We study the gradient flow of the Riemannian functional F(g) := ∫ M |Rm| . This flow corresponds to a fourth-order degenerate parabolic equation for a Riemannian metric. We prove that, as with the Ricci flow, the degeneracies may be accounted for entirely by diffeomorphism flow, and hence we show short-time existence using the DeTurck method. We prove L2 derivative estimates of Bernstein-Bando-...

We compute the group element of SO(2,2) associated with the spinning black hole found by Bañados, Teitelboim and Zanelli in (2+1)-dimensional anti-de Sitter space-time. We show that their metric is built with SO(2,2) gauge invariant quantities and satisfies Einstein’s equations with negative cosmological constant everywhere except at r = 0. Moreover, although the metric is singular on the horiz...

We present numerical experiments that test the predictions of a conjecture Gaiotto–Moore–Neitzke and Gaiotto concerning monodromy map for opers, non-Abelian Hodge correspondence, restriction hyperkähler L2 metric to Hitchin section. These are conducted in setting polynomial holomorphic differentials on complex plane, where take form conjectural formulas Stokes data tensor. Overall, results our ...

A twin bounded support vector machine (TBSVM) is a phenomenon of symmetry that improves the performance traditional classification algorithm. In this paper, we propose an improved model based on TBSVM, called Welsch loss with capped L2,p-norm distance metric robust (WCTBSVM). On one hand, by introducing in problem non-sparse output regularization term solved; thus, generalization and robustness...

to enrich our understanding of the attitudinal/motivational basis of foreign language learning at junior high school level, this study investigated the students’ status of l2 motivation, the relationship between motivational factors, and the possibility of predicting their motivated learning behavior in light of dörnyei’s (2005, 2009) theory of l2 motivational self system. to this end, 1462 jun...

As language rhythm relies partly on general acoustic properties, such as intensity and duration, mastering two languages with distinct rhythmic properties (i.e., stress position) may enhance musical rhythm perception. We investigated whether competence in a second language (L2) with different rhythmic properties than a L1 affects musical rhythm aptitude. Turkish early (TELG) and late learners (...

We study minimization of the difference of l1 and l2 norms as a non-convex and Lipschitz continuous metric for solving constrained and unconstrained compressed sensing problems. We establish exact (stable) sparse recovery results under a restricted isometry property (RIP) condition for the constrained problem, and a full-rank theorem of the sensing matrix restricted to the support of the sparse...

Consider the standard linear regression model Y = Xβ+w, where Y ∈ R is an observation vector, X ∈ R is a design matrix, β ∈ R is the unknown regression vector, and w ∼ N (0, σI) is additive Gaussian noise. This paper studies the minimax rates of convergence for estimation of β for lp-losses and in the l2-prediction loss, assuming that β belongs to an lq-ball Bq(Rq) for some q ∈ [0, 1]. We show ...

Matching a pair of affine invariant regions between images results in estimation of the affine transformation between the regions. However, the parameters of the affine transformations are rarely used directly for matching images, mainly due to the lack of an appropriate error metric of the distance between them. In this paper we derive a novel metric for measuring the distance between affine t...

The information metric arises in statistics as a natural inner product on a space of probability distributions. In general this inner product is positive semi-definite but is potentially degenerate. By associating to an instanton its energy density, we can examine the information metric g on the moduli spaces M of self-dual connections over Riemannian 4-manifolds. Compared with the more widely ...