We construct finite dimensional families of non-steady solutions to the Euler equations, existing for all time, and exhibiting kinds qualitative dynamics in phase space, example: strange attractors chaos, invariant manifolds arbitrary topology, quasiperiodic tori any dimension. The main theorem paper, from which these are obtained, states that given vector field X on a closed manifold N, there ...

We investigate percolation in the Boolean model with convex grains high dimension. For each dimension d, one fixes a compact, and symmetric set K⊂Rd non empty interior. In first setting, is reunion of translates K. second K or ρK for further parameter ρ∈(1,2). give asymptotic behavior probability threshold two settings.

Feature selection is an NP-hard combinatorial problem, in which the number of possible feature subsets increases exponentially with features. In case large dimensionality, goal to determine smallest features considering most informative subset. this paper, we proposed a hybrid optimization model for Cancer Classification called, ENSVM. Our based on using Elastic Net (EN) method that regulates a...

We steered comparative analysis of manifold supervised dimension reduction methods by assimilating customary multiobjective standard metrics and validated the efficacy learning algorithms in reliance on data sample complexity. The question intricacy is deliberated dependence automating selection user-purposed instances. Different techniques are responsive to different scales measurement supervi...

This paper offers a methodological contribution for computing the distance between two empirical distributions in an Euclidean space of very large dimension. We propose to use decision trees instead of relying on standard quantifi10 cation of the feature space. Our contribution is two-fold: We first define a new distance between empirical distributions, based on the Kullback-Leibler (KL) diverg...

In this paper, we propose a new estimator: the Slope SVM, which minimizes the hinge loss with the Slope penalization introduced by [3]. We study the asymptotical behavior of the `2 error between the theoretical hinge loss minimizer and the Slope estimator. We prove Slope achieves a (k/n) log(p/k) rate with high probability and in expectation under the Weighted Restricted Eigenvalue Condition. T...

Deep neural networks (DNN) have achieved breakthroughs in applications with large sample size. However, when facing high dimension, low sample size (HDLSS) data, such as the phenotype prediction problem using genetic data in bioinformatics, DNN suffers from overfitting and high-variance gradients. In this paper, we propose a DNN model tailored for the HDLSS data, named Deep Neural Pursuit (DNP)...

High dimension, low sample size data are emerging in various areas of science. We find a common structure underlying many such data sets by using a non-standard type of asymptotics: the dimension tends to 1 while the sample size is fixed. Our analysis shows a tendency for the data to lie deterministically at the vertices of a regular simplex. Essentially all the randomness in the data appears o...

This paper considers the maximum likelihood estimation of factor models of high dimension, where the number of variables (N) is comparable with or even greater than the number of observations (T ). An inferential theory is developed. We establish not only consistency but also the rate of convergence and the limiting distributions. Five different sets of identification conditions are considered....

Let A be a d by n matrix, d < n. Let C be the regular cross polytope (octahedron) in R. It has recently been shown that properties of the centrosymmetric polytope P = AC are of interest for finding sparse solutions to the underdetermined system of equations y = Ax; [9]. In particular, it is valuable to know that P is centrally k-neighborly. We study the face numbers of randomly-projected cross-...