Ensemble clustering in the belief functions framework

In this paper, belief functions, defined on the lattice of intervals partitions of a set of objects, are investigated as a suitable framework for combining multiple clusterings. We first show how to represent clustering results as masses of evidence allocated to sets of partitions. Then a consensus belief function is obtained using a suitable combination rule. Tools for synthesizing the results are also proposed. The approach is illustrated using synthetic and real data sets.     

Existence and construction of shifted lattice rules with an arbitrary number of points and bounded weighted star discrepancy for general decreasing weights

We study the problem of constructing shifted rank-1 lattice rules for the approximation of high-dimensional integrals with a low weighted star discrepancy, for classes of functions having bounded weighted variation, where the weighted variation is defined as the weighted sum of Hardy–Krause variations over all lower-dimensional projections of the integrand. Under general conditions on the weights, we prove the existence of rank-1 lattice rules such that for any δ>0, the general weighted star discrepancy is O(n^−1+δ) for any number of points n>1 (not necessarily prime), any shift of the lattice, general (decreasing) weights, and uniformly in the dimension. We also show that these rules can be constructed by a component-by-component strategy. This implies in particular that a single infinite-dimensional generating vector can be used for integrals in any number of dimensions, and even for infinite-dimensional integrands when they have bounded weighted variation. These same lattices are also good with respect to the worst-case error in weighted Korobov spaces with the same types of general weights. Similar results were already available for various special cases, such as general weights and prime n, or arbitrary n and product weights, but not for the most general combination of n composite, general weights, arbitrary shift, and star discrepancy, considered here. Our results imply tractability or strong tractability of integration for classes of integrands with finite weighted variation when the weights satisfy the conditions we give. These classes are a strict superset of those covered by earlier sufficient tractability conditions.     

Pairs of chiral quarks on the lattice from staggered fermions

A new formulation of chiral fermions on the lattice is presented. It is a version of overlap fermions, but built from the computationally efficient staggered fermions rather than the previously used Wilson fermions. The construction reduces the four quark flavors described by the staggered fermion to two quark flavors; this pair can be taken as the up and down quarks in Lattice QCD. A domain wall formulation giving a truncation of this overlap construction is also outlined.     

Towards finite density QCD with Taylor expansions

Convergence properties of Taylor expansions of observables, which are also used in lattice QCD calculations at non-zero chemical potential, are analyzed in an effective Nf=2+1$N_f=2+1$ flavor Polyakov quark–meson model. A recently developed algorithmic technique allows the calculation of higher-order Taylor expansion coefficients in functional approaches. This novel technique is for the first time applied to an effective Nf=2+1$N_f=2+1$ flavor Polyakov quark–meson model and the findings are compared with the full model solution at finite densities. The results are used to discuss prospects for locating the QCD phase boundary and a possible critical endpoint in the phase diagram.     

When hadrons become unstable: A novel type of non-analyticity in chiral extrapolations

Hadron masses show a specific dependence on the quark masses. Therefore, the variation of these masses can cause a resonance in a hadronic scattering amplitude to become a bound state. Consequently, the amplitude exhibits a non-analytic behavior at this transition. Crossed amplitudes, where the resonance can be exchanged in the t-channel, can be shown to exhibit the same phenomenon by s→t analytic continuation. This entails possible kinks in lattice quark-mass extrapolations needed to compute hadronic observables.     

A study on the inclusion of body forces in the lattice Boltzmann BGK equation to recover steady-state hydrodynamics

When the lattice Boltzmann (LB) method is used to solve hydrodynamic problems containing a body force term varying in space and/or time, its modelling at the mesoscopic scale must be verified in terms of consistency in order to avoid the appearance of non-hydrodynamic error terms at the macroscopic scale. In the present work it is shown that the modelling of spatially varying steady body force terms in the LB equation must be different from the time-dependent case, when a steady-state flow solution is sought. For that, the Chapman-Enskog analysis is used to derive the LB body force model for the LB BGK equations in a steady-state flow problem. The theoretical findings are supported by numerical tests performed on two different 2D steady-state laminar flows driven by spatially varying body forces with known analytical solutions.     

A method for resummation of perturbative series based on the stochastic solution of Schwinger-Dyson equations

We propose a numerical method for resummation of perturbative series, which is based on the stochastic perturbative solution of Schwinger-Dyson equations. The method stochastically estimates the coefficients of perturbative series, and incorporates Borel resummation in a natural way. Similarly to the “worm” algorithm, the method samples open Feynman diagrams, but with an arbitrary number of external legs. As a test of our numerical algorithm, we study the scale dependence of the renormalized coupling constant in a theory of one-component scalar field with quartic interaction. We confirm the triviality of this theory in four and five space-time dimensions, and the instability of the trivial fixed point in three dimensions.     

High pressure lattice dynamics, dielectric and thermodynamic properties of SrO

Using density functional theory and density functional perturbation theory we have studied the effects of hydrostatic pressure on lattice dynamics, dielectric and thermodynamic properties of the rocksalt (NaCl) and CsCl phases of SrO. The stability of the NiAs type structure, experimentally confirmed to be stable in BaO, is also investigated. Studying the lattice dynamics of the NaCl and CsCl phases at various pressures, in the range of the phase stability, we have found the lattice dynamical instabilities which govern the phase transitions between NaCl and CsCl phases with increasing and decreasing pressure. By monitoring the behaviour of the found soft modes, we have calculated the transition pressures upon compression and decompression of SrO crystal. Lattice dynamics calculations reveal that the rocksalt and CsCl structures are unstable with respect to the soft transversal acoustic modes at single points of the Brillouin zone, which points to the fact that the transitions are of displacive type. Responses to electric fields and thermodynamic properties at high pressures are also given and discussed. All our results are in a good agreement with experimental data where applicable.     

First-principles study of the high pressure phase transition and lattice dynamics of cerium

We present a first-principles study of the phase transition and lattice dynamics of Ce within the framework of the density functional theory using the GGA+U method. Our calculated results denote that under pressure the transition path is α-Ce (fcc)→α″-Ce (monoclinic, with two atoms per unit cell)→bct-Ce (body centered tetragonal), and the transition pressures are located at 5.36 and 14.37 GPa, respectively. The equation of state in a wide range of pressure is consistent with the experimental data. During the γ-α phase transition, the magnetic moment disappears gradually, which is mainly due to the strong interaction between the 4f and 5d electrons. By calculating the free energies from phonon dispersions including electronic contribution, the obtained γ-α transition temperature at zero pressure is 148 K. From the Blackman diagram of dimensionless elastic constant ratios, we can find that both γ- and α-Ce show negative Cauchy pressure—C₄₄>C₁₂.     

Structural and magnetic properties of Li-Cu mixed spinel ferrites

Li_0.5−x/2Cu_xFe_2.5−x/2O₄ (where x=0.0-1.0) ferrites have been prepared by solid-state reaction. X-ray diffraction was used to study the structure of the above investigated ferrites at various sintering temperatures. Samples were sintered at 1000, 1100 and 1200 °C for 3 h in the atmosphere. For the sintering temperature of 1000 °C, Li_0.5−x/2Cu_xFe_2.5−x/2O₄ undergoes cubic to tetragonal transformation for higher Cu content. However, for the sintering temperature of 1100 and 1200 °C, X-ray diffraction patterns are mainly characterized by fcc structure, though presence of tetragonal distortion was found by other temperature dependence of initial permeability curves. The lattice parameter, X-ray density and bulk density were calculated for different compositions. Curie temperature was measured from the temperature dependence of initial permeability curves. Curie temperatures of Li-Cu mixed ferrites were found to decrease with the increase in Cu²⁺ content due to the reduction of A-B interaction. As mentioned earlier, temperature dependence of initial permeability curves was characterized by tetragonal deformation for the samples containing higher at% of Cu. The complex initial permeability has been studied for different samples. The B-H loops were measured at constant frequency, f=1200 Hz, at room temperature (298 K). Coercivity and hysteresis loss were estimated for different Cu contents.