Extracting useful information from high-dimensional data is an important focus of today's statistical research and practice. Penalized loss function minimization has been shown to be effective for this task both theoretically and empirically. With the virtues of both regularization and sparsity, the L1-penalized squared error minimization method Lasso has been popular in regression models and beyond.In this paper, we combine different norms including L1 to form an intelligent penalty in order to add side information to the fitting of a regression or classification model to obtain reasonable estimates. Specifically, we introduce the Composite Absolute Penalties (CAP) family, which allows given grouping and hierarchical relationships between the predictors to be expressed. CAP penalties are built by defining groups and combining the properties of norm penalties at the across-group and within-group levels. Grouped selection occurs for nonoverlapping groups. Hierarchical variable selection is reached by defining groups with particular overlapping patterns. We propose using the BLASSO and cross-validation to compute CAP estimates in general. For a subfamily of CAP estimates involving only the L1 and L∞ norms, we introduce the iCAP algorithm to trace the entire regularization path for the grouped selection problem. Within this subfamily, unbiased estimates of the degrees of freedom (df) are derived so that the regularization parameter is selected without crossvalidation. CAP is shown to improve on the predictive performance of the LASSO in a series of simulated experiments, including cases with p ≫ n and possibly mis-specified groupings. When the complexity of a model is properly calculated, iCAP is seen to be parsimonious in the experiments.

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A numerical model based on one-dimensional balance laws and ad hoc zero-dimensional boundary conditions is tested against experimental data. The study concentrates on the circle of Willis, a vital subnetwork of the cerebral vasculature. The main goal is to obtain efficient and reliable numerical tools with predictive capabilities. The flow is assumed to obey the Navier-Stokes equations, while the mechanical reactions of the arterial walls follow a viscoelastic model. Like many previous studies, a dimension reduction is performed through averaging. Unlike most previous work, the resulting model is both calibrated and validated against in vivo data, more precisely transcranial Doppler data of cerebral blood velocity. The network considered has three inflow vessels and six outflow vessels. Inflow conditions come from the data, while outflow conditions are modeled. Parameters in the outflow conditions are calibrated using a subset of the data through ensemble Kalman filtering techniques. The rest of the data is used for validation. The results demonstrate the viability of the proposed approach.

Cerebral autoregulation (CA) is an most important mechanism responsible for the relatively constant blood flow supply to brain when cerebral perfusion pressure varies. Its assessment in nonacute cases has been relied on the quantification of the relationship between noninvasive beat-to-beat blood pressure (BP) and blood flow velocity (BFV). To overcome the nonstationary nature of physiological signals such as BP and BFV, a computational method called multimodal pressure-flow (MMPF) analysis was recently developed to study the nonlinear BP-BFV relationship during the Valsalva maneuver (VM). The present study aimed to determine (i) whether this method can estimate autoregulation from spontaneous BP and BFV fluctuations during baseline rest conditions; (ii) whether there is any difference between the MMPF measures of autoregulation based on intra-arterial BP (ABP) and based on cerebral perfusion pressure (CPP); and (iii) whether the MMPF method provides reproducible and reliable measure for noninvasive assessment of autoregulation. To achieve these aims, we analyzed data from existing databases including: (i) ABP and BFV of 12 healthy control, 10 hypertensive, and 10 stroke subjects during baseline resting conditions and during the Valsalva maneuver, and (ii) ABP, CPP, and BFV of 30 patients with traumatic brain injury (TBI) who were being paralyzed, sedated, and ventilated. We showed that autoregulation in healthy control subjects can be characterized by specific phase shifts between BP and BFV oscillations during the Valsalva maneuver, and the BP-BFV phase shifts were reduced in hypertensive and stroke subjects (P < 0.01), indicating impaired autoregulation. Similar results were found during baseline condition from spontaneous BP and BFV oscillations. The BP-BFV phase shifts obtained during baseline and during VM were highly correlated (R > 0.8, P < 0.0001), showing no statistical difference (pairedt test P > 0.47). In TBI patients there were strong correlations between phases of ABP and CPP oscillations (R = 0.99, P < 0.0001) and, thus, between ABP-BFV and CPP-BFV phase shifts (P < 0.0001, R = 0.76). By repeating the MMPF 4 times on data of TBI subjects, each time on a selected cycle of spontaneous BP and BFV oscillations, we showed that MMPF had better reproducibility than traditional autoregulation index. These results indicate that the MMPF method, based on instantaneous phase relationships between cerebral blood flow velocity and peripheral blood pressure, has better performance than the traditional standard method, and can reliably assess cerebral autoregulation dynamics from ambulatory blood pressure and cerebral blood flow during supine rest conditions.