In stochastic quantisation, quantum mechanical expectation values are computed as averages over the time history of a stochastic process described by a Langevin equation. Complex stochastic quantisation, though theoretically not rigorously established, extends this idea to cases where the action is complex-valued by complexifying the basic degrees of freedom, all observables and allowing the stochastic process to probe the complexified configuration space. We review the method for a previously studied one-dimensional toy model, the U(1) one link model. We confirm that complex Langevin dynamics only works for a certain range of parameters, misestimating observables otherwise. A curious effect is observed where all moments of the basic stochastic variable are misestimated, although these misestimated moments may be used to construct, by a Taylor series, other observables that are reproduced correctly. This suggests a subtle but not completely resolved relationship between the original complex integration measure and the higher-dimensional probability distribution in the complexified configuration space, generated by the complex Langevin process.

In this paper, we propose a paradigm of control, called a maximum hands-off control. A hands-off control is defined as a control that has a short support per unit time. The maximum hands-off control is the minimum support (or sparsest) per unit time among all controls that achieve control objectives. For finite horizon continuous-time control, we show the equivalence between the maximum hands-off control and L1-optimal control under a uniqueness assumption called normality. This result rationalizes the use of L1 optimality in computing a maximum hands-off control. The same result is obtained for discrete-time hands-off control. We also propose an L1/L2-optimal control to obtain a smooth hands-off control. Furthermore, we give a self-triggered feedback control algorithm for linear time-invariant systems, which achieves a given sparsity rate and practical stability in the case of plant disturbances. An example is included to illustrate the effectiveness of the proposed control.

Background: Joint replacement is a procedure with a major impact on the quality of life of patients with joint degenerative disease or traumatic injuries. However, some patients develop symptoms after the intervention caused by mechanical loosening or infection. Metabolic imaging by 18F-FDG-PET investigated in these patients isoften hampered by low specificity for diagnosis of possible septic vs. mechanical loosening. The reason for this shortcoming is to our opinion the unawareness of physiological remodeling processes that could be seen in asymptomatic patients. Objectives: In order to overcome this drawback, we aimed to find out the physiological metabolic functional pattern in asymptomatic patients with implanted hip prosthesis Patients and Methods: Twelve patients (6 males, 6 females); mean age 73 ± 7 (range 58 - 91) years were prospectively enrolled in the study. The patients were admitted to our department for oncological referral with implanted hip prostheses. All patients explained no symptoms with regard to their implanted prosthesis. The attenuation corrected images were used for analysis. Results: Fourteen hip prostheses in 12 patients were visually analyzed. Seven out of 14 prostheses among 12 patients showed focal periprosthetic enhanced metabolism, two of which showed two sites of enhanced uptake; whereas, the remaining five prostheses showed singular hypermetabolic areas within the periprosthetic site. The remaining seven prostheses in the other five patients showed no periprosthetic-enhanced uptake. Conclusion: Of the asymptomatic patients investigated, 58% showed focal enhanced periprosthetic glucose metabolism. This finding should be taken into consideration as a more probable unspecific metabolic pattern for correct interpretation of 18F-FDG-PET studies in patients with suspected septic loosening of the hip prosthesis.