The last decade has witnessed a growing interest in random forest models which are recognized to exhibit good practical performance, especially in high-dimensional settings. On the theoretical side, however, their predictive power remains largely unexplained, thereby creating a gap between theory and practice. The aim of this paper is twofold. Firstly, we provide theoretical guarantees to link ...

The statistical quality control process on raw materials and/or the final product of traditional Chinese medicine (TCM) is examined. We develop a statistical quality control (QC) method to assess a proposed consistency index of raw materials from different sources and/or final products manufactured at different sites. The idea is to construct a 95% confidence interval for a proposed consistency...

We investigate Matrix theory in the large-N limit following the conjectured correspondence between Matrix theory and supergravity on the near-horizon limit of the D0-brane background. We analyze the complete fermionic spectrum of supergravity and obtain two-point functions of the supercurrents in Matrix theory. By examining the large-N scaling properties of the correlators, we discuss the consi...

We obtain a limit of a hierarchical Bayes estimator of a finite population mean when the sample size is large. The limit is in the sense of ordinary calculus, where the sample observations are treated as fixed quantities. Our result suggests a simple way to correct the hierarchical Bayes estimator to achieve design-consistency, a well-known property in the traditional randomization approach to ...

We investigate the possibility of incorporating a chiral fourth generation into a GUT model. We find that in order to do so, precision fits to electroweak observables demand the introduction of light (< MZ) su-persymmetric particles. This also enables us to provide decay channels to the fourth-generation quarks. Perturbative consistency sets an upper bound on the coloured supersymmetric spectru...

We investigate properties of the color space of SU(Nc) gauge theories in the limit of small number of colors (Nc → 0) and large number of flavors. More generally, we introduce a rescaling of αs and nf which assigns a finite limit to colored quantities as Nc → 0, which reproduces their known large-Nc limit, and which expresses them as an analytic function of N2 c for arbitrary value of Nc. The v...

1. BASIC PROBABILITY THEORY 1.1 Measure-theoretical foundation of probability theory 1.2 Independence 1.3 Borel measurable functions 1.4 Mathematical expectatlon 1.5 Characteristic functions 1.6 Random functions 2. CONVERGENCE 2.1 Heak and strong convergence of random variables 2.2 Convergence of mathematical expectations 2.3 Convergence of distributions 2.4 Central limit theoreras 2.5 Further ...

Current multi-core network protocol stack designs use lock-based and scheduler-based approaches to leverage multiple processors. Unfortunately, these approaches limit protocol stack scalability on multicore systems both for high-bandwidth connections and large numbers of concurrent connections. In this paper, we propose a new approach to parallelizing network protocol stacks based on state repl...

The present study focuses on a class of games with reinforcement-learning agents that adaptively choose their actions to locally maximize their rewards. By analyzing a limit model with a special type of learning, previous studies suggested that dynamics of games with learners may become chaotic. We evaluated the generality of this model by analyzing the consistency of this limit model in compar...

Here we assume that the logarithmic asset price is given by a semimartingale. Jacod (2006) has derived an infeasible central limit theorem for the realised variance in such a general framework. However, here we focus on constructing a feasible limit theorem. We propose a new estimator for the asymptotic variance of the realised variance. This new estimator is based on generalised versions of th...