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- Lopes-Lima, M., et al.
(författare)
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Integrative phylogenetic, phylogeographic and morphological characterisation of the Unio crassus species complex reveals cryptic diversity with important conservation implications
- 2024
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Ingår i: Molecular Phylogenetics and Evolution. - : Academic Press Inc.. - 1055-7903 .- 1095-9513. ; 195
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Tidskriftsartikel (refereegranskat)abstract
- The global decline of freshwater mussels and their crucial ecological services highlight the need to understand their phylogeny, phylogeography and patterns of genetic diversity to guide conservation efforts. Such knowledge is urgently needed for Unio crassus, a highly imperilled species originally widespread throughout Europe and southwest Asia. Recent studies have resurrected several species from synonymy based on mitochondrial data, revealing U. crassus to be a complex of cryptic species. To address long-standing taxonomic uncertainties hindering effective conservation, we integrate morphometric, phylogenetic, and phylogeographic analyses to examine species diversity within the U. crassus complex across its entire range. Phylogenetic analyses were performed using cytochrome c oxidase subunit I (815 specimens from 182 populations) and, for selected specimens, whole mitogenome sequences and Anchored Hybrid Enrichment (AHE) data on ∼ 600 nuclear loci. Mito-nuclear discordance was detected, consistent with mitochondrial DNA gene flow between some species during the Pliocene and Pleistocene. Fossil-calibrated phylogenies based on AHE data support a Mediterranean origin for the U. crassus complex in the Early Miocene. The results of our integrative approach support 12 species in the group: the previously recognised Unio bruguierianus, Unio carneus, Unio crassus, Unio damascensis, Unio ionicus, Unio sesirmensis, and Unio tumidiformis, and the reinstatement of five nominal taxa: Unio desectus stat. rev., Unio gontierii stat. rev., Unio mardinensis stat. rev., Unio nanus stat. rev., and Unio vicarius stat. rev. Morphometric analyses of shell contours reveal important morphospace overlaps among these species, highlighting cryptic, but geographically structured, diversity. The distribution, taxonomy, phylogeography, and conservation of each species are succinctly described.
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- Alaghmandan, Mahmood, 1983, et al.
(författare)
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Completely bounded maps and invariant subspaces
- 2020
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Ingår i: Mathematische Zeitschrift. - : Springer Science and Business Media LLC. - 1432-1823 .- 0025-5874. ; 294:1-2, s. 471-489
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Tidskriftsartikel (refereegranskat)
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- Brannan, Michael, et al.
(författare)
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Quantum no-signalling bicorrelations
- 2024
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Ingår i: Advances in Mathematics. - 1090-2082 .- 0001-8708. ; 449
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Tidskriftsartikel (refereegranskat)abstract
- We introduce classical and quantum no-signalling bicorrelations and characterise the different types thereof in terms of states on operator system tensor products, exhibiting connections with bistochastic operator matrices and with dilations of quantum magic squares. We define concurrent bicorrelations as a quantum input-output generalisation of bisynchronous correlations. We show that concurrent bicorrelations of quantum commuting type correspond to tracial states on the universal C*-algebra of the projective free unitary quantum group, showing that in the quantum input-output setup, quantum permutations of finite sets must be replaced by quantum automorphisms of matrix algebras. We apply our results to study the quantum graph isomorphism game, describing the game C*-algebra in this case, and make precise connections with the algebraic notions of quantum graph isomorphism, existing presently in the literature.
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- Brannan, Michael, et al.
(författare)
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Synchronicity for quantum non-local games
- 2023
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Ingår i: Journal of Functional Analysis. - : Elsevier BV. - 0022-1236 .- 1096-0783. ; 284:2
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Tidskriftsartikel (refereegranskat)abstract
- We introduce concurrent quantum non-local games, quantum output mirror games and concurrent classical-to-quantum non-local games, as quantum versions of synchronous non-local games, and provide tracial characterisations of their perfect strategies belonging to various correlation classes. We define *-algebras and C*-algebras of concurrent classical-to-quantum and concurrent quantum non-local games, and algebraic versions of the orthogonal rank of a graph. We show that quantum homomorphisms of quantum graphs can be viewed as entanglement assisted classical homomorphisms of the graphs, and give descriptions of the perfect quantum commuting and the perfect approximately quantum strategies for the quantum graph homomorphism game. We specialise the latter results to the case where the inputs of the game are based on a classical graph.
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- He, W. J., et al.
(författare)
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Completely Compact Herz-Schur Multipliers of Dynamical Systems
- 2022
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Ingår i: Journal of Fourier Analysis and Applications. - : Springer Science and Business Media LLC. - 1069-5869 .- 1531-5851. ; 28:3
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Tidskriftsartikel (refereegranskat)abstract
- We prove that if G is a discrete group and (A, G, alpha) is a C*-dynamical system such that the reduced crossed product A (sic)(r,alpha) G possesses property (SOAP) then every completely compact Herz-Schur (A, G, alpha)-multiplier can be approximated in the completely bounded norm by Herz-Schur (A, G, alpha)-multipliers of finite rank. As a consequence, if G has the approximation property (AP) then the completely compact Herz-Schur multipliers of A(G) coincide with the closure of A(G) in the completely bounded multiplier norm. We study the class of invariant completely compact Herz-Schur multipliers of A (sic)(r,alpha) G and provide a description of this class in the case of the irrational rotation algebra.
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- Le Merdy, Christian, et al.
(författare)
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Bilinear operator multipliers into the trace class
- 2020
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Ingår i: Journal of Functional Analysis. - : Elsevier BV. - 0022-1236 .- 1096-0783. ; 279:7
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Tidskriftsartikel (refereegranskat)abstract
- Given Hilbert spaces H1,H2,H3, we consider bilinear maps defined on the cartesian product S2(H2,H3)×S2(H1,H2) of spaces of Hilbert-Schmidt operators and valued in either the space B(H1,H3) of bounded operators, or in the space S1(H1,H3) of trace class operators. We introduce modular properties of such maps with respect to the commutants of von Neumann algebras Mi⊂B(Hi), i=1,2,3, as well as an appropriate notion of complete boundedness for such maps. We characterize completely bounded module maps u:S2(H2,H3)×S2(H1,H2)→B(H1,H3) by the membership of a natural symbol of u to the von Neumann algebra tensor product M1⊗‾M2op⊗‾M3. In the case when M2 is injective, we characterize completely bounded module maps u:S2(H2,H3)×S2(H1,H2)→S1(H1,H3) by a weak factorization property, which extends to the bilinear setting a famous description of bimodule linear mappings going back to Haagerup, Effros-Kishimoto, Smith and Blecher-Smith. We make crucial use of a theorem of Sinclair-Smith on completely bounded bilinear maps valued in an injective von Neumann algebra, and provide a new proof of it, based on Hilbert C⁎-modules.
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- McKee, Andrew, et al.
(författare)
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Central and convolution Herz-Schur multipliers
- 2022
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Ingår i: New York Journal of Mathematics. - 1076-9803 .- 1076-9803. ; 28, s. 1-43
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Tidskriftsartikel (refereegranskat)abstract
- In this paper we obtain descriptions of central operator-valued Schur and Herz-Schur multipliers, akin to a classical characterisation due to Grothendieck, that reveals a close link between central (linear) multipliers and bilinear multipliers into the trace class. Restricting to dynamical systems where a locally compact group acts on itself by translation, we identify their convolution multipliers as the right completely bounded multipliers, in the sense of Junge-Neufang-Ruan, of a canonical quantum group associated with the underlying group. We provide characterisations of contractive idempotent operator-valued Schur and Herz-Schur multipliers. Exploiting the link between Herz-Schur multipliers and multipliers on transformation groupoids, we provide a combinatorial characterisation of groupoid multipliers that are contractive and idempotent.
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