We propose a neural-network based survival model (SurvSurf) specifically designed for direct and simultaneous probabilistic prediction of the first hitting time of sequential events from baseline. Unlike existing models, SurvSurf is theoretically guaranteed to never violate the monotonic relationship between the cumulative incidence functions of sequential events, while allowing nonlinear influence from predictors. It also incorporates implicit truths for unobserved intermediate events in model fitting, and supports both discrete and continuous time and events. We also identified a variant of the Integrated Brier Score (IBS) that showed robust correlation with the mean squared error (MSE) between the true and predicted probabilities by accounting for implied truths about the missing intermediate events. We demonstrated the superiority of SurvSurf compared to modern and traditional predictive survival models in two simulated datasets and two real-world datasets, using MSE, the more robust IBS and by measuring the extent of monotonicity violation.

When it comes to probability theory we all would have heard of joint distribution, marginal distribution, independence etc. In this article I will focus my attention onto independence specially conditional independence. In others words if the happening of event A doesn't affect the probability of event B happening, both events are said to be independent. From the view of information theory it can be interpreted as: if knowing A doesn't provide any additional information about B, then A and B are said to be independent. These are the different interpretations for the concept of independence.

In this paper we present a textual description, in terms of Description Logics, of the BPMN Ontology, which provides a clear semantic formalisation of the structural components of the Business Process Modelling Notation (BPMN), based on the latest stable BPMN specifications from OMG [BPMN Version 1.1 -- January 2008]. The development of the ontology was guided by the description of the complete set of BPMN Element Attributes and Types contained in Annex B of the BPMN specifications.