We use differential geometry techniques to estimate the class probability P (y = l|x) for learning both binary and multiclass plug-in classifiers. We propose a geometric regularization technique to find the optimal submanifold corresponding to the estimator of P (y = l|x). The regularization term measures the volume of this submanifold, based on the intuition that overfitting produces fast osci...

Let X be a Stein manifold of dimension at least 3. Given a compact codimension 2 real analytic submanifold M of X, that is the boundary of a compact Levi-flat hypersurface H, we study the regularity of H. Suppose that the CR singularities of M are an O(X)-convex set. For example, suppose M has only finitely many CR singularities, which is a generic condition. Then H must in fact be a real analy...

We revisit the Lagrange and Delaunay systems of equations for the orbital elements, and point out a previously neglected aspect of these equations: in both cases the orbit resides on a certain 9-dimensional submanifold of the 12dimensional space spanned by the orbital elements and their time derivatives. We demonstrate that there exists a vast freedom in choosing this submanifold. This freedom ...

The present work is a continuation of [5] and [6]. In [5] we have obtained derivational equations of a submanifold XM of a generalized Riemannian space GRN . Since the basic tensor in GRN is asymmetric and in this way the connection is also asymmetric, in a submanifold the connection is generally asymmetric too. By reason of this, we define 4 kinds of covariant derivative and obtain 4 kinds of ...

We give a holomorphic extension result from non generic CR submanifold of C of positive CR dimension. We consider N a non generic CR submanifold given by N = {N, h(N)} where N is a generic submanifold of some C and h is a CR map from N into C. We prove that if N is a hypersurface then any CR distribution on N extends holomorphically to a complex transversal wedge, we then generalize this result...

The integrability of the N -cosine model, a N -field generalization of the sine-Gordon model, is investigated. We establish to first order in conformal perturbation theory that, for arbitrary N , the model possesses a quantum conserved current of Lorentz spin 3 on a submanifold of the parameter space where the interaction becomes marginal. The integrability of the model on this submanifold is f...

Abstract: In this paper, firstly, manifold PD(n) consisting of all n× n symmetric positive-definite matrices is introduced based on matrix information geometry; Secondly, the geometrical structures of information submanifold of PD(n) are presented including metric, geodesic and geodesic distance; Thirdly, the information resolution with sensor networks is presented by three classical measuremen...

We revisit the Lagrange and Delaunay systems of equations of celestial mechanics, and point out a previously neglected aspect of these equations: in both cases the orbit resides on a certain 9(N-1)-dimensional submanifold of the 12(N-1)-dimensional space spanned by the orbital elements and their time derivatives. We demonstrate that there exists a vast freedom in choosing this submanifold. This...

Gastric cancer (GC) is one of the most common types of cancer and the second leading cause of cancer-associated mortality. Identification of novel biomarkers is critical to prolonging patient survival. MicroRNAs (miRNAs) proved to play diverse roles in the physiological and pathological state in cancers including GC. Herein we were aimed at performing a meta-analysis on miRNA profiling studies ...

Our main results are: (1) The complex and Lagrangian points of a non-complex and nonLagrangian 2n-dimensional submanifold F :M →N , immersed with parallel mean curvature and with equal Kähler angles into a Kähler-Einstein manifold (N, J, g) of complex dimension 2n, are zeros of finite order of sin θ and cos θ respectively, where θ is the common J-Kähler angle. (2) If M is a Cayley submanifold o...