The paper investigates the acceleration of t-SNE—an embedding technique that is commonly used for the visualization of high-dimensional data in scatter plots—using two treebased algorithms. In particular, the paper develops variants of the Barnes-Hut algorithm and of the dual-tree algorithm that approximate the gradient used for learning t-SNE embeddings in O(N logN). Our experiments show that ...

Abstract. We study a factorization of bounded linear maps from an operator space A to its dual space A∗. It is shown that T : A −→ A∗ factors through a pair of a column Hilbert spaces Hc and its dual space if and only if T is a bounded linear form on A ⊗ A by the canonical identification equipped with a numerical radius type Haagerup norm. As a consequence, we characterize a bounded linear map ...

If X is the dual space of a given Banach space E , X = E*, we say that X has the weak* fixed point property (w*-fpp) if for every nonempty weak* compact (that is, cr(X, E)-co~npact) convex subset C of X and every nonexpansive mapping T : C + C we have Fix(T) # 0. Which subsets of X are weak* compact depends on the choice of pre-dual. Thus, when discussing the w*-fpp it is important that we have...

It has recently been proposed that certain nonsupersymmetric type II orbifolds have vanishing perturbative contributions to the cosmological constant. We show that techniques of Sen and Vafa allow one to construct dual type II descriptions of these models (some of which have no weakly coupled heterotic dual). The dual type II models are given by the same orbifolds with the string coupling S and...

This paper discusses system identification of dual-rate systems. In particular, a dual-rate system with control interval T and output sampling interval nT is considered. At first the problem of identifying a fast single-rate model with sampling period T based on dual-rate input-output data is studied in the polynomial domain. Then the proposed algorithm is applied to model an industrial process...

Let w 1 = d, w 2 , ... , w s be the weights of the nonzero codewords in a binary linear [n , k, d] code C, and let w1′ , w2′ , ... , ws ′ ′ be the nonzero weights in the dual code C ⊥ . Let t be an integer in the range 0 < t < d such that there are at most d − t weights wi′ with 0 < wi′ ≤ n − t. Assmus and Mattson proved that the words of any weight w i in C form a t-design. We show that if w 2...

BACKGROUND Considerable numbers of HIV-1-infected men who have sex with men (MSM) show a relatively rapid disease progression in China; however, the cause remains elusive. HIV-1 dual infection was reported to occur commonly among the MSM population, and its contribution to clinical prognosis remains controversial. We investigated the occurrence and impact on disease progression of dual infectio...

in this paper, we study spacelike dual biharmonic curves. we characterize spacelike dual biharmonic curves in terms of their curvature and torsion in the lorentzian dual heisenberg group . we give necessary and sufficient conditions for spacelike dual biharmonic curves in the lorentzian dual heisenberg group . therefore, we prove that all spacelike dual biharmonic curves are spacelike dual heli...