Synthesis of a Glyoxalase I Inhibitor from Streptomyces griseosporeus NIIDAet OGASAWARA

The pseudolactones 6 and 12 were prepared in a straightforward way from methyl α-D -glucopyranoside and methyl α-D -mannopyranoside, respectively. The pseudolactone 6 reacted with tert-butyl lithioacetate to give the protected, trihydroxylated cyclohexenone carboxylate 7 (51 %). The sterically hindered, L-ribo-configurated pseudolactone 12 reacted with diethyl ethylphosphonate and dimethyl methylphosphonate to give the protected trihydroxycyclohexenones 17 (49 %) and 18 (62 %), respectively. The hydroxymethylated cyclohexenone 21 was obtained from 18 by treatment with Me₂AlSPh and then formaldehyde, oxidation of the product 19 , and elimination. Deprotection of 21 gave 2 , identical with KD16-Ul. Esterification of 2 gave 1 , identical with the title compound. Alternatively, 1 was obtained in higher yields by esterification of 21 , followed by deprotection of the hydroxy groups. This synthesis gave 1 and 2 from methyl α-D -mannopyranoside in an overall yield of 18 and 20 %, respectively, confirming their absolute configuration.     

Short-Range Spin Glasses and Random Overlap Structures

Properties of Random Overlap Structures (ROSt)’s constructed from the Edwards-Anderson (EA) Spin Glass model on ℤ ^d with periodic boundary conditions are studied. ROSt’s are ℕ×ℕ random matrices whose entries are the overlaps of spin configurations sampled from the Gibbs measure. Since the ROSt construction is the same for mean-field models (like the Sherrington-Kirkpatrick model) as for short-range ones (like the EA model), the setup is a good common ground to study the effect of dimensionality on the properties of the Gibbs measure. In this spirit, it is shown, using translation invariance, that the ROSt of the EA model possesses a local stability that is stronger than stochastic stability, a property known to hold at almost all temperatures in many spin glass models with Gaussian couplings. This fact is used to prove stochastic stability for the EA spin glass at all temperatures and for a wide range of coupling distributions. On the way, a theorem of Newman and Stein about the pure state decomposition of the EA model is recovered and extended.     

Homology of Fortuin–Kasteleyn Clusters of Potts Models on the Torus

Topological properties of Fortuin–Kasteleyn clusters are studied on the torus. Namely, the probability that their topology yields a given subgroup of the first homology group of the torus is computed for Q=1, 2, 3 and 4. The expressions generalize those obtained by Pinson for percolation (Q=1). Numerical results are also presented for three tori of different moduli. They agree with the theoretical predictions for Q=1, 2 and 3. For Q=4 agreement is not ruled out but logarithmic corrections are probably present and they make it harder to decide.     

Small Perturbations of a Spin Glass System

We show through a simple example that perturbations of the Hamiltonian of a spin glass which cannot be detected at the level of the free energy can completely alter the behavior of the overlap. In particular, perturbations of order O(log?N), with N→∞ the size of the system, suffice to have ultrametricity emerge in the thermodynamical limit.     

Spin Glass Computations and Ruelle’s Probability Cascades

We study the Parisi functional, appearing in the Parisi formula for the pressure of the SK model, as a functional on Ruelle's Probability Cascades (RPC). Computation techniques for the RPC formulation of the functional are developed. They are used to derive continuity and monotonicity properties of the functional retrieving a theorem of Guerra. We also detail the connection between the Aizenman-Sims-Starr variational principle and the Parisi formula. As a final application of the techniques, we rederive the Almeida-Thouless line in the spirit of Toninelli but relying on the RPC structure.     

Random overlap structures: properties and applications to spin glasses

Random overlap structures (ROSt’s) are random elements on the space of probability measures on the unit ball of a Hilbert space, where two measures are identified if they differ by an isometry. In spin glasses, they arise as natural limits of Gibbs measures under the appropriate algebra of functions. We prove that the so called ‘cavity mapping’ on the space of ROSt’s is continuous, leading to a proof of the stochastic stability conjecture for the limiting Gibbs measures of a large class of spin glass models. Similar arguments yield the proofs of a number of other properties of ROSt’s that may be useful in future attempts at proving the ultrametricity conjecture. Lastly, assuming that the ultrametricity conjecture holds, the setup yields a constructive proof of the Parisi formula for the free energy of the Sherrington–Kirkpatrick model by making rigorous a heuristic of Aizenman, Sims and Starr.     

Uniqueness of Ground States for Short-Range Spin Glasses in the Half-Plane

We consider the Edwards-Anderson Ising spin glass model on the half-plane \mathbbZ ×\mathbbZ⁺{\mathbb{Z} \times \mathbb{Z}^+} with zero external field and a wide range of choices, including mean zero Gaussian for the common distribution of the collection J of i.i.d. nearest neighbor couplings. The infinite-volume joint distribution K(J,a){\mathcal{K}(J,\alpha)} of couplings J and ground state pairs α with periodic (respectively, free) boundary conditions in the horizontal (respectively, vertical) coordinate is shown to exist without need for subsequence limits. Our main result is that for almost every J, the conditional distribution K(a | J){\mathcal{K}(\alpha\,|\,J)} is supported on a single ground state pair.     

Maximum of the Riemann Zeta Function on a Short Interval of the Critical Line

We prove the leading order of a conjecture by Fyodorov, Hiary, and Keating about the maximum of the Riemann zeta function on random intervals along the critical line. More precisely, as T → ∞ for a set of t ∊ [T, 2T] of measure (1–o(1)) T, we have © 2018 Wiley Periodicals, Inc.     

Spin lattice coupling in multiferroic hexagonal YMnO3

Aiming to shed light on the possible existence of hybrid phonon-magnon excitations in multiferroic manganites, neutron scattering measurements have been undertaken at LLB and ILL on the particular case of hexagonal YMnO₃. Our experiments focused on a transverse acoustic phonon mode polarized along the ferroelectric axis. The neutron data show that below the magnetic transition, this particular phonon mode splits in two different branches. The upper branch is found to coincide with a spin wave mode. This manifestation of a strong spin-lattice coupling is discussed in terms of a possible hybridization between the two types of elementary excitations, the phonon and magnons.