Ensemble Of Outcomes Research Articles

Incoherence: A Generalized Measure of Complexity to Quantify Ensemble Divergence in Multi-Trial Experiments and Simulations.

Complex systems pose significant challenges to traditional scientific and statistical methods due to their inherent unpredictability and resistance to simplification. Accurately detecting complex behavior and the uncertainty which comes with it is therefore essential. Using the context of previous studies, we introduce a new information-theoretic measure, termed "incoherence". By using an adapted Jensen-Shannon Divergence across an ensemble of outcomes, we quantify the aleatoric uncertainty of the system. First we compared this measure to established statistical tests using both continuous and discrete data. Before demonstrating how incoherence can be applied to identify key characteristics of complex systems, including sensitivity to initial conditions, criticality, and response to perturbations.

Implications of the link between the Periodic Table and the Standard Model

The mathematics of quantum physics from the standard model using groups U(1)xSU(2)xSU(3) and the Pauli principle produces two sets of time independent quantum states n(n+1) and n(n-1) where n is the principal quantum number. Oscillations between these states result in a one to one mapping with the Roberts-Janet Nuclear Periodic Table by interpretation of n>0 for condensed matter and n<0 for plasma prior to fusion. The mechanism provides a framework for Periodic Tables for every supernova by excluding mass number. In the lower half of the table occupation by bosons leads to increased energy densities in which an ensemble of outcomes is discussed. An hypothesis of string theory is proposed at the nuclear end of the table merging into quantum loop gravity at the condensed matter at the top end of the table.

Implications of the Link between the Periodic Table and the Standard Model

The mathematics of quantum physics from the standard model using groups U(1)xSU(2)xSU(3) and the Pauli principle produces two sets of time independent quantum states n(n+1) and n(n-1) where n is the principal quantum number. Oscillations between these states result in a one to one mapping with the Roberts-Janet Nuclear Periodic Table by interpretation of n>0 for condensed matter and n<0 for plasma prior to fusion. The mechanism provides a framework for Periodic Tables for every supernova by excluding mass number. In the lower half of the table occupation by bosons leads to increased energy densities in which an ensemble of outcomes is discussed. An hypothesis of string theory is proposed at the nuclear end of the table merging into quantum loop gravity at the condensed matter at the top end of the table.

Importance of anthropogenic climate impact, sampling error and urban development in sewer system design

Urban drainage design relying on observed precipitation series neglects the uncertainties associated with current and indeed future climate variability. Urban drainage design is further affected by the large stochastic variability of precipitation extremes and sampling errors arising from the short observation periods of extreme precipitation. Stochastic downscaling addresses anthropogenic climate impact by allowing relevant precipitation characteristics to be derived from local observations and an ensemble of climate models. This multi-climate model approach seeks to reflect the uncertainties in the data due to structural errors of the climate models. An ensemble of outcomes from stochastic downscaling allows for addressing the sampling uncertainty. These uncertainties are clearly reflected in the precipitation-runoff predictions of three urban drainage systems. They were mostly due to the sampling uncertainty. The contribution of climate model uncertainty was found to be of minor importance. Under the applied greenhouse gas emission scenario (A1B) and within the period 2036–2065, the potential for urban flooding in our Swiss case study is slightly reduced on average compared to the reference period 1981–2010. Scenario planning was applied to consider urban development associated with future socio-economic factors affecting urban drainage. The impact of scenario uncertainty was to a large extent found to be case-specific, thus emphasizing the need for scenario planning in every individual case. The results represent a valuable basis for discussions of new drainage design standards aiming specifically to include considerations of uncertainty.