The distribution of pairwise relative peculiar velocities, f(u;r), on small non-linear scales, r, is derived from the Press{Schechter approach. This derivation assumes that Press{Schechter clumps are virialized and isothermal. The virialized assumption requires that the circular velocity V c / M 1=3 , where M denotes the mass of the clump. The isothermal assumption means that the circular veloc...

Non-negative Matrix Factorisation (NMF) has been extensively used in machine learning and data analytics applications. Most existing variations of NMF only consider how each row/column vector of factorised matrices should be shaped, and ignore the relationship among pairwise rows or columns. In many cases, such pairwise relationship enables better factorisation, for example, image clustering an...

Landmark Multidimensional Scaling (LMDS) The O(N) memory complexity of cMDS makes it an impractical choice when N is the number of pixels. Randomized approaches sample rows of the distance matrix to build approximate representatives of the entire matrix [4]. Depending on the coherence of the right singular vectors of D, it has been shown [2] that the Nyström approximation is the original matrix...

We systematically study pairwise counter-monotonicity, an extremal notion of negative dependence. A stochastic representation and invariance property are established for this dependence structure. show that counter-monotonicity implies association, it is equivalent to joint mix if both possible the same marginal distributions. find intimate connection between risk sharing problems quantile agen...

Non-negative matrix factorization (NMF) is a powerful feature extraction method for finding parts-based, linear representations of non-negative data . Inherently, it is unsupervised learning algorithm. That is to say, the classical NMF algorithm does not respect the class-specific information. This paper presents an improvement of the classical NMF approach by imposing Fisher constraints. This ...

Pairwise maximum-entropy models have been used in neuroscience to predict the activity of neuronal populations, given only the time-averaged correlations of the neuron activities. This paper provides evidence that the pairwise model, applied to experimental recordings, would produce a bimodal distribution for the population-averaged activity, and for some population sizes the second mode would ...

We construct an uncountable family of smooth ergodic zero-entropy diffeomorphisms that are pairwise non-Kakutani equivalent, on any smooth compact connected manifold of dimension greater than two, on which there exists an effective smooth circle action preserving a positive smooth volume. To that end, we first construct a smooth ergodic zero-entropy and non-Loosely Bernoulli diffeomorphism, by ...