Irreducible compositions and the first return to the origin of a random walk

Let $n = b_1 + ... + b_k = b_1' + \cdot + b_k'$ be a pair of compositions of $n$ into $k$ positive parts. We say this pair is {\em irreducible} if there is no positive $j < k$ for which $b_1 + ... b_j = b_1' + ... b_j'$. The probability that a random pair of compositions of $n$ is irreducible is shown to be asymptotic to $8/n$. This problem leads to a problem in probability theory. Two players move along a game board by rolling a die, and we ask when the two players will first coincide. A natural extension is to show that the probability of a first return to the origin at time $n$ for any mean-zero variance $V$ random walk is asymptotic to $\sqrt{V/(2 \pi)} n^{-3/2}$. We prove this via two methods, one analytic and one probabilistic

Phylogenetic Investigation of the Aliphatic, Non-hydrolyzable Biopolymer Algaenan, with a Focus on Green Algae

Algaenan, an aliphatic biopolymer found in various microalgae, has been implicated as the source of a sizable proportion of the aliphatic refractory organic matter in sedimentary rocks. Because of its recalcitrant nature, algaenan is thought to be preserved selectively in the formation of kerogen and microfossils. Its taxonomic distribution in organisms has not been studied in detail or in a phylogenetic context. Here, we evaluate the distribution and phylogenetic relationships of algaenan-producing organisms from a broad, eukaryote-wide perspective down to the level of genus and species. We focus on the kingdom Plantae, as most described algaenan producers belong to this superkingdom. The phylogenetic distribution of algaenan producers within the Plantae is actually quite limited and a detailed phylogenetic analysis of the two classes that include all green algal algaenan producers suggests that there is no finer-grained pattern of phylogenetic distribution to the production of this biopolymer. Our results suggest that the biopolymer is not widespread ecologically or phylogenetically, is not found abundantly in marine organisms and likely represents a functional description of molecular class, rather than a biomarker for green algae. This adds to a growing body of literature that questions the selective preservation hypothesis for insoluble organic matter and calls for a more detailed chemical and structural analysis of algaenan.Organismic and Evolutionary Biolog

Production of tetra-methylpyrazine using engineered Corynebacterium glutamicum.

Corynebacterium glutamicum ATCC 13032 is an established and industrially-relevant microbial host that has been utilized for the expression of many desirable bioproducts. Tetra-methylpyrazine (TMP) is a naturally occurring alkylpyrazine with broad applications spanning fragrances to resins. We identified an engineered strain of C.&nbsp;glutamicum which produces 5&nbsp;​g/L TMP and separately, a strain which can co-produce both TMP and the biofuel compound isopentenol. Ionic liquids also stimulate TMP production in engineered strains. Using a fed batch-mode feeding strategy, ionic liquid stimulated strains produced 2.2&nbsp;​g/L of tetra-methylpyrazine. We show that feedback from a specific heterologous gene pathway on host physiology leads to acetoin accumulation and the production of TMP

Description of a New Blood-fluke, \u3ci\u3eCruoricola lates\u3c/i\u3e n. g., n. sp. (Digenea: Sanguinicolidae), from Sea-bass \u3ci\u3eLates calcarifer\u3c/i\u3e (Bloch, 1790) (Centropomidae)

A new blood-fluke, Cruoricola lates n. g., n. sp., is described from sea-bass Lates calcarifer cultured in Malaysia. It is also found in Thailand and Australia. All fish examined over 15 cm in length were infected in the type-locality. This sanguinicolid is differentiated from other genera by the spherical seminal vesicle; the large, single testis extending beyond the intestinal caeca; the medial, bi-lobed ovary; and the single column of submarginal, laterally directed, evenly spaced spines. It has separate genital pores which are close together. Adults are found predominantly in the mesenteric venules of the venous circulation. Juveniles are commonest in the caudal kidney

Digital innovation management for entrepreneurial ecosystems: services and functionalities as drivers of innovation management software adoption

Innovation Management Software can promote Entrepreneurial Ecosystems by consolidating an organization’s innovation programs, stakeholders, and resources in one place. In this study, we highlighted the digitalization of innovation processes. We focus particularly on the factors influencing the adoption of a specific class of software tools called Innovation Management Software (IMS) or Digital Innovation Management System to support innovation management methods and activities. Specifically, we address the two questions (a) which specific functionality drives the adoption of IMS tools, and (b) which services of IMS providers are valuable in supporting the adoption of IMS by organizations aiming to digitalize their innovation processes. By using an online questionnaire, we gathered survey data from 199 innovation managers of German firms. We used regression analysis to test our hypotheses. While the overall IMS adoption is considered to positively affect the new product development (NPD) efficiency, our results indicate that especially idea management functionalities and services for updates and upgrades improve the IMS adoption. Surprisingly, offering complementary consulting services together with IMS offerings to support the digitalization of innovation processes reduces the likelihood of IMS adoption. These findings are important for managers, consultants, and developers in order to choose and leverage the right options for improving the adoption of IT tools in the NPD process and therefore increase NPD performance and thus also promote Entrepreneurial Ecosystems