Algorithmic Analysis of Qualitative and Quantitative Termination Problems for Affine Probabilistic Programs

In this paper, we consider termination of probabilistic programs with real-valued variables. The questions concerned are: 1. qualitative ones that ask (i) whether the program terminates with probability 1 (almost-sure termination) and (ii) whether the expected termination time is finite (finite termination); 2. quantitative ones that ask (i) to approximate the expected termination time (expectation problem) and (ii) to compute a bound B such that the probability to terminate after B steps decreases exponentially (concentration problem). To solve these questions, we utilize the notion of ranking supermartingales which is a powerful approach for proving termination of probabilistic programs. In detail, we focus on algorithmic synthesis of linear ranking-supermartingales over affine probabilistic programs (APP's) with both angelic and demonic non-determinism. An important subclass of APP's is LRAPP which is defined as the class of all APP's over which a linear ranking-supermartingale exists. Our main contributions are as follows. Firstly, we show that the membership problem of LRAPP (i) can be decided in polynomial time for APP's with at most demonic non-determinism, and (ii) is NP-hard and in PSPACE for APP's with angelic non-determinism; moreover, the NP-hardness result holds already for APP's without probability and demonic non-determinism. Secondly, we show that the concentration problem over LRAPP can be solved in the same complexity as for the membership problem of LRAPP. Finally, we show that the expectation problem over LRAPP can be solved in 2EXPTIME and is PSPACE-hard even for APP's without probability and non-determinism (i.e., deterministic programs). Our experimental results demonstrate the effectiveness of our approach to answer the qualitative and quantitative questions over APP's with at most demonic non-determinism.Comment: 24 pages, full version to the conference paper on POPL 201

Identification of low and very high-risk patients with non-WNT/non-SHH medulloblastoma by improved clinico-molecular stratification of the HIT2000 and I-HIT-MED cohorts

Molecular groups of medulloblastoma (MB) are well established. Novel risk stratification parameters include Group 3/4 (non-WNT/non-SHH) methylation subgroups I-VIII or whole-chromosomal aberration (WCA) phenotypes. This study investigates the integration of clinical and molecular parameters to improve risk stratification of non-WNT/non-SHH MB. Non-WNT/non-SHH MB from the HIT2000 study and the HIT-MED registries were selected based on availability of DNA-methylation profiling data. MYC or MYCN amplification and WCA of chromosomes 7, 8, and 11 were inferred from methylation array-based copy number profiles. In total, 403 non-WNT/non-SHH MB were identified, 346/403 (86%) had a methylation class family Group 3/4 methylation score (classifier v11b6) ≥ 0.9, and 294/346 (73%) were included in the risk stratification modeling based on Group 3 or 4 score (v11b6) ≥ 0.8 and subgroup I-VIII score (mb_g34) ≥ 0.8. Group 3 MB (5y-PFS, survival estimation ± standard deviation: 41.4 ± 4.6%; 5y-OS: 48.8 ± 5.0%) showed poorer survival compared to Group 4 (5y-PFS: 68.2 ± 3.7%; 5y-OS: 84.8 ± 2.8%). Subgroups II (5y-PFS: 27.6 ± 8.2%) and III (5y-PFS: 37.5 ± 7.9%) showed the poorest and subgroup VI (5y-PFS: 76.6 ± 7.9%), VII (5y-PFS: 75.9 ± 7.2%), and VIII (5y-PFS: 66.6 ± 5.8%) the best survival. Multivariate analysis revealed subgroup in combination with WCA phenotype to best predict risk of progression and death. The integration of clinical (age, M and R status) and molecular (MYC/N, subgroup, WCA phenotype) variables identified a low-risk stratum with a 5y-PFS of 94 ± 5.7 and a very high-risk stratum with a 5y-PFS of 29 ± 6.1%. Validation in an international MB cohort confirmed the combined stratification scheme with 82.1 ± 6.0% 5y-PFS in the low and 47.5 ± 4.1% in very high-risk groups, and outperformed the clinical model. These newly identified clinico-molecular low-risk and very high-risk strata, accounting for 6%, and 21% of non-WNT/non-SHH MB patients, respectively, may improve future treatment stratification

Clinical and molecular characterization of isolated M1 disease in pediatric medulloblastoma: experience from the German HIT-MED studies

PURPOSE: To evaluate the clinical impact of isolated spread of medulloblastoma cells into cerebrospinal fluid without additional macroscopic metastases (M1-only). METHODS: The HIT-MED database was searched for pediatric patients with M1-only medulloblastoma diagnosed from 2000 to 2019. Corresponding clinical and molecular data was evaluated. Treatment was stratified by age and changed over time for older patients. RESULTS: 70 patients with centrally reviewed M1-only disease were identified. Clinical data was available for all and molecular data for 45/70 cases. 91% were non-WNT/non-SHH medulloblastoma (Grp3/4). 5-year PFS for 52 patients ≥ 4 years was 59.4 (± 7.1) %, receiving either upfront craniospinal irradiation (CSI) or SKK-sandwich chemotherapy (CT). Outcomes did not differ between these strategies (5-year PFS: CSI 61.7 ± 9.9%, SKK-CT 56.7 ± 6.1%). For patients < 4 years (n = 18), 5-year PFS was 50.0 (± 13.2) %. M1-persistence occurred exclusively using postoperative CT and was a strong negative predictive factor (p$_{PFS/OS}$ < 0.01). Patients with additional clinical or molecular high-risk (HR) characteristics had worse outcomes (5-year PFS 42.7 ± 10.6% vs. 64.0 ± 7.0%, p = 0.03). In n = 22 patients ≥ 4 years with full molecular information and without additional HR characteristics, risk classification by molecular subtyping had an effect on 5-year PFS (HR 16.7 ± 15.2%, SR 77.8 ± 13.9%; p = 0.01). CONCLUSIONS: Our results confirm that M1-only is a high-risk condition, and further underline the importance of CSF staging. Specific risk stratification of affected patients needs attention in future discussions for trials and treatment recommendations. Future patients without contraindications may benefit from upfront CSI by sparing risks related to higher cumulative CT applied in sandwich regimen

Clinical and molecular characterization of isolated M1 disease in pediatric medulloblastoma: experience from the German HIT-MED studies

PURPOSE: To evaluate the clinical impact of isolated spread of medulloblastoma cells into cerebrospinal fluid without additional macroscopic metastases (M1-only). METHODS: The HIT-MED database was searched for pediatric patients with M1-only medulloblastoma diagnosed from 2000 to 2019. Corresponding clinical and molecular data was evaluated. Treatment was stratified by age and changed over time for older patients. RESULTS: 70 patients with centrally reviewed M1-only disease were identified. Clinical data was available for all and molecular data for 45/70 cases. 91% were non-WNT/non-SHH medulloblastoma (Grp3/4). 5-year PFS for 52 patients ≥ 4 years was 59.4 (± 7.1) %, receiving either upfront craniospinal irradiation (CSI) or SKK-sandwich chemotherapy (CT). Outcomes did not differ between these strategies (5-year PFS: CSI 61.7 ± 9.9%, SKK-CT 56.7 ± 6.1%). For patients < 4 years (n = 18), 5-year PFS was 50.0 (± 13.2) %. M1-persistence occurred exclusively using postoperative CT and was a strong negative predictive factor (p(PFS/OS) < 0.01). Patients with additional clinical or molecular high-risk (HR) characteristics had worse outcomes (5-year PFS 42.7 ± 10.6% vs. 64.0 ± 7.0%, p = 0.03). In n = 22 patients ≥ 4 years with full molecular information and without additional HR characteristics, risk classification by molecular subtyping had an effect on 5-year PFS (HR 16.7 ± 15.2%, SR 77.8 ± 13.9%; p = 0.01). CONCLUSIONS: Our results confirm that M1-only is a high-risk condition, and further underline the importance of CSF staging. Specific risk stratification of affected patients needs attention in future discussions for trials and treatment recommendations. Future patients without contraindications may benefit from upfront CSI by sparing risks related to higher cumulative CT applied in sandwich regimen. SUPPLEMENTARY INFORMATION: The online version contains supplementary material available at 10.1007/s11060-021-03913-5

The Biochemical Abstract Machine {BIOCHAM}

http://www.springerlink.com/index/NVWWRAN9W4RUA03NIn this article we present the Biochemical Abstract Machine BIOCHAM and advocate its use as a formal modeling environment for networks biology. Biocham provides a precise semantics to biomolecular interaction maps. Based on this formal semantics, the Biocham system offers automated reasoning to ols for querying the temporal properties of the system under all its possible behavi ors. We present the main features of Biocham, provide details on a simple example of the MAPK signaling cascade and prove some results on the equivalence of model s w.r.t. their temporal properties