Exact and approximate mean first passage times on trees and other necklace structures: a local equilibrium approach

Förster, Yanik-Pascal; Gamberi, Luca; Tzanis, Evan; Vivo, Pierpaolo; Annibale, Alessia

doi:10.1088/1751-8121/ac4ece

Cited by 7 publications

(3 citation statements)

References 33 publications

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“…For tree-graphs, which we consider in this manuscript, and generally for graphs in which two sets of nodes exist that are connected by a single edge, one can find more explicit formulae for MFPTs. As we have shown elsewhere [34], if we can coarse-grain the network into clusters 0, . .…”

Section: Brief Review Of Mfptsmentioning

confidence: 87%

Information retrieval and structural complexity of legal trees

Förster¹,

Annibale²,

Gamberi³

et al. 2022

J. Phys. Complex.

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We introduce a model for the retrieval of information hidden in legal texts. These are typically organised in a hierarchical (tree) structure, which a reader interested in a given provision needs to explore down to the “deepest” level (articles, clauses,...). We assess the structural complexity of legal trees by computing the mean ﬁrst-passage time a random reader takes to retrieve information planted in the leaves. The reader is assumed to skim through the content of a legal text based on their interests/keywords, and be drawn towards the sought information based on keywords aﬃnity, i.e. how well the Chapters/Section headers of the hierarchy seem to match the informational content of the leaves. Using randomly generated keyword patterns, we investigate the eﬀect of two main features of the text – the horizontal and vertical coherence – on the searching time, and consider ways to validate our results using real legal texts. We obtain numerical and analytical results, the latter based on a mean-ﬁeld approximation on the level of patterns, which lead to an explicit expression for the complexity of legal trees as a function of the structural parameters of the model.

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Section: Brief Review Of Mfptsmentioning

confidence: 87%

Information retrieval and structural complexity of legal trees

Förster¹,

Annibale²,

Gamberi³

et al. 2022

J. Phys. Complex.

Self Cite

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“…Correct pseudotemporal ordering is an essential and computationally intensive part of the TI algorithms. Here we use a particular formulation (and modification) of the idea of expected hitting time 42 . We calculate the expected number of random steps necessary to reach any cell in a dataset from the cell of origin.…”

Section: Pseudotime and Random Walks Simulationmentioning

confidence: 99%

Deconstructing Complexity: A Computational Topology Approach to Trajectory Inference in the Human Thymus withtviblindi

Stuchly,

Novak,

Brdickova

et al. 2023

Preprint

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Interpreting and understanding complex, organ-level mass cytometry datasets represents a formidable interdisciplinary challenge. This study aims to identify, describe, and interpret potential developmental trajectories of thymocytes and mature T cells. We developedtviblindi, a trajectory inference algorithm that integrates several autonomous modules - pseudotime inference, random walk simulations, real-time topological classification using persistence homology, and autoencoder-based 2D visualization using thevaevictisalgorithm. This integration facilitates an interactive exploration of developmental trajectories. The utility and proficiency oftviblindiare demonstrated through comprehensive analysis of the thymic and peripheral T-cell compartment. Our approach not only uncovers and elucidates the canonical CD4 and CD8 development but also offers insights into various checkpoints such as TCRβ selection and positive/negative selection, elucidating the crossroads between further development and apoptosis. Finally, we identify and thoroughly characterize thymic regulatory T cells, tracing their development from the negative selection stage to mature thymic regulatory T cells with an extensive proliferation history and an immunophenotype of activated and recirculating cells.tviblindiis a versatile and generic approach suitable for any single-cell dataset, equipping biologists with an effective tool for interpreting complex data.

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“…where E[T FP |SPATH] is given by equation ( 48) and E[T FP |¬SPATH] is given by equation ( 65). The mean first passage time T FP was recently calculated for specific network instances and a given pair of initial and target nodes [17,[38][39][40]. These calculations were done using matrix methods that apply to a wide range of network structures including weighted networks.…”

Section: The Overall Distribution Of First-passage Timesmentioning

confidence: 99%

Analytical results for the distribution of first-passage times of random walks on random regular graphs

2022

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We present analytical results for the distribution of first-passage (FP) times of random walks (RWs) on random regular graphs that consist of N nodes of degree c ⩾ 3. Starting from a random initial node at time t = 0, at each time step t ⩾ 1 an RW hops into a random neighbor of its previous node. In some of the time steps the RW may hop into a yet-unvisited node while in other time steps it may revisit a node that has already been visited before. We calculate the distribution P(T FP = t) of first-passage times from a random initial node i to a random target node j, where j ≠ i. We distinguish between FP trajectories whose backbone follows the shortest path (SPATH) from the initial node i to the target node j and FP trajectories whose backbone does not follow the shortest path (¬SPATH). More precisely, the SPATH trajectories from the initial node i to the target node j are defined as trajectories in which the subnetwork that consists of the nodes and edges along the trajectory is a tree network. Moreover, the shortest path between i and j on this subnetwork is the same as in the whole network. The SPATH scenario is probable mainly when the length ℓ ij of the shortest path between the initial node i and the target node j is small. The analytical results are found to be in very good agreement with the results obtained from computer simulations.

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Exact and approximate mean first passage times on trees and other necklace structures: a local equilibrium approach

Cited by 7 publications

References 33 publications

Information retrieval and structural complexity of legal trees

Information retrieval and structural complexity of legal trees

Deconstructing Complexity: A Computational Topology Approach to Trajectory Inference in the Human Thymus withtviblindi

Analytical results for the distribution of first-passage times of random walks on random regular graphs

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