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We present a comprehensive study of stationary states in a coherent medium with a quadratic or Kerr nonlinearity in the presence of localized potentials in one dimension for both positive and negative signs of the nonlinear term as well as for barriers and wells. The description is in terms of the nonlinear Schrödinger equation and hence applicable to a variety of systems, including interacting ultracold atoms in the mean field regime and light propagation in optical fibers. We determine the full landscape of solutions in terms of a potential step and build solutions for rectangular barrier and well potentials. It is shown that all the solutions can be expressed in terms of a Jacobi elliptic function with the inclusion of a complex-valued phase shift. Our solution method relies on the roots of a cubic polynomial associated with a hydrodynamic picture, which provides a simple classification of all the solutions, both bounded and unbounded, while the boundary conditions are intuitively visualized as intersections of phase space curves. We compare solutions for open boundary conditions with those for a barrier potential on a ring, and also show that numerically computed solutions for smooth barriers agree qualitatively with analytical solutions for rectangular barriers. A stability analysis of solutions based on the Bogoliubov equations for fluctuations shows that persistent instabilities are localized at sharp boundaries and are predicated by the relation of the mean density change across the boundary to the value of the derivative of the density at the edge. We examine the scattering of a wave packet by a barrier potential and show that at any instant the scattered states are well described by the stationary solutions we obtain, indicating applications of our results and methods to nonlinear scattering problems. 

Mobile devices have been an integral part of our everyday lives. Users' increasing interaction with mobile devices brings in significant concerns on various types of potential privacy leakage, among which location privacy draws the most attention. Specifically, mobile users' trajectories constructed by location data may be captured by adversaries to infer sensitive information. In previous studies, differential privacy has been utilized to protect published trajectory data with rigorous privacy guarantee. Strong protection provided by differential privacy distorts the original locations or trajectories using stochastic noise to avoid privacy leakage. In this paper, we propose a novel location inference attack framework, iTracker, which simultaneously recovers multiple trajectories from differentially private trajectory data using the structured sparsity model. Compared with the traditional recovery methods based on single trajectory prediction, iTracker, which takes advantage of the correlation among trajectories discovered by the structured sparsity model, is more effective in recovering multiple private trajectories simultaneously. iTracker successfully attacks the existing privacy protection mechanisms based on differential privacy. We theoretically demonstrate the near-linear runtime of iTracker, and the experimental results using two real-world datasets show that iTracker outperforms existing recovery algorithms in recovering multiple trajectories. 

We present Variational Aspect-based Latent Topic Allocation (VALTA), a family of autoencoding topic models that learn aspect-based representations of reviews. VALTA defines a user-item encoder that maps bag-of-words vectors for combined reviews associated with each paired user; item onto structured embeddings, which in turn define per-aspect topic weights. We model individual reviews in a structured manner by inferring an aspect assignment for each sentence in a given review, where the per-aspect topic weights obtained by the user-item encoder serve to define a mixture over topics, conditioned on the aspect. The result is an autoencoding neural topic model for reviews, which can be trained in a fully unsupervised manner to learn topics that are structured into aspects. Experimental evaluation on large number of datasets demonstrates that aspects are interpretable, yield higher coherence scores than non-structured autoencoding topic model variants,; can be utilized to perform aspect-based comparison; genre discovery. 

Abstract Prostate cancer treatment planning is largely dependent upon examination of core-needle biopsies. The microscopic architecture of the prostate glands forms the basis for prognostic grading by pathologists. Interpretation of these convoluted three-dimensional (3D) glandular structures via visual inspection of a limited number of two-dimensional (2D) histology sections is often unreliable, which contributes to the under- and overtreatment of patients. To improve risk assessment and treatment decisions, we have developed a workflow for nondestructive 3D pathology and computational analysis of whole prostate biopsies labeled with a rapid and inexpensive fluorescent analogue of standard hematoxylin and eosin (H&E) staining. This analysis is based on interpretable glandular features and is facilitated by the development of image translation–assisted segmentation in 3D (ITAS3D). ITAS3D is a generalizable deep learning–based strategy that enables tissue microstructures to be volumetrically segmented in an annotation-free and objective (biomarker-based) manner without requiring immunolabeling. As a preliminary demonstration of the translational value of a computational 3D versus a computational 2D pathology approach, we imaged 300 ex vivo biopsies extracted from 50 archived radical prostatectomy specimens, of which, 118 biopsies contained cancer. The 3D glandular features in cancer biopsies were superior to corresponding 2D features for risk stratification of patients with low- to intermediate-risk prostate cancer based on their clinical biochemical recurrence outcomes. The results of this study support the use of computational 3D pathology for guiding the clinical management of prostate cancer. Significance:An end-to-end pipeline for deep learning–assisted computational 3D histology analysis of whole prostate biopsies shows that nondestructive 3D pathology has the potential to enable superior prognostic stratification of patients with prostate cancer. 

Abstract Prostate cancer treatment decisions rely heavily on subjective visual interpretation [assigning Gleason patterns or International Society of Urological Pathology (ISUP) grade groups] of limited numbers of two‐dimensional (2D) histology sections. Under this paradigm, interobserver variance is high, with ISUP grades not correlating well with outcome for individual patients, and this contributes to the over‐ and undertreatment of patients. Recent studies have demonstrated improved prognostication of prostate cancer outcomes based on computational analyses of glands and nuclei within 2D whole slide images. Our group has also shown that the computational analysis of three‐dimensional (3D) glandular features, extracted from 3D pathology datasets of whole intact biopsies, can allow for improved recurrence prediction compared to corresponding 2D features. Here we seek to expand on these prior studies by exploring the prognostic value of 3D shape‐based nuclear features in prostate cancer (e.g. nuclear size, sphericity). 3D pathology datasets were generated using open‐top light‐sheet (OTLS) microscopy of 102 cancer‐containing biopsies extractedex vivofrom the prostatectomy specimens of 46 patients. A deep learning‐based workflow was developed for 3D nuclear segmentation within the glandular epithelium versus stromal regions of the biopsies. 3D shape‐based nuclear features were extracted, and a nested cross‐validation scheme was used to train a supervised machine classifier based on 5‐year biochemical recurrence (BCR) outcomes. Nuclear features of the glandular epithelium were found to be more prognostic than stromal cell nuclear features (area under the ROC curve [AUC] = 0.72 versus 0.63). 3D shape‐based nuclear features of the glandular epithelium were also more strongly associated with the risk of BCR than analogous 2D features (AUC = 0.72 versus 0.62). The results of this preliminary investigation suggest that 3D shape‐based nuclear features are associated with prostate cancer aggressiveness and could be of value for the development of decision‐support tools. © 2023 The Pathological Society of Great Britain and Ireland.