Using machine learning to predict statistical properties of non-stationary dynamical processes: System climate,regime transitions, and the effect of stochasticity

We develop and test machine learning techniques for successfully using past state time series data and knowledge of a time-dependent system parameter to predict the evolution of the "climate" associated with the long-term behavior of a non-stationary dynamical system, where the non-stationary dynamical system is itself unknown. By the term climate, we mean the statistical properties of orbits rather than their precise trajectories in time. By the term non-stationary, we refer to systems that are, themselves, varying with time. We show that our methods perform well on test systems predicting both continuous gradual climate evolution as well as relatively sudden climate changes (which we refer to as "regime transitions"). We consider not only noiseless (i.e., deterministic) non-stationary dynamical systems, but also climate prediction for non-stationary dynamical systems subject to stochastic forcing (i.e., dynamical noise), and we develop a method for handling this latter case. The main conclusion of this paper is that machine learning has great promise as a new and highly effective approach to accomplishing data driven prediction of non-stationary systems.

Effectiveness of Breast-Conserving Surgery and 3-Dimensional Conformal Partial Breast Reirradiation for Recurrence of Breast Cancer in the Ipsilateral Breast: The NRG Oncology/RTOG 1014 Phase 2 Clinical Trial

Importance

Mastectomy is standard for recurrence of breast cancer after breast conservation therapy with whole breast irradiation. The emergence of partial breast irradiation led to consideration of its application for reirradiation after a second lumpectomy for treatment of recurrence of breast cancer in the ipsilateral breast.

Objectives

To assess the effectiveness and adverse effects of partial breast reirradiation after a second lumpectomy and whether the treatment is an acceptable alternative to mastectomy.

Design, Setting, and Participants

The NRG Oncology/Radiation Therapy Oncology Group 1014 trial is a phase 2, single-arm, prospective clinical trial of 3-dimensional, conformal, external beam partial breast reirradiation after a second lumpectomy for recurrence of breast cancer in the ipsilateral breast after previous whole breast irradiation. The study opened on June 4, 2010, and closed June 18, 2013. Median follow-up was 5.5 years. This analysis used all data received at NRG Oncology through November 18, 2018. Eligible patients experienced a recurrence of breast tumor that was less than 3 cm and unifocal in the ipsilateral breast more than 1 year after breast-conserving therapy with whole breast irradiation and who had undergone excision with negative margins.

Interventions

Adjuvant partial breast reirradiation, 1.5 Gy twice daily for 30 treatments during 15 days (45 Gy), using a 3-dimensional conformal technique.

Main Outcomes and Measures

The main outcomes of the present study were the predefined secondary study objectives of recurrence of breast cancer in the ipsilateral breast, late adverse events (>1 year after treatment), mastectomy incidence, distant metastasis-free survival, overall survival, and circulating tumor cell incidence.

Results

A total of 65 women were enrolled, with 58 evaluable for analysis (mean [SD] age, 65.12 [9.95] years; 48 [83%] white). Of the recurrences of breast cancer in the ipsilateral breast, 23 (40%) were noninvasive and 35 (60%) were invasive. In all 58 patients, 53 (91%) had tumors 2 cm or smaller. All tumors were clinically node negative. A total of 44 patients (76%) tested positive for estrogen receptor, 33 (57%) for progesterone receptor, and 10 (17%) for ERBB2 (formerly HER2 or HER2/neu) overexpression. Four patients had breast cancer recurrence, with a 5-year cumulative incidence of 5% (95% CI, 1%-13%). Seven patients underwent ipsilateral mastectomies for a 5-year cumulative incidence of 10% (95% CI, 4%-20%). Both distant metastasis-free survival and overall survival rates were 95% (95% CI, 85%-98%). Four patients (7%) had grade 3 and none had grade 4 or higher late treatment adverse events.

Conclusions and Relevance

For patients experiencing recurrence of breast cancer in the ipsilateral breast after lumpectomy and whole breast irradiation, a second breast conservation was achievable in 90%, with a low risk of re-recurrence of cancer in the ipsilateral breast using adjuvant partial breast reirradiation. This finding suggests that this treatment approach is an effective alternative to mastectomy.

Rapid time series prediction with a hardware-based reservoir computer

Reservoir computing is a neural network approach for processing time-dependent signals that has seen rapid development in recent years. Physical implementations of the technique using optical reservoirs have demonstrated remarkable accuracy and processing speed at benchmark tasks. However, these approaches require an electronic output layer to maintain high performance, which limits their use in tasks such as time-series prediction, where the output is fed back into the reservoir. We present here a reservoir computing scheme that has rapid processing speed both by the reservoir and the output layer. The reservoir is realized by an autonomous, time-delay, Boolean network configured on a field-programmable gate array. We investigate the dynamical properties of the network and observe the fading memory property that is critical for successful reservoir computing. We demonstrate the utility of the technique by training a reservoir to learn the short- and long-term behavior of a chaotic system. We find accuracy comparable to state-of-the-art software approaches of a similar network size, but with a superior real-time prediction rate up to 160 MHz.