LSTM Neural Networks: Input to State Stability and Probabilistic Safety Verification

The goal of this paper is to analyze Long Short Term Memory (LSTM) neural networks from a dynamical system perspective. The classical recursive equations describing the evolution of LSTM can be recast in state space form, resulting in a time-invariant nonlinear dynamical system. A sufficient condition guaranteeing the Input-to-State (ISS) stability property of this class of systems is provided. The ISS property entails the boundedness of the output reachable set of the LSTM. In light of this result, a novel approach for the safety verification of the network, based on the Scenario Approach, is devised. The proposed method is eventually tested on a pH neutralization process.Comment: Accepted for Learning for dynamics & control (L4DC) 202

Learning-based predictive control for linear systems: a unitary approach

A comprehensive approach addressing identification and control for learningbased Model Predictive Control (MPC) for linear systems is presented. The design technique yields a data-driven MPC law, based on a dataset collected from the working plant. The method is indirect, i.e. it relies on a model learning phase and a model-based control design one, devised in an integrated manner. In the model learning phase, a twofold outcome is achieved: first, different optimal p-steps ahead prediction models are obtained, to be used in the MPC cost function; secondly, a perturbed state-space model is derived, to be used for robust constraint satisfaction. Resorting to Set Membership techniques, a characterization of the bounded model uncertainties is obtained, which is a key feature for a successful application of the robust control algorithm. In the control design phase, a robust MPC law is proposed, able to track piece-wise constant reference signals, with guaranteed recursive feasibility and convergence properties. The controller embeds multistep predictors in the cost function, it ensures robust constraints satisfaction thanks to the learnt uncertainty model, and it can deal with possibly unfeasible reference values. The proposed approach is finally tested in a numerical example

Robust multi-rate predictive control using multi-step prediction models learned from data

This note extends a recently proposed algorithm for model identification and robust MPC of asymptotically stable, linear time-invariant systems subject to process and measurement disturbances. Independent output predictors for different steps ahead are estimated with Set Membership methods. It is here shown that the corresponding prediction error bounds are the least conservative in the considered model class. Then, a new multi-rate robust MPC algorithm is developed, employing said multi-step predictors to robustly enforce constraints and stability against disturbances and model uncertainty, and to reduce conservativeness. A simulation example illustrates the effectiveness of the approach

On multi-step prediction models for receding horizon control

The derivation of multi-step-ahead prediction models from sampled data of a linear system is considered. A dedicated prediction model is built for each future time step of interest. In addition to a nominal model, the set of all models consistent with data and prior information is derived as well, making the approach suitable for robust control design within a Model Predictive Control framework. The resulting parameter identification problem is solved through a sequence of convex programs, overcoming the non-convexity arising when identifying 1-step prediction models with an output-error criterion. At the same time, the derived models guarantee a worst-case error which is always smaller than the one obtained by iterating models identified with a 1-step prediction error criterion.Comment: This manuscript contains technical details of recent results developed by the authors on learning-based model predictive control for linear time invariant system

Copy number variation at the HvCBF4–HvCBF2 genomic segment is a major component of frost resistance in barley

A family of CBF transcription factors plays a major role in reconfiguring the plant transcriptome in response to low-freezing temperature in temperate cereals. In barley, more than 13 HvCBF genes map coincident with the major QTL FR-H2 suggesting them as candidates to explain the function of the locus. Variation in copy number (CNV) of specific HvCBFs was assayed in a panel of 41 barley genotypes using RT-qPCR. Taking advantage of an accurate phenotyping that combined Fv/Fm and field survival, resistance-associated variants within FR-H2 were identified. Genotypes with an increased copy number of HvCBF4 and HvCBF2 (at least ten and eight copies, respectively) showed greater frost resistance. A CAPS marker able to distinguish the CBF2A, CBF2B and CBF2A/B forms was developed and showed that all the higher-ranking genotypes in term of resistance harbour only CBF2A, while other resistant winter genotypes harbour also CBF2B, although at a lower CNV. In addition to the major involvement of the HvCBF4-HvCBF2 genomic segment in the proximal cluster of CBF elements, a negative role of HvCBF3 in the distal cluster was identified. Multiple linear regression models taking into account allelic variation at FR-H1/VRN-H1 explained 0.434 and 0.550 (both at p < 0.001) of the phenotypic variation for Fv/Fm and field survival respectively, while no interaction effect between CNV at the HvCBFs and FR-H1/VRN-H1 was found. Altogether our data suggest a major involvement of the CBF genes located in the proximal cluster, with no apparent involvement of the central cluster contrary to what was reported for wheat

PD-L1 expression heterogeneity in non-small cell lung cancer: Evaluation of small biopsies reliability

Immunotherapy with checkpoint inhibitors, allowing recovery of effector cells function, has demonstrated to be highly effective in many tumor types and represents a true revolution in oncology. Recently, the anti-PD1 agent pembrolizumab was granted FDA approval for the first line treatment of patients with advanced non-small cell lung cancer (NSCLC) whose tumors show PD-L1 expression in \ue2\u89\ua5 50% of neoplastic cells and as a second line treatment for patients with NSCLC expressing PD-L1 in \ue2\u89\ua51% of neoplastic cells, evaluated with a validated assay. For the large majority of patients such evaluation is made on small biopsies. However, small tissue samples such as core biopsies might not be representative of tumors and may show divergent results given the possible heterogeneous immunoexpression of the biomarker. We therefore sought to evaluate PD-L1 expression concordance in a cohort of 239 patients using tissue microarrays (TMA) as surrogates of biopsies stained with a validated PD-L1 immunohistochemical assay (SP263) and report the degree of discordance among tissue cores in order to understand how such heterogeneity could affect decisions regarding therapy. We observed a discordance rate of 20% and 7.9% and a Cohen's \uce\uba value of 0.53 (moderate) and 0,48 (moderate) for \ue2\u89\ua5 1% and \ue2\u89\ua5 50% cutoffs, respectively. Our results suggest that caution must be taken when evaluating single biopsies from patients with advanced NSCLC eligible for immunotherapy; moreover, at least 4 biopsies are necessary in order to minimize the risk of tumor misclassification

Pathological and clinical features of multiple cancers and lung adenocarcinoma: a multicentre study

OBJECTIVES: Lung cancer is increasingly diagnosed as a second cancer. Our goal was to analyse the characteristics and outcomes of early-stage resected lung adenocarcinomas in patients with previous cancers (PC) and correlations with adenocarcinoma subtypes.METHODS: We retrospectively reviewed data of patients radically operated on for stage I-II lung adenocarcinoma in 9 thoracic surgery departments between 2014 and 2017. Overall survival (OS) and time to disease relapse were evaluated between subgroups.RESULTS: We included 700 consecutive patients. PC were present in 260 (37.1%). Breast adenocarcinoma, lung cancer and prostate cancer were the most frequent (21.5%, 11.5% and 11.2%, respectively). No significant differences in OS were observed between the PC and non-PC groups (P = 0.378), with 31 and 75 deaths, respectively. Patients with PC had smaller tumours and were more likely to receive sublobar resection and to be operated on with a minimally invasive approach. Previous gastric cancer (P = 0.042) and synchronous PC (when diagnosed up to 6 months before lung adenocarcinoma; P = 0.044) were related, with a worse OS. Colon and breast adenocarcinomas and melanomas were significantly related to a lower incidence of high grade (solid or micropapillary, P = 0.0039, P = 0.005 and P = 0.028 respectively), whereas patients affected by a previous lymphoma had a higher incidence of a micropapillary pattern (P = 0.008).CONCLUSIONS: In patients with PC, we found smaller tumours more frequently treated with minimally invasive techniques and sublobar resection, probably due to a more careful follow-up. The impact on survival is not uniform and predictable; however, breast and colon cancers and melanoma showed a lower incidence of solid or micropapillary patterns whereas patients with lymphomas had a higher incidence of a micropapillary pattern

Impact of High‑Grade Patterns in Early‑Stage Lung Adenocarcinoma: A Multicentric Analysis

Objective The presence of micropapillary and solid adenocarcinoma patterns leads to a worse survival and a signifcantly higher tendency to recur. This study aims to assess the impact of pT descriptor combined with the presence of high-grade components on long-term outcomes in early-stage lung adenocarcinomas. Methods We retrospectively collected data of consecutive resected pT1-T3N0 lung adenocarcinoma from nine European Thoracic Centers. All patients who underwent a radical resection with lymph-node dissection between 2014 and 2017 were included. Diferences in Overall Survival (OS) and Disease-Free Survival (DFS) and possible prognostic factors associated with outcomes were evaluated also after performing a propensity score matching to compare tumors containing non-highgrade and high-grade patterns. Results Among 607 patients, the majority were male and received a lobectomy. At least one high-grade histological pattern was seen in 230 cases (37.9%), of which 169 solid and 75 micropapillary. T1a-b-c without high-grade pattern had a signifcant better prognosis compared to T1a-b-c with high-grade pattern (p=0.020), but the latter had similar OS compared to T2a (p=0.277). Concurrently, T1a-b-c without micropapillary or solid patterns had a signifcantly better DFS compared to those with high-grade patterns (p=0.034), and it was similar to T2a (p=0.839). Multivariable analysis confrms the role of T descriptor according to high-grade pattern both for OS (p=0.024; HR 1.285 95% CI 1.033–1.599) and DFS (p=0.003; HR 1.196, 95% CI 1.054–1.344, respectively). These results were confrmed after the propensity score matching analysis. Conclusions pT1 lung adenocarcinomas with a high-grade component have similar prognosis of pT2a tumors