Statistical mechanical systems on complete graphs, infinite exchangeability, finite extensions and a discrete finite moment problem

We show that a large collection of statistical mechanical systems with quadratically represented Hamiltonians on the complete graph can be extended to infinite exchangeable processes. This extends a known result for the ferromagnetic Curie--Weiss Ising model and includes as well all ferromagnetic Curie--Weiss Potts and Curie--Weiss Heisenberg models. By de Finetti's theorem, this is equivalent to showing that these probability measures can be expressed as averages of product measures. We provide examples showing that ``ferromagnetism'' is not however in itself sufficient and also study in some detail the Curie--Weiss Ising model with an additional 3-body interaction. Finally, we study the question of how much the antiferromagnetic Curie--Weiss Ising model can be extended. In this direction, we obtain sharp asymptotic results via a solution to a new moment problem. We also obtain a ``formula'' for the extension which is valid in many cases.Comment: Published at http://dx.doi.org/10.1214/009117906000001033 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org

Synchronization versus stability of the invariant distribution for a class of globally coupled maps

We study a class of globally coupled maps in the continuum limit, where the individual maps are expanding maps of the circle. The circle maps in question are such that the uncoupled system admits a unique absolutely continuous invariant measure (acim), which is furthermore mixing. Interaction arises in the form of diffusive coupling, which involves a function that is discontinuous on the circle. We show that for sufficiently small coupling strength the coupled map system admits a unique absolutely continuous invariant distribution, which depends on the coupling strength $\varepsilon$. Furthermore, the invariant density exponentially attracts all initial distributions considered in our framework. We also show that the dependence of the invariant density on the coupling strength $\varepsilon$ is Lipschitz continuous in the BV norm. When the coupling is sufficiently strong, the limit behavior of the system is more complex. We prove that a wide class of initial measures approach a point mass with support moving chaotically on the circle. This can be interpreted as synchronization in a chaotic state

Validation of the Estimated Torques of an Open-chain Kinematic Model of the Human Body

The standing human body is frequently modeled as an inverted double pendulum restricted to a single plane. In order to capture the coordination efforts and interplay between spatial dimensions, the model has to capture motion and joint torques in all spatial dimensions. Our two-segment model covers two degrees of freedom (ML and AP revolutions) at the ankle and the hip level and utilizes the Denavit-Hartenberg convention. This work aimed to validate the model's torque estimation on a diverse group of participants (11 women, 22–56 years, 11 men, 22–61 years). The inverse dynamic calculations provide estimated joint torques for a motion capture recorded trial, while standing on a force platform enables the indirect measurement of ankle torques. A 60-second-long visually guided balancing task was recorded and repeated three times. The estimated and the indirectly measured torques were compared, and offset and variance type errors ( normalized RMSE and R2 ) were analyzed. The R2-values were excellent (R2 > 0.90) 64 out of the 66 cases (97%) for AP torques and 58 out of the 66 cases (88%) for ML torques. Normalized RMSE values were dominantly under the 0.35 value with some outliers. RMSE showed no evident connection with age, body height, body mass, or BMI. An open-chain kinematic model with two segments, following the Denavit-Hartenberg convention, is well suited to estimate the control torque traces of the human body during standing balancing and needs only three tracked positions

Erdőszegélyek fajösszetételét és szerkezetét meghatározó tényezők

Vizsgálatainkat két eltérő termőhelyi viszonyok között kialakult e rdőtársulás esetében az erdőállomány és a szomszédos nyílt terület átmeneti zónájában végeztük. A Budai-hegységben két cseres- kocsánytalan tölgyes ( Quercetum petraeae-cerris S oó 1963) erdőállomány, illetve a szomszédos parlag - területek határán található, különböző égtáji kitettségű (ÉK, ÉNY, DK, DNY) erdőszegélyeket vizsgáltunk. Csáfordjánosfa határában egy síkvidéki üde tölgy-kőris-szil ligeterdő ( Fraxino pannonicae-Ulmetum S oó in A S zód 1935 corr. 1963), illetve a szomszédos dunántúli mocsárrét ( Deschampsietum caespitosae ) határán ki - alakult, az előbbiekkel megegyező égtáji kitettségű erdőszegélyeket vizsgáltuk. Célunk volt annak megállapítása, hogy van-e határozott különbség az átmeneti zóna egyes szerkezeti ele - meinek (nyílt terület, lágyszárú szegély, cserjés szegély, erdőköpeny, erdőbelső) fajösszetétele között, az egyes erdőtársulások, illetve a különböző égtáji kitettségű szegélyek esetében. Eredményeink alapján a cseres-kocsánytalan tölgyes és a tölgy-kőris-szil ligeterdő állományok szegélyei - nek fajösszetétele teljes mértékben eltér egymástól. Az erdőszegélyek fajösszetétele és szerkezete minden eset - ben az égtáji kitettségtől függően alakul

Synthesis of Homogeneous Manganese-Doped Titanium Oxide Nanotubes from Titanate Precursors

We report a novel synthesis route of homogeneously manganese-doped titanium dioxide nanotubes in a broad concentration range. The scroll-type trititanate (H(2)Ti(3)O(7)) nanotubes prepared by hydrothermal synthesis were used as precursors. Mn2+ ions were introduced by an ion exchange method resulting Mn(x)H(2-x)Ti(3)O(7). In a subsequent heat-treatment they were transformed into Mn(y)Ti(1-y)O(2) where y=x/(3+x). The state and the local environment of the Mn2+ ions in the precursor and final products were studied by Electron Spin Resonance (ESR) technique. It was found that the Mn2+ ions occupy two positions: the first having an almost perfect cubic symmetry while the other is in a strongly distorted octahedral site. The ratio of the two Mn2+ sites is independent of the doping level and amounts to 15:85 in Mn(x)H(2-x)Ti(3)O(7) and to 5:95 in Mn(y)Ti(1-y)O(2). SQUID magnetometry does not show long-range magnetic order in the homogeneously Mn2+-doped nanotubes.Comment: 7 pages, 6 figure

Calm Multi-Baryon Operators

Outstanding problems in nuclear physics require input and guidance from lattice QCD calculations of few baryons systems. However, these calculations suffer from an exponentially bad signal-to-noise problem which has prevented a controlled extrapolation to the physical point. The variational method has been applied very successfully to two-meson systems, allowing for the extraction of the two-meson states very early in Euclidean time through the use of improved single hadron operators. The sheer numerical cost of using the same techniques in two-baryon systems has been prohibitive. We present an alternate strategy which offers some of the same advantages as the variational method while being significantly less numerically expensive. We first use the Matrix Prony method to form an optimal linear combination of single baryon interpolating fields generated from the same source and different sink interpolators. Very early in Euclidean time this linear combination is numerically free of excited state contamination, so we coin it a calm baryon. This calm baryon operator is then used in the construction of the two-baryon correlation functions. To test this method, we perform calculations on the WM/JLab iso-clover gauge configurations at the SU(3) flavor symmetric point with m{\pi} $\sim$ 800 MeV --- the same configurations we have previously used for the calculation of two-nucleon correlation functions. We observe the calm baryon removes the excited state contamination from the two-nucleon correlation function to as early a time as the single-nucleon is improved, provided non-local (displaced nucleon) sources are used. For the local two-nucleon correlation function (where both nucleons are created from the same space-time location) there is still improvement, but there is significant excited state contamination in the region the single calm baryon displays no excited state contamination.Comment: 8 pages, 3 figures, proceedings for LATTICE 201