Improving the Variational Quantum Eigensolver Using Variational Adiabatic Quantum Computing

The variational quantum eigensolver (VQE) is a hybrid quantum-classical algorithm for finding the minimum eigenvalue of a Hamiltonian that involves the optimization of a parameterized quantum circuit. Since the resulting optimization problem is in general nonconvex, the method can converge to suboptimal parameter values that do not yield the minimum eigenvalue. In this work, we address this shortcoming by adopting the concept of variational adiabatic quantum computing (VAQC) as a procedure to improve VQE. In VAQC, the ground state of a continuously parameterized Hamiltonian is approximated via a parameterized quantum circuit. We discuss some basic theory of VAQC to motivate the development of a hybrid quantum-classical homotopy continuation method. The proposed method has parallels with a predictor-corrector method for numerical integration of differential equations. While there are theoretical limitations to the procedure, we see in practice that VAQC can successfully find good initial circuit parameters to initialize VQE. We demonstrate this with two examples from quantum chemistry. Through these examples, we provide empirical evidence that VAQC, combined with other techniques (an adaptive termination criteria for the classical optimizer and a variance-based resampling method for the expectation evaluation), can provide more accurate solutions than “plain” VQE, for the same amount of effort.

Comparison of cascade P-PI controller tuning methods for PMDC motor based on intelligence techniques

In this paper, there are two contributions: The first contribution is to design a robust cascade P-PI controller to control the speed and position of the permanent magnet DC motor (PMDC). The second contribution is to use three methods to tuning the parameter values for this cascade controller by making a comparison between them to obtain the best results to ensure accurate tracking trajectory on the axis to reach the desired position. These methods are the classical method (CM) and it requires some assumptions, the genetic algorithm (GA), and the particle swarm optimization algorithm (PSO). The simulation results show the system becomes unstable after applying the load when using the classical method because it assumes cancellation of the load effect. Also, an overshoot of about 3.763% is observed, and a deviation from the desired position of about 12.03 degrees is observed when using the GA algorithm, while no deviation or overshoot is observed when using the PSO algorithm. Therefore, the PSO algorithm has superiority as compared to the other two methods in improving the performance of the PMDC motor by extracting the best parameters for the cascade P-PI controller to reach the desired position at a regular speed.

Tree Inference: Response Time and Other Measures in a Binary Multinomial Processing Tree, Representation and Uniqueness of Parameters

A Multinomial Processing Tree (MPT) is a directed tree with a probability associated with each arc and partitioned terminal vertices. We consider an additional parameter for each arc, a measure such as time. Each vertex represents a process. An arc descending from a vertex represents selection of a process outcome. A source vertex represents processing beginning with stimulus presentation and a terminal vertex represents a response. An experimental factor selectively influences a vertex if changing the factor level changes parameter values on arcs descending from that vertex and no others. Earlier work shows that if each of two factors selectively influences a different vertex in an arbitrary MPT it is equivalent to one of two simple MPTs. Which applies depends on whether the two selectively influenced vertices are ordered by the factors or not. A special case, the Standard Binary Tree for Ordered Processes, arises if the vertices are ordered and the factor selectively influencing the first vertex changes parameter values on only two arcs. We derive necessary and sufficient conditions, testable by bootstrapping, for this case. Parameter values are not unique. We give admissible transformations for them. We calculate degrees of freedom needed for goodness of fit tests.

Investigation of Posture/Balance Disorder and Pd-related Pain by Using Diffusion Tensor Imaging and Transcranial Doppler

Background: Posture/balance disorder and pain are both present in Parkinson's patients, but their neural basis remain unclear. To investigate the central mechanism of posture/balance disorder and PD-related pain in Parkinson's disease by using diffusion tensor imaging (DTI) and tract-based spatial statistics (TBSS), combined with Transcranial Doppler (TCD). Results: It was found that the dose of levodopa, UPDRSⅡ and UPDRSⅢ were higher value in the group with higher score of posture/balance. In the more severe posture/balance disorder group, the fiber bundles of the prefrontal cortex, anterior cingulate cortex and basal ganglia were more likely to be affected. In addition, the DTI parameter values of the three brain regions had a significant correlation with the parameter values of the corresponding arteries. In the analysis of PD-related pain, the white matter fiber bundles from the midbrain to the basal ganglia increased in patients with PD-related pain. There were no statistic difference in prevalence of PD-related pain was found between different groups according to posture/balance. Conclusions: Posture and balance in PD were correlated with the severity of the disease and the dosage of compound levodopa. Posture and balance in PD were related to changes in the white matter integrity of the prefrontal cortex, anterior cingulate cortex and basal ganglia. The function of cerebral arteries had contributions to white matter integrity of these area and posture/balance. PD-related pain was positively correlated with sleep score. Patients with PD-related pain had an increase in the fiber projection from the midbrain to the basal ganglia. No relation was found between posture/balance disorder with PD-related pain.

Kinetic Modeling of Saccharomyces cerevisiae Central Carbon Metabolism: Achievements, Limitations, and Opportunities

Central carbon metabolism comprises the metabolic pathways in the cell that process nutrients into energy, building blocks and byproducts. To unravel the regulation of this network upon glucose perturbation, several metabolic models have been developed for the microorganism Saccharomyces cerevisiae. These dynamic representations have focused on glycolysis and answered multiple research questions, but no commonly applicable model has been presented. This review systematically evaluates the literature to describe the current advances, limitations, and opportunities. Different kinetic models have unraveled key kinetic glycolytic mechanisms. Nevertheless, some uncertainties regarding model topology and parameter values still limit the application to specific cases. Progressive improvements in experimental measurement technologies as well as advances in computational tools create new opportunities to further extend the model scale. Notably, models need to be made more complex to consider the multiple layers of glycolytic regulation and external physiological variables regulating the bioprocess, opening new possibilities for extrapolation and validation. Finally, the onset of new data representative of individual cells will cause these models to evolve from depicting an average cell in an industrial fermenter, to characterizing the heterogeneity of the population, opening new and unseen possibilities for industrial fermentation improvement.

Does Model Calibration Reduce Uncertainty in Climate Projections?

Uncertainty in climate projections is large as shown by the likely uncertainty ranges in Equilibrium Climate Sensitivity (ECS) of 2.5-4K and in the Transient Climate Response (TCR) of 1.4-2.2K. Uncertainty in model projections could arise from the way in which unresolved processes are represented, the parameter values used, or the targets for model calibration. We show that, in two climate model ensembles which were objectively calibrated to minimise differences from observed large scale atmospheric climatology, uncertainties in ECS and TCR are about two to six times smaller than in the CMIP5 or CMIP6 multi-model ensemble. We also find that projected uncertainties in surface temperature, precipitation and annual extremes are relatively small. Residual uncertainty largely arises from unconstrained sea-ice feedbacks. The 20+ year old HadAM3 standard model configuration simulates observed hemispheric scale observations and pre-industrial surface temperatures about as well as the median CMIP5 and CMIP6 ensembles while the optimised configurations simulates these better than almost all the CMIP5 and CMIP6 models. Hemispheric scale observations and pre-industrial temperatures are not systematically better simulated in CMIP6 than in CMIP5 though the CMIP6 ensemble seems to better simulate patterns of large-scale observations than the CMIP5 ensemble and the optimised HadAM3 configurations. Our results suggest that most CMIP models could be improved in their simulation of large scale observations by systematic calibration. However, the uncertainty in climate projections (for a given scenario) likely largely arises from the choice of parametrisation schemes for unresolved processes (“structural uncertainty”), with different tuning targets another possible contributor.

Combining Physiology-Based Modeling and Evolutionary Algorithms for Personalized, Noninvasive Cardiovascular Assessment Based on Electrocardiography and Ballistocardiography

Purpose: This study proposes a novel approach to obtain personalized estimates of cardiovascular parameters by combining (i) electrocardiography and ballistocardiography for noninvasive cardiovascular monitoring, (ii) a physiology-based mathematical model for predicting personalized cardiovascular variables, and (iii) an evolutionary algorithm (EA) for searching optimal model parameters.Methods: Electrocardiogram (ECG), ballistocardiogram (BCG), and a total of six blood pressure measurements are recorded on three healthy subjects. The R peaks in the ECG are used to segment the BCG signal into single BCG curves for each heart beat. The time distance between R peaks is used as an input for a validated physiology-based mathematical model that predicts distributions of pressures and volumes in the cardiovascular system, along with the associated BCG curve. An EA is designed to search the generation of parameter values of the cardiovascular model that optimizes the match between model-predicted and experimentally-measured BCG curves. The physiological relevance of the optimal EA solution is evaluated a posteriori by comparing the model-predicted blood pressure with a cuff placed on the arm of the subjects to measure the blood pressure.Results: The proposed approach successfully captures amplitudes and timings of the most prominent peak and valley in the BCG curve, also known as the J peak and K valley. The values of cardiovascular parameters pertaining to ventricular function can be estimated by the EA in a consistent manner when the search is performed over five different BCG curves corresponding to five different heart-beats of the same subject. Notably, the blood pressure predicted by the physiology-based model with the personalized parameter values provided by the EA search exhibits a very good agreement with the cuff-based blood pressure measurement.Conclusion: The combination of EA with physiology-based modeling proved capable of providing personalized estimates of cardiovascular parameters and physiological variables of great interest, such as blood pressure. This novel approach opens the possibility for developing quantitative devices for noninvasive cardiovascular monitoring based on BCG sensing.

Conditions for realizing one-point interactions from a multi-layer structure model

A heterostructure composed of N parallel homogeneous layers is studied in the limit as their widths l1, . . . , lN shrink to zero. The problem is investigated in one dimension and the piecewise constant potential in the Schrödinger equation is given by the strengths V1, . . . , VN as functions of l1, . . . , lN, respectively. The key point is the derivation of the conditions on the functions V1(l1), . . . , VN(lN) for realizing a family of one-point interactions as l1, . . . , lN tend to zero along available paths in the N-dimensional space. The existence of equations for a squeezed structure, the solution of which determines the system parameter values, under which the non-zero tunneling of quantum particles through a multi-layer structure occurs, is shown to exist and depend on the paths. This tunneling appears as a result of an appropriate cancellation of divergences.

Cost Problems for Parametric Time Petri Nets*

We investigate the problem of parameter synthesis for time Petri nets with a cost variable that evolves both continuously with time, and discretely when firing transitions. More precisely, parameters are rational symbolic constants used for time constraints on the firing of transitions and we want to synthesise all their values such that some marking is reachable, with a cost that is either minimal or simply less than a given bound. We first prove that the mere existence of values for the parameters such that the latter property holds is undecidable. We nonetheless provide symbolic semi-algorithms for the two synthesis problems and we prove them both sound and complete when they terminate. We also show how to modify them for the case when parameter values are integers. Finally, we prove that these modified versions terminate if parameters are bounded. While this is to be expected since there are now only a finite number of possible parameter values, our algorithms are symbolic and thus avoid an explicit enumeration of all those values. Furthermore, the results are symbolic constraints representing finite unions of convex polyhedra that are easily amenable to further analysis through linear programming. We finally report on the implementation of the approach in Romeo, a software tool for the analysis of time Petri nets.

A Mathematical Model for Transport in Poroelastic Materials with Variable Volume: Derivation, Lie Symmetry Analysis and Examples. Part 2

The model for perfused tissue undergoing deformation taking into account the local exchange between tissue and blood and lymphatic systems is presented. The Lie symmetry analysis in order to identify its symmetry properties is applied. Several families of steady-state solutions in closed formulae are derived. An analysis of the impact of the parameter values and boundary conditions on the distribution of hydrostatic pressure, osmotic agent concentration and deformation of perfused tissue is provided applying the solutions obtained in examples describing real-world processes.