<p>By sequencing the cells in several samples of a cancer mass, we can obtain the frequency of mutations occurring in the samples genomes. The variant allele frequencies factorization problem which leads to finding a phylogenetic tree showing the ancestral relationships between clones has attracted many researchers. Since real data are obtained from sequencing cells, they are prone to errors and suffer from uncertainty. In this paper, the robust mathematical formulations of this problem are proposed with different uncertainty sets. The robust model is defined under the uncertainty sets proposed by Bertsimas and Sim, the ellipsoidal, the interval, and the intersection of the ellipsoidal and interval uncertainty sets, then the results are compared. Since the interval uncertainty set is more conservative than the ellipsoidal and the intersection of the ellipsoidal and interval, it demonstrates greater robustness against data uncertainty. Consequently, in such problems, the resulting phylogenetic tree that illustrates the progression of cancer is more reliable. In the robust model under ellipsoidal and interval uncertainty sets, adjusting the parameters to increase model robustness yields a more reliable output.</p>

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Robust mathematical formulations for the two state phylogenetic tree reconstruction

  • Razieh Enayatsefat,
  • Mehri Bagherian,
  • Hamidreza Vaziri

摘要

By sequencing the cells in several samples of a cancer mass, we can obtain the frequency of mutations occurring in the samples genomes. The variant allele frequencies factorization problem which leads to finding a phylogenetic tree showing the ancestral relationships between clones has attracted many researchers. Since real data are obtained from sequencing cells, they are prone to errors and suffer from uncertainty. In this paper, the robust mathematical formulations of this problem are proposed with different uncertainty sets. The robust model is defined under the uncertainty sets proposed by Bertsimas and Sim, the ellipsoidal, the interval, and the intersection of the ellipsoidal and interval uncertainty sets, then the results are compared. Since the interval uncertainty set is more conservative than the ellipsoidal and the intersection of the ellipsoidal and interval, it demonstrates greater robustness against data uncertainty. Consequently, in such problems, the resulting phylogenetic tree that illustrates the progression of cancer is more reliable. In the robust model under ellipsoidal and interval uncertainty sets, adjusting the parameters to increase model robustness yields a more reliable output.