Polyelectrolyte Adsorption on Charged Substrate

The behavior of a polyelectrolyte adsorbed on a charged substrate of high-dielectric constant is studied by both Monte-Carlo simulation and analytical methods. It is found that in a low enough ionic strength medium, the adsorption transition is first-order where the substrate surface charge still keeps repulsive. The monomer density at the adsorbed surface is identified as the order parameter. It follows a linear relation with substrate surface charge density because of the electrostatic boundary condition at the charged surface. During the transition, the adsorption layer thickness remains finite. A new scaling law for the layer thickness is derived and verified by simulation.Comment: Proceedings of the 3rd Symposium on Slow Dynamics in Complex Systems, 3-8 November 2003, Sendai, Japa

Purchasing Power Parity and Country Characteristics: Evidence from Time Series Analysis

This paper investigates the relationships between country characteristics and the validity of PPP. We use three alternative time series methods to test for the stationarity of real exchange rates for each of the 72 countries over the period from 1976 to 2005. Our result shows that the evidence of PPP exhibits geographic difference. It is most likely to find stationary real exchange rates for European countries, whereas it is least likely to obtain the result of supporting PPP for Asian countries. We then use a probit regression model to examine if county characteristics are related to the validity of PPP. The probit regression result reveals that the validity of PPP decreases with inflation rate and increases with nominal exchange rate volatility.Purchasing power parity, Country characteristics, Unit root tests

On Searching a Table Consistent with Division Poset

Suppose $P_n=\{1,2,...,n\}$ is a partially ordered set with the partial order defined by divisibility, that is, for any two distinct elements $i,j\in P_n$ satisfying $i$ divides $j$, $i<_{P_n} j$. A table $A_n=\{a_i|i=1,2,...,n\}$ of distinct real numbers is said to be \emph{consistent} with $P_n$, provided for any two distinct elements $i,j\in \{1,2,...,n\}$ satisfying $i$ divides $j$, $a_i< a_j$. Given an real number $x$, we want to determine whether $x\in A_n$, by comparing $x$ with as few entries of $A_n$ as possible. In this paper we investigate the complexity $\tau(n)$, measured in the number of comparisons, of the above search problem. We present a $\frac{55n}{72}+O(\ln^2 n)$ search algorithm for $A_n$ and prove a lower bound $({3/4}+{17/2160})n+O(1)$ on $\tau(n)$ by using an adversary argument.Comment: 16 pages, no figure; same results, representation improved, add reference

Bayesian Semi-supervised Learning with Graph Gaussian Processes

We propose a data-efficient Gaussian process-based Bayesian approach to the semi-supervised learning problem on graphs. The proposed model shows extremely competitive performance when compared to the state-of-the-art graph neural networks on semi-supervised learning benchmark experiments, and outperforms the neural networks in active learning experiments where labels are scarce. Furthermore, the model does not require a validation data set for early stopping to control over-fitting. Our model can be viewed as an instance of empirical distribution regression weighted locally by network connectivity. We further motivate the intuitive construction of the model with a Bayesian linear model interpretation where the node features are filtered by an operator related to the graph Laplacian. The method can be easily implemented by adapting off-the-shelf scalable variational inference algorithms for Gaussian processes.Comment: To appear in NIPS 2018 Fixed an error in Figure 2. The previous arxiv version contains two identical sub-figure