\begin{algorithmic}[1]
\Statex Input: The underlying linear dynamical systems matrices $\tilde{B}$ and $\tilde{B'}$ and the correlations between each of the coordinates (corresponding to genes) and the two phenotypes of interest.
\Statex Output: A set of pathways of a given length $L$ that are prominently different between the two phenotypes.
\Statex $\triangleright$ Algorithm starts:
\State Compute and sort the list of genes in descending order in terms of the absolute value of their correlation coefficient with the pathological phenotype, denote this list as $\vec{g}$
\State Compute $C:= \mathrm{Diag}(\vec{g})(\tilde{B'}-\tilde{B})$
\State Fix a positive threshold $\theta$ and set $C_{ij}=0$ if $C_{ij}<\theta$, denote the resulting matrix as $\Pi_\theta$ 
\State Compute the set of paths of length $L$ in the graph with adjacency matrix $\Pi_\theta$ and return them.
\end{algorithmic}

\begin{algorithmic}
[1]
\Statex Input: The underlying linear dynamical systems matrices $\tilde{B}$ and $\tilde{B'}$ and the correlations between each of the coordinates (corresponding to genes) and the two phenotypes of interest.
\Statex Output: A set of pathways of a given length $L$ that are prominently different between the two phenotypes.
\Statex $\triangleright$ Algorithm starts:
\State Compute and sort the list of genes in descending order in terms of the absolute value of their correlation coefficient with the pathological phenotype, denote this list as $\vec{g}$
\State Compute $C:= \mathrm{Diag}(\vec{g})(\tilde{B'}-\tilde{B})$
\State Fix a positive threshold $\theta$ and set $C_{ij}=0$ if $C_{ij}<\theta$, denote the resulting matrix as $\Pi_\theta$
\State Compute the set of paths of length $L$ in the graph with adjacency matrix $\Pi_\theta$ and return them.
\end{algorithmic}
{
    "title": "approximating a linear dynamical system from non-sequential data",
    "id": "2401.11858",
    "abstract": "given non-sequential snapshots from instances of a dynamical system, we design a compressed sensing based algorithm that reconstructs the dynamical system. we formally prove that successful reconstruction is possible under the assumption that we can construct an approximate clock from a subset of the coordinates of the underlying system.   as an application, we argue that our assumption is likely true for genomic datasets, and we recover the underlying nuclear receptor networks and predict pathways, as opposed to genes, that may differentiate phenotypes in some publicly available datasets.",
    "categories": "q-bio.gn",
    "doi": "",
    "created": "2024-01-22",
    "updated": "",
    "authors": [
        "cliff stein",
        "pratik worah"
    ],
    "affiliation": [],
    "url": "https://arxiv.org/abs/2401.11858"
}
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