Friends or Foes? The Problem of South Florida’s Invasive Mangroves

A recent global review on the impacts of climate change on mangroves concluded that different regions will experience varying degrees of impacts due to the variability of expected changes in climate (shifts in precipitation, frequency and intensity of storms, droughts, sea level rise, change of ocean currents, increases in CO2 concentrations, etc.) and the variety of types and mangrove assemblages growing in these regions, including different species composition of mangrove forests. In North America and the Caribbean, these changes are dependent upon a predicted higher frequency (and intensity) of tropical storms, sea level rise, changes in patterns of precipitation, and higher temperatures. Located at the land-sea interface, mangroves in this region are expected to expand their ranges poleward (towards North Florida), or migrate into other coastal ecosystems (e.g., the Everglades), provided no natural or urban center barriers are present to prevent this expansion. If rains increase, as is anticipated, along the United States-Mexico border, mangroves may likely begin to thrive in places currently occupied by unvegetated salt flats. However, a lack of rain may also be of benefit in areas such as Louisiana where marsh diebacks have been linked to droughts, which directly increases the likelihood of mangrove migrations into these ecosystems. Given the services that mangroves provide and the legal protections that mangroves receive, it is shocking to discover that their future existence may be compromised or threatened. Certainly, the greatest threats to mangroves in Florida are from direct and indirect human impacts of development, including pollution and habitat destruction. Mangroves may also be naturally damaged and destroyed from disturbance events such as tropical storms and hurricanes. However, a new threat to native mangroves has recently emerged: the introduction of invasive mangrove species. These non-native species may threaten the ecosystem dynamics of mangrove forests and may alter the natural coastal landscape of South Florida unless eradicated

Two Generalizations of Homogeneity in Groups with Applications to Regular Semigroups

Let $X$ be a finite set such that $|X|=n$ and let $i\leq j \leq n$. A group G\leq \sym is said to be $(i,j)$-homogeneous if for every $I,J\subseteq X$, such that $|I|=i$ and $|J|=j$, there exists $g\in G$ such that $Ig\subseteq J$. (Clearly $(i,i)$-homogeneity is $i$-homogeneity in the usual sense.) A group G\leq \sym is said to have the $k$-universal transversal property if given any set $I\subseteq X$ (with $|I|=k$) and any partition $P$ of $X$ into $k$ blocks, there exists $g\in G$ such that $Ig$ is a section for $P$. (That is, the orbit of each $k$-subset of $X$ contains a section for each $k$-partition of $X$.) In this paper we classify the groups with the $k$-universal transversal property (with the exception of two classes of 2-homogeneous groups) and the $(k-1,k)$-homogeneous groups (for $2<k\leq \lfloor \frac{n+1}{2}\rfloor$). As a corollary of the classification we prove that a $(k-1,k)$-homogeneous group is also $(k-2,k-1)$-homogeneous, with two exceptions; and similarly, but with no exceptions, groups having the $k$-universal transversal property have the $(k-1)$-universal transversal property. A corollary of all the previous results is a classification of the groups that together with any rank $k$ transformation on $X$ generate a regular semigroup (for $1\leq k\leq \lfloor \frac{n+1}{2}\rfloor$). The paper ends with a number of challenges for experts in number theory, group and/or semigroup theory, linear algebra and matrix theory.Comment: Includes changes suggested by the referee of the Transactions of the AMS. We gratefully thank the referee for an outstanding report that was very helpful. We also thank Peter M. Neumann for the enlightening conversations at the early stages of this investigatio

Primitive Groups Synchronize Non-uniform Maps of Extreme Ranks

Let $\Omega$ be a set of cardinality $n$, $G$ a permutation group on $\Omega$, and $f:\Omega\to\Omega$ a map which is not a permutation. We say that $G$ synchronizes $f$ if the semigroup $\langle G,f\rangle$ contains a constant map. The first author has conjectured that a primitive group synchronizes any map whose kernel is non-uniform. Rystsov proved one instance of this conjecture, namely, degree $n$ primitive groups synchronize maps of rank $n-1$ (thus, maps with kernel type $(2,1,\ldots,1)$). We prove some extensions of Rystsov's result, including this: a primitive group synchronizes every map whose kernel type is $(k,1,\ldots,1)$. Incidentally this result provides a new characterization of imprimitive groups. We also prove that the conjecture above holds for maps of extreme ranks, that is, ranks 3, 4 and $n-2$. These proofs use a graph-theoretic technique due to the second author: a transformation semigroup fails to contain a constant map if and only if it is contained in the endomorphism semigroup of a non-null (simple undircted) graph. The paper finishes with a number of open problems, whose solutions will certainly require very delicate graph theoretical considerations.Comment: Includes changes suggested by the referee of the Journal of Combinatorial Theory, Series B - Elsevier. We are very grateful to the referee for the detailed, helpful and careful repor

Opinion Dynamics and Communication Networks

This paper examines the interplay of opinion exchange dynamics and communication network formation. An opinion formation procedure is introduced which is based on an abstract representation of opinions as $k$--dimensional bit--strings. Individuals interact if the difference in the opinion strings is below a defined similarity threshold $d_I$. Depending on $d_I$, different behaviour of the population is observed: low values result in a state of highly fragmented opinions and higher values yield consensus. The first contribution of this research is to identify the values of parameters $d_I$ and $k$, such that the transition between fragmented opinions and homogeneity takes place. Then, we look at this transition from two perspectives: first by studying the group size distribution and second by analysing the communication network that is formed by the interactions that take place during the simulation. The emerging networks are classified by statistical means and we find that non--trivial social structures emerge from simple rules for individual communication. Generating networks allows to compare model outcomes with real--world communication patterns.Comment: 14 pages 6 figure

The impact of the oil spill of the tanker “Aragon” on the littoral fish fauna of Porto Santo (NE Atlantic Ocean) in 1991 and ten years later

Bocagiana, 217: 1-8Em Janeiro de 1990, a Ilha de Porto Santo (Arquipélago da Madeira), foi atingida por uma maré negra proveniente de um derrame do navio petroleiro “Aragon”. Um ano depois, avaliou-se a ictiofauna costeira. Dez anos depois da maré negra, uma nova amostragem foi realizada com a mesma metodologia, de forma a comparar com os dados recolhidos anteriormente. A análise dos resultados obtidos parece revelar que os efeitos da maré negra nos peixes litorais foram reduzidos. Este trabalho constitui a primeira contribuição para a “check-list” da ictiofauna costeira da Ilha de Porto Santo.In January 1990, the tanker “Aragon” oil spill reached Porto Santo Island (Madeira Archipelago). One year later, in 1991 the littoral fish fauna was evaluated. Ten years after the “Aragon” oil spill, a new survey was made using the same methods, to compare data. From the results it seems that the effects of the oil were rather small. As a result of this work, as a check-list of the littoral fish fauna of this Island is presented

Orbits of primitive k-homogenous groups on (N − k)-partitions with applications to semigroups

© 2018 American Mathematical Society. The purpose of this paper is to advance our knowledge of two of the most classic and popular topics in transformation semigroups: automorphisms and the size of minimal generating sets. In order to do this, we examine the k-homogeneous permutation groups (those which act transitively on the subsets of size k of their domain X) where |X| = n and k < n/2. In the process we obtain, for k-homogeneous groups, results on the minimum numbers of generators, the numbers of orbits on k-partitions, and their normalizers in the symmetric group. As a sample result, we show that every finite 2-homogeneous group is 2-generated. Underlying our investigations on automorphisms of transformation semigroups is the following conjecture: If a transformation semigroup S contains singular maps and its group of units is a primitive group G of permutations, then its automorphisms are all induced (under conjugation) by the elements in the normalizer of G in the symmetric group. For the special case that S contains all constant maps, this conjecture was proved correct more than 40 years ago. In this paper, we prove that the conjecture also holds for the case of semigroups containing a map of rank 3 or less. The effort in establishing this result suggests that further improvements might be a great challenge. This problem and several additional ones on permutation groups, transformation semigroups, and computational algebra are proposed at the end of the paper