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Transmon qubits are the predominant element in circuit-based quantum information processing, such as existing quantum computers, due to their controllability and ease of engineering implementation. But more than qubits, transmons are multilevel nonlinear oscillators that can be used to investigate fundamental physics questions. Here, they are explored as simulators of excited state quantum phase transitions (ESQPTs), which are generalizations of quantum phase transitions to excited states. We show that the spectral kissing (coalescence of pairs of energy levels) experimentally observed in the effective Hamiltonian of a driven SNAIL-transmon is an ESQPT precursor. We explore the dynamical consequences of the ESQPT, which include the exponential growth of out-of-time-ordered correlators, followed by periodic revivals, and the slow evolution of the survival probability due to localization. These signatures of ESQPT are within reach for current superconducting circuits platforms and are of interest to experiments with cold atoms and ion traps. [ABSTRACT FROM AUTHOR]

Nucleus incertus (NI) neurons in the pontine tegmentum give rise to ascending forebrain projections and express the neuropeptide relaxin-3 (RLN3) which acts via the relaxin-family peptide 3 receptor (RXFP3). Activity in the hippocampus and entorhinal cortex can be driven from the medial septum (MS), and the NI projects to all these centers, where a prominent pattern of activity is theta rhythm, which is related to spatial memory processing. Therefore, we examined the degree of collateralization of NI projections to the MS and the medial temporal lobe (MTL), comprising medial and lateral entorhinal cortex (MEnt, LEnt) and dentate gyrus (DG), and the ability of the MS to drive entorhinal theta in the adult rat. We injected fluorogold and cholera toxin-B into the MS septum and either MEnt, LEnt or DG, to determine the percentage of retrogradely labeled neurons in the NI projecting to both or single targets, and the relative proportion of these neurons that were RLN3-positive (+). The projection to the MS was threefold stronger than that to the MTL. Moreover, a majority of NI neurons projected independently to either MS or the MTL. However, RLN3 + neurons collateralize significantly more than RLN3-negative (–) neurons. In in vivo studies, electrical stimulation of the NI induced theta activity in the MS and the entorhinal cortex, which was impaired by intraseptal infusion of an RXFP3 antagonist, R3(BΔ23-27)R/I5, particularly at ~ 20 min post-injection. These findings suggest that the MS plays an important relay function in the NI-induced generation of theta within the entorhinal cortex. [ABSTRACT FROM AUTHOR]

This work designs a methodology to quantify the uncertainty of a volatility parameter in a stochastic control problem arising in energy management. The difficulty lies in the non-linearity of the underlying scalar Hamilton-Jacobi-Bellman equation. We proceed by decomposing the unknown solution on a Hermite polynomial basis (of the unknown volatility), whose different coefficients are solutions to a system of second order parabolic non-linear PDEs. Numerical tests show that computing the first basis elements may be enough to get an accurate approximation with respect to the uncertain volatility parameter. We provide an example of the methodology in the context of a swing contract (energy contract with flexibility in purchasing energy power), this allows us to introduce the concept of Uncertainty Value Adjustment (UVA), whose aim is to value the risk of misspecification of the volatility model. [ABSTRACT FROM AUTHOR]

Despite its generality and powerful convergence properties, Milstein's method for functionals of spatially bounded stochastic differential equations is widely regarded as difficult to implement. This has likely prevented it from being utilised in applications. In this paper, we design and analyse in detail one such implementation. The presented method turns out to be on par with other, popular schemes in terms of computational cost—but with a (nearly) linear weak convergence rate under the usual smoothness requirements on coefficients and boundary. Two byproducts of theoretical interest are a new, non-standard rank-one update formula, and a connection between numerics of bounded diffusions and Eikonal equations. Three examples are worked out, confirming the accuracy and robustness of the method. [ABSTRACT FROM AUTHOR]

We present a polyad-preserving algebraic approach to molecular structure and, as an application, we fit the model parameters to reproduce an extensive experimental data set of vibrational energies of carbon dioxide in its ground electronic state. The data set includes levels with vibrational angular momentum ℓ = 1, ...,6 and some recently obtained term values that have not been previously considered. The obtained results are close to experimental uncertainty and we compare the results obtained making use of the three most common polyad schemes that can be found in the literature for this molecular species. Graphical abstract: [ABSTRACT FROM AUTHOR]