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

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

Maîtrise foncière, pratiques agricoles durables et protection de la ressource en eau : quels outils d’intervention sur les AAC ?

Enjeu de santé publique et de préservation des milieux, la protection des captages et de la ressource en eau fait l’objet d’une série de dispositifs mis en oeuvre à la fois de façon règlementaire et volontaire. Les acteurs de la protection, à l’échelon local, ont notamment recours à toute la gamme d’outils fonciers : de la maîtrise de l’usage du sol à l’acquisition foncière en propriété. En plus, la mise en oeuvre de pratiques agricoles durables, par le biais du bail environnemental notamment, est une orientation forte pour concilier activité agricole et protection des ressources en eau. Les expériences observables en Île-de-France font état des obstacles rencontrés pour la mise en oeuvre de ce type d’actions. La principale difficulté, en dehors de la capacité des gestionnaires, concerne le rapport entre la profession agricole et l’instrument foncier. En Île-de-France, la situation est exacerbée compte tenu du contexte de pression foncière forte

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

Tuning magnetic frustration on the diamond lattice of the A-site magnetic spinels CoAl2−x_{2-x}Gax_xO4_4: Lattice expansion and site disorder

The spinels CoB$_2$O$_4$ with magnetic Co$^{2+}$ ions on the diamond lattice A site can be frustrated because of competing near-neighbor ($J_1$) and next-near neighbor ($J_2$) interactions. Here we describe attempts to tune the relative strengths of these interactions by substitution on the non-magnetic B-site. The system we employ is CoAl$_{2-x}$Ga$_x$O$_4$, where Al is systematically replaced by the larger Ga, ostensibly on the B site. As expected, Ga substitution expands the lattice, resulting in Co atoms on the A-site being pushed further from one other and thereby weakening magnetic interactions. In addition, Ga distributes between the B and the A site in a concentration dependent manner displacing an increasing amount of Co from the A site with increasing $x$. This increased inversion, which is confirmed by neutron diffraction studies carried out at room temperature, affects magnetic ordering very significantly, and changes the nature of the ground state. Modeling of the magnetic coupling illustrates the complexity that arises from the cation site disorder.Comment: 9 pages, 10 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

Determining conductivity and mobility values of individual components in multiphase composite Cu_(1.97)Ag_(0.03)Se

The intense interest in phase segregation in thermoelectrics as a means to reduce the lattice thermal conductivity and to modify the electronic properties from nanoscale size effects has not been met with a method for separately measuring the properties of each phase assuming a classical mixture. Here, we apply effective medium theory for measurements of the in-line and Hall resistivity of a multiphase composite, in this case Cu_(1.97) Ag_(0.03)Se. The behavior of these properties with magnetic field as analyzed by effective medium theory allows us to separate the conductivity and charge carrier mobility of each phase. This powerful technique can be used to determine the matrix properties in the presence of an unwanted impurity phase, to control each phase in an engineered composite, and to determine the maximum carrier concentration change by a given dopant, making it the first step toward a full optimization of a multiphase thermoelectric material and distinguishing nanoscale effects from those of a classical mixture