Nonsquare Spectral Factorization for Nonlinear Control Systems

This paper considers nonsquare spectral factorization of nonlinear input affine state space systems in continuous time. More specifically, we obtain a parametrization of nonsquare spectral factors in terms of invariant Lagrangian submanifolds and associated solutions of Hamilton–Jacobi inequalities. This inequality is a nonlinear analogue of the bounded real lemma and the control algebraic Riccati inequality. By way of an application, we discuss an alternative characterization of minimum and maximum phase spectral factors and introduce the notion of a rigid nonlinear system.

Identifying Cancer-Related Cognitive Impairment Using the FACT-Cog Perceived Cognitive Impairment.

Cancer-related cognitive impairment (CRCI) is a concerning problem for many cancer survivors. Evaluating patients for CRCI has been a challenge, in part because of a lack of standardized practices. Self-report instruments are often used to assess CRCI, but there are no validated cutpoints. We present the results of receiver operating characteristic curve analysis identifying cutpoints of the Functional Assessment of Cancer Therapy-Cognition perceived cognitive impairment (PCI) in female breast cancer survivors for identifying CRCI cases. We defined presence of CRCI based on elevated complaints on the Patient's Assessment of Own Functioning Inventory compared with healthy control scores. Our results indicate that scores less than 54 in PCI scores using 18 items and scores less than 60 in PCI scores using 20 items exhibited good ability to discriminate CRCI cases from noncases (area under the receiver operating characteristic curve was 0.84 [95% CI = 0.73 to 0.94]). These preliminary results represent an important contribution toward standardizing practices across CRCI studies

Sliding mode control of quantum systems

This paper proposes a new robust control method for quantum systems with uncertainties involving sliding mode control (SMC). Sliding mode control is a widely used approach in classical control theory and industrial applications. We show that SMC is also a useful method for robust control of quantum systems. In this paper, we define two specific classes of sliding modes (i.e., eigenstates and state subspaces) and propose two novel methods combining unitary control and periodic projective measurements for the design of quantum sliding mode control systems. Two examples including a two-level system and a three-level system are presented to demonstrate the proposed SMC method. One of main features of the proposed method is that the designed control laws can guarantee desired control performance in the presence of uncertainties in the system Hamiltonian. This sliding mode control approach provides a useful control theoretic tool for robust quantum information processing with uncertainties.Comment: 18 pages, 4 figure

Maximization of Regional probabilities using Optimal Surface Graphs: Application to Carotid Artery Segmentation in MRI

__Purpose__ We present a segmentation method that maximizes regional probabilities enclosed by coupled surfaces using an Optimal Surface Graph (OSG) cut approach. This OSG cut determines the globally optimal solution given a graph constructed around an initial surface. While most methods for vessel wall segmentation only use edge information, we show that maximizing regional probabilities using an OSG improves the segmentation results. We applied this to automatically segment the vessel wall of the carotid artery in magnetic resonance images. __Methods__ First, voxel-wise regional probability maps were obtained using a Support Vector Machine classifier trained on local image features. Then the OSG segments the regions which maximizes the regional probabilities considering smoothness and topological constraints. __Results__ The method was evaluated on 49 carotid arteries from 30 subjects. The proposed method shows good accuracy with a Dice wall overlap of 74:1%+-4:3%, and significantly outperforms a published method based on an OSG using only surface information, the obtained segmentations using voxel-wise classification alone, and another published artery wall segmentation method based on a deformable surface model. Intra-class correlations (ICC) with manually measured lumen and wall volumes were similar to those obtained between observers. Finally, we show a good reproducibility of the method with ICC = 0:86 between the volumes measured in scans repeated within a short time interval. __Conclusions__ In this work a new segmentation method that uses both an OSG and regional probabilities is presented. The method shows good segmentations of the carotid artery in MRI and outperformed another segmentation method that uses OSG and edge information and the voxel-wise segmentation using the probability maps

Single-machine scheduling with stepwise tardiness costs and release times

We study a scheduling problem that belongs to the yard operations component of the railroad planning problems, namely the hump sequencing problem. The scheduling problem is characterized as a single-machine problem with stepwise tardiness cost objectives. This is a new scheduling criterion which is also relevant in the context of traditional machine scheduling problems. We produce complexity results that characterize some cases of the problem as pseudo-polynomially solvable. For the difficult-to-solve cases of the problem, we develop mathematical programming formulations, and propose heuristic algorithms. We test the formulations and heuristic algorithms on randomly generated single-machine scheduling problems and real-life datasets for the hump sequencing problem. Our experiments show promising results for both sets of problems

Estimating Nuisance Parameters in Inverse Problems

Many inverse problems include nuisance parameters which, while not of direct interest, are required to recover primary parameters. Structure present in these problems allows efficient optimization strategies - a well known example is variable projection, where nonlinear least squares problems which are linear in some parameters can be very efficiently optimized. In this paper, we extend the idea of projecting out a subset over the variables to a broad class of maximum likelihood (ML) and maximum a posteriori likelihood (MAP) problems with nuisance parameters, such as variance or degrees of freedom. As a result, we are able to incorporate nuisance parameter estimation into large-scale constrained and unconstrained inverse problem formulations. We apply the approach to a variety of problems, including estimation of unknown variance parameters in the Gaussian model, degree of freedom (d.o.f.) parameter estimation in the context of robust inverse problems, automatic calibration, and optimal experimental design. Using numerical examples, we demonstrate improvement in recovery of primary parameters for several large- scale inverse problems. The proposed approach is compatible with a wide variety of algorithms and formulations, and its implementation requires only minor modifications to existing algorithms.Comment: 16 pages, 5 figure