Morten Brun

On the multiplicative structure of topological Hochschild homology

We show that the topological Hochschild homology THH.R/ of an En ‐ring spectrum R is an En 1 ‐ring spectrum. The proof is based on the fact that the tensor product of the operad Ass for monoid structures and the little n‐cubes operad Cn is an EnC1 ‐operad, a result which is of independent interest. 55P43; 18D50

The use of heuristics in intuitive mathematical judgment

Anecdotal evidence points to the use of beauty as an indication of truth in mathematical problem solving. In the two experiments of the present study, we examined the use of heuristics and tested the assumption that participants use symmetry as a cue for correctness in an arithmetic verification task. We manipulated the symmetry of sets of dot pattern addition equations. Speeded decisions about the correctness of these equations led to higher endorsements for both correct and incorrect equations when the addend and sum dot patterns were symmetrical. Therefore, this effect is not due to the fact that symmetry facilitates calculation or estimation. We found systematic evidence for the use of heuristics in solving mathematical tasks, and we discuss how these findings relate to a processing-fluency account of intuition in mathematical judgment.

The Auslander–Reiten translate on monomial rings

Abstract For t in N n , E. Miller has defined a category of positively t-determined modules over the polynomial ring S in n variables. We consider the Auslander–Reiten translate, N t , on the (derived) category of such modules. A monomial ideal I is t-determined if each generator x a has a ⩽ t . We compute the multigraded cohomology and Betti spaces of N t k ( S / I ) for every iterate k and also the S-module structure of these cohomology modules. This comprehensively generalizes results of Hochster and Grabe on local cohomology of Stanley–Reisner rings.

Betti Numbers of ℤ n -Graded Modules

Abstract Let S = K[X 1,…, X n ] be the polynomial ring over a field K. For bounded below ℤ n -graded S-modules M and N we show that if , then for 0 ≤ i ≤ p, the dimension of the K-vector space is at least . In particular, we get lower bounds for the total Betti numbers of such modules. These results are related to a conjecture of Buchsbaum and Eisenbud.

RNA-Seq analysis of transcriptome responses in Atlantic cod (Gadus morhua) precision-cut liver slices exposed to benzo[a]pyrene and 17α-ethynylestradiol

Polycyclic aromatic hydrocarbons such as benzo[a]pyrene (BaP) that activate the aryl hydrocarbon receptor (Ahr) pathway, and endocrine disruptors acting through the estrogen receptor pathway are among environmental pollutants of major concern. In this work, we exposed Atlantic cod (Gadus morhua) precision-cut liver slices (PCLS) to BaP (10 nM and 1000 nM), ethynylestradiol (EE2) (10 nM and 1000 nM), and equimolar mixtures of BaP and EE2 (10 nM and 1000 nM) for 48 h, and performed RNA-Seq based transcriptome mapping followed by systematic bioinformatics analyses. Our gene expression analysis showed that several genes were differentially expressed in response to BaP and EE2 treatments in PCLS. Strong up-regulation of genes coding for the cytochrome P450 1a (Cyp1a) enzyme and the Ahr repressor (Ahrrb) was observed in BaP treated PCLS. EE2 treatment of liver slices strongly up-regulated genes coding for precursors of vitellogenin (Vtg) and eggshell zona pellucida (Zp) proteins. As expected, pathway enrichment and network analysis showed that the Ahr and estrogen receptor pathways are among the top affected by BaP and EE2 treatments, respectively. Interestingly, two genes coding for fibroblast growth factor 3 (Fgf3) and fibroblast growth factor 4 (Fgf4) were up-regulated by EE2 in this study. To our knowledge, the fgf3 and fgf4 genes have not previously been described in relation to estrogen signaling in fish liver, and these results suggest the modulation of the FGF signaling pathway by estrogens in fish. The signature expression profiles of top differentially expressed genes in response to the single compound (BaP or EE2) treatment were generally maintained in the expression responses to the equimolar binary mixtures. However, in the mixture-treated groups, BaP appeared to have anti-estrogenic effects as observed by lower number of differentially expressed putative EE2 responsive genes. Our in-depth quantitative analysis of changes in liver transcriptome in response to BaP and EE2, using PCLS tissue culture provides further mechanistic insights into effects of the compounds. Moreover, the analyses demonstrate the usefulness of PCLS in cod for omics experiments.