Comprehensive quantum Monte Carlo study of the quantum critical points in planar dimerized/quadrumerized Heisenberg models

We study two planar square lattice Heisenberg models with explicit dimerization or quadrumerization of the couplings in the form of ladder and plaquette arrangements. We investigate the quantum critical points of those models by means of (stochastic series expansion) quantum Monte Carlo simulations as a function of the coupling ratio $\alpha = J^\prime/J$. The critical point of the order-disorder quantum phase transition in the ladder model is determined as $\alpha_\mathrm{c} = 1.9096(2)$ improving on previous studies. For the plaquette model we obtain $\alpha_\mathrm{c} = 1.8230(2)$ establishing a first benchmark for this model from quantum Monte Carlo simulations. Based on those values we give further convincing evidence that the models are in the three-dimensional (3D) classical Heisenberg universality class. The results of this contribution shall be useful as references for future investigations on planar Heisenberg models such as concerning the influence of non-magnetic impurities at the quantum critical point.Comment: 10+ pages, 7 figures, 4 table

A nonparametric empirical Bayes framework for large-scale multiple testing

We propose a flexible and identifiable version of the two-groups model, motivated by hierarchical Bayes considerations, that features an empirical null and a semiparametric mixture model for the non-null cases. We use a computationally efficient predictive recursion marginal likelihood procedure to estimate the model parameters, even the nonparametric mixing distribution. This leads to a nonparametric empirical Bayes testing procedure, which we call PRtest, based on thresholding the estimated local false discovery rates. Simulations and real-data examples demonstrate that, compared to existing approaches, PRtest's careful handling of the non-null density can give a much better fit in the tails of the mixture distribution which, in turn, can lead to more realistic conclusions.Comment: 18 pages, 4 figures, 3 table

Gross Job Flows in Ukraine: Size, Ownership and Trade Effects

This paper documents and analyses gross job flows and their determinants in Ukraine using a unique data set of more than 2200 Ukrainian firms operating in both the manufacturing and the non-manufacturing sector for the years 1998-2000. There are several important findings in the paper. Job destruction is dominating job creation in both 1999 and 2000. In connection with other evidence we infer from this that Ukraine is only at the beginning of the restructuring process. The most clear-cut result of our analysis is the strong positive effect of new private firms on net employment growth, a finding established for other transition economies as well. At the same time, we do not find differences in the employment growth of state-owned and privatised firms. Apart from ownership effects we also find, at the firm level, an inverse correlation of size and net employment growth and of size and job reallocation. Finally, we establish that strong foreign trade links force firms to shed labour more aggressively and to engage in more restructuring when trade is directed to and originating from Western economies. This disciplining function is absent when the trade flows are confined to CIS countries.http://deepblue.lib.umich.edu/bitstream/2027.42/39906/3/wp521.pd

The Generic, Incommensurate Transition in the two-dimensional Boson Hubbard Model

The generic transition in the boson Hubbard model, occurring at an incommensurate chemical potential, is studied in the link-current representation using the recently developed directed geometrical worm algorithm. We find clear evidence for a multi-peak structure in the energy distribution for finite lattices, usually indicative of a first order phase transition. However, this multi-peak structure is shown to disappear in the thermodynamic limit revealing that the true phase transition is second order. These findings cast doubts over the conclusion drawn in a number of previous works considering the relevance of disorder at this transition.Comment: 13 pages, 10 figure

High-Dimensional Stochastic Design Optimization by Adaptive-Sparse Polynomial Dimensional Decomposition

This paper presents a novel adaptive-sparse polynomial dimensional decomposition (PDD) method for stochastic design optimization of complex systems. The method entails an adaptive-sparse PDD approximation of a high-dimensional stochastic response for statistical moment and reliability analyses; a novel integration of the adaptive-sparse PDD approximation and score functions for estimating the first-order design sensitivities of the statistical moments and failure probability; and standard gradient-based optimization algorithms. New analytical formulae are presented for the design sensitivities that are simultaneously determined along with the moments or the failure probability. Numerical results stemming from mathematical functions indicate that the new method provides more computationally efficient design solutions than the existing methods. Finally, stochastic shape optimization of a jet engine bracket with 79 variables was performed, demonstrating the power of the new method to tackle practical engineering problems.Comment: 18 pages, 2 figures, to appear in Sparse Grids and Applications--Stuttgart 2014, Lecture Notes in Computational Science and Engineering 109, edited by J. Garcke and D. Pfl\"{u}ger, Springer International Publishing, 201

Slip-velocity of large neutrally-buoyant particles in turbulent flows

We discuss possible definitions for a stochastic slip velocity that describes the relative motion between large particles and a turbulent flow. This definition is necessary because the slip velocity used in the standard drag model fails when particle size falls within the inertial subrange of ambient turbulence. We propose two definitions, selected in part due to their simplicity: they do not require filtration of the fluid phase velocity field, nor do they require the construction of conditional averages on particle locations. A key benefit of this simplicity is that the stochastic slip velocity proposed here can be calculated equally well for laboratory, field, and numerical experiments. The stochastic slip velocity allows the definition of a Reynolds number that should indicate whether large particles in turbulent flow behave (a) as passive tracers; (b) as a linear filter of the velocity field; or (c) as a nonlinear filter to the velocity field. We calculate the value of stochastic slip for ellipsoidal and spherical particles (the size of the Taylor microscale) measured in laboratory homogeneous isotropic turbulence. The resulting Reynolds number is significantly higher than 1 for both particle shapes, and velocity statistics show that particle motion is a complex non-linear function of the fluid velocity. We further investigate the nonlinear relationship by comparing the probability distribution of fluctuating velocities for particle and fluid phases

Cross-correlations in scaling analyses of phase transitions

Thermal or finite-size scaling analyses of importance sampling Monte Carlo time series in the vicinity of phase transition points often combine different estimates for the same quantity, such as a critical exponent, with the intent to reduce statistical fluctuations. We point out that the origin of such estimates in the same time series results in often pronounced cross-correlations which are usually ignored even in high-precision studies, generically leading to significant underestimation of statistical fluctuations. We suggest to use a simple extension of the conventional analysis taking correlation effects into account, which leads to improved estimators with often substantially reduced statistical fluctuations at almost no extra cost in terms of computation time.Comment: 4 pages, RevTEX4, 3 tables, 1 figur

Computational algebraic methods in efficient estimation

A strong link between information geometry and algebraic statistics is made by investigating statistical manifolds which are algebraic varieties. In particular it it shown how first and second order efficient estimators can be constructed, such as bias corrected Maximum Likelihood and more general estimators, and for which the estimating equations are purely algebraic. In addition it is shown how Gr\"obner basis technology, which is at the heart of algebraic statistics, can be used to reduce the degrees of the terms in the estimating equations. This points the way to the feasible use, to find the estimators, of special methods for solving polynomial equations, such as homotopy continuation methods. Simple examples are given showing both equations and computations. *** The proof of Theorem 2 was corrected by the latest version. Some minor errors were also corrected.Comment: 21 pages, 5 figure

Pengaruh Model Pembelajaran CTL (Contextual Teaching and Learning) terhadap Kemampuan Berpikir Kritis Matematis Siswa pada Materi Sistem Persamaan Linear Dua Variabel

Penelitian ini bertujuan untuk mengetahui Pengaruh Model Pembelajaran Contextual Teaching and Learning (CTL) terhadap Kemampuan Berpikir Kritis Matematis Siswa pada materi Sistem Persamaan Linear Dua Variabel (SPLDV) di Kelas VIII SMP Sw Bukit Cahaya Sidikalang T.A. 2021/2022. Jenis penelitian ini adalah penelitian quasi eksperimen. Dari analisis data diperoleh persamaan regresi untuk kemampuan berpikir kritis . Pada persamaan regresi tersebut, diperoleh nilai b bertanda positif, yang mempunyai hubungan linear yang positif. Dengan uji Koefisien Korelasi, model pembelajaran Contextual Teaching and Learning (X) terhadap kemampuan berpikir kritis siswa (Y) diperoleh koefisien korelasi atau rhitung sebesar 0,877 sehingga dapat disimpulkan berdasarkan tingkat keeratan hubungan dari Guilford Emperical Rulesi bahwa variabel X (model pembelajaran Contextual Teaching and Learning) dan variabel Y (kemampuan berpikir kritis) memiliki hubungan yang kuat/tinggi. Dari uji keberartian koefisien korelasi diperoleh thitung sebesar 7,743 dengan taraf signifikan 5% dk = N – 2, maka harga ttabel sebesar 2,101. Ternyata harga thitung > ttabel (7,743 > 2,101) sehingga Ha diterima dan Ho ditolak. Dalam uji keberartian regresi pada kemampuan berpikir kritis diperoleh Fhitung > Ftabel atau 59,75 > 4,41. Sehingga Ha diterima yang berarti ada pengaruh dari model pembelajaran Contextual Teaching and Learning (CTL) terhadap Kemampuan Berpikir Kritis Matematis siswa pada materi Sistem Persamaan Linear Dua Variabel (SPLDV)