Random Forests and Networks Analysis

D. Wilson~\cite{[Wi]} in the 1990's described a simple and efficient algorithm based on loop-erased random walks to sample uniform spanning trees and more generally weighted trees or forests spanning a given graph. This algorithm provides a powerful tool in analyzing structures on networks and along this line of thinking, in recent works~\cite{AG1,AG2,ACGM1,ACGM2} we focused on applications of spanning rooted forests on finite graphs. The resulting main conclusions are reviewed in this paper by collecting related theorems, algorithms, heuristics and numerical experiments. A first foundational part on determinantal structures and efficient sampling procedures is followed by four main applications: 1) a random-walk-based notion of well-distributed points in a graph 2) how to describe metastable dynamics in finite settings by means of Markov intertwining dualities 3) coarse graining schemes for networks and associated processes 4) wavelets-like pyramidal algorithms for graph signals.Comment: Survey pape

Neutron monitors and muon detectors for solar modulation studies: 2. ϕ\phi time series

The level of solar modulation at different times (related to the solar activity) is a central question of solar and galactic cosmic-ray physics. In the first paper of this series, we have established a correspondence between the uncertainties on ground-based detectors count rates and the parameter $\phi$ (modulation level in the force-field approximation) reconstructed from these count rates. In this second paper, we detail a procedure to obtain a reference $\phi$ time series from neutron monitor data. We show that we can have an unbiased and accurate $\phi$ reconstruction ($\Delta\phi/\phi\simeq 10\%$). We also discuss the potential of Bonner spheres spectrometers and muon detectors to provide $\phi$ time series. Two by-products of this calculation are updated $\phi$ values for the cosmic-ray database and a web interface to retrieve and plot $\phi$ from the 50's to today (\url{http://lpsc.in2p3.fr/crdb}).Comment: 15 pages, 5 figures, 2 tables. AdSR, in press. Web interface to get modulation parameter phi(t): new tab in http://lpsc.in2p3.fr/crd

Real space investigation of structural changes at the metal-insulator transition in VO2

Synchrotron X-ray total scattering studies of structural changes in rutile VO2 at the metal-insulator transition temperature of 340 K reveal that monoclinic and tetragonal phases of VO2 coexist in equilibrium, as expected for a first-order phase transition. No evidence for any distinct intermediate phase is seen. Unbiased local structure studies of the changes in V--V distances through the phase transition, using reverse Monte Carlo methods, support the idea of phase coexistence and point to the high degree of correlation in the dimerized low-temperature structure. No evidence for short range V--V correlations that would be suggestive of local dimers is found in the metallic phase.Comment: 4 pages, 5 figure

Regioselective trans-Hydrostannation of Boron-Capped Alkynes

Alkynyl-B(aam) (aam=anthranilamidato) derivatives are readily available bench-stable compounds that undergo remarkably selective reactions with Bu3SnH in the presence of [Cp*RuCl]4 as the catalyst. The addition follows a stereochemically unorthodox trans-selective course; in terms of regioselectivity, the Bu3Sn- unit is delivered with high fidelity to the C-atom of the triple bond adjacent to the boracyclic head group (“alpha,trans-addition”). This outcome is deemed to reflect a hydrogen bonding interaction between the protic −NH groups of the benzo-1,3,2-diazaborininone ring system and the polarized [Ru−Cl] bond in the loaded catalyst, which locks the substrate in place in a favorable orientation relative to the incoming reagent. The resulting isomerically (almost) pure gem-dimetalated building blocks are amenable to numerous downstream functionalizations; most remarkable is the ability to subject the −B(aam) moiety to Suzuki-Miyaura cross coupling without need for prior hydrolysis while keeping the adjacent Bu3Sn- group intact. Alternatively, the tin residue can be engaged in selective tin/halogen exchange without touching the boron substituent; the fact that the two -NH entities of −B(aam) do not protonate organozinc reagents and hence do not interfere with Negishi reactions of the alkenyl halides thus formed is another virtue of this so far underutilized boracycle. Overall, the ruthenium catalyzed trans-hydrostannation of alkynyl-B(aam) derivatives opens a practical gateway to isomerically pure trisubstituted alkenes of many different substitution patterns by sequential functionalization of the 1-alkenyl-1,1-heterobimetallic adducts primarily formed

Dielectric anomalies and spiral magnetic order in CoCr2O4

We have investigated the structural, magnetic, thermodynamic, and dielectric properties of polycrystalline CoCr$_2$O$_4$, an insulating spinel exhibiting both ferrimagnetic and spiral magnetic structures. Below $T_c$ = 94 K the sample develops long-range ferrimagnetic order, and we attribute a sharp phase transition at $T_N$ $\approx$ 25 K with the onset of long-range spiral magnetic order. Neutron measurements confirm that while the structure remains cubic at 80 K and at 11 K; there is complex magnetic ordering by 11 K. Density functional theory supports the view of a ferrimagnetic semiconductor with magnetic interactions consistent with non-collinear ordering. Capacitance measurements on CoCr$_2$O$_4$, show a sharp decrease in the dielectric constant at $T_N$, but also an anomaly showing thermal hysteresis falling between approximately $T$ = 50 K and $T$ = 57 K. We tentatively attribute the appearance of this higher temperature dielectric anomaly to the development of \textit{short-range} spiral magnetic order, and discuss these results in the context of utilizing dielectric spectroscopy to investigate non-collinear short-range magnetic structures.Comment: & Figure

Understanding complex magnetic order in disordered cobalt hydroxides through analysis of the local structure

In many ostensibly crystalline materials, unit-cell-based descriptions do not always capture the complete physics of the system due to disruption in long-range order. In the series of cobalt hydroxides studied here, Co(OH)$_{2-x}$(Cl)$_x$(H$_2$O)$_{n}$, magnetic Bragg diffraction reveals a fully compensated N\'eel state, yet the materials show significant and open magnetization loops. A detailed analysis of the local structure defines the aperiodic arrangement of cobalt coordination polyhedra. Representation of the structure as a combination of distinct polyhedral motifs explains the existence of locally uncompensated moments and provides a quantitative agreement with bulk magnetic measurements and magnetic Bragg diffraction