Unshuffling Permutations: Trivial Bijections and Compositions

International audienc

Pattern Matching for k-Track Permutations

International audienceGiven permutations τ and π, the permutation pattern (PP) problem is to decide whether π occurs in τ as an order-isomorphic subsequence. Although an FPT algorithm is known for PP parameterized by the size of the pattern |π| [Guillemot and Marx 2014], the high complexity of this algorithm makes it impractical for most instances. In this paper we approach the PP problem from k-track permutations, i.e. those permutations that are the union of k increasing patterns or, equivalently, those permutation that avoid the decreasing pattern (k+1)k…1. Recently, k-track permutations have been shown to be central combinatorial objects in the study of the PP problem. Indeed, the PP problem is NP-complete when π is 321-avoiding and τ is 4321-avoiding but is solvable in polynomial-time if both π and τ avoid 321. We propose and implement an exact algorithm, FPT for parameters k and |π|, which allows to solve efficiently some large instances

Nrf2-interacting nutrients and COVID-19 : time for research to develop adaptation strategies

There are large between- and within-country variations in COVID-19 death rates. Some very low death rate settings such as Eastern Asia, Central Europe, the Balkans and Africa have a common feature of eating large quantities of fermented foods whose intake is associated with the activation of the Nrf2 (Nuclear factor (erythroid-derived 2)-like 2) anti-oxidant transcription factor. There are many Nrf2-interacting nutrients (berberine, curcumin, epigallocatechin gallate, genistein, quercetin, resveratrol, sulforaphane) that all act similarly to reduce insulin resistance, endothelial damage, lung injury and cytokine storm. They also act on the same mechanisms (mTOR: Mammalian target of rapamycin, PPAR gamma:Peroxisome proliferator-activated receptor, NF kappa B: Nuclear factor kappa B, ERK: Extracellular signal-regulated kinases and eIF2 alpha:Elongation initiation factor 2 alpha). They may as a result be important in mitigating the severity of COVID-19, acting through the endoplasmic reticulum stress or ACE-Angiotensin-II-AT(1)R axis (AT(1)R) pathway. Many Nrf2-interacting nutrients are also interacting with TRPA1 and/or TRPV1. Interestingly, geographical areas with very low COVID-19 mortality are those with the lowest prevalence of obesity (Sub-Saharan Africa and Asia). It is tempting to propose that Nrf2-interacting foods and nutrients can re-balance insulin resistance and have a significant effect on COVID-19 severity. It is therefore possible that the intake of these foods may restore an optimal natural balance for the Nrf2 pathway and may be of interest in the mitigation of COVID-19 severity.Peer reviewe