Time reparametrization invariance in arbitrary range p-spin models: symmetric versus non-symmetric dynamics

We explore the existence of time reparametrization symmetry in p-spin models. Using the Martin-Siggia-Rose generating functional, we analytically probe the long-time dynamics. We perform a renormalization group analysis where we systematically integrate over short timescale fluctuations. We find three families of stable fixed points and study the symmetry of those fixed points with respect to time reparametrizations. One of those families is composed entirely of symmetric fixed points, which are associated with the low temperature dynamics. The other two families are composed entirely of non-symmetric fixed points. One of these two non-symmetric families corresponds to the high temperature dynamics. Time reparametrization symmetry is a continuous symmetry that is spontaneously broken in the glass state and we argue that this gives rise to the presence of Goldstone modes. We expect the Goldstone modes to determine the properties of fluctuations in the glass state, in particular predicting the presence of dynamical heterogeneity.Comment: v2: Extensively modified to discuss both high temperature (non-symmetric) and low temperature (symmetric) renormalization group fixed points. Now 16 pages with 1 figure. v1: 13 page

On the strategy frequency problem in batch Minority Games

Ergodic stationary states of Minority Games with S strategies per agent can be characterised in terms of the asymptotic probabilities $\phi_a$ with which an agent uses $a$ of his strategies. We propose here a simple and general method to calculate these quantities in batch canonical and grand-canonical models. Known analytic theories are easily recovered as limiting cases and, as a further application, the strategy frequency problem for the batch grand-canonical Minority Game with S=2 is solved. The generalization of these ideas to multi-asset models is also presented. Though similarly based on response function techniques, our approach is alternative to the one recently employed by Shayeghi and Coolen for canonical batch Minority Games with arbitrary number of strategies.Comment: 17 page

Structure–Spectroscopy Correlations for Intermediate Q of Soluble Methane Monooxygenase: Insights from QM/MM Calculations

The determination of the diiron core intermediate structures involved in the catalytic cycle of soluble methane monooxygenase (sMMO), the enzyme that selectively catalyzes the conversion of methane to methanol, has been a subject of intense interest within the bioinorganic scientific community. Particularly, the specific geometry and electronic structure of the intermediate that precedes methane binding, known as intermediate Q (or MMOHQ), has been debated for over 30 years. Some reported studies support a bis-μ-oxo-bridged Fe(IV)2O2 closed-core conformation Fe(IV)2O2 core, whereas others favor an open-core geometry, with a longer Fe–Fe distance. The lack of consensus calls for a thorough re-examination and reinterpretation of the spectroscopic data available on the MMOHQ intermediate. Herein, we report extensive simulations based on a hybrid quantum mechanics/molecular mechanics approach (QM/MM) approach that takes into account the complete enzyme to explore possible conformations for intermediates MMOHox and MMOHQ of the sMMOH catalytic cycle. High-level quantum chemical approaches are used to correlate specific structural motifs with geometric parameters for comparison with crystallographic and EXAFS data, as well as with spectroscopic data from Mössbauer spectroscopy, Fe K-edge high-energy resolution X-ray absorption spectroscopy (HERFD XAS), and resonance Raman 16O–18O difference spectroscopy. The results provide strong support for an open-core-type configuration in MMOHQ, with the most likely topology involving mono-oxo-bridged Fe ions and alternate terminal Fe-oxo and Fe-hydroxo groups that interact via intramolecular hydrogen bonding. The implications of an open-core intermediate Q on the reaction mechanism of sMMO are discussed

Analogue neural networks on correlated random graphs

We consider a generalization of the Hopfield model, where the entries of patterns are Gaussian and diluted. We focus on the high-storage regime and we investigate analytically the topological properties of the emergent network, as well as the thermodynamic properties of the model. We find that, by properly tuning the dilution in the pattern entries, the network can recover different topological regimes characterized by peculiar scalings of the average coordination number with respect to the system size. The structure is also shown to exhibit a large degree of cliquishness, even when very sparse. Moreover, we obtain explicitly the replica symmetric free energy and the self-consistency equations for the overlaps (order parameters of the theory), which turn out to be classical weighted sums of 'sub-overlaps' defined on all possible sub-graphs. Finally, a study of criticality is performed through a small-overlap expansion of the self-consistencies and through a whole fluctuation theory developed for their rescaled correlations: Both approaches show that the net effect of dilution in pattern entries is to rescale the critical noise level at which ergodicity breaks down.Comment: 34 pages, 3 figure

On the transition to efficiency in Minority Games

The existence of a phase transition with diverging susceptibility in batch Minority Games (MGs) is the mark of informationally efficient regimes and is linked to the specifics of the agents' learning rules. Here we study how the standard scenario is affected in a mixed population game in which agents with the `optimal' learning rule (i.e. the one leading to efficiency) coexist with ones whose adaptive dynamics is sub-optimal. Our generic finding is that any non-vanishing intensive fraction of optimal agents guarantees the existence of an efficient phase. Specifically, we calculate the dependence of the critical point on the fraction $q$ of `optimal' agents focusing our analysis on three cases: MGs with market impact correction, grand-canonical MGs and MGs with heterogeneous comfort levels.Comment: 12 pages, 3 figures; contribution to the special issue "Viewing the World through Spin Glasses" in honour of David Sherrington on the occasion of his 65th birthda

Synthesis Of Ag@silica Nanoparticles By Assisted Laser Ablation

This paper reports the synthesis of silver nanoparticles coated with porous silica (Ag@Silica NPs) using an assisted laser ablation method. This method is a chemical synthesis where one of the reagents (the reducer agent) is introduced in nanometer form by laser ablation of a solid target submerged in an aqueous solution. In a first step, a silicon wafer immersed in water solution was laser ablated for several minutes. Subsequently, an AgNO3 aliquot was added to the aqueous solution. The redox reaction between the silver ions and ablation products leads to a colloidal suspension of core-shell Ag@Silica NPs. The influence of the laser pulse energy, laser wavelength, ablation time, and Ag+ concentration on the size and optical properties of the Ag@Silica NPs was investigated. Furthermore, the colloidal suspensions were studied by UV-VIS-NIR spectroscopy, X-Ray diffraction, and high-resolution transmission electron microscopy (HRTEM).10Mexican founding agency CONACyT [CB183728, CB 176705]Instituto Politecnico Nacional [SIP20130216, SIP20141409, SIP 20151327]Brasilian founding agency FACEPEConselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq