Ginzburg-Landau models on a spatial lattice Z(d). The spectrum has a quasiparticle interpretation. Depending on d and on the specific interaction, by solving the Bethe-Salpeter equation in the ladder approximation, we show the existence of a stable particle above the upper envelope of the two-particle band, possessing a concave dispersion curve. This result furthers our knowledge about the spectrum of the stochastic dynamics generator.