On the nonexistence of k reptile simplices in ℝ^3 and ℝ^4

A d-dimensional simplex S is called a k-reptile (or a k-reptile simplex) if it can be tiled by k simplices with disjoint interiors that are all mutually congruent and similar to S. For d = 2, triangular k-reptiles exist for all k of the form a^2, 3a^2 or a^2+b^2 and they have been completely characterized by Snover, Waiveris, and Williams. On the other hand, the only k-reptile simplices that are known for d ≥ 3, have k = m^d, where m is a positive integer. We substantially simplify the proof by Matoušek and the second author that for d = 3, k-reptile tetrahedra can exist only for k = m^3. We then prove a weaker analogue of this result for d = 4 by showing that four-dimensional k-reptile simplices can exist only for k = m^2

Leibniz International Proceedings in Information, LIPIcs

We prove that for every d ≥ 2, deciding if a pure, d-dimensional, simplicial complex is shellable is NP-hard, hence NP-complete. This resolves a question raised, e.g., by Danaraj and Klee in 1978. Our reduction also yields that for every d ≥ 2 and k ≥ 0, deciding if a pure, d-dimensional, simplicial complex is k-decomposable is NP-hard. For d ≥ 3, both problems remain NP-hard when restricted to contractible pure d-dimensional complexes

Scientific opinion on the safety of monacolins in red yeast rice

The Panel on Food Additives and Nutrient Sources added to Food (ANS) was asked to deliver a scientific opinion on the safety of monacolins in red yeast rice (RYR) and to provide advice on a dietary intake of monacolins that does not give rise to concerns about harmful effects to health. The Panel reviewed the scientific evidences available as well as the information provided by interested parties in response of a public ‘Call for data’ launched by EFSA. The Panel considered that monacolin K in lactone form is identical to lovastatin, the active ingredient of several medicinal products authorised for the treatment of hypercholesterolaemia in the EU. On the basis of the information available, the Panel concluded that intake of monacolins from RYR via food supplements, could lead to estimated exposure to monacolin K within the range of the therapeutic doses of lovastatin. The Panel considered that the available information on the adverse effects reported in humans were judged to be sufficient to conclude that monacolins from RYR when used as food supplements were of significant safety concern at the use level of 10 mg/day. The Panel further considered that individual cases of severe adverse reactions have been reported for monacolins from RYR at intake levels as low as 3 mg/day. The Panel concluded that exposure to monacolin K from RYR could lead to severe adverse effects on musculoskeletal system, including rhabdomyolysis, and on the liver. In the reported cases, the product contained other ingredients in addition to RYR. However, these reported effects in particular musculoskeletal effects, have both occurred after ingestion of monacolin K and lovastatin independently. On the basis of the information available and several uncertainties highlighted in this opinion, the Panel was unable to identify a dietary intake of monacolins from RYR that does not give rise to concerns about harmful effects to health, for the general population, and as appropriate, for vulnerable subgroups of the population

Talaromyces atroroseus, a new species efficiently producing industrially relevant red pigments

Some species of Talaromyces secrete large amounts of red pigments. Literature has linked this character to species such as Talaromyces purpurogenus, T. albobiverticillius, T. marneffei, and T. minioluteus often under earlier Penicillium names. Isolates identified as T. purpurogenus have been reported to be interesting industrially and they can produce extracellular enzymes and red pigments, but they can also produce mycotoxins such as rubratoxin A and B and luteoskyrin. Production of mycotoxins limits the use of isolates of a particular species in biotechnology. Talaromyces atroroseus sp. nov., described in this study, produces the azaphilone biosynthetic families mitorubrins and Monascus pigments without any production of mycotoxins. Within the red pigment producing clade, T. atroroseus resolved in a distinct clade separate from all the other species in multigene phylogenies (ITS, β-tubulin and RPB1), which confirm its unique nature. Talaromyces atroroseus resembles T. purpurogenus and T. albobiverticillius in producing red diffusible pigments, but differs from the latter two species by the production of glauconic acid, purpuride and ZG-1494α and by the dull to dark green, thick walled ellipsoidal conidia produced. The type strain of Talaromyces atroroseus is CBS 133442

Mathematical modelling of clostridial acetone-butanol-ethanol fermentation

Clostridial acetone-butanol-ethanol (ABE) fermentation features a remarkable shift in the cellular metabolic activity from acid formation, acidogenesis, to the production of industrial-relevant solvents, solventogensis. In recent decades, mathematical models have been employed to elucidate the complex interlinked regulation and conditions that determine these two distinct metabolic states and govern the transition between them. In this review, we discuss these models with a focus on the mechanisms controlling intra- and extracellular changes between acidogenesis and solventogenesis. In particular, we critically evaluate underlying model assumptions and predictions in the light of current experimental knowledge. Towards this end, we briefly introduce key ideas and assumptions applied in the discussed modelling approaches, but waive a comprehensive mathematical presentation. We distinguish between structural and dynamical models, which will be discussed in their chronological order to illustrate how new biological information facilitates the ‘evolution’ of mathematical models. Mathematical models and their analysis have significantly contributed to our knowledge of ABE fermentation and the underlying regulatory network which spans all levels of biological organization. However, the ties between the different levels of cellular regulation are not well understood. Furthermore, contradictory experimental and theoretical results challenge our current notion of ABE metabolic network structure. Thus, clostridial ABE fermentation still poses theoretical as well as experimental challenges which are best approached in close collaboration between modellers and experimentalists