Function-Oriented and Modular (+/−)-cis-Pseudoguaianolide Synthesis: Discovery of New Nrf2 Activators and NF-κB Inhibitors

Described herein is a function-oriented synthesis route and biological evaluation of pseudoguaianolide analogues. The 10-step synthetic route developed retains the topological complexity of the natural product, installs functional handles for late-stage diversification, and forges the key bioactive Michael acceptors early in the synthesis. The analogues were found to be low-micromolar Nrf2 activators and micromolar NF-κB inhibitors and dependent on the local environment of the Michael acceptor moieties.     

On oriented supersingular elliptic curves

We revisit theoretical background on OSIDH (Oriented Supersingular Isogeny Diffie-Hellman protocol), which is an isogeny-based key-exchange protocol proposed by Colò and Kohel at NutMiC 2019. We give a proof of a fundamental theorem for OSIDH. The theorem was stated by Colò and Kohel without proof. Furthermore, we consider parameters of OSIDH, give a sufficient condition on the parameters for the protocol to work, and estimate the size of the parameters for a certain security level.     

Sharp Dirac's theorem for DP‐critical graphs

Correspondence coloring, or DP‐coloring, is a generalization of list coloring introduced recently by Dvořák and Postle [11]. In this article, we establish a version of Dirac's theorem on the minimum number of edges in critical graphs [9] in the framework of DP‐colorings. A corollary of our main result answers a question posed by Kostochka and Stiebitz [15] on classifying list‐critical graphs that satisfy Dirac's bound with equality.     

Verlinde模性范畴上的Casimir数及其应用

本文计算了秩为n+1的一类特殊的Verlinde模性范畴L的Casimir数,计算结果表明该Casimir数为2n+4.作为应用,由Higman定理知域K上的Grothendieck代数Gr(L)_Z K是半单代数当且仅当2n+4在域K中不为零.这也给出了第二类型n+1次Dickson多项式E_(n+1)(X)在K[X]中无重因式的一个等价刻画.如果2n+4在域K中为零,借助于Dickson多项式的有关因式分解定理,本文完全给出了Grothendieck代数Gr(L)_Z K的Jacobson根.     

Postman problems on series–parallel mixed graphs

Given a strongly connected, mixed graph with costs on its edges and arcs, the mixed postman problem is to find a minimum cost closed walk traversing its edges and arcs at least once. This problem is NP-hard even on planar graphs but is solvable in polynomial time on series–parallel graphs. We give $O\left(n{m}^2\right)$ dynamic programming algorithms for the mixed postman problem and other similar problems on series–parallel graphs with $n$ vertices and $m$ edges and arcs.     

Learning marginal AMP chain graphs under faithfulness revisited

Marginal AMP chain graphs are a recently introduced family of models that is based on graphs that may have undirected, directed and bidirected edges. They unify and generalize the AMP and the multivariate regression interpretations of chain graphs. In this paper, we present a constraint based algorithm for learning a marginal AMP chain graph from a probability distribution which is faithful to it. We show that the marginal AMP chain graph returned by our algorithm is a distinguished member of its Markov equivalence class. We also show that our algorithm performs well in practice. Finally, we show that the extension of Meek's conjecture to marginal AMP chain graphs does not hold, which compromises the development of efficient and correct score+search learning algorithms under assumptions weaker than faithfulness.     

Algebraic Cayley graphs over finite fields

A new algebraic Cayley graph is constructed using finite fields. It provides a more flexible source of expander graphs. Its connectedness, the number of connected components, and diameter bound are studied via Weil's estimate for character sums. Furthermore, we study the algorithmic problem of computing the number of connected components and establish a link to the integer factorization problem.