In this article, we show that magnitude homology and path are closely related, give some applications. We define differentials MH k ℓ ( G ) ⟶ − 1 $\operatorname{MH}^{\ell }_k(G) \longrightarrow \operatorname{MH}^{\ell -1}_{k-1}(G)$ between homologies of a digraph $G$ , which make them chain complexes. Then its $\mathcal {MH}^{\ell }_k(G)$ is non-trivial homotopy invariant in the context ‘homoto...

background: lipophosphoglycan 3 (lpg3) is required for the lpg assembly, a well known virulent molecule. in this study, the lpg3 gene of the lizard and mammalian leishmania species were cloned and sequenced. a three-dimensional structure (3d) for the target sequence was also predicted by comparative (homology) modeling. materials and methods: an optimization pcr amplification was performed on g...

background: luxi is a component of the quorum sensing signaling pathway in vibrio fischeri responsible for the inducer synthesis that is essential for bioluminescence. methods: homology modeling of luxi was carried out using phyre2 and refined with the galaxyweb server. five models were generated and evaluated by errat, anolea, qmean6, and procheck. results: five refined models were generated b...

medicinal use of the opium poppy (papaver somniferum l) has ancient history, but the isolation of morphine was not described until the early nineteenth century. morphine is the most important alkaloid of opium poppy in the last 50 years. in the morphine pathway has been reported to generate morphine in this species, codm has a crucial role as the gene coding the enzyme responsible for demethyla...

In this paper, we prove an $\mathbb{A}^1$-homology version of the Whitehead theorem with dimension bound. We also excision for $\mathbb{A}^1$-homology, Suslin homology, and $\mathbb{A}^1$-homotopy sheaves. order to these results, develop a general theory relative sheaves establish weak comparison result between $\mathbb{A}^1$- homology. As example as application results above, compute hyperplan...