scholarly journals DReSS: A difference measurement based on reachability between state spaces of Boolean networks

2020 ◽  
Author(s):  
Ziqiao Yin ◽  
Binghui Guo ◽  
Shuangge Steven Ma ◽  
Yifan Sun ◽  
Zhilong Mi ◽  
...  
Keyword(s):  
State Space ◽  
Regulatory Network ◽  
Biological Systems ◽  
Boolean Networks ◽  
Random Networks ◽  
Biological Factors ◽  
Related Factors ◽  
State Spaces ◽  
Structural Perturbations ◽  
Dynamical Features

AbstractResearches on dynamical features of biological systems are mostly based on fixed network structure. However, both biological factors and data factors can cause structural perturbations to biological regulatory networks. There are researches focus on the influence of such structural perturbations to the systems’ dynamical features. Reachability is one of the most important dynamical features, which describe whether a state can automatically evolve into another state. However, there is still no method can quantitively describe the reachability differences of two state spaces caused by structural perturbations. DReSS, Difference based on Reachability between State Spaces, is proposed in this research to solve this problem. First, basic properties of DReSS such as non-negativity, symmetry and subadditivity are proved based on the definition. And two more indexes, diagDReSS and iDReSS are proposed based on the definition of DReSS. Second, typical examples like DReSS = 0 or 1 are shown to explain the meaning of DReSS family, and the differences between DReSS and traditional graph distance are shown based on the calculation steps of DReSS. Finally, differences of DReSS distribution between real biological regulatory network and random networks are compared. Multiple interaction positions in real biological regulatory network show significant different DReSS value with those in random networks while none of them show significant different diagDReSS value, which illustrates that the structural perturbations tend to affect reachability inside and between attractor basins rather than to affect attractor set itself.Author summaryBoolean network is a kind of networks which is widely used to model biological regulatory systems. There are structural perturbations in biological systems based on both biological factors and data-related factors. We propose a measurement called DReSS to describe the difference between state spaces of Boolean networks, which can be used to evaluate the influence of specific structural perturbations of a network to its state space quantitively. We can use DReSS to detect the sensitive interactions in a regulatory network, where structural perturbations can influence its state space significantly. We proved properties of DReSS including non-negativity, symmetry and subadditivity, and gave examples to explain the meaning of some special DReSS values. Finally, we present an example of using DReSS to detect sensitive vertexes in yeast cell cycle regulatory network. DReSS can provide a new perspective on how different interactions affect the state space of a specific regulatory network differently.

DReSS: a method to quantitatively describe the influence of structural perturbations on state spaces of genetic regulatory networks

2020 ◽  
Author(s):  
Ziqiao Yin ◽  
Binghui Guo ◽  
Shuangge Ma ◽  
Yifan Sun ◽  
Zhilong Mi ◽  
...  
Keyword(s):  
Biological Networks ◽  
Regulatory Networks ◽  
Genetic Regulatory Networks ◽  
Random Networks ◽  
Graph Distance ◽  
State Spaces ◽  
Biological Regulatory Networks ◽  
Structural Perturbations ◽  
The Relationship ◽  
Index Family

Abstract Structures of genetic regulatory networks are not fixed. These structural perturbations can cause changes to the reachability of systems’ state spaces. As system structures are related to genotypes and state spaces are related to phenotypes, it is important to study the relationship between structures and state spaces. However, there is still no method can quantitively describe the reachability differences of two state spaces caused by structural perturbations. Therefore, Difference in Reachability between State Spaces (DReSS) is proposed. DReSS index family can quantitively describe differences of reachability, attractor sets between two state spaces and can help find the key structure in a system, which may influence system’s state space significantly. First, basic properties of DReSS including non-negativity, symmetry and subadditivity are proved. Then, typical examples are shown to explain the meaning of DReSS and the differences between DReSS and traditional graph distance. Finally, differences of DReSS distribution between real biological regulatory networks and random networks are compared. Results show most structural perturbations in biological networks tend to affect reachability inside and between attractor basins rather than to affect attractor set itself when compared with random networks, which illustrates that most genotype differences tend to influence the proportion of different phenotypes and only a few ones can create new phenotypes. DReSS can provide researchers with a new insight to study the relation between genotypes and phenotypes.

State Space Properties of Boolean Networks Trained for Sequence Tasks

2013 ◽  
pp. 235-240
Author(s):  
Andrea Roli ◽  
Matteo Amaducci ◽  
Lorenzo Garattoni ◽  
Carlo Pinciroli ◽  
Mauro Birattari
Keyword(s):  
State Space ◽  
Boolean Networks

scholarly journals Tangible visual analytics: the integration of tangible interactions and computational techniques for biological data visualization and modelling with experts in the loop

2021 ◽  
Author(s):  
Roozbeh Manshaei
Keyword(s):  
Unique Solution ◽  
Gene Regulatory Network ◽  
Regulatory Network ◽  
Biological Systems ◽  
Network Reconstruction ◽  
Biological Data ◽  
Tangible Interaction ◽  
Survival Prediction ◽  
New Approach ◽  
Gene Regulatory

Understanding and interpreting the inherently uncertain nature of complex biological systems, as well as the time to an event in these systems, are notable challenges in the field of bioinformatics. Overcoming these challenges could potentially lead to scientific discoveries, for example paving the path for the design of new drugs to target specific diseases such as cancer, or helping to apply more effective treatment for these diseases. In general, reverse engineering of these types of biological systems using online datasets is difficult. In particular, finding a unique solution to these systems is hard due to their complexity and the small sample size of datasets. This remains an unsolved problem due to such uncertainty, and the often intractable solution space of these systems. The term"uncertainty" describes the application-based margin of significance, validity, and efficiency of inferred or predictive models in their ability to extract characteristic properties and features describing the observed state of a given biological system. In this work, uncertainties within two specific bioinformatics domains are considered, namely "gene regulatory network reconstruction" (in which gene interactions/relationships within a biological entity are inferred from gene expression data); and "cancer survivorship prediction" (in which patient survival rates are predicted based on clinical factors and treatment outcomes). One approach to reduce uncertainty is to apply different constraints that have particular relevance to each application domain. In gene network reconstruction for instance, the consideration of constraints such as sparsity, stability and modularity, can inform and reduce uncertainty in the inferred reconstructions. While in cancer survival prediction, there is uncertainty in determining which clinical features (or feature aggregates) can improve associated prediction models. The inherent lack of understanding of how, why and when such constraints should be applied, however, prompts the need for a radically new approach. In this dissertation, a new approach is thus considered to aid human expert users in understanding and exploring inherent uncertainties associated with these two bioinformatics domains. Specifically, a novel set of tools is introduced and developed to assist in evidence gathering, constraint definition, and refinement of models toward the discovery of better solutions. This dissertation employs computational approaches, including convex optimization and feature selection/aggregation, in order to increase the chances of finding a unique solution. These approaches are realized through three novel interactive tools that employ tangible interaction in combination with graphical visualization to enable experts to query and manipulate the data. Tangible interaction provides physical embodiments of data and computational functions in support of learning and collaboration. Using these approaches, the dissertation demonstrates: (1) a modified stability constraint for reconstructing gene regulatory network that shows improvement in accuracy of predicted networks, (2) a novel modularity constraint (neighbor norm) for extracting available structures in the data which is validated with Laplacian eigenvalue spectrum, and (3) a hybrid method for estimating overall survival and inferring effective prognosis factors for patients with advanced prostate cancer that improves the accuracy of survival analysis.

scholarly journals Observing extreme events in incomplete state spaces with application to rainfall estimation from satellite images

2005 ◽  
Vol 12 (2) ◽  
pp. 195-200 ◽  
Author(s):  
A. A. Tsonis ◽  
K. P. Georgakakos
Keyword(s):  
Nonlinear Systems ◽  
State Space ◽  
Satellite Imagery ◽  
Extreme Events ◽  
State Vector ◽  
Satellite Images ◽  
Rainfall Estimation ◽  
State Spaces ◽  
Complete Knowledge ◽  
Complete State

Abstract. Reconstructing the dynamics of nonlinear systems from observations requires the complete knowledge of its state space. In most cases, this is either impossible or at best very difficult. Here, by using a toy model, we investigate the possibility of deriving useful insights about the variability of the system from only a part of the complete state vector. We show that while some of the details of the variability might be lost, other details, especially extreme events, are successfully recovered. We then apply these ideas to the problem of rainfall estimation from satellite imagery. We show that, while reducing the number of observables reduces the correlation between actual and inferred precipitation amounts, good estimates for extreme events are still recoverable.

scholarly journals A Novel Antifragility Measure Based on Satisfaction and Its Application to Random and Biological Boolean Networks

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-10 ◽  
Author(s):  
Omar K. Pineda ◽  
Hyobin Kim ◽  
Carlos Gershenson
Keyword(s):  
Biological Systems ◽  
Treatment Strategies ◽  
Boolean Networks ◽  
Genetic Mechanism ◽  
Engineering Systems ◽  
Random Boolean Networks ◽  
External Perturbations ◽  
Before And After ◽  
New Treatment ◽  
Practical Measure

Antifragility is a property that enhances the capability of a system in response to external perturbations. Although the concept has been applied in many areas, a practical measure of antifragility has not been developed yet. Here we propose a simply calculable measure of antifragility, based on the change of “satisfaction” before and after adding perturbations, and apply it to random Boolean networks (RBNs). Using the measure, we found that ordered RBNs are the most antifragile. Also, we demonstrated that seven biological systems are antifragile. Our measure and results can be used in various applications of Boolean networks (BNs) including creating antifragile engineering systems, identifying the genetic mechanism of antifragile biological systems, and developing new treatment strategies for various diseases.

scholarly journals The morphological state space revisited: what do phylogenetic patterns in homoplasy tell us about the number of possible character states?

2015 ◽  
Vol 5 (6) ◽  
pp. 20150049 ◽  
Author(s):  
Jennifer F. Hoyal Cuthill
Keyword(s):  
State Space ◽  
Morphological Evolution ◽  
Character Evolution ◽  
Character State ◽  
State Spaces ◽  
Phylogenetic Constraints ◽  
Finite State ◽  
Finite States ◽  
Close Relatives ◽  
Morphological State

Biological variety and major evolutionary transitions suggest that the space of possible morphologies may have varied among lineages and through time. However, most models of phylogenetic character evolution assume that the potential state space is finite. Here, I explore what the morphological state space might be like, by analysing trends in homoplasy (repeated derivation of the same character state). Analyses of ten published character matrices are compared against computer simulations with different state space models: infinite states, finite states, ordered states and an ‘inertial' model, simulating phylogenetic constraints. Of these, only the infinite states model results in evolution without homoplasy, a prediction which is not generally met by real phylogenies. Many authors have interpreted the ubiquity of homoplasy as evidence that the number of evolutionary alternatives is finite. However, homoplasy is also predicted by phylogenetic constraints on the morphological distance that can be traversed between ancestor and descendent. Phylogenetic rarefaction (sub-sampling) shows that finite and inertial state spaces do produce contrasting trends in the distribution of homoplasy. Two clades show trends characteristic of phylogenetic inertia, with decreasing homoplasy (increasing consistency index) as we sub-sample more distantly related taxa. One clade shows increasing homoplasy, suggesting exhaustion of finite states. Different clades may, therefore, show different patterns of character evolution. However, when parsimony uninformative characters are excluded (which may occur without documentation in cladistic studies), it may no longer be possible to distinguish inertial and finite state spaces. Interestingly, inertial models predict that homoplasy should be clustered among comparatively close relatives (parallel evolution), whereas finite state models do not. If morphological evolution is often inertial in nature, then homoplasy (false homology) may primarily occur between close relatives, perhaps being replaced by functional analogy at higher taxonomic scales.

On the Construction of Relativistic Representation Spaces in Functional Quantum Theory of the Nonlinear Spinor Field

1975 ◽  
Vol 30 (11) ◽  
pp. 1361-1371 ◽  
Author(s):  
H. Stumpf ◽  
K. Scheerer
Keyword(s):  
Quantum Theory ◽  
State Space ◽  
Functional State ◽  
Spinor Field ◽  
Function Spaces ◽  
The State ◽  
Nonlinear Spinor ◽  
Spinor Theory ◽  
State Spaces ◽  
Representation Spaces

Functional quantum theory is defined by an isomorphism of the state space H of a conventional quantum theory into an appropriate functional state space D It is a constructive approach to quantum theory in those cases where the state spaces H of physical eigenstates cannot be calculated explicitly like in nonlinear spinor field quantum theory. For the foundation of functional quantum theory appropriate functional state spaces have to be constructed which have to be representation spaces of the corresponding invariance groups. In this paper, this problem is treated for the spinor field. Using anticommuting source operator, it is shown that the construction problem of these spaces is tightly connected with the construction of appropriate relativistic function spaces. This is discussed in detail and explicit representations of the function spaces are given. Imposing no artificial restrictions it follows that the resulting functional spaces are indefinite. Physically the indefiniteness results from the inclusion of tachyon states. It is reasonable to assume a tight connection of these tachyon states with the ghost states introduced by Heisenberg for the regularization of the nonrenormalizable spinor theory

scholarly journals Evolving Functional and Structural Dynamism in Coupled Boolean Networks

2014 ◽  
Vol 20 (4) ◽  
pp. 441-455 ◽  
Author(s):  
Larry Bull
Keyword(s):  
Network Model ◽  
Significant Role ◽  
Regulatory Network ◽  
Boolean Networks ◽  
Network Node ◽  
Mobile Dna ◽  
Natural Systems ◽  
Node Connectivity ◽  
And Function

This article uses a recently presented abstract, tunable Boolean regulatory network model to further explore aspects of mobile DNA, such as transposons. The significant role of mobile DNA in the evolution of natural systems is becoming increasingly clear. This article shows how dynamically controlling network node connectivity and function via transposon-inspired mechanisms can be selected for to significant degrees under coupled regulatory network scenarios, including when such changes are heritable. Simple multicellular and coevolutionary versions of the model are considered.

scholarly journals Modular State Space Analysis of Coloured Petri Nets

1997 ◽  
Vol 26 (524) ◽  
Author(s):  
Søren Christensen ◽  
Laure Petrucci
Keyword(s):  
Petri Nets ◽  
State Space ◽  
The State ◽  
Total System ◽  
Entire System ◽  
State Spaces ◽  
Space Analysis ◽  
State Space Analysis ◽  
Full State ◽  
Local Properties

<p>State Space Analysis is one of the most developed analysis methods for Petri Nets. The main problem of state space analysis is the size of the state spaces. Several ways to reduce it have been proposed but cannot yet handle industrial size systems.</p><p>Large models often consist of a set of modules. Local properties of each module can be checked separately, before checking the validity of the entire system. We want to avoid the construction of a single state space of the entire system.</p><p>When considering transition sharing, the behaviour of the total system can be capture by the state spaces of modules combined with a Synchronisation Graph. To verify that we do not lose information we show how the full state space can be conctructed.</p><p>We show how it is possible to determine usual Petri Nets properites, without unfolding to the ordinary state space.</p>

Sign in / Sign up

Export Citation Format

Share Document