SCATTERING STATISTICS OF GENERALIZED SPATIAL POISSON POINT PROCESSES.

We present a machine learning model for the analysis of randomly generated discrete signals, modeled as the points of an inhomogeneous, compound Poisson point process. Like the wavelet scattering transform introduced by Mallat, our construction is naturally invariant to translations and reflections, but it decouples the roles of scale and frequency, replacing wavelets with Gabor-type measurements. We show that, with suitable nonlinearities, our measurements distinguish Poisson point processes from common self-similar processes, and separate different types of Poisson point processes.

A Combined CRISP3 and SPINK1 Prognostic Grade in EPS-Urine and Establishment of Models to Predict Prognosis of Patients With Prostate Cancer.

BACKGROUND: Prostate cancer (PCa) is characterized by significant heterogeneity. Thus, novel prognostic indicators are required to improve prognosis and treatment. METHODS: Cysteine rich secretory protein 3 (CRISP3) and serine peptidase inhibitor Kazal type 1 (SPINK1) levels in expressed prostatic secretion (EPS)-urine collected during digital rectal examination of 496 patients histologically diagnosed with PCa were detected via enzyme-linked immunosorbent assay. A combined CRISP3 and SPINK1 prognostic grade (CSPG) was defined using cut-off values from receiver operating characteristic curves. Log-rank Kaplan-Meier survival curves investigated differences in prognosis between groups. Univariate and multivariate Cox analyses investigated the CSPG relationship with biochemical recurrence (BCR), cancer-specific survival (CSS), and overall survival (OS). Three prognostic models were developed and validated. CONCLUSIONS: CRISP3 and SPINK1 levels increased with Gleason score progression, pathological T stage, and metastasis status. CSPG in EPS-urine, which was an effective independent prognostic variable, accurately predicted the prognosis of patients with PCa. Three clinical prognostic models using the CSPG for BCR, CSS, and OS were developed and validated.

Establishment of Novel Prostate Cancer Risk Subtypes and A Twelve-Gene Prognostic Model.

Prostate cancer (PCa) is the most common malignancy among men worldwide. However, its complex heterogeneity makes treatment challenging. In this study, we aimed to identify PCa subtypes and a gene signature associated with PCa prognosis. In particular, nine PCa-related pathways were evaluated in patients with PCa by a single-sample gene set enrichment analysis (ssGSEA) and an unsupervised clustering analysis (i.e., consensus clustering). We identified three subtypes with differences in prognosis (Risk_H, Risk_M, and Risk_L). Differences in the proliferation status, frequencies of known subtypes, tumor purity, immune cell composition, and genomic and transcriptomic profiles among the three subtypes were explored based on The Cancer Genome Atlas database. Our results clearly revealed that the Risk_H subtype was associated with the worst prognosis. By a weighted correlation network analysis of genes related to the Risk_H subtype and least absolute shrinkage and selection operator, we developed a 12-gene risk-predicting model. We further validated its accuracy using three public datasets. Effective drugs for high-risk patients identified using the model were predicted. The novel PCa subtypes and prognostic model developed in this study may improve clinical decision-making.

Establishment of Novel DNA Methylation-Based Prostate Cancer Subtypes and a Risk-Predicting Eight-Gene Signature.

Prostate cancer (PCa) is the most common malignant tumor affecting males worldwide. The substantial heterogeneity in PCa presents a major challenge with respect to molecular analyses, patient stratification, and treatment. Least absolute shrinkage and selection operator was used to select eight risk-CpG sites. Using an unsupervised clustering analysis, called consensus clustering, we found that patients with PCa could be divided into two subtypes (Methylation_H and Methylation_L) based on the DNA methylation status at these CpG sites. Differences in the epigenome, genome, transcriptome, disease status, immune cell composition, and function between the identified subtypes were explored using The Cancer Genome Atlas database. This analysis clearly revealed the risk characteristics of the Methylation_H subtype. Using a weighted correlation network analysis to select risk-related genes and least absolute shrinkage and selection operator, we constructed a prediction signature for prognosis based on the subtype classification. We further validated its effectiveness using four public datasets. The two novel PCa subtypes and risk predictive signature developed in this study may be effective indicators of prognosis.

A Hybrid Scattering Transform for Signals with Isolated Singularities.

The scattering transform is a wavelet-based model of Convolutional Neural Networks originally introduced by S. Mallat. Mallat's analysis shows that this network has desirable stability and invariance guarantees and therefore helps explain the observation that the filters learned by early layers of a Convolutional Neural Network typically resemble wavelets. Our aim is to understand what sort of filters should be used in the later layers of the network. Towards this end, we propose a two-layer hybrid scattering transform. In our first layer, we convolve the input signal with a wavelet filter transform to promote sparsity, and, in the second layer, we convolve with a Gabor filter to leverage the sparsity created by the first layer. We show that these measurements characterize information about signals with isolated singularities. We also show that the Gabor measurements used in the second layer can be used to synthesize sparse signals such as those produced by the first layer.

Immune-Related Gene-Based Novel Subtypes to Establish a Model Predicting the Risk of Prostate Cancer.

BACKGROUND: There is significant heterogeneity in prostate cancer (PCa), but immune status can reflect its prognosis. This study aimed to explore immune-related gene-based novel subtypes and to use them to create a model predicting the risk of PCa. METHODS: We downloaded the data of 487 PCa patients from The Cancer Genome Atlas (TCGA) database. We used immunologically relevant genes as input for consensus clustering and applied survival analysis and principal component analysis to determine the properties of the subtypes. We also explored differences of somatic variations, copy number variations, TMPRSS2-ERG fusion, and androgen receptor (AR) scores among the subtypes. Then, we examined the infiltration of different immune cells into the tumor microenvironment in each subtype. We next performed Gene Set Enrichment Analysis (GSEA) to illustrate the characteristics of the subtypes. Finally, based on the subtypes, we constructed a risk predictive model and verified it in TCGA, Gene Expression Omnibus (GEO), cBioPortal, and International Cancer Genome Consortium (ICGC) databases. RESULTS: Four PCa subtypes (C1, C2, C3, and C4) were identified on immune status. Patients with the C3 subtype had the worst prognosis, while the other three groups did not differ significantly from each other in terms of their prognosis. Principal component analysis clearly distinguished high-risk (C3) and low-risk (C1 + 2 + 4) patients. Compared with the case in the low-risk subtype, the Speckle-type POZ Protein (SPOP) had a higher mutation frequency and lower transcriptional level in the high-risk subtype. In C3, there was also a higher frequency of copy number alterations (CNA) of Clusterin (CLU) and lower CLU expression. In addition, C3 had a higher frequency of TMPRSS2-ERG fusion and higher AR scores. M2 macrophages also showed significantly higher infiltration in the high-risk subtype, while CD8+ T cells and dendritic cells had significantly higher infiltration in the low-risk subtype. GSEA revealed that MYC, androgen, and KRAS were relatively activated and p53 was relatively suppressed in high-risk subtype, compared with the levels in the low-risk subtype. Finally, we trained a six-gene signature risk predictive model, which performed well in TCGA, GEO, cBioPortal, and ICGC databases. CONCLUSION: PCa can be divided into four subtypes based on immune-related genes, among which the C3 subtype is associated with a poor prognosis. Based on these subtypes, a risk predictive model was developed, which could indicate patient prognosis.