Externally positive linear systems from transfer function properties

The characterisation of single-input-single-output externally positive linear systems is considered. A complete characterisation of the class of externally positive second-order and a class of underdamped third-order systems is given and connections to negative-imaginary systems are highlighted. It is shown that negative-imaginary systems have non-negative step responses, leading to a condition for external positivity based on negative imaginary systems theory. Finally, a class of externally positive systems which can be verified using the developed results but which fail a recently developed numerical test for external positivity based upon linear matrix inequalities are introduced. These results extend the class of system for which external positivity can be verified, facilitating large-scale control and less conservative absolute stability analysis

Reduced-order neural network synthesis with robustness guarantees

In the wake of the explosive growth in smartphones and cyber-physical systems, there has been an accelerating shift in how data are generated away from centralized data toward on-device-generated data. In response, machine learning algorithms are being adapted to run locally on board, potentially hardware-limited, devices to improve user privacy, reduce latency, and be more energy efficient. However, our understanding of how these device-orientated algorithms behave and should be trained is still fairly limited. To address this issue, a method to automatically synthesize reduced-order neural networks (having fewer neurons) approximating the input-output mapping of a larger one is introduced. The reduced-order neural network's weights and biases are generated from a convex semidefinite program that minimizes the worst case approximation error with respect to the larger network. Worst case bounds for this approximation error are obtained and the approach can be applied to a wide variety of neural networks architectures. What differentiates the proposed approach to existing methods for generating small neural networks, e.g., pruning, is the inclusion of the worst case approximation error directly within the training cost function, which should add robustness to out-of-sample data points. Numerical examples highlight the potential of the proposed approach. The overriding goal of this article is to generalize recent results in the robustness analysis of neural networks to a robust synthesis problem for their weights and biases

Exponential input-to-state stability for Lur’e systems via Integral Quadratic Constraints and Zames–Falb multipliers

Absolute stability criteria that are sufficient for global exponential stability are shown, under a Lipschitz assumption, to be sufficient for the a priori stronger exponential input-to-state stability property. Important corollaries of this result are as follows: (i) absolute stability results obtained using Zames–Falb multipliers for systems containing slope-restricted nonlinearities provide exponential input-to-state-stability under a mild detectability assumption; and (ii) more generally, many absolute stability results obtained via Integral Quadratic Constraint methods provide, with the additional Lipschitz assumption, this stronger property

quasiharmonic equations of state for dynamically-stabilized soft-mode materials

We introduce a method for treating soft modes within the analytical framework of the quasiharmonic equation of state. The corresponding double-well energy-displacement relation is fitted to a functional form that is harmonic in both the low- and high-energy limits. Using density-functional calculations and statistical physics, we apply the quasiharmonic methodology to solid periclase. We predict the existence of a B1--B2 phase transition at high pressures and temperatures

The cost-effectiveness of an adjuvanted quadrivalent influenza vaccine in the United Kingdom

In the United Kingdom (UK), both the MF59-adjuvanted quadrivalent influenza vaccine (aQIV) and the high-dose QIV (QIV-HD) are preferred for persons aged 65 years and older but only aQIV is reimbursed by the National Health Service (NHS). The objective was to determine the potential cost-effectiveness of vaccinating adults aged 65 years and above with aQIV compared with QIV-HD in the UK. A dynamic transmission model, calibrated to match infection data from the UK, was used to estimate the impact of vaccination in 10 influenza seasons. Vaccine effectiveness was based on a meta-analysis that concluded the vaccines were not significantly different. Vaccine coverage, physician visits, hospitalizations, deaths, utility losses and NHS costs were estimated using published UK sources. The list price of aQIV was £11.88 while a range of prices were tested for QIV-HD. The price of the trivalent high-dose vaccine (TIV-HD) is £20.00 but a list price for QIV-HD is not yet available. The projected differences between the vaccines in terms of clinical cases and influenza treatment costs are minimal. Our analysis demonstrates that in order to be cost-effective, the price of QIV-HD must be similar to that of aQIV and may range from £7.57 to £12.94 depending on the relative effectiveness of the vaccines. The results of the analysis were most sensitive to variation in vaccine effectiveness and the rate of hospitalization due to influenza. Given the evidence, aQIV is cost-saving unless QIV-HD is priced lower than the existing list price of TIV-HD

The Cost-Effectiveness of Expanding Vaccination with a Cell-Based Influenza Vaccine to Low Risk Adults Aged 50 to 64 Years in the United Kingdom

Background: In response to COVID-19, the UK National Health Service (NHS) extended influenza vaccination in 50- to 64-year-olds from at-risk only to all in this age group for the 2020/21 season. The objective of this research is to determine the cost-effectiveness of continuing to vaccinate all with a quadrivalent cell-based vaccine (QIVc) compared to returning to an at-risk only policy after the pandemic resolves. Methods: A dynamic transmission model, calibrated to match infection data from the UK, was used to estimate the clinical and economic impact of vaccination across 10 influenza seasons. The base case effectiveness of QIVc was 63.9% and the list price was GBP 9.94. Results: Vaccinating 50% of all 50- to 64-year-olds with QIVc reduced the average annual number of clinical infections (−682,000), hospitalizations (−5800) and deaths (−740) in the UK. The base case incremental cost per quality-adjusted life-year gained (ICER) of all compared to at-risk only was GBP6000 (NHS perspective). When the cost of lost productivity was considered, vaccinating all 50-to 64-year-olds with QIVc became cost-saving. Conclusion: Vaccinating all 50- to 64-year-olds with QIVc is likely to be cost-effective. The NHS should consider continuing this policy in future seasons

Entanglement of two-mode Bose-Einstein condensates

We investigate the entaglement characteristics of two general bimodal Bose-Einstein condensates - a pair of tunnel-coupled Bose-Einstein condensates and the atom-molecule Bose-Einstein condensate. We argue that the entanglement is only physically meaningful if the system is viewed as a bipartite system, where the subsystems are the two modes. The indistinguishibility of the particles in the condensate means that the atomic constituents are physically inaccessible and thus the degree of entanglement between individual particles, unlike the entanglement between the modes, is not experimentally relevant so long as the particles remain in the condensed state. We calculate the entanglement between the modes for the exact ground state of the two bimodal condensates and consider the dynamics of the entanglement in the tunnel-coupled case.Comment: 11 pages, 8 figures, submitted to Physical Review A, to be presented at the third UQ Mathematical Physics workshop, Oct. 4-6; changes made in response to referee comment

Quantum properties of transverse pattern formation in second-harmonic generation

We investigate the spatial quantum noise properties of the one dimensional transverse pattern formation instability in intra-cavity second-harmonic generation. The Q representation of a quasi-probability distribution is implemented in terms of nonlinear stochastic Langevin equations. We study these equations through extensive numerical simulations and analytically in the linearized limit. Our study, made below and above the threshold of pattern formation, is guided by a microscopic scheme of photon interaction underlying pattern formation in second-harmonic generation. Close to the threshold for pattern formation, beams with opposite direction of the off-axis critical wave numbers are shown to be highly correlated. This is observed for the fundamental field, for the second harmonic field and also for the cross-correlation between the two fields. Nonlinear correlations involving the homogeneous transverse wave number, which are not identified in a linearized analysis, are also described. The intensity differences between opposite points of the far fields are shown to exhibit sub-Poissonian statistics, revealing the quantum nature of the correlations. We observe twin beam correlations in both the fundamental and second-harmonic fields, and also nonclassical correlations between them.Comment: 18 pages, 17 figures, submitted to Phys. Rev.

Super-Hubbard models and applications

We construct XX- and Hubbard- like models based on unitary superalgebras gl(N|M) generalising Shastry's and Maassarani's approach of the algebraic case. We introduce the R-matrix of the gl(N|M) XX model and that of the Hubbard model defined by coupling two independent XX models. In both cases, we show that the R-matrices satisfy the Yang--Baxter equation, we derive the corresponding local Hamiltonian in the transfer matrix formalism and we determine the symmetry of the Hamiltonian. Explicit examples are worked out. In the cases of the gl(1|2) and gl(2|2) Hubbard models, a perturbative calculation at two loops a la Klein and Seitz is performed.Comment: 26 page

Chaos in a double driven dissipative nonlinear oscillator

We propose an anharmonic oscillator driven by two periodic forces of different frequencies as a new time-dependent model for investigating quantum dissipative chaos. Our analysis is done in the frame of statistical ensemble of quantum trajectories in quantum state diffusion approach. Quantum dynamical manifestation of chaotic behavior, including the emergence of chaos, properties of strange attractors, and quantum entanglement are studied by numerical simulation of ensemble averaged Wigner function and von Neumann entropy.Comment: 9 pages, 18 figure