Improved Typelog Alignment for Automated Geosteering Using Multi-Stage Penalized Optimization

Automated geosteering relies on logging-while-drilling data from offset wells to make inferences about the geological formation and help guide directional drilling of the subject well. When data from multiple offset wells are available, it is desirable to consistently combine data typelogs from these wells to better estimate the 3D geological formation around the drilling path. We develop a quantitative typelog alignment method based on a Bayesian approach, where the alignment map between pairs of typelogs are modeled as a random function with a prior distribution. A multi-stage penalized procedure is developed that optimizes this alignment map to minimize a misfit function, while taking the prior knowledge into consideration.

A Rank-Deficient and Sparse Penalized Optimization Model for Compressive Indoor Radar Target Localization

This paper proposes a rank-deficient and sparse penalized optimization method for addressing the problem of through-wall radar imaging (TWRI) in the presence of structured wall clutter. Compressive TWRI enables fast data collection and accurate target localization, but faces with the challenges of incomplete data measurements and strong wall clutter. This paper handles these challenges by formulating the task of wall-clutter removal and target image reconstruction as a joint low-rank and sparse regularized minimization problem. In this problem, the low-rank regularization is used to capture the low-dimensional structure of the wall signals and the sparse penalty is employed to represent the image of the indoor targets. We introduce an iterative algorithm based on the forward-backward proximal gradient technique to solve the large-scale optimization problem, which simultaneously removes unwanted wall clutter and reconstruct an image of indoor targets. Simulated and real radar data are used to validate the effectiveness of the proposed rank-deficient and sparse regularized optimization approach.

Origins of atrophy in Parkinson linked to early onset and local transcription patterns

There is enormous clinical value in inferring the brain regions initially atrophied in Parkinson disease for individual patients and understanding its relationship with clinical and genetic risk factors. The aim of this study is to leverage a new seed-inference algorithm demonstrated for Alzheimer’s disease to the Parkinsonian context and to cluster patients in meaningful subgroups based on these incipient atrophy patterns. Instead of testing brain regions separately as the likely initiation site for each patient, we solve an L1-penalized optimization problem that can return a more predictive heterogeneous, multi-locus seed patterns. A cluster analysis of the individual seed patterns reveals two distinct subgroups (S1 versus S2). The S1 subgroup is characterized by the involvement of the brainstem and ventral nuclei, and S2 by cortex and striatum. Post hoc analysis in features not included in the clustering shows significant differences between subgroups regarding age of onset and local transcriptional patterns of Parkinson-related genes. Top genes associated with regional microglial abundance are strongly associated with subgroup S1 but not with S2. Our results suggest two distinct aetiological mechanisms operative in Parkinson disease. The interplay between immune-related genes, lysosomal genes, microglial abundance and atrophy initiation sites may explain why the age of onset for patients in S1 is on average 4.5 years later than for those in S2. We highlight and compare the most prominently affected brain regions for both subgroups. Altogether, our findings may improve current screening strategies for early Parkinson onsetters.

Heterogeneity of Incipient Atrophy Patterns in Parkinson’s Disease

Parkinson’s Disease (PD) is a the second most common neurodegenerative disorder after Alzheimer’s disease and is characterized by cell death in the amygdala and in substructures of the basal ganglia such as the substantia nigra. Since neuronal loss in PD leads to measurable atrophy patterns in the brain, there is clinical value in understanding where exactly the pathology emerges in each patient and how incipient atrophy relates to the future spread of disease. A recent seed-inference algorithm combining an established network-diffusion model with an L1-penalized optimization routine led to new insights regarding the non-stereotypical origins of Alzheimer’s pathologies across individual subjects. Here, we leverage the same technique to PD patients, demonstrating that the high variability in their atrophy patterns also translates into heterogeneous seed locations. Our individualized seeds are significantly more predictive of future atrophy than a single seed placed at the substantia nigra or the amygdala. We also found a clear distinction in seeding patterns between two PD subgroups – one characterized by predominant involvement of brainstem and ventral nuclei, and the other by more widespread frontal and striatal cortices. This might be indicative of two distinct etiological mechanisms operative in PD. Ultimately, our methods demonstrate that the early stages of the disease may exhibit incipient atrophy patterns that are more complex and variable than generally appreciated.

THE l1 PENALTY FUNCTION METHOD FOR NONCONVEX DIFFERENTIABLE OPTIMIZATION PROBLEMS WITH INEQUALITY CONSTRAINTS

In this paper, some new results on the l1 exact penalty function method are presented. A simple optimality characterization is given for the nonconvex differentiable optimization problems with inequality constraints via the l1 exact penalty function method. The equivalence between sets of optimal solutions in the original mathematical programming problem and its associated exact penalized optimization problem is established under suitable r-invexity assumption. The penalty parameter is given, above which this equivalence holds. Furthermore, the equivalence between a saddle point in the considered nonconvex mathematical programming problem with inequality constraints and a minimizer in its penalized optimization problem with the l1 exact penalty function is also established.