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Input-output maps are strongly biased towards simple outputs.

ABSTRACT: Many systems in nature can be described using discrete input-output maps. Without knowing details about a map, there may seem to be no a priori reason to expect that a randomly chosen input would be more likely to generate one output over another. Here, by extending fundamental results from algorithmic information theory, we show instead that for many real-world maps, the a priori probability P(x) that randomly sampled inputs generate a particular output x decays exponentially with the approximate Kolmogorov complexity [Formula: see text] of that output. These input-output maps are biased towards simplicity. We derive an upper bound P(x)???[Formula: see text], which is tight for most inputs. The constants a and b, as well as many properties of P(x), can be predicted with minimal knowledge of the map. We explore this strong bias towards simple outputs in systems ranging from the folding of RNA secondary structures to systems of coupled ordinary differential equations to a stochastic financial trading model.

SUBMITTER: Dingle K

PROVIDER: S-EPMC5823903 | biostudies-other | 2018 Feb

REPOSITORIES: biostudies-other

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Input-output maps are strongly biased towards simple outputs.

Dingle Kamaludin K Camargo Chico Q CQ Louis Ard A AA

Nature communications 20180222 1

Many systems in nature can be described using discrete input-output maps. Without knowing details about a map, there may seem to be no a priori reason to expect that a randomly chosen input would be more likely to generate one output over another. Here, by extending fundamental results from algorithmic information theory, we show instead that for many real-world maps, the a priori probability P(x) that randomly sampled inputs generate a particular output x decays exponentially with the approxima ...[more]

PMID: 29472533

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Project description:BACKGROUND: Statistical approaches to describing the behaviour, including the complex relationships between input parameters and model outputs, of nonlinear dynamic models (referred to as metamodelling) are gaining more and more acceptance as a means for sensitivity analysis and to reduce computational demand. Understanding such input-output maps is necessary for efficient model construction and validation. Multi-way metamodelling provides the opportunity to retain the block-wise structure of the temporal data typically generated by dynamic models throughout the analysis. Furthermore, a cluster-based approach to regional metamodelling allows description of highly nonlinear input-output relationships, revealing additional patterns of covariation. RESULTS: By presenting the N-way Hierarchical Cluster-based Partial Least Squares Regression (N-way HC-PLSR) method, we here combine multi-way analysis with regional cluster-based metamodelling, together making a powerful methodology for extensive exploration of the input-output maps of complex dynamic models. We illustrate the potential of the N-way HC-PLSR by applying it both to predict model outputs as functions of the input parameters, and in the inverse direction (predicting input parameters from the model outputs), to analyse the behaviour of a dynamic model of the mammalian circadian clock. Our results display a more complete cartography of how variation in input parameters is reflected in the temporal behaviour of multiple model outputs than has been previously reported. CONCLUSIONS: Our results indicated that the N-way HC-PLSR metamodelling provides a gain in insight into which parameters that are related to a specific model output behaviour, as well as variations in the model sensitivity to certain input parameters across the model output space. Moreover, the N-way approach allows a more transparent and detailed exploration of the temporal dimension of complex dynamic models, compared to alternative 2-way methods.

Project description:Nitrogen (N) presents an important challenge for sustainability. Human intervention in the global nitrogen cycle has been pivotal in in providing goods and services to society. However, release of N beyond its intended societal use has many negative health and environmental consequences. Several systems modeling approaches have been developed to understand the trade-offs between the beneficial and harmful effects of N. These efforts include life cycle modeling, integrated management practices and sustainability metrics for individuals and communities. However, these approaches do not connect economic and ecological N flows in physical units throughout the system, which could better represent these trade-offs for decision-makers. Physical Input-Output Table (PIOT) based models present a viable complementary solution to overcome this limitation. We developed a N-PIOT for Illinois representing the interdependence of sectors in 2002, using N mass units. This allows studying the total N flow required to produce a certain amount of N in the final product. An Environmentally Extended Input Output (EEIO) based approach was used to connect the physical economic production to environmental losses; allowing quantification of total environmental impact to support agricultural production in Illinois. A bottom up approach was used to develop the N-PIOT using Material Flow Analysis (MFA) tracking N flows associated with top 3 commodities (Corn, Soybean and Wheat). These three commodities cover 99% of N fertilizer use in Illinois. The PIOT shows that of all the N inputs to corn production the state exported 68% of N embedded in useful products, 9% went to animal feed manufacturing and only 0.03% was consumed directly within the state. Approximately 35% of N input to soybean farming ended up in animal feed. Release of N to the environment was highest from corn farming, at about 21.8% of total N fertilizer inputs, followed by soybean (9.2%) and wheat farming (4.2%). The model also allowed the calculation of life cycle N use efficiency for N based on physical flows in the economy. Hence, PIOTs prove to be a viable tool for developing a holistic approach to manage disrupted biogeochemical cycles, since these provide a detailed insight into physical flows in economic systems and allow physical coupling with ecological N flows.

Dataset Information

Input-output maps are strongly biased towards simple outputs.

Publications

Input-output maps are strongly biased towards simple outputs.

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