We prove that finiteness of the index of the intersection of a finite set of finite index subalgebras in a von Neumann algebra (with small centre) is equivalent to the finite dimensionality of the algebra generated by the conditional expectations onto the subalgebras. Supported in part by NSF gramt DMS-9322675 and Marsden grant UOA520. Supported in part by NSF grant DMS-0200770.

26 The structure of the human brain changes in a variety of ways as we age. While a sizeable 27 literature has examined age-related differences in cortical thickness, and to a lesser 28 degree, gyrification, here we examined differences in cortical complexity, as indexed by 29 fractal dimensionality in a sample of over 400 individuals across the adult lifespan. While 30 prior studies have shown...

We propose a single-index di usion model in this paper. This model can avoid the `curse of dimensionality' in estimating a multivariate nonparametric conditional variance. We adopt an absolute deviation estimation method to estimate the model. Comparing with the commonly used estimators, the absolute deviation estimator is more stable and efcient. Some simulations and applications to real data ...

Conditional independence testing is an important problem, especially in Bayesian network learning and causal discovery. Due to the curse of dimensionality the case of continuous variables is particularly challenging. We propose a Kernel-based Conditional Independence test (KCI-test), by constructing an appropriate test statistic and deriving its asymptotic distribution under the null hypothesis...

Parameter estimation becomes difficult in high-dimensional spaces due to the increasing sparseness of the data. Therefore, when a low-dimensional representation is embedded in the data, dimensionality reduction methods become useful. One such method-projection pursuit regression (Friedman and Stuetzle 1981 (PPR)-is capable of performing dimensionality reduction by composition, namely, it constr...

Electric power SCADA (Supervisory Control and Data Acquisition) system gradually transforming from a separate private network to an open public network, seriously increases the vulnerability risk in electric power SCADA. In order to assess the vulnerability risk in electric power SCADA system, the paper firstly uses Delphi method and AHP (Analytic Hierarchy Process) to build an index system of ...

With the proliferation of mobile computing, the ability to index efficiently the movements of mobile objects becomes important. Objects are typically seen as moving in two-dimensional (x, y) space, which means that their movements across time may be embedded in the three-dimensional (x, y, t) space. Further, the movements are typically represented as trajectories, sequences of connected line se...

In the absence of a single composite measure to assess, rank, and test disability and functional needs in the context of disaster, this study undertook an interdisciplinary approach to develop a composite index based on C-MIST theory. An examination into how well the CMIST index represents the multidimensional nature of disability and functional needs was conducted, as well as illustrating any ...

let g be a simple graph with vertex set v(g) {v1,v2 ,...vn} . for every vertex i v , ( ) i  vrepresents the degree of vertex i v . the h-th order of randić index, h r is defined as the sumof terms1 2 11( ), ( )... ( ) i i ih  v  v  vover all paths of length h contained (as sub graphs) in g . inthis paper , some bounds for higher randić index and a method for computing the higherrandic ind...

In this paper, several two-dimensional extensions of principal component analysis (PCA) and linear discriminant analysis (LDA) techniques has been applied in a lossless dimensionality reduction framework, for face recognition application. In this framework, the benefits of dimensionality reduction were used to improve the performance of its predictive model, which was a support vector machine (...