Gain Bounds for Multiple Model Switched Adaptive Control of General MIMO LTI Systems

For the class of MIMO minimal LTI systems controlled by an estimation based multiple model switched adaptive controller (EMMSAC), bounds are obtained for the closed loop lp gain, 1 ? p ? ?, from the input and output disturbances to the internal signals

A dosimetric comparison of real-time adaptive and non-adaptive radiotherapy: A multi-institutional study encompassing robotic, gimbaled, multileaf collimator and couch tracking

AbstractPurposeA study of real-time adaptive radiotherapy systems was performed to test the hypothesis that, across delivery systems and institutions, the dosimetric accuracy is improved with adaptive treatments over non-adaptive radiotherapy in the presence of patient-measured tumor motion.Methods and materialsTen institutions with robotic(2), gimbaled(2), MLC(4) or couch tracking(2) used common materials including CT and structure sets, motion traces and planning protocols to create a lung and a prostate plan. For each motion trace, the plan was delivered twice to a moving dosimeter; with and without real-time adaptation. Each measurement was compared to a static measurement and the percentage of failed points for γ-tests recorded.ResultsFor all lung traces all measurement sets show improved dose accuracy with a mean 2%/2mm γ-fail rate of 1.6% with adaptation and 15.2% without adaptation (p<0.001). For all prostate the mean 2%/2mm γ-fail rate was 1.4% with adaptation and 17.3% without adaptation (p<0.001). The difference between the four systems was small with an average 2%/2mm γ-fail rate of <3% for all systems with adaptation for lung and prostate.ConclusionsThe investigated systems all accounted for realistic tumor motion accurately and performed to a similar high standard, with real-time adaptation significantly outperforming non-adaptive delivery methods

Three-points interfacial quadrature for geometrical source terms on nonuniform grids

International audienceThis paper deals with numerical (finite volume) approximations, on nonuniform meshes, for ordinary differential equations with parameter-dependent fields. Appropriate discretizations are constructed over the space of parameters, in order to guarantee the consistency in presence of variable cells' size, for which $L^p$-error estimates, $1\le p < +\infty$, are proven. Besides, a suitable notion of (weak) regularity for nonuniform meshes is introduced in the most general case, to compensate possibly reduced consistency conditions, and the optimality of the convergence rates with respect to the regularity assumptions on the problem's data is precisely discussed. This analysis attempts to provide a basic theoretical framework for the numerical simulation on unstructured grids (also generated by adaptive algorithms) of a wide class of mathematical models for real systems (geophysical flows, biological and chemical processes, population dynamics)

Oracle Complexity Classes and Local Measurements on Physical Hamiltonians

The canonical problem for the class Quantum Merlin-Arthur (QMA) is that of estimating ground state energies of local Hamiltonians. Perhaps surprisingly, [Ambainis, CCC 2014] showed that the related, but arguably more natural, problem of simulating local measurements on ground states of local Hamiltonians (APX-SIM) is likely harder than QMA. Indeed, [Ambainis, CCC 2014] showed that APX-SIM is P^QMA[log]-complete, for P^QMA[log] the class of languages decidable by a P machine making a logarithmic number of adaptive queries to a QMA oracle. In this work, we show that APX-SIM is P^QMA[log]-complete even when restricted to more physical Hamiltonians, obtaining as intermediate steps a variety of related complexity-theoretic results. We first give a sequence of results which together yield P^QMA[log]-hardness for APX-SIM on well-motivated Hamiltonians: (1) We show that for NP, StoqMA, and QMA oracles, a logarithmic number of adaptive queries is equivalent to polynomially many parallel queries. These equalities simplify the proofs of our subsequent results. (2) Next, we show that the hardness of APX-SIM is preserved under Hamiltonian simulations (a la [Cubitt, Montanaro, Piddock, 2017]). As a byproduct, we obtain a full complexity classification of APX-SIM, showing it is complete for P, P^||NP, P^||StoqMA, or P^||QMA depending on the Hamiltonians employed. (3) Leveraging the above, we show that APX-SIM is P^QMA[log]-complete for any family of Hamiltonians which can efficiently simulate spatially sparse Hamiltonians, including physically motivated models such as the 2D Heisenberg model. Our second focus considers 1D systems: We show that APX-SIM remains P^QMA[log]-complete even for local Hamiltonians on a 1D line of 8-dimensional qudits. This uses a number of ideas from above, along with replacing the "query Hamiltonian" of [Ambainis, CCC 2014] with a new "sifter" construction.Comment: 38 pages, 3 figure