Microscopic Characterization of the Mucous Cells and Their Mucin Secretions in the Alimentary Canal of the Blackmouth Catshark Galeus melastomus (Chondrichthyes: Elasmobranchii)

Sharks belong to the most primitive group of jawed vertebrates and have some special structural and functional features such as a cartilaginous skeleton, a spiral intestinal valve, and a rectal gland for osmoregulation. In January 2020, ten specimens of Galeus melastomus, the Blackmouth catshark, were collected from the Gulf of Asinara (North Sardinia, Italy) and the entire alimentary canal was studied using histochemical reactions to characterize the mucous cell types. In the alimentary canal of G. melastomus, mucous cells mainly secrete a mixture of acidic and neutral mucins. Of the acidic mucins, only the carboxylated type was present in mucous cells of the stomach, while the sulfated type predominated in the esophagus and the intestines. The use of lectins revealed a distribution of sugar residues in mucins related to cellular activities of the different regions of the catshark alimentary canal. The current study is the first report to characterize the intestinal mucous cells of G. melastomus and to provide quantitative data on their different populations in the alimentary canal.

On valency problems of Saxl graphs

Let 𝐺 be a permutation group on a set Ω, and recall that a base for 𝐺 is a subset of Ω such that its pointwise stabiliser is trivial. In a recent paper, Burness and Giudici introduced the Saxl graph of 𝐺, denoted Σ ⁢ ( G ) \Sigma(G) , with vertex set Ω and two vertices adjacent if and only if they form a base for 𝐺. If 𝐺 is transitive, then Σ ⁢ ( G ) \Sigma(G) is vertex-transitive, and it is natural to consider its valency (which we refer to as the valency of 𝐺). In this paper, we present a general method for computing the valency of any finite transitive group, and we use it to calculate the exact valency of every primitive group with stabiliser a Frobenius group with cyclic kernel. As an application, we calculate the valency of every almost simple primitive group with an alternating socle and soluble stabiliser, and we use this to extend results of Burness and Giudici on almost simple primitive groups with prime-power or odd valency.

A generalization of Sims’ conjecture for finite primitive groups and two point stabilizers in primitive groups

In this paper, we propose a refinement of Sims’ conjecture concerning the cardinality of the point stabilizers in finite primitive groups, and we make some progress towards this refinement. In this process, when dealing with primitive groups of diagonal type, we construct a finite primitive group 𝐺 on Ω and two distinct points α , β ∈ Ω \alpha,\beta\in\Omega with G α ⁢ β ⊴ G α G_{\alpha\beta}\unlhd G_{\alpha} and G α ⁢ β ≠ 1 G_{\alpha\beta}\neq 1 , where G α G_{\alpha} is the stabilizer of 𝛼 in 𝐺 and G α ⁢ β G_{\alpha\beta} is the stabilizer of 𝛼 and 𝛽 in 𝐺. In particular, this example gives an answer to a question raised independently by Cameron and by Fomin in the Kourovka Notebook.

On quasiprimitive edge-transitive graphs of odd order and twice prime valency

A graph is edge-transitive if its automorphism group acts transitively on the edge set. In this paper, we investigate the automorphism groups of edge-transitive graphs of odd order and twice prime valency. Let {\varGamma} be a connected graph of odd order and twice prime valency, and let G be a subgroup of the automorphism group of {\varGamma}. In the case where G acts transitively on the edge set and quasiprimitively on the vertex set of {\varGamma}, we prove that either G is almost simple, or G is a primitive group of affine type. If further G is an almost simple primitive group, then, with two exceptions, the socle of G acts transitively on the edge set of {\varGamma}.

Classification and evolution of the burrowing sea anemones (Anthozoa: Actiniaria: Athenaria): a review of the past and current views

The opinions of systematists about the classification and evolution of burrowing sea anemones have repeatedly changed over the long-term study of Actiniaria. Four stages can be distinguished over the course of the classification history. Each system was characterized by the use of mainly one particular feature. These features were: (1) characters of the external morphology, (2) arrangement of the mesenteries, (3) presence or absence of the basilar muscles and (4) molecular markers. The views on the origin and the evolution of the burrowing sea anemones were also altered more than once, that led to the emergence of several hypotheses. The burrowing sea anemones were considered as a primitive group or, on the contrary, as more advanced descendants of large hexamerous actinians.

On the Saxl graph of a permutation group

Let G be a permutation group on a set Ω. A subset of Ω is a base for G if its pointwise stabiliser in G is trivial. In this paper we introduce and study an associated graph Σ(G), which we call the Saxl graph of G. The vertices of Σ(G) are the points of Ω, and two vertices are adjacent if they form a base for G. This graph encodes some interesting properties of the permutation group. We investigate the connectivity of Σ(G) for a finite transitive group G, as well as its diameter, Hamiltonicity, clique and independence numbers, and we present several open problems. For instance, we conjecture that if G is a primitive group with a base of size 2, then the diameter of Σ(G) is at most 2. Using a probabilistic approach, we establish the conjecture for some families of almost simple groups. For example, the conjecture holds when G = Sn or An (with n > 12) and the point stabiliser of G is a primitive subgroup. In contrast, we can construct imprimitive groups whose Saxl graph is disconnected with arbitrarily many connected components, or connected with arbitrarily large diameter.

Primitivity of PRESENT and other lightweight ciphers

We provide two sufficient conditions to guarantee that the round functions of a translation-based cipher generate a primitive group. Furthermore, under the same hypotheses, and assuming that a round of the cipher is strongly proper and consists of [Formula: see text]-bit S-Boxes, with [Formula: see text] or [Formula: see text], we prove that such a group is the alternating group. As an immediate consequence, we deduce that the round functions of some lightweight translation-based ciphers, such as the PRESENT cipher, generate the alternating group.

Connected Components of H_(r,g)^A (G)

The Hurwitz space is the space of genus g covers of the Riemann sphere with branch points and the monodromy group . In this paper, we enumerate the connected components of the Hurwitz spaces for a finite primitive group of degree 7 and genus zero except . We achieve this with the aid of the computer algebra system GAP and the MAPCLASS package.

A revision of Taraxacum sect. Atrata, a dandelion group centred in the Middle Asia, and the problem of Taraxacum brevirostre

The two most primitive Taraxacum sections (Asteraceae, Cichorieae-Crepidinae) in high mountains of Middle Asia and adjacent regions are characterized by almost smooth achenes, frequent absence of discernible cone and a thick beak. One of them, a recently recognized T. sect. Atrata was studied, characterized in detail and its members reviewed. The section is centred in Kyrgyzstan and SE. Kazakhstan and extends to NW. Mongolia in the north, to Pakistan and Ladakh in the southeast and W. China in the east. Eighteen species were found to belong to T. sect. Atrata, nine of them are described as new. All taxa were revised nomenclaturally and the names newly interpreted. Taraxacum sect. Atrata is compared with T. subsect. Epyramidata Orazova (= sect. Oligantha auct.), the other primitive group, also with the highest species diversity in Middle Asia. A special analysis was carried out of T. brevirostre; its syntypes studied and the lectotype described in detail and interpreted as a taxon marginal to T. subsect. Epyramidata.