Retinoic acid production, regulation and containment through Zic1, Pitx2c and Cyp26c1 control cranial placode specification

ABSTRACTAll paired sensory organs arise from a common precursor domain called the pre-placodal region (PPR). In Xenopus, Zic1 non-cell autonomously regulates PPR formation by activating retinoic acid (RA) production. Here, we have identified two Zic1 targets, the RA catabolizing enzyme Cyp26c1 and the transcription factor Pitx2c, expressed in the vicinity of the PPR as being crucially required for maintaining low RA levels in a spatially restricted, PPR-adjacent domain. Morpholino- or CRISPR/Cas9-mediated Cyp26c1 knockdown abrogated PPR gene expression, yielding defective cranial placodes. Direct measurement of RA levels revealed that this is mediated by a mechanism involving excess RA accumulation. Furthermore, we show that pitx2c is activated by RA and required for Cyp26c1 expression in a domain-specific manner through induction of FGF8. We propose that Zic1 anteriorly establishes a program of RA containment and regulation through activation of Cyp26c1 and Pitx2c that cooperates to promote PPR specification in a spatially restricted domain.

Faceted Classifications as Linked Data: A Logical Analysis

Faceted knowledge organization systems have sophisticated logical structures, making their representation as linked data a demanding task. The term facet is often used in ambiguous ways: while in thesauri facets only work as semantic categories, in classification schemes they also have syntactic functions. The need to convert the Integrative Levels Classification (ILC) into SKOS stimulated a more general analysis of the different kinds of syntactic facets, as can be represented in terms of RDF properties and their respective domain and range. A nomenclature is proposed, distinguishing between common facets, which can be appended to any class, that is, have an unrestricted domain; and special facets, which are exclusive to some class, that is, have a restricted domain. In both cases, foci can be taken from any other class (unrestricted range: free facets), or only from subclasses of an existing class (parallel facets), or be defined specifically for the present class (bound facets). Examples are given of such cases in ILC and in the Dewey Decimal Classification (DDC).

ON THE HYPERSTABILITY OF THE DRYGAS FUNCTIONAL EQUATION ON A RESTRICTED DOMAIN

We prove hyperstability results for the Drygas functional equation on a restricted domain (a certain subset of a normed space). Our results are more general than the ones proposed by Aiemsomboon and Sintunavarat [‘Two new generalised hyperstability results for the Drygas functional equation’, Bull. Aust. Math. Soc.95 (2017), 269–280] and our proof does not rely on the fixed point theorem of Brzdęk as was the case there. A characterisation of the Drygas functional equation in terms of its asymptotic behaviour is given. Several examples are given to illustrate our generalisations. Finally, we point out a misleading statement in the proof of the second result in the paper by Aiemsomboon and Sintunavarat and propose its correction.

Exhaustive Search for Various Types of MDS Matrices

MDS matrices are used in the design of diffusion layers in many block ciphers and hash functions due to their optimal branch number. But MDS matrices, in general, have costly implementations. So in search for efficiently implementable MDS matrices, there have been many proposals. In particular, circulant, Hadamard, and recursive MDS matrices from companion matrices have been widely studied. In a recent work, recursive MDS matrices from sparse DSI matrices are studied, which are of interest due to their low fixed cost in hardware implementation. In this paper, we present results on the exhaustive search for (recursive) MDS matrices over GL(4, F2). Specifically, circulant MDS matrices of order 4, 5, 6, 7, 8; Hadamard MDS matrices of order 4, 8; recursive MDS matrices from companion matrices of order 4; recursive MDS matrices from sparse DSI matrices of order 4, 5, 6, 7, 8 are considered. It is to be noted that the exhaustive search is impractical with a naive approach. We first use some linear algebra tools to restrict the search to a smaller domain and then apply some space-time trade-off techniques to get the solutions. From the set of solutions in the restricted domain, one can easily generate all the solutions in the full domain. From the experimental results, we can see the (non) existence of (involutory) MDS matrices for the choices mentioned above. In particular, over GL(4, F2), we provide companion matrices of order 4 that yield involutory MDS matrices, circulant MDS matrices of order 8, and establish the nonexistence of involutory circulant MDS matrices of order 6, 8, circulant MDS matrices of order 7, sparse DSI matrices of order 4 that yield involutory MDS matrices, and sparse DSI matrices of order 5, 6, 7, 8 that yield MDS matrices. To the best of our knowledge, these results were not known before. For the choices mentioned above, if such MDS matrices exist, we provide base sets of MDS matrices, from which all the MDS matrices with the least cost (with respect to d-XOR and s-XOR counts) can be obtained. We also take this opportunity to present some results on the search for sparse DSI matrices over finite fields that yield MDS matrices. We establish that there is no sparse DSI matrix S of order 8 over F28 such that S8 is MDS.

Preferences Single-Peaked on a Tree: Sampling and Tree Recognition

In voting theory, impossibility results and computational hardness results are often circumvented by recognising that voters' preferences are not arbitrary, but lie within a restricted domain. Uncovering the structure of the underlying domain often provides useful insights about the nature of the alternative space, and may be helpful in identifying a collective choice. Preferences single-peaked on a tree are an example of a relatively broad domain that nonetheless exhibits several desirable properties. We consider the setting where voters' preferences are independently sampled from rankings that are single-peaked on a given tree, and study the problem of reliably identifying the tree that generated the observed votes. We test our algorithm empirically; to this end, we develop an algorithm to uniformly sample preferences that are single-peaked on a given tree.