Topological properties of hierarchical networks

Hierarchical networks are attracting a renewal interest for modelling the organization of a number of biological systems and for tackling the complexity of statistical mechanical models beyond mean-field limitations. Here we consider the Dyson hierarchical construction for ferromagnets, neural networks and spin-glasses, recently analyzed from a statistical-mechanics perspective, and we focus on the topological properties of the underlying structures. In particular, we find that such structures are weighted graphs that exhibit high degree of clustering and of modularity, with small spectral gap; the robustness of such features with respect to link removal is also studied. These outcomes are then discussed and related to the statistical mechanics scenario in full consistency. Lastly, we look at these weighted graphs as Markov chains and we show that in the limit of infinite size, the emergence of ergodicity breakdown for the stochastic process mirrors the emergence of meta-stabilities in the corresponding statistical mechanical analysis

Meta-stable states in the hierarchical Dyson model drive parallel processing in the hierarchical Hopfield network

In this paper we introduce and investigate the statistical mechanics of hierarchical neural networks: First, we approach these systems \`a la Mattis, by thinking at the Dyson model as a single-pattern hierarchical neural network and we discuss the stability of different retrievable states as predicted by the related self-consistencies obtained from a mean-field bound and from a bound that bypasses the mean-field limitation. The latter is worked out by properly reabsorbing fluctuations of the magnetization related to higher levels of the hierarchy into effective fields for the lower levels. Remarkably, mixing Amit's ansatz technique (to select candidate retrievable states) with the interpolation procedure (to solve for the free energy of these states) we prove that (due to gauge symmetry) the Dyson model accomplishes both serial and parallel processing. One step forward, we extend this scenario toward multiple stored patterns by implementing the Hebb prescription for learning within the couplings. This results in an Hopfield-like networks constrained on a hierarchical topology, for which, restricting to the low storage regime (where the number of patterns grows at most logarithmical with the amount of neurons), we prove the existence of the thermodynamic limit for the free energy and we give an explicit expression of its mean field bound and of the related improved boun

Hierarchical neural networks perform both serial and parallel processing

In this work we study a Hebbian neural network, where neurons are arranged according to a hierarchical architecture such that their couplings scale with their reciprocal distance. As a full statistical mechanics solution is not yet available, after a streamlined introduction to the state of the art via that route, the problem is consistently approached through signal- to-noise technique and extensive numerical simulations. Focusing on the low-storage regime, where the amount of stored patterns grows at most logarithmical with the system size, we prove that these non-mean-field Hopfield-like networks display a richer phase diagram than their classical counterparts. In particular, these networks are able to perform serial processing (i.e. retrieve one pattern at a time through a complete rearrangement of the whole ensemble of neurons) as well as parallel processing (i.e. retrieve several patterns simultaneously, delegating the management of diff erent patterns to diverse communities that build network). The tune between the two regimes is given by the rate of the coupling decay and by the level of noise affecting the system. The price to pay for those remarkable capabilities lies in a network's capacity smaller than the mean field counterpart, thus yielding a new budget principle: the wider the multitasking capabilities, the lower the network load and viceversa. This may have important implications in our understanding of biological complexity

From Dyson to Hopfield: Processing on hierarchical networks

We consider statistical-mechanical models for spin systems built on hierarchical structures, which provide a simple example of non-mean-field framework. We show that the coupling decay with spin distance can give rise to peculiar features and phase diagrams much richer that their mean-field counterpart. In particular, we consider the Dyson model, mimicking ferromagnetism in lattices, and we prove the existence of a number of meta-stabilities, beyond the ordered state, which get stable in the thermodynamic limit. Such a feature is retained when the hierarchical structure is coupled with the Hebb rule for learning, hence mimicking the modular architecture of neurons, and gives rise to an associative network able to perform both as a serial processor as well as a parallel processor, depending crucially on the external stimuli and on the rate of interaction decay with distance; however, those emergent multitasking features reduce the network capacity with respect to the mean-field counterpart. The analysis is accomplished through statistical mechanics, graph theory, signal-to-noise technique and numerical simulations in full consistency. Our results shed light on the biological complexity shown by real networks, and suggest future directions for understanding more realistic models

Simulation of the AGILE gamma-ray imaging detector performance: Part II

In this paper (Paper II) we complete our discussion on the results of a comprehensive GEANT simulation of the scientific performance of the AGILE Gamma-Ray Imaging Detector (GRID), operating in the 30 MeV - 50 GeV energy range in an equatorial orbit of height near 550 km. Here we focus on the on-board Level-2 data processing and discuss possible alternative strategies for event selection and their optimization. We find that the dominant particle background components after our Level-2 processing are electrons and positrons of kinetic energies between 10 and 100 MeV penetrating the GRID instrument from directions almost parallel to the Tracker planes (incidence angles > 90 degrees) or from below. The analog (charge) information available on-board in the GRID Tracker is crucial for a reduction by almost three orders of magnitude of protons (and heavier ions) with kinetic energies near 100 MeV. We also present in this paper the telemetry structure of the GRID photon and particle events, and obtain the on-board effective area for photon detection in the energy range ~30 MeV - 50 GeV.Comment: 24 pages, 10 figures, accepted for publication in Nuclear Instruments and Methods in Physics Research, Section A. See also astro-ph/0202221 and astro-ph/020222

P K-Edge XANES Calculations of Mineral Standards: Exploring the Potential of Theoretical Methods in the Analysis of Phosphorus Speciation

Phosphorus K-edge X-ray absorption near-edge structure(XANES)spectroscopy is a technique routinely employed in the qualitativeand quantitative analysis of phosphorus speciation in many scientificfields. The data analysis is, however, often performed in a qualitativemanner, relying on linear combination fitting protocols or simplecomparisons between the experimental data and the spectra of standards,and little quantitative structural and electronic information is thusretrieved. Herein, we report a thorough theoretical investigationof P K-edge XANES spectra of NaH2PO4 & BULL;H2O, AlPO4, & alpha;-Ti(HPO4)(2)& BULL;H2O, and FePO4 & BULL;2H(2)O showingexcellent agreement with the experimental data. We find that differentcoordination shells of phosphorus, up to a distance of 5-6 & ANGS; from the photoabsorber, contribute to distinct features inthe XANES spectra. This high structural sensitivity enables P K-edgeXANES spectroscopy to even distinguish between nearly isostructuralcrystal phases of the same compound. Additionally, we provide a rationalizationof the pre-edge transitions observed in the spectra of & alpha;-Ti(HPO4)(2)& BULL;H2O and FePO4 & BULL;2H(2)O through density of states calculations. These pre-edge transitionsare found to be enabled by the covalent mixing of phosphorus s andp orbitals and titanium or iron d orbitals, which happens even thoughneither metal ion is directly bound to phosphorus in the two systems.Calculating a P K-edge XANES spectrumwith the FDMNES programstarting from a crystallographic structure leads to excellent agreementwith the experimental data and DOS calculations that enable accurateinterpretation of the observed transitions

Direct structural and mechanistic insights into fast bimolecular chemical reactions in solution through a coupled XAS/UV-Vis multivariate statistical analysis

In this work, we obtain detailed mechanistic and structural information on bimolecular chemical reactions occurring in solution on the second to millisecond time scales through the combination of a statistical, multivariate and theoretical analysis of time-resolved coupled X-ray Absorption Spectroscopy (XAS) and UV-Vis data. We apply this innovative method to investigate the sulfoxidation of p-cyanothioanisole and p-methoxythioanisole by the nonheme FeIV oxo complex [N4Py·FeIV(O)]2+ (N4Py = N,N-bis(2-pyridylmethyl)-N-bis(2-pyridyl)methylamine) in acetonitrile at room temperature. By employing statistical and multivariate techniques we determine the number of key chemical species involved along the reaction paths and derive spectral and concentration profiles for the reaction intermediates. From the quantitative analysis of the XAS spectra we obtain accurate structural information for all reaction intermediates and provide the first structural characterization in solution of complex [N4Py·FeIII(OH)]2+. The employed strategy is promising for the spectroscopic characterization of transient species formed in redox reactions. © The Royal Society of Chemistry

Activation of C-H bonds by a nonheme iron(iv)-oxo complex: mechanistic evidence through a coupled EDXAS/UV-Vis multivariate analysis

The understanding of reactive processes involving organic substrates is crucial to chemical knowledge and requires multidisciplinary efforts for its advancement. Herein, we apply a combined multivariate, statistical and theoretical analysis of coupled time-resolved X-ray absorption (XAS)/UV-Vis data to obtain detailed mechanistic information for on the C-H bond activation of 9,10-dihydroanthracene (DHA) and diphenylmethane (Ph2CH2) by the nonheme FeIV-oxo complex [N4Py·FeIV(O)]2+ (N4Py = N,N-bis(2-pyridylmethyl)-N-bis(2-pyridyl)methylamine) in CH3CN at room temperature. Within this approach, we determine the number of key chemical species present in the reaction mixtures and derive spectral and concentration profiles for the reaction intermediates. From the quantitative analysis of the XAS spectra the transient intermediate species are structurally determined. As a result, it is suggested that, while DHA is oxidized by [N4Py·FeIV(O)]2+ with a hydrogen atom transfer-electron transfer (HAT-ET) mechanism, Ph2CH2 is oxidized by the nonheme iron-oxo complex through a HAT-radical dissociation pathway. In the latter process, we prove that the intermediate FeIII complex [N4Py·FeIII(OH)]2+ is not able to oxidize the diphenylmethyl radical and we provide its structural characterization in solution. The employed combined experimental and theoretical strategy is promising for the spectroscopic characterization of transient intermediates as well as for the mechanistic investigation of redox chemical transformations on the second to millisecond time scales. This journal i

Caught while Dissolving: Revealing the Interfacial Solvation of the Mg2+ Ions on the MgO Surface

Interfaces between water and materials are ubiquitous and are crucial in materials sciences and in biology, where investigating the interaction of water with the surface under ambient conditions is key to shedding light on the main processes occurring at the interface. Magnesium oxide is a popular model system to study the metal oxide-water interface, where, for sufficient water loadings, theoretical models have suggested that reconstructed surfaces involving hydrated Mg2+ metal ions may be energetically favored. In this work, by combining experimental and theoretical surface-selective ambient pressure X-ray absorption spectroscopy with multivariate curve resolution and molecular dynamics, we evidence in real time the occurrence of Mg2+ solvation at the interphase between MgO and solvating media such as water and methanol (MeOH). Further, we show that the Mg2+ surface ions undergo a reversible solvation process, we prove the dissolution/redeposition of the Mg2+ ions belonging to the MgO surface, and we demonstrate the formation of octahedral [Mg(H2O)6]2+ and [Mg(MeOH)6]2+ intermediate solvated species. The unique surface, electronic, and structural sensitivity of the developed technique may be beneficial to access often elusive properties of low-Z metal ion intermediates involved in interfacial processes of chemical and biological interest