Cleft Extensions and Quotients of Twisted Quantum Doubles

Given a pair of finite groups $F, G$ and a normalized 3-cocycle $\omega$ of $G$, where $F$ acts on $G$ as automorphisms, we consider quasi-Hopf algebras defined as a cleft extension $\Bbbk^G_\omega\#_c\,\Bbbk F$ where $c$ denotes some suitable cohomological data. When $F\rightarrow \overline{F}:=F/A$ is a quotient of $F$ by a central subgroup $A$ acting trivially on $G$, we give necessary and sufficient conditions for the existence of a surjection of quasi-Hopf algebras and cleft extensions of the type $\Bbbk^G_\omega\#_c\, \Bbbk F\rightarrow \Bbbk^G_\omega\#_{\overline{c}} \, \Bbbk \overline{F}$. Our construction is particularly natural when $F=G$ acts on $G$ by conjugation, and $\Bbbk^G_\omega\#_c \Bbbk G$ is a twisted quantum double $D^{\omega}(G)$. In this case, we give necessary and sufficient conditions that Rep($\Bbbk^G_\omega\#_{\overline{c}} \, \Bbbk \overline{G}$) is a modular tensor category.Comment: LaTex; 14 page

Little Golden Blond : Morceau de Salon

https://digitalcommons.library.umaine.edu/mmb-ps/1216/thumbnail.jp

Molecular diversity of the Metarhizium anisopliae lineage in an agricultural field

Entomopathogenic fungal isolates identified by morphology as Metarhizium anisopliae may belong to different species when identified by molecular characters. We isolated Metarhizium spp. from an experimental agricultural field under both conventional and organic farming regimes using Tenebrio molitor as bait insect to assess the molecular diversity within the soil. Isolates were analyzed using DNA sequencing and applying SSR markers. Within the former M. anisopliae lineage, we found M. brunneum (86.3%), M. robertsii (11.3%) and M. majus (3.4%) in the soil samples. Several genotypes of each species were identified based on SSR markers. Differences in abundance of the species and their genotypes suggest different adaptations to the soil environment of the agricultural field. There were no effects of conventinal or organic farming regimes on diversity of the fungi

Green's Relations in Finite Transformation Semigroups

We consider the complexity of Green's relations when the semigroup is given by transformations on a finite set. Green's relations can be defined by reachability in the (right/left/two-sided) Cayley graph. The equivalence classes then correspond to the strongly connected components. It is not difficult to show that, in the worst case, the number of equivalence classes is in the same order of magnitude as the number of elements. Another important parameter is the maximal length of a chain of components. Our main contribution is an exponential lower bound for this parameter. There is a simple construction for an arbitrary set of generators. However, the proof for constant alphabet is rather involved. Our results also apply to automata and their syntactic semigroups.Comment: Full version of a paper submitted to CSR 2017 on 2016-12-1

On the Disambiguation of Weighted Automata

We present a disambiguation algorithm for weighted automata. The algorithm admits two main stages: a pre-disambiguation stage followed by a transition removal stage. We give a detailed description of the algorithm and the proof of its correctness. The algorithm is not applicable to all weighted automata but we prove sufficient conditions for its applicability in the case of the tropical semiring by introducing the *weak twins property*. In particular, the algorithm can be used with all acyclic weighted automata, relevant to applications. While disambiguation can sometimes be achieved using determinization, our disambiguation algorithm in some cases can return a result that is exponentially smaller than any equivalent deterministic automaton. We also present some empirical evidence of the space benefits of disambiguation over determinization in speech recognition and machine translation applications

On groups and counter automata

We study finitely generated groups whose word problems are accepted by counter automata. We show that a group has word problem accepted by a blind n-counter automaton in the sense of Greibach if and only if it is virtually free abelian of rank n; this result, which answers a question of Gilman, is in a very precise sense an abelian analogue of the Muller-Schupp theorem. More generally, if G is a virtually abelian group then every group with word problem recognised by a G-automaton is virtually abelian with growth class bounded above by the growth class of G. We consider also other types of counter automata.Comment: 18 page

Categorical Foundation of Quantum Mechanics and String Theory

The unification of Quantum Mechanics and General Relativity remains the primary goal of Theoretical Physics, with string theory appearing as the only plausible unifying scheme. In the present work, in a search of the conceptual foundations of string theory, we analyze the relational logic developed by C. S. Peirce in the late nineteenth century. The Peircean logic has the mathematical structure of a category with the relation $R_{ij}$ among two individual terms $S_i$ and $S_j$, serving as an arrow (or morphism). We introduce a realization of the corresponding categorical algebra of compositions, which naturally gives rise to the fundamental quantum laws, thus indicating category theory as the foundation of Quantum Mechanics. The same relational algebra generates a number of group structures, among them $W_{\infty}$. The group $W_{\infty}$ is embodied and realized by the matrix models, themselves closely linked with string theory. It is suggested that relational logic and in general category theory may provide a new paradigm, within which to develop modern physical theories.Comment: To appear in International Journal of Modern Physics

Within-host competition between two entomopathogenic fungi and a granulovirus in Diatraea saccharalis (Lepidoptera: Crambidae).

Abstract: We provide insights into how the interactions of two entomopathogenic fungi and a virus play a role in virulence, disease development, and pathogen reproduction for an economically important insect crop pest, the sugarcane borer Diatraea saccharalis (Fabricius) (Lepidoptera: Crambidae). In our model system, we highlight the antagonistic effects of the co-inoculation of Beauveria bassiana and granulovirus (DisaGV) on virulence, compared to their single counterparts. By contrast, combinations of Metarhizium anisopliae and B. bassiana, or M. anisopliae and DisaGV, have resulted in additive effects against the insect. Intriguingly, most cadavers that were derived from dual or triple infections, produced signs/symptoms of only one species after the death of the infected host. In the combination of fungi and DisaGV, there was a trend where a higher proportion of viral infection bearing conspicuous symptoms occurred, except when the larvae were inoculated with M. anisopliae and DisaGV at the two highest inoculum rates. Co-infections with B. bassiana and M. anisopliae did not affect pathogen reproduction, since the sporulation from co-inoculated larvae did not differ from their single counterparts

Conjugacy and Equivalence of Weighted Automata and Functional Transducers

International audienceWe show that two equivalent K-automata are conjugate to a third one, when K is equal to B, N, Z, or any (skew) ¯eld and that the same holds true for functional tranducers as well