Enhancing Predictive Capabilities in Data-Driven Dynamical Modeling with Automatic Differentiation: Koopman and Neural ODE Approaches

Data-driven approximations of the Koopman operator are promising for predicting the time evolution of systems characterized by complex dynamics. Among these methods, the approach known as extended dynamic mode decomposition with dictionary learning (EDMD-DL) has garnered significant attention. Here we present a modification of EDMD-DL that concurrently determines both the dictionary of observables and the corresponding approximation of the Koopman operator. This innovation leverages automatic differentiation to facilitate gradient descent computations through the pseudoinverse. We also address the performance of several alternative methodologies. We assess a 'pure' Koopman approach, which involves the direct time-integration of a linear, high-dimensional system governing the dynamics within the space of observables. Additionally, we explore a modified approach where the system alternates between spaces of states and observables at each time step -- this approach no longer satisfies the linearity of the true Koopman operator representation. For further comparisons, we also apply a state space approach (neural ODEs). We consider systems encompassing two and three-dimensional ordinary differential equation systems featuring steady, oscillatory, and chaotic attractors, as well as partial differential equations exhibiting increasingly complex and intricate behaviors. Our framework significantly outperforms EDMD-DL. Furthermore, the state space approach offers superior performance compared to the 'pure' Koopman approach where the entire time evolution occurs in the space of observables. When the temporal evolution of the Koopman approach alternates between states and observables at each time step, however, its predictions become comparable to those of the state space approach

BRAF Mutations in Advanced Cancers: Clinical Characteristics and Outcomes

BACKGROUND: Oncogenic BRAF mutations have been found in diverse malignancies and activate RAF/MEK/ERK signaling, a critical pathway of tumorigenesis. We examined the clinical characteristics and outcomes of patients with mutant (mut) BRAF advanced cancer referred to phase 1 clinic. METHODS: We reviewed the records of 80 consecutive patients with mutBRAF advanced malignancies and 149 with wild-type (wt) BRAF (matched by tumor type) referred to the Clinical Center for Targeted Therapy and analyzed their outcome. RESULTS: Of 80 patients with mutBRAF advanced cancer, 56 had melanoma, 10 colorectal, 11 papillary thyroid, 2 ovarian and 1 esophageal cancer. Mutations in codon 600 were found in 77 patients (62, V600E; 13, V600K; 1, V600R; 1, unreported). Multivariate analysis showed less soft tissue (Odds ratio (OR) = 0.39, 95%CI: 0.20-0.77, P = 0.007), lung (OR = 0.38, 95%CI: 0.19-0.73, p = 0.004) and retroperitoneal metastases (OR = 0.34, 95%CI: 0.13-0.86, p = 0.024) and more brain metastases (OR = 2.05, 95%CI: 1.02-4.11, P = 0.043) in patients with mutBRAF versus wtBRAF. Comparing to the corresponding wtBRAF, mutBRAF melanoma patients had insignificant trend to longer median survival from diagnosis (131 vs. 78 months, p = 0.14), while mutBRAF colorectal cancer patients had an insignificant trend to shorter median survival from diagnosis (48 vs. 53 months, p = 0.22). In melanoma, V600K mutations in comparison to other BRAF mutations were associated with more frequent brain (75% vs. 36.3%, p = 0.02) and lung metastases (91.6% vs. 47.7%, p = 0.007), and shorter time from diagnosis to metastasis and to death (19 vs. 53 months, p = 0.046 and 78 vs. 322 months, p = 0.024 respectively). Treatment with RAF/MEK targeting agents (Hazard ratio (HR) = 0.16, 95%CI: 0.03-0.89, p = 0.037) and any decrease in tumor size after referral (HR = 0.07, 95%CI: 0.015-0.35, p = 0.001) correlated with longer survival in mutBRAF patients. CONCLUSIONS: BRAF appears to be a druggable mutation that also defines subgroups of patients with phenotypic overlap, albeit with differences that correlate with histology or site of mutation

Analytical model of a self-complementary connected array on high impedance surface

International audienc

Overweight is associated to a better prognosis in metastatic colorectal cancer: A pooled analysis of FFCD trials

IF 7.191 (2017)International audienceBACKGROUND:Previous studies showed that high and low body mass index (BMI) was associated with worse prognosis in early-stage colorectal cancer (CRC), and low BMI was associated with worse prognosis in metastatic CRC (mCRC). We aimed to assess efficacy outcomes according to BMI.PATIENTS AND METHODS:A pooled analysis of individual data from 2085 patients enrolled in eight FFCD first-line mCRC trials from 1991 to 2013 was performed. Comparisons were made according to the BMI cut-off: Obese (BMI ≥30), overweight patients (BMI ≥ 25), normal BMI patients (BMI: 18.5-24) and thin patients (BMI <18.5). Interaction tests were performed between BMI effect and sex, age and the addition of antiangiogenics to chemotherapy.RESULTS:The rate of BMI ≥25 patients was 41.5%, ranging from 37.6% (1991-1999 period) to 41.5% (2000-2006 period) and 44.8% (2007-2013 period). Comparison of overweight patients versus normal BMI range patients revealed a significant improvement of median overall survival (OS) (18.5 versus 16.3 months, HR = 0.88 [0.80-0.98] p = 0.02) and objective response rate (ORR) (42% versus 36% OR = 1.23 [1.01-1.50] p = 0.04) but a comparable median progression-free survival (PFS) (7.8 versus 7.2 months, HR = 0.96 [0.87-1.05] p = 0.35). Subgroup analyses revealed that overweight was significantly associated with better OS in men. OS and PFS were significantly shorter in thin patients.CONCLUSION:Overweight patients had a prolonged OS compared with normal weight patients with mCRC. The association of overweight with better OS was only observed in men. The pejorative prognosis of BMI <18.5 was confirmed.Copyright © 2018 The Authors. Published by Elsevier Ltd.. All rights reserve