Irreducible free energy expansion and overlaps locking in mean field spin glasses

We introduce a diagrammatic formulation for a cavity field expansion around the critical temperature. This approach allows us to obtain a theory for the overlap's fluctuations and, in particular, the linear part of the Ghirlanda-Guerra relationships (GG) (often called Aizenman-Contucci polynomials (AC)) in a very simple way. We show moreover how these constraints are "superimposed" by the symmetry of the model with respect to the restriction required by thermodynamic stability. Within this framework it is possible to expand the free energy in terms of these irreducible overlaps fluctuations and in a form that simply put in evidence how the complexity of the solution is related to the complexity of the entropy.Comment: 19 page

Order Parameter Flow in the SK Spin-Glass I: Replica Symmetry

We present a theory to describe the dynamics of the Sherrington- Kirkpatrick spin-glass with (sequential) Glauber dynamics in terms of deterministic flow equations for macroscopic parameters. Two transparent assumptions allow us to close the macroscopic laws. Replica theory enters as a tool in the calculation of the time- dependent local field distribution. The theory produces in a natural way dynamical generalisations of the AT- and zero-entropy lines and of Parisi's order parameter function $P(q)$. In equilibrium we recover the standard results from equilibrium statistical mechanics. In this paper we make the replica-symmetric ansatz, as a first step towards calculating the order parameter flow. Numerical simulations support our assumptions and suggest that our equations describe the shape of the local field distribution and the macroscopic dynamics reasonably well in the region where replica symmetry is stable.Comment: 41 pages, Latex, OUTP-94-29S, 14 figures available in hardcop

Coupled dynamics of sequence selection and compactification in mean-field hetero-polymers

We study a simple solvable model describing the genesis of monomer sequences for hetero-polymers (such as proteins), as the result of the equilibration of a slow stochastic genetic selection process which is assumed to be driven by the competing demands of functionality and reproducibility of the polymer's folded structure. Since reproducibility is defined in terms of properties of the folding process, one is led to the analysis of the coupled dynamics of (fast) polymer folding and (slow) genetic sequence selection. For the present mean-field model this analysis can be carried out using the finite-dimensional replica method, leading to exact results for (first- and second-order) transitions and to rich phase diagrams.Comment: 21 pages, 7 figure

Dynamics of a spherical minority game

We present an exact dynamical solution of a spherical version of the batch minority game (MG) with random external information. The control parameters in this model are the ratio of the number of possible values for the public information over the number of agents, and the radius of the spherical constraint on the microscopic degrees of freedom. We find a phase diagram with three phases: two without anomalous response (an oscillating versus a frozen state), and a further frozen phase with divergent integrated response. In contrast to standard MG versions, we can also calculate the volatility exactly. Our study reveals similarities between the spherical and the conventional MG, but also intriguing differences. Numerical simulations confirm our analytical results.Comment: 16 pages, 3 figures; submitted to J. Phys.

Possible Glassiness in a Periodic Long-Range Josephson Array

We present an analytic study of a periodic Josephson array with long-range interactions in a transverse magnetic field. We find that this system exhibits a first-order transition into a phase characterized by an extensive number of states separated by barriers that scale with the system size; the associated discontinuity is small in the limit of weak applied field, thus permitting an explicit analysis in this regime.Comment: 4 pages, 2 Postscript figures in a separate file

p>2 spin glasses with first order ferromagnetic transitions

We consider an infinite-range spherical p-spin glass model with an additional r-spin ferromagnetic interaction, both statically using a replica analysis and dynamically via a generating functional method. For r>2 we find that there are first order transitions to ferromagnetic phases. For r<p there are two ferromagnetic phases, one non-glassy replica symmetric and one exhibiting glassy one-step replica symmetry breaking and aging, whereas for r>=p only the replica symmetric phase exists.Comment: AMSLaTeX, 13 pages, 23 EPS figures ; one figure correcte

Modification of chiral dimethyl tartrate through transesterification : immobilisation on POSS and enantioselectivity reversion in Sharpless asymmetric epoxidation

Modification of dimethyl tartrate has been investigated through transesterification with aminoalcohols to provide reactive functionalities for the covalent bonding of chiral tartrate to polyhedral oligomeric silsesquioxanes. The transesterification of dimethyl tartrate has been widely studied by means of using different catalytic systems and reaction conditions. Through the proper selection of both, the catalytic system and the reaction conditions, it is possible to achieve the mono- or the bis-substituted tartrate derivative as sole products. All the intermediate chiral tartrate-derived ligands were successfully used in the homogeneous enantioselective epoxidation of allylic alcohols providing moderate enantiomeric excess over the products. Attached amine groups have been used to support the modified tartrate ligands onto a haloaryl-functionalized silsesquioxane moiety. This final chiral tartrate ligand displays enantioselectivity reversion in the asymmetric epoxidation of allylic alcohols with regards to the starting dimethyl tartrate ligand, having both molecules them the same chiral sign. However, the POSS-containing ligand can be easily recovered in almost quantitative yield and reused in asymmetric epoxidation reactions. In addition, recovered silsesquioxane-pendant ligand, though displaying decreasing catalytic activity in recycling epoxidation tests, showed very stable enantioselective behavior

Exercise for falls prevention in community-dwelling older adults: Trial and participant characteristics, interventions and bias in clinical trials from a systematic review

IntroductionThere is strong evidence that exercise prevents falls in community-dwelling older people. This review summarises trial and participant characteristics, intervention contents and study quality of 108 randomised trials evaluating exercise interventions for falls prevention in community-dwelling older adults.MethodsMEDLINE, EMBASE, CENTRAL and three other databases sourced randomised controlled trials of exercise as a single intervention to prevent falls in community-dwelling adults aged 60+ years to May 2018.Results108 trials with 146 intervention arms and 23 407 participants were included. Trials were undertaken in 25 countries, 90% of trials had predominantly female participants and 56% had elevated falls risk as an inclusion criterion. In 72% of trial interventions attendance rates exceeded 50% and/or 75% of participants attended 50% or more sessions. Characteristics of the trials within the three types of intervention programme that reduced falls were: (1) balance and functional training interventions lasting on average 25 weeks (IQR 16–52), 39% group based, 63% individually tailored; (2) Tai Chi interventions lasting on average 20 weeks (IQR 15–43), 71% group based, 7% tailored; (3) programmes with multiple types of exercise lasting on average 26 weeks (IQR 12–52), 54% group based, 75% tailored. Only 35% of trials had low risk of bias for allocation concealment, and 53% for attrition bias.ConclusionsThe characteristics of effective exercise interventions can guide clinicians and programme providers in developing optimal interventions based on current best evidence. Future trials should minimise likely sources of bias and comply with reporting guidelines