Specular sets

We introduce the notion of specular sets which are subsets of groups called here specular and which form a natural generalization of free groups. These sets are an abstract generalization of the natural codings of linear involutions. We prove several results concerning the subgroups generated by return words and by maximal bifix codes in these sets.Comment: arXiv admin note: substantial text overlap with arXiv:1405.352

Investigating the antiparasitic potential of the marine sesquiterpene avarone, its reduced form avarol, and the novel semisynthetic thiazinoquinone analogue thiazoavarone

The chemical analysis of the sponge Dysidea avara afforded the known sesquiterpene quinone avarone, along with its reduced form avarol. To further explore the role of the thiazinoquinone scaffold as an antiplasmodial, antileishmanial and antischistosomal agent, we converted the quinone avarone into the thiazinoquinone derivative thiazoavarone. The semisynthetic compound, as well as the natural metabolites avarone and avarol, were pharmacologically investigated in order to assess their antiparasitic properties against sexual and asexual stages of Plasmodium falciparum, larval and adult developmental stages of Schistosomamansoni (eggs included), and also against promastigotes and amastigotes of Leishmania infantum and Leishmania tropica. Furthermore, in depth computational studies including density functional theory (DFT) calculations were performed. A toxic semiquinone radical species which can be produced starting both from quinone- and hydroquinone-based compounds could mediate the anti-parasitic effects of the tested compounds

Return words of linear involutions and fundamental groups

We investigate the natural codings of linear involutions. We deduce from the geometric representation of linear involutions as Poincar\'e maps of measured foliations a suitable definition of return words which yields that the set of first return words to a given word is a symmetric basis of the free group on the underlying alphabet $A$. The set of first return words with respect to a subgroup of finite index $G$ of the free group on $A$ is also proved to be a symmetric basis of $G$

Direct Differential Photometric Stereo Shape Recovery of Diffuse and Specular Surfaces

This is the author accepted manuscript. The final version is available from Springer via http://dx.doi.org/10.1007/s10851-016-0633-0Recovering the 3D shape of an object from shading is a challenging problem due to the complexity of modeling light propagation and surface reflections. Photometric Stereo (PS) is broadly considered a suitable approach for high-resolution shape recovery, but its functionality is restricted to a limited set of object surfaces and controlled lighting setup. In particular, PS models generally consider reflection from objects as purely diffuse, with specularities being regarded as a nuisance that breaks down shape reconstruction. This is a serious drawback for implementing PS approaches, since most common materials have prominent specular components. In this paper, we propose a PS model that solves the problem for both diffuse and specular components aimed at shape recovery of generic objects with the approach being independent of the albedo values thanks to the image ratio formulation used. Notably, we show that by including specularities, it is possible to solve the PS problem for a minimal number of three images using a setup with three calibrated lights and a standard industrial camera. Even if an initial separation of diffuse and specular components is still required for each input image, experimental results on synthetic and real objects demonstrate the feasibility of our approach for shape reconstruction of complex geometries.The first author acknowledges the support of INDAM under the GNCS research Project “Metodi numerici per la regolarizzazione nella ricostruzione feature-preserving di dati.

On morphisms preserving palindromic richness

It is known that each word of length $n$ contains at most $n+1$ distinct palindromes. A finite rich word is a word with maximal number of palindromic factors. The definition of palindromic richness can be naturally extended to infinite words. Sturmian words and Rote complementary symmetric sequences form two classes of binary rich words, while episturmian words and words coding symmetric $d$-interval exchange transformations give us other examples on larger alphabets. In this paper we look for morphisms of the free monoid, which allow to construct new rich words from already known rich words. We focus on morphisms in Class $P_{ret}$. This class contains morphisms injective on the alphabet and satisfying a particular palindromicity property: for every morphism $\varphi$ in the class there exists a palindrome $w$ such that $\varphi(a)w$ is a first complete return word to $w$ for each letter $a$. We characterize $P_{ret}$ morphisms which preserve richness over a binary alphabet. We also study marked $P_{ret}$ morphisms acting on alphabets with more letters. In particular we show that every Arnoux-Rauzy morphism is conjugated to a morphism in Class $P_{ret}$ and that it preserves richness

Selected Papers from XVI MaNaPro and XI ECMNP

The oceans harbor the majority of the Earth´s biodiversity. Marine organisms/microorganisms provide a diverse array of natural products, which are important sources of biologically active agents with unique chemical structures and a broad range of medical and biotechnological applications. The XVI MaNaPro and XI ECMNP conferences aim to present advances and future perspectives on marine natural product research to the scientific community by gathering scientists who work in marine chemistry and related scientific fields from all over the world and at different seniority levels. This Special Issue was organized on the occasion of the 2nd joint XVI MaNaPro and XI ECMNP meeting (http://wmnp2019.ipleiria.pt/) held in Peniche, Portugal, in 2019. It comprises 12 original research articles that exemplify research performed in the scope of the conference topic

Solutions to twisted word equations and equations in virtually free groups

It is well known that the problem solving equations in virtually free groups can be reduced to the problem of solving twisted word equations with regular constraints over free monoids with involution. In this paper, we prove that the set of all solutions of a twisted word equation is an EDT0L language whose specification can be computed in [Formula: see text]. Within the same complexity bound we can decide whether the solution set is empty, finite, or infinite. In the second part of the paper we apply the results for twisted equations to obtain in [Formula: see text] an EDT0L description of the solution set of equations with rational constraints for finitely generated virtually free groups in standard normal forms with respect to a natural set of generators. If the rational constraints are given by a homomorphism into a fixed (or “small enough”) finite monoid, then our algorithms can be implemented in [Formula: see text], that is, in quasi-quadratic nondeterministic space. Our results generalize the work by Lohrey and Sénizergues (ICALP 2006) and Dahmani and Guirardel (J. of Topology 2010) with respect to both complexity and expressive power. Neither paper gave any concrete complexity bound and the results in these papers are stated for subsets of solutions only, whereas our results concern all solutions. </jats:p