Fractional Gradient Descent-Based Auxiliary Model Algorithm for FIR Models with Missing Data

Tang, Jia

doi:10.1155/2023/7527478

Cited by 1 publication

(1 citation statement)

References 32 publications

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“…We can then proceed to compute the fractional gradient descent, post hoc, to a preliminary imputation step to estimate missing or latent data points 62 , 63 , 69 , 70 . We can combine a small learning rate with a constant (stochastic) or mini-batch update protocol concomitantly with several novel algorithmic approaches to accomplish these steps 62 , 63 , 69 , 70 , …”

Section: Resultsmentioning

confidence: 99%

A mathematically rigorous algorithm to define, compute and assess relevance of the probable dissociation constants in characterizing a biochemical network

Kundu

2024

Sci Rep

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Metabolism results from enzymatic- and non-enzymatic interactions of several molecules, is easily parameterized with the dissociation constant and occurs via biochemical networks. The dissociation constant is an empirically determined parameter and cannot be used directly to investigate in silico models of biochemical networks. Here, we develop and present an algorithm to define, compute and assess the relevance of the probable dissociation constant for every reaction of a biochemical network. The reactants and reactions of this network are modelled by a stoichiometry number matrix. The algorithm computes the null space and then serially generates subspaces by combinatorially summing the spanning vectors that are non-trivial and unique. This is done until the terms of each row either monotonically diverge or form an alternating sequence whose terms can be partitioned into subsets with almost the same number of oppositely signed terms. For a selected null space-generated subspace the algorithm utilizes several statistical and mathematical descriptors to select and bin terms from each row into distinct outcome-specific subsets. The terms of each subset are summed, mapped to the real-valued open interval $$\left(0,\infty \right)$$ 0 , ∞ and used to populate a reaction-specific outcome vector. The p1-norm for this vector is then the probable dissociation constant for this reaction. These steps are continued until every reaction of a modelled network is unambiguously annotated. The assertions presented are complemented by computational studies of a biochemical network for aerobic glycolysis. The fundamental premise of this work is that every row of a null space-generated subspace is a valid reaction and can therefore, be modelled as a reaction-specific sequence vector with a dimension that corresponds to the cardinality of the subspace after excluding all trivial- and redundant-vectors. A major finding of this study is that the row-wise sum or the sum of the terms contained in each reaction-specific sequence vector is mapped unambiguously to a positive real number. This means that the probable dissociation constants, for all reactions, can be directly computed from the stoichiometry number matrix and are suitable indicators of outcome for every reaction of the modelled biochemical network. Additionally, we find that the unambiguous annotation for a biochemical network will require a minimum number of iterations and will determine computational complexity.

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Section: Resultsmentioning

confidence: 99%

A mathematically rigorous algorithm to define, compute and assess relevance of the probable dissociation constants in characterizing a biochemical network

Kundu

2024

Sci Rep

View full text Add to dashboard Cite

show abstract

Fractional Gradient Descent-Based Auxiliary Model Algorithm for FIR Models with Missing Data

Cited by 1 publication

References 32 publications

A mathematically rigorous algorithm to define, compute and assess relevance of the probable dissociation constants in characterizing a biochemical network

A mathematically rigorous algorithm to define, compute and assess relevance of the probable dissociation constants in characterizing a biochemical network

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