The work in this report describes the syntheses, characterization, crystal structures and magnetic properties of eight linear trinickel(ii) compounds of the composition [Ni(II)3(L(sal-pyr))2(propionate)4] (), [Ni(II)3(L(sal-pyr))2(benzoate)4]·CH3CN (), [Ni(II)3(L(sal-pip))2(acetate)4]·2CH3CN (), [Ni(II)3(L(sal-pip))2(propionate)4] (), [Ni(II)3(L(sal-pip))2(benzoate)4]·CH2Cl2 (), [Ni(II)3(L(sal-...

We prove that the combinatorial distance between any two reduced expressions of a given permutation of {1, ..., n} in terms of transpositions lies in O(n4), a sharp bound. Using a connection with the intersection numbers of certain curves in van Kampen diagrams, we prove that this bound is sharp, and give a practical criterion for proving that the derivations provided by the reversing algorithm...

Factorizing low-rank matrices has many applications in machine learning and statistics. For probabilistic models in the Bayes optimal setting, a general expression for the mutual information has been proposed using heuristic statistical physics computations, and proven in few specific cases. Here, we show how to rigorously prove the conjectured formula for the symmetric rank-one case. This allo...

– We analyse the eigenvalue structure of the replicated transfer matrix of onedimensional disordered Ising models. In the limit of n → 0 replicas, an infinite sequence of transfer matrices is found, each corresponding to a different irreducible representation (labelled by a positive integer ρ) of the permutation group. We show that the free energy can be calculated from the replica-symmetric su...

There are many combinatorial expressions for evaluating characters of the Hecke algebra of type A. However, with rare exceptions, they give simple results only for permutations that have minimal length in their conjugacy class. For other permutations, a recursive formula has to be applied. Consequently, quantum immanants are complicated objects when expressed in the standard basis of the quantu...

We present a Monte Carlo calculation of the effect of small site or bond dilution in a nn/nnn Ising model in two dimensions. Whereas the Harris criterion for the cross-over exponent, 4 = a, is satisfied by the ferromagnetic system, the calculated value of 4 for the antiferromagnet is consistent with 4 = y 2P. It has been predicted by Harris [I] that the critical behaviour of ferromagnetic syste...

We observe that, for fixed n ≥ 3, each of the Artin groups of finite type An, Bn = Cn, and affine type Ãn−1 and C̃n−1 is a central extension of a finite index subgroup of the mapping class group of the (n + 2)-punctured sphere. (The centre is trivial in the affine case and infinite cyclic in the finite type cases). Using results of Ivanov and Korkmaz on abstract commensurators of surface mapping...

I briefly review the three nonperturbative methods for the treatment of disordered systems — supersymmetry, replicas and dynamics — with a parallel presentation that highlights their connections and differences. Disordered systems need to be treated with a method that allows to perform averages over the sample realisation. There is no universal way to do this that can be applied efficiently to ...

A statistical physics model for the time evolutions of stock portfolios is proposed. In this model the time series of price changes are coded into the sequences of up and down spins. The Hamiltonian of the system is introduced and is expressed by spin-spin interactions as in spin glass models of disordered magnetic systems. The interaction coefficients between two stocks are determined by empir...