Ladderpath Approach: How Tinkering and Reuse Increase Complexity and Information

Liu, Yu; Di, Zengru; Gerlee, Philip

doi:10.3390/e24081082

Cited by 11 publications

(20 citation statements)

References 40 publications

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“…The Ladderpath approach, detailed in 15,31 , offers a quantitative approach to analyze structural information in systems, ranging from sequences, molecules to images. It iteratively identifies repeating substructures, called ladderons, which are essentially reused modules.…”

Section: A Ladderpath Characterizes Hierarchical Structuresmentioning

confidence: 99%

“…From this, we can establish a hierarchical relationship (and illustrate the laddergraph): the red substructure is encompassed within both the yellow and green ones. Nevertheless, directly calculating the laddergraph is quite challenging (and this problem is inherently NP-hard 15 ). Hence, we first transform the network into a set of sequences and then compute it (the method for this transformation will be detailed in Section III C, and there are already algorithms developed for computing laddergraphs of sequences up to 10,000 elements in length 31 ).…”

Section: A Ladderpath Characterizes Hierarchical Structuresmentioning

confidence: 99%

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Correlating Measures of Hierarchical Structures in Artificial Neural Networks with Their Performance

Xu,

Zhu,

Hong

et al. 2024

Preprint

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This study employs the recently developed Ladderpath approach, within the broader category of Algorithmic Information Theory, which characterizes the hierarchical and nesting relationships among repeating substructures, to explore the structure-function relationship in neural networks. The metric order-rate η, derived from the approach, is a measure of structural orderliness: when η is in the middle range (around 0.5), the structure exhibits the richest hierarchical relationships, corresponding to the highest complexity. We hypothesize that the highest structural complexity correlates with optimal functionality. Our experiments support this hypothesis in several ways: networks with η values in the middle range show superior performance, and the training processes tend to naturally adjust η towards this range; additionally, starting neural networks with η values in this middle range appears to boost performance. Intriguingly, these findings align with observations in other distinct systems, including chemical molecules and protein sequences, hinting at a hidden regularity encapsulated by this theoretical framework.

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Section: A Ladderpath Characterizes Hierarchical Structuresmentioning

confidence: 99%

Section: A Ladderpath Characterizes Hierarchical Structuresmentioning

confidence: 99%

Correlating Measures of Hierarchical Structures in Artificial Neural Networks with Their Performance

Xu,

Zhu,

Hong

et al. 2024

Preprint

Self Cite

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“…Note that there are various angles to characterize the 'complexity' of ecosystems [32][33][34], here the 'complexity' portrays the network connectance in our model [1,2]. Thus Community matrix of the unstructured ecosystem in (a), and the colour in each element corresponds to the interaction type shown in (a).…”

Section: Impact Of Connectance Within the Same Layer And Between Diff...mentioning

confidence: 99%

Stability of multi-layer ecosystems

Wang

Yang

et al. 2023

J. R. Soc. Interface.

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Community structure is reported to play a critical role in ecosystem stability, which indicates the ability of a system to return to equilibrium after perturbations. However, current studies rely on the assumption that the community consists of only a single-layer structure. In practice, multi-layer structures are common in ecosystems, e.g. the distributions of both microorganisms in strata and fish in the ocean usually stratify into multi-layer structures. Here we use multi-layer networks to model species interactions within each layer and between different layers, and study the stability of multi-layer ecosystems under different interaction types. We show that competitive interactions within each layer have a more substantial stabilizing effect in multi-layer ecosystems relative to their impact in single-layer ecosystems. Surprisingly, between different layers, we find that competition between species destabilizes the ecosystem. We further provide a theoretical analysis of the stability of multi-layer ecosystems and confirm the robustness of our findings for different connectances between layers, numbers of species in each layer, and numbers of layers. Our work provides a general framework for investigating the stability of multi-layer ecosystems and uncovers the double-sided role of competitive interactions in the stability of multi-layer ecosystems.

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“…As shown in Figure 3, an ideal gas THEORETICAL PERSPECTIVE ON MAN-MADE LIFE system and a crystal are two representative extreme cases: The former is close to the x-axis, indicating high λ but low ω, and the latter is close to the y-axis, indicating high ω but low λ (referring to ref. [136] for how to calculate the indices of the exemplified black dot patterns); while living systems have both high λ and high ω, resulting in high complexity.…”

Section: How To Evolve From Simple To Complex: Ladderpath Systemmentioning

confidence: 99%

“…The former, λ, quantitatively measures the cost and difficulty of constructing a target system, while the latter, ω, quantifies the degree of organization and hierarchical structures exhibited in the target system. Complexity can then be quantified by combining λ and ω in a certain way, for example, taking the product of the two [135,136]. As shown in Figure 3, an ideal gas THEORETICAL PERSPECTIVE ON MAN-MADE LIFE system and a crystal are two representative extreme cases: The former is close to the x-axis, indicating high λ but low ω, and the latter is close to the y-axis, indicating high ω but low λ (referring to ref.…”

Section: How To Evolve From Simple To Complex: Ladderpath Systemmentioning

confidence: 99%

Theoretical perspective on synthetic man‐made life: Learning from the origin of life

Peng,

Zhang,

Wang

et al. 2023

Quant. Biol.

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Creating a man‐made life in the laboratory is one of life science’s most intriguing yet challenging problems. Advances in synthetic biology and related theories, particularly those related to the origin of life, have laid the groundwork for further exploration and understanding in this field of artificial life or man‐made life. But there remains a wealth of quantitative mathematical models and tools that have yet to be applied to this area. In this paper, we review the two main approaches often employed in the field of man‐made life: the top‐down approach that reduces the complexity of extant and existing living systems and the bottom‐up approach that integrates well‐defined components, by introducing the theoretical basis, recent advances, and their limitations. We then argue for another possible approach, namely “bottom‐up from the origin of life”: Starting with the establishment of autocatalytic chemical reaction networks that employ physical boundaries as the initial compartments, then designing directed evolutionary systems, with the expectation that independent compartments will eventually emerge so that the system becomes free‐living. This approach is actually analogous to the process of how life originated. With this paper, we aim to stimulate the interest of synthetic biologists and experimentalists to consider a more theoretical perspective, and to promote the communication between the origin of life community and the synthetic man‐made life community.

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Ladderpath Approach: How Tinkering and Reuse Increase Complexity and Information

Cited by 11 publications

References 40 publications

Correlating Measures of Hierarchical Structures in Artificial Neural Networks with Their Performance

Correlating Measures of Hierarchical Structures in Artificial Neural Networks with Their Performance

Stability of multi-layer ecosystems

Theoretical perspective on synthetic man‐made life: Learning from the origin of life

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