Diel vertical migration in marine dinoflagellates

Increasing precipitation and surface water temperature due to global change may strengthen stratification in coastal regions, which could influence the behavior of dinoflagellate diel vertical migration (DVM). DVM is a behavioral mechanism by which dinoflagellates can access photosynthetically active radiation near the surface, and nutrients at depth. During this process, cells may need to cross both salinity and temperature gradients (haloclines and thermoclines, respectively). My results show that different dinoflagellate species display unique DVM behaviors in stratified waters and increasing halo- and thermocline strength may act as barriers between the surface- and bottom water. There is, however, large variation in how dinoflagellates cope with stratification and even closely related species have different strategies. Different DVM strategies may lead to a niche separation among species, which was also observed in my research. Moreover, during powerful mixing of the water column i.e. during strong winds in situ, the continuous DVM behavior was disrupted. In addition, as indicated by my experiments, dinoflagellates were influenced by the combination of salinity and temperature. An increase in temperature had no significant effect on growth rate if cells were grown in low salinity environments. The results indicate higher growth rates for two bloom-forming species when growing in salinities corresponding to bottom water conditions on the west coast of Sweden. Thus, there is a trade-off for dinoflagellates between low-salinity light-rich surface conditions and high-nutrient, low-light and high salinity bottom water conditions. If different species have different optimal growth conditions, a geographical separation among species is to be expected. Furthermore, the results indicate that the primary trigger for vertical migration is light in combination with an internal clock controlling the behavior. I show that there is a positive phototactic response to both white, blue and red light and demonstrate that the non-photosynthetic photoreceptor rhodopsin gene exists and is expressed in the cells. Harmful algal blooms (HABs) affect nearly every coastal region of the world and dinoflagellate blooms is a major problem for the shellfish industry. Efforts are made into designing accurate models that predict harmful algae blooms and these models need to be derived from reliable experimental and observational data. High resolution sampling and repeated measurements in time is needed to be able to detect DVM behavior in the field and species-specific data may need to be coordinated and integrated in the models. To predict harmful algal blooms of vertically migrating species, the migration patterns and the growth rates in the natural environment should be further clarified for each species. If increasing precipitation and temperature strengthen the gradient in coastal regions, the nutrient-rich bottom water will be inaccessible to cells unable to migrate through the gradient. Thus, stronger stratification will benefit migrating species able to cross the gradient during DVM and generate more variability in were we can expect to find specific species in situ

'Is a Market Orientation necessary for a Small Firm with Limited Competion?

The purpose of this study is to attempt to identify the importance of market orientation to a firm with limited competition. It has been suggested within some aspects of the literature that the necessary strength of a firm’s market orientation, as well as that of its various components, alters with the market in which it operates. This study will attempt to ascertain whether a market with a small amount of competition necessitates a market orientation at all, or whether some aspects are more important than others. It will attempt to discover whether other factors prove to be more important than market orientation, and indeed whether being market oriented in such an environment leads to improved financial performance. It will try to ascertain whether the evidence for positive performance gains within large companies holds true for small companies. It will also analyse to what extent a market orientation can be observed within small companies, particularly if they have no marketing department and formal barriers between units do not exist to the same extent. Although this has been researched at length before, the unique nature of this study is the element of limited competition. With one, or very few competitors, does the case for the importance of market orientation hold true? It is hoped that this study will contribute to new knowledge through analysis of this question, as well pinpointing whether other factors prove to be more important

Permutation groups and transformation semigroups : results and problems

J.M. Howie, the influential St Andrews semigroupist, claimed that we value an area of pure mathematics to the extent that (a) it gives rise to arguments that are deep and elegant, and (b) it has interesting interconnections with other parts of pure mathematics. This paper surveys some recent results on the transformation semigroup generated by a permutation group G and a single non-permutation a. Our particular concern is the influence that properties of G (related to homogeneity, transitivity and primitivity) have on the structure of the semigroup. In the first part of the paper, we consider properties of S= such as regularity and generation. The second is a brief report on the synchronization project, which aims to decide in what circumstances S contains an element of rank 1. The paper closes with a list of open problems on permutation groups and linear groups, and some comments about the impact on semigroups are provided. These two research directions outlined above lead to very interesting and challenging problems on primitive permutation groups whose solutions require combining results from several different areas of mathematics, certainly fulfilling both of Howie's elegance and value tests in a new and fascinating way.PostprintPeer reviewe

The classification of partition homogeneous groups with applications to semigroup theory

Let λ=(λ1,λ2,...) be a partition of n, a sequence of positive integers in non-increasing order with sum n. Let Ω:={1,...,n}. An ordered partition P=(A1,A2,...) of Ω has type λ if |Ai|=λi.Following Martin and Sagan, we say that G is λ-transitive if, for any two ordered partitions P=(A1,A2,...) and Q=(B1,B2,...) of Ω of type λ, there exists g ∈ G with Aig=Bi for all i. A group G is said to be λ-homogeneous if, given two ordered partitions P and Q as above, inducing the sets P'={A1,A2,...} and Q'={B1,B2,...}, there exists g ∈ G such that P'g=Q'. Clearly a λ-transitive group is λ-homogeneous.The first goal of this paper is to classify the λ-homogeneous groups (Theorems 1.1 and 1.2). The second goal is to apply this classification to a problem in semigroup theory.Let Tn and Sn denote the transformation monoid and the symmetric group on Ω, respectively. Fix a group H<=Sn. Given a non-invertible transformation a in Tn-Sn and a group G<=Sn, we say that (a,G) is an H-pair if the semigroups generated by {a} ∪ H and {a} ∪ G contain the same non-units, that is, {a,G}\G= {a,H}\H. Using the classification of the λ-homogeneous groups we classify all the Sn-pairs (Theorem 1.8). For a multitude of transformation semigroups this theorem immediately implies a description of their automorphisms, congruences, generators and other relevant properties (Theorem 8.5). This topic involves both group theory and semigroup theory; we have attempted to include enough exposition to make the paper self-contained for researchers in both areas. The paper finishes with a number of open problems on permutation and linear groups.PostprintPeer reviewe

Constructing flag-transitive, point-imprimitive designs

We give a construction of a family of designs with a specified point-partition and determine the subgroup of automorphisms leaving invariant the point-partition. We give necessary and sufficient conditions for a design in the family to possess a flag-transitive group of automorphisms preserving the specified point-partition. We give examples of flag-transitive designs in the family, including a new symmetric 2-(1408,336,80) design with automorphism group 2^12:((3⋅M22):2) and a construction of one of the families of the symplectic designs (the designs S^−(n) ) exhibiting a flag-transitive, point-imprimitive automorphism group.PostprintPeer reviewe

'Is a Market Orientation necessary for a Small Firm with Limited Competion?

The purpose of this study is to attempt to identify the importance of market orientation to a firm with limited competition. It has been suggested within some aspects of the literature that the necessary strength of a firm’s market orientation, as well as that of its various components, alters with the market in which it operates. This study will attempt to ascertain whether a market with a small amount of competition necessitates a market orientation at all, or whether some aspects are more important than others. It will attempt to discover whether other factors prove to be more important than market orientation, and indeed whether being market oriented in such an environment leads to improved financial performance. It will try to ascertain whether the evidence for positive performance gains within large companies holds true for small companies. It will also analyse to what extent a market orientation can be observed within small companies, particularly if they have no marketing department and formal barriers between units do not exist to the same extent. Although this has been researched at length before, the unique nature of this study is the element of limited competition. With one, or very few competitors, does the case for the importance of market orientation hold true? It is hoped that this study will contribute to new knowledge through analysis of this question, as well pinpointing whether other factors prove to be more important

Between primitive and 2-transitive : synchronization and its friends

The second author was supported by the Fundação para a Ciência e Tecnologia (Portuguese Foundation for Science and Technology) through the project CEMAT-CIÊNCIAS UID/Multi/ 04621/2013An automaton (consisting of a finite set of states with given transitions) is said to be synchronizing if there is a word in the transitions which sends all states of the automaton to a single state. Research on this topic has been driven by the Černý conjecture, one of the oldest and most famous problems in automata theory, according to which a synchronizing n-state automaton has a reset word of length at most (n − 1)2 . The transitions of an automaton generate a transformation monoid on the set of states, and so an automaton can be regarded as a transformation monoid with a prescribed set of generators. In this setting, an automaton is synchronizing if the transitions generate a constant map. A permutation group G on a set Ω is said to synchronize a map f if the monoid (G, f) generated by G and f is synchronizing in the above sense; we say G is synchronizing if it synchronizes every non-permutation. The classes of synchronizing groups and friends form an hierarchy of natural and elegant classes of groups lying strictly between the classes of primitive and 2-homogeneous groups. These classes have been floating around for some years and it is now time to provide a unified reference on them. The study of all these classes has been prompted by the Černý conjecture, but it is of independent interest since it involves a rich mix of group theory, combinatorics, graph endomorphisms, semigroup theory, finite geometry, and representation theory, and has interesting computational aspects as well. So as to make the paper self-contained, we have provided background material on these topics. Our purpose here is to present recent work on synchronizing groups and related topics. In addition to the results that show the connections between the various areas of mathematics mentioned above, we include a new result on the Černý conjecture (a strengthening of a theorem of Rystsov), some challenges to finite geometers (which classical polar spaces can be partitioned into ovoids?), some thoughts about infinite analogues, and a long list of open problems to stimulate further work.PostprintPeer reviewe

Generating sets of finite groups

We investigate the extent to which the exchange relation holds in finite groups G. We define a new equivalence relation ≡m, where two elements are equivalent if each can be substituted for the other in any generating set for G. We then refine this to a new sequence ≡(r)/m of equivalence relations by saying that x≡(r)/m y if each can be substituted for the other in any r-element generating set. The relations ≡(r)/m become finer as r increases, and we define a new group invariant ψ(G) to be the value of r at which they stabilise to ≡m. Remarkably, we are able to prove that if G is soluble then ψ(G) ∈ {d(G),d(G)+1}, where d(G) is the minimum number of generators of G, and to classify the finite soluble groups G for which ψ(G)=d(G). For insoluble G, we show that d(G) ≤ ψ(G) ≤ d(G)+5. However, we know of no examples of groups G for which ψ(G) > d(G)+1. As an application, we look at the generating graph of G, whose vertices are the elements of G, the edges being the 2-element generating sets. Our relation ≡(2)m enables us to calculate Aut(Γ(G)) for all soluble groups G of nonzero spread, and give detailed structural information about Aut(Γ(G)) in the insoluble case.PostprintPeer reviewe

Integrals of groups

Funding: Fundação para a Ciência e a Tecnologia (CEMAT-Ciências FCT project UID/Multi/04621/2013).An integral of a group G is a group H whose derived group (commutator subgroup) is isomorphic to G. This paper discusses integrals of groups, and in particular questions about which groups have integrals and how big or small those integrals can be. Our main results are: - If a finite group has an integral, then it has a finite integral. - A precise characterization of the set of natural numbers n for which every group of order n is integrable: these are the cubefree numbers n which do not have prime divisors p and q with q | p-1. - An abelian group of order n has an integral of order at most n1+o(1), but may fail to have an integral of order bounded by cn for constant c. - A finite group can be integrated n times (in the class of finite groups) for every n if and only if it is a central product of an abelian group and a perfect group. There are many other results on such topics as centreless groups, groups with composition length 2, and infinite groups. We also include a number of open problems.PostprintPeer reviewe