Fast Bayesian parameter estimation for stochastic logistic growth models

The transition density of a stochastic, logistic population growth model with multiplicative intrinsic noise is analytically intractable. Inferring model parameter values by fitting such stochastic differential equation (SDE) models to data therefore requires relatively slow numerical simulation. Where such simulation is prohibitively slow, an alternative is to use model approximations which do have an analytically tractable transition density, enabling fast inference. We introduce two such approximations, with either multiplicative or additive intrinsic noise, each derived from the linear noise approximation of the logistic growth SDE. After Bayesian inference we find that our fast LNA models, using Kalman filter recursion for computation of marginal likelihoods, give similar posterior distributions to slow arbitrarily exact models. We also demonstrate that simulations from our LNA models better describe the characteristics of the stochastic logistic growth models than a related approach. Finally, we demonstrate that our LNA model with additive intrinsic noise and measurement error best describes an example set of longitudinal observations of microbial population size taken from a typical, genome-wide screening experiment.Comment: 24 pages, 5 figures and 2 table

The effect of sertraline and 8-OH-DPAT on the PTZinduced seizure threshold: Role of the nitrergic system

Purpose Serotonin is a key regulatory neurotransmitter in the CNS which plays an important role in seizure through different receptors, especially the 5HT1A subtype. The role of sertraline through the 5HT1A receptor and nitric oxide interaction on the PTZ-induced seizure threshold was investigated in this study. Method In this study, 70 white male mice were randomly divided into 10 groups including intact control, sham-control and eight experimental groups which received sertraline, 8-OH-DPAT, WAY100635, WAY100635 + sertraline, WAY100635 + 8-OH-DPAT, L-NAME, L-NAME + sertraline and L-NAME + 8-OH-DPAT. After 14 days of treatment in different groups, the PTZ-induced seizure threshold was assessed and the measurement of nitric oxide metabolites in the brain tissue was done with the Greiss method. Results The seizure threshold was significantly increased in the sertraline and 8OH-DPAT receiving groups compared to the sham group (P < 0.001). In the presence of WAY100635, the effect of both sertraline and 8-OH-DPAT in raising the seizure threshold was more prominent (P < 0.001) but on the other hand, in the presence of L-NAME, an increase in the anticonvulsant effect of 8-OH-DPAT was observed, while L-NAME alone had no effect on the seizure threshold (P < 0.001). The NOX concentration was significantly decreased in the 8-OH-DPATtreated group (P < 0.01), while the WAY100657 reversed it and the combination of 8-OH-DPAT with L-NAME reduced the NOX levels (P < 0.001). Conclusions These findings support the anticonvulsant effect of SSRIs and selective 5HT1A receptors, although serotonin receptors other than 5HT1A subtype may be involved and also it is probable that some anticonvulsant effects of the sertraline and 8-OH-DPAT are through the modulation of nitrergic system. © 2016 British Epilepsy Associatio

Effect of acute caffeine administration on PTZ-induced seizure threshold in mice: Involvement of adenosine receptors and NO-cGMP signaling pathway

Abstract Purpose: Caffeine is a non-selective antagonist of A1 and A2A adenosine receptors (ARs). In this regard, nitric oxide (NO) is partly involved in the central effects of caffeine. In this study, we examined the effect of acute caffeine administration on pentylenetetrazole (PTZ)-induced seizure threshold by focusing on A1Rs, A2ARs, and NO-cGMP signaling pathway. Methods: NMRI male mice (25–30 g) received caffeine (5, 50, and 100 mg/kg) alone, whereas 8-CPT (1 and 5 mg/kg, a selective A1Rs antagonist), SCH-442416 (5 and 10 mg/kg, a selective A2ARs antagonist) or sildenafil (5 and 10 mg/kg, a phosphodiesterase 5 inhibitor) were administrated alone or as pre-treatment before caffeine. Seizure threshold was assessed by intravenous infusion of PTZ. Nitric oxide metabolites (NOx) were measured with the Griess method. Results: When administrated alone, caffeine (5 and 50 mg/kg) and 8-CPT (1 and 5 mg/kg) significantly decreased seizure threshold, while 100 mg/kg of caffeine, SCH-442416 or sildenafil did not change it. Only pre-treatment with SCH-442416 (5 and 10 mg/kg) or sildenafil (5 and 10 mg/kg) before 100 mg/kg of caffeine significantly decreased seizure threshold. Moreover, NOx levels significantly decreased following alone administration of caffeine (100 mg/kg) or 8-CPT (5 mg/kg). Conclusion: The results of present study showed that 5 and 50 mg/kg of caffeine had a proconvulsant effect but caffeine at a dose of 100 mg/kg had no effect on seizure threshold. In addition, it seems that the effect caffeine on seizure threshold is partly mediated through ARs or modulation of the NO-cGMP signaling pathway. Keywords: Seizure Caffeine Nitric oxide Adenosine receptors Pentylenetetrazol

The invariant-comb approach and its relation to the balancedness of multipartite entangled states

The invariant-comb approach is a method to construct entanglement measures for multipartite systems of qubits. The essential step is the construction of an antilinear operator that we call {\em comb} in reference to the {\em hairy-ball theorem}. An appealing feature of this approach is that for qubits (or spins 1/2) the combs are automatically invariant under SL(2,\CC), which implies that the obtained invariants are entanglement monotones by construction. By asking which property of a state determines whether or not it is detected by a polynomial SL(2,\CC) invariant we find that it is the presence of a {\em balanced part} that persists under local unitary transformations. We present a detailed analysis for the maximally entangled states detected by such polynomial invariants, which leads to the concept of {\em irreducibly balanced} states. The latter indicates a tight connection with SLOCC classifications of qubit entanglement. \\ Combs may also help to define measures for multipartite entanglement of higher-dimensional subsystems. However, for higher spins there are many independent combs such that it is non-trivial to find an invariant one. By restricting the allowed local operations to rotations of the coordinate system (i.e. again to the SL(2,\CC)) we manage to define a unique extension of the concurrence to general half-integer spin with an analytic convex-roof expression for mixed states.Comment: 17 pages, revtex4. Substantially extended manuscript (e.g. proofs have been added); title and abstract modified