We analyze the Blume-Emery-Griffiths (BEG) associative memory with sparse
patterns and at zero temperature. We give bounds on its storage capacity
provided that we want the stored patterns to be fixed points of the retrieval
dynamics. We compare our results to that of other models of sparse neural
networks and show that the BEG model has a superior performance compared to
them.Comment: 23 p

Christophe Volkringer (1434343)

Natacha Henry (1434346)

Stéphane Grandjean (1444216)

Thierry Loiseau (1434349)

English

arXiv

A series of uranyl and lanthanide (trivalent Ce, Nd)
mellitates
(mel) has been hydrothermally synthesized in aqueous
solvent. Mixtures of these 4f and 5f elements also revealed the formation
of a rare case of lanthanide–uranyl coordination polymers.
Their structures, determined by XRD single-crystal analysis, exhibit
three distinct architectures. The pure lanthanide mellitate Ln2(H2O)6(mel) possesses
a 3D framework built up from the connection of isolated LnO6(H2O)3 polyhedra (tricapped trigonal prism)
through the mellitate ligand. The structure of the uranyl mellitate
(UO2)3(H2O)6(mel)·11.5H2O is lamellar and consists of 8-fold coordinated
uranium atoms linked to each other through the organic ligand giving
rise to the formation of a 2D 36 net. The third structural
type, (UO2)2Ln­(OH)­(H2O)3(mel)·2.5H2O, involves direct oxygen
bondings between the lanthanide and uranyl centers, with the isolation
of a heterometallic dinuclear motif. The 9-fold coordinated Ln cation,
LnO5(OH)­(H2O)3, is linked to the
7-fold coordinated uranyl (UO2)­O4(OH) (pentagonal
bipyramid) via one μ2-hydroxo group and one μ2-oxo group. The latter is shared between the uranyl bonding
(UO = 1.777(4)/1.779(6) Å) and a long Ln–O bonding
(Ce–O = 2.822(4) Å; Nd–O = 2.792(6) Å). This
unusual linkage is a unique illustration of the so-called cation–cation
interaction associating 4f and 5f metals. The dinuclear motif is then
further connected through the mellitate ligand, and this generates
organic–inorganic layers that are linked to each other via
discrete uranyl (UO2)­O4 units (square bipyramid),
which ensure the three-dimensional cohesion of the structure. The
mixed U–Ln carboxylate is thermally decomposed from 260 to
280 °C and then transformed into the basic uranium oxide (U3O8) together with U–Ln oxide with the fluorite
structural type (“(Ln,U)­O2”). At 1400 °C,
only fluorite type “(Ln,U)­O2” is formed with
the measured stoichiometry of U0.63Ce0.37O2 and U0.60Nd0.40O2−δ

FigShare

Uranyl and/or Rare-Earth
Mellitates in Extended Organic–Inorganic
Networks: A Unique Case of Heterometallic Cation–Cation Interaction
with UVIO–LnIII Bonding (Ln =
Ce, Nd)

The sparse Blume-Emery-Griffiths model of associative memories

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