An Algebraic Framework for the Real-Time Solution of Inverse Problems on Embedded Systems

This article presents a new approach to the real-time solution of inverse problems on embedded systems. The class of problems addressed corresponds to ordinary differential equations (ODEs) with generalized linear constraints, whereby the data from an array of sensors forms the forcing function. The solution of the equation is formulated as a least squares (LS) problem with linear constraints. The LS approach makes the method suitable for the explicit solution of inverse problems where the forcing function is perturbed by noise. The algebraic computation is partitioned into a initial preparatory step, which precomputes the matrices required for the run-time computation; and the cyclic run-time computation, which is repeated with each acquisition of sensor data. The cyclic computation consists of a single matrix-vector multiplication, in this manner computation complexity is known a-priori, fulfilling the definition of a real-time computation. Numerical testing of the new method is presented on perturbed as well as unperturbed problems; the results are compared with known analytic solutions and solutions acquired from state-of-the-art implicit solvers. The solution is implemented with model based design and uses only fundamental linear algebra; consequently, this approach supports automatic code generation for deployment on embedded systems. The targeting concept was tested via software- and processor-in-the-loop verification on two systems with different processor architectures. Finally, the method was tested on a laboratory prototype with real measurement data for the monitoring of flexible structures. The problem solved is: the real-time overconstrained reconstruction of a curve from measured gradients. Such systems are commonly encountered in the monitoring of structures and/or ground subsidence.Comment: 24 pages, journal articl

Deep brain and cortical stimulation for epilepsy

Background : Despite optimal medical treatment, including epilepsy surgery, many epilepsy patients have uncontrolled seizures. In the last decades, interest has grown in invasive intracranial neurostimulation as a treatment for these patients. Intracranial stimulation includes both deep brain stimulation (DBS) (stimulation through depth electrodes) and cortical stimulation (subdural electrodes). Objectives : To assess the efficacy, safety and tolerability of deep brain and cortical stimulation for refractory epilepsy based on randomized controlled trials. Search methods : We searched PubMed (6 August 2013), the Cochrane Epilepsy Group Specialized Register (31 August 2013), Cochrane Central Register of Controlled Trials (CENTRAL) (The Cochrane Library 2013, Issue 7 of 12) and reference lists of retrieved articles. We also contacted device manufacturers and other researchers in the field. No language restrictions were imposed. Selection criteria : Randomized controlled trials (RCTs) comparing deep brain or cortical stimulation to sham stimulation, resective surgery or further treatment with antiepileptic drugs. Data collection and analysis : Four review authors independently selected trials for inclusion. Two review authors independently extracted the relevant data and assessed trial quality and overall quality of evidence. The outcomes investigated were seizure freedom, responder rate, percentage seizure frequency reduction, adverse events, neuropsychological outcome and quality of life. If additional data were needed, the study investigators were contacted. Results were analysed and reported separately for different intracranial targets for reasons of clinical heterogeneity. Main results : Ten RCTs comparing one to three months of intracranial neurostimulation to sham stimulation were identified. One trial was on anterior thalamic DBS (n = 109; 109 treatment periods); two trials on centromedian thalamic DBS (n = 20; 40 treatment periods), but only one of the trials (n = 7; 14 treatment periods) reported sufficient information for inclusion in the quantitative meta-analysis; three trials on cerebellar stimulation (n = 22; 39 treatment periods); three trials on hippocampal DBS (n = 15; 21 treatment periods); and one trial on responsive ictal onset zone stimulation (n = 191; 191 treatment periods). Evidence of selective reporting was present in four trials and the possibility of a carryover effect complicating interpretation of the results could not be excluded in 4 cross-over trials without any washout period. Moderate-quality evidence could not demonstrate statistically or clinically significant changes in the proportion of patients who were seizure-free or experienced a 50% or greater reduction in seizure frequency (primary outcome measures) after 1 to 3 months of anterior thalamic DBS in (multi) focal epilepsy, responsive ictal onset zone stimulation in (multi) focal epilepsy patients and hippocampal DBS in (medial) temporal lobe epilepsy. However, a statistically significant reduction in seizure frequency was found for anterior thalamic DBS (-17.4% compared to sham stimulation; 95% confidence interval (CI) -32.1 to -1.0; high-quality evidence), responsive ictal onset zone stimulation (-24.9%; 95% CI -40.1 to 6.0; high-quality evidence)) and hippocampal DBS (-28.1%; 95% CI -34.1 to -22.2; moderate-quality evidence). Both anterior thalamic DBS and responsive ictal onset zone stimulation do not have a clinically meaningful impact on quality life after three months of stimulation (high-quality evidence). Electrode implantation resulted in asymptomatic intracranial haemorrhage in 3% to 4% of the patients included in the two largest trials and 5% to 13% had soft tissue infections; no patient reported permanent symptomatic sequelae. Anterior thalamic DBS was associated with fewer epilepsy-associated injuries (7.4 versus 25.5%; P = 0.01) but higher rates of self-reported depression (14.8 versus 1.8%; P = 0.02) and subjective memory impairment (13.8 versus 1.8%; P = 0.03); there were no significant differences in formal neuropsychological testing results between the groups. Responsive ictal-onset zone stimulation was well tolerated with few side effects but SUDEP rate should be closely monitored in the future (4 per 340 [= 11.8 per 1000] patient-years; literature: 2.2-10 per 1000 patient-years). The limited number of patients preclude firm statements on safety and tolerability of hippocampal DBS. With regards to centromedian thalamic DBS and cerebellar stimulation, no statistically significant effects could be demonstrated but evidence is of only low to very low quality. Authors' conclusions : Only short term RCTs on intracranial neurostimulation for epilepsy are available. Compared to sham stimulation, one to three months of anterior thalamic DBS ((multi) focal epilepsy), responsive ictal onset zone stimulation ((multi) focal epilepsy) and hippocampal DBS (temporal lobe epilepsy) moderately reduce seizure frequency in refractory epilepsy patients. Anterior thalamic DBS is associated with higher rates of self-reported depression and subjective memory impairment. SUDEP rates require careful monitoring in patients undergoing responsive ictal onset zone stimulation. There is insufficient evidence to make firm conclusive statements on the efficacy and safety of hippocampal DBS, centromedian thalamic DBS and cerebellar stimulation. There is a need for more, large and well-designed RCTs to validate and optimize the efficacy and safety of invasive intracranial neurostimulation treatments

Probing the quantumness of channels with mixed states

We present an alternative approach to the derivation of benchmarks for quantum channels, such as memory or teleportation channels. Using the concept of effective entanglement and the verification thereof, a testing procedure is derived which demands very few experimental resources. The procedure is generalized by allowing for mixed test states. By constructing optimized measure & re-prepare channels, the benchmarks are found to be very tight in the considered experimental regimes.Comment: 11 Pages, 9 Figures, published versio

Fundamentals of 3-D Neutron Kinetics and Current Status

This lecture includes the following topics: 1) A summary of the cell and lattice calculations used to generate the neutron reaction data for neutron kinetics, including the spectral and burn up calculations of LWR cells and fuel assembly lattices, and the main nodal kinetics parameters: mean neutron generation time and delayed neutron fraction; 2) the features of the advanced nodal methods for 3-D LWR core physics, including the treatment of partially inserted control rods, fuel assembly grids, fuel burn up and xenon and samarium transients, and ex core detector responses, that are essential for core surveillance, axial offset control and operating transient analysis; 3) the advanced nodal methods for 3-D LWR core neutron kinetics (best estimate safety analysis, real time simulation); and 4) example applications to 3-D neutron kinetics problems in transient analysis of PWR cores, including model, benchmark and operational transients without, or with simple, thermal-hydraulics feedback