Joint min-max distribution and Edwards-Anderson's order parameter of the circular 1/f1 / f-noise model

We calculate the joint min--max distribution and the Edwards-Anderson's order parameter for the circular model of $1 / f$-noise. Both quantities, as well as generalisations, are obtained exactly by combining the freezing-duality conjecture and Jack-polynomial techniques. Numerical checks come with significantly improved control of finite-size effects in the glassy phase, and the results convincingly validate the freezing-duality conjecture. Application to diffusive dynamics is discussed. We also provide a formula for the pre-factor ratio of the joint/marginal Carpentier-Le Doussal tail for minimum/maximum which applies to any logarithmic random energy model.Comment: 6 pages, 3 figure

Regression with respect to sensing actions and partial states

In this paper, we present a state-based regression function for planning domains where an agent does not have complete information and may have sensing actions. We consider binary domains and employ the 0-approximation [Son & Baral 2001] to define the regression function. In binary domains, the use of 0-approximation means using 3-valued states. Although planning using this approach is incomplete with respect to the full semantics, we adopt it to have a lower complexity. We prove the soundness and completeness of our regression formulation with respect to the definition of progression. More specifically, we show that (i) a plan obtained through regression for a planning problem is indeed a progression solution of that planning problem, and that (ii) for each plan found through progression, using regression one obtains that plan or an equivalent one. We then develop a conditional planner that utilizes our regression function. We prove the soundness and completeness of our planning algorithm and present experimental results with respect to several well known planning problems in the literature.Comment: 38 page

Log-correlated Random Energy Models with extensive free energy fluctuations: pathologies caused by rare events as signatures of phase transitions

We address systematically an apparent non-physical behavior of the free energy moment generating function for several instances of the logarithmically correlated models: the Fractional Brownian Motion with Hurst index $H = 0$ (fBm0) (and its bridge version), a 1D model appearing in decaying Burgers turbulence with log-correlated initial conditions, and finally, the two-dimensional logREM introduced in [Cao et al., Phys.Rev.Lett.,118,090601] based on the 2D Gaussian free field (GFF) with background charges and directly related to the Liouville field theory. All these models share anomalously large fluctuations of the associated free energy, with a variance proportional to the log of the system size. We argue that a seemingly non-physical vanishing of the moment generating function for some values of parameters is related to the termination point transition (a.k.a pre-freezing). We study the associated universal log corrections in the frozen phase, both for log-REMs and for the standard REM, filling a gap in the literature. For the above mentioned integrable instances of logREMs, we predict the non-trivial free energy cumulants describing non-Gaussian fluctuations on the top of the Gaussian with extensive variance. Some of the predictions are tested numerically.Comment: 17 pages, 4 figure

Determinants of Capital Structure: Evidence from China Public Listed Industrial Companies

This paper examines determinants of capital structure of China-Listed companies in Shang Hai Stock Exchange. Profitability, size, growth rate and liquidity are the variables used as the independent variables, while capital structure is proxied by leverage.The capital market of China went through a remarkable growth from 2006 to 2008, but currently it is in deep recession. This study looks at the factors that influence China's industrial companies' capital structure in a ten-year period, from 1998 to 2010. The findings show that size is positively and significantly correlated to leverage, whilst liquidity is negatively but significantly influences leverage. Both profitability and growth rates do not have any effect on capital structure of the 967 industrial companies examined. The findings also demonstrate that neither the pecking order theory nor trade-off theory derived from the western setting could provide convincing explanation for the capital structure choices of the China's companies. The differences in the choices may be attributed to the fundamental institutional assumptions in the western models that are not valid in China