We discuss the detection of two Gaussian clusters given a cloud of points. The optimal learning curve for this unsupervised learning scenario is determined with a replica calculation. A comparison with principal component analysis and supervised learning allows to understand the three diierent learning phases observed.

This paper considers a decomposition framework as a mechanism for information hiding for secure communication via open network channels. Two varieties of this framework are provided: one is based on Gaussian arithmetic with complex modulus and another on an elliptic curve modular equation. The proposed algorithm is illustrated in a numerical example.

For triangles with linear vertex motion, common practice is to backface cull a triangle if it is backfacing at both the start and end of the motion. However, this is not conservative. We derive conservative tests that guarantee that a moving triangle is backfacing over an entire time interval and over the area of a lens. In addition, we present tests for the special cases of only motion blur an...

This note is about the geometry of holomorphic foliations. Let X be a polynomial vector field with isolated singularities on C2. We announce some results regarding two problems: 1. Given a finitely curved orbit L of X, under which conditions is L algebraic? 2. If X has some non-algebraic finitely curved orbit L what is the classification of X? Problem 1 is related to the following question: Let...

Principal curves are smooth curves that minimize the average squared orthogonal distance to each point in a data set. Fitting a principal curve is a maximum-likelihood technique for nonlinear regression in the presence of Gaussian noise on both x and y. We choose two definitions of principal curves in the literature and then present experimental results to discuss over them.

Let C be a curve of genus g over a field k. We describe probabilistic algorithms for addition and inversion of the classes of rational divisors in the Jacobian of C. After a precomputation, which is done only once for the curve C, the algorithms use only linear algebra in vector spaces of dimension at most O(g log g), and so take O(g3+ ) field operations in k, using Gaussian elimination. Using ...

A quantitative analytical method, using a spreadsheet, has been developed that allows the determination of values of the three parameters that characterize the Hubbert-style Gaussian error curve that best fits the conventional oil production data both for the U.S. and the world. The three parameters are the total area under the Gaussian, which represents the estimated ultimate (oil) recovery (E...

We provide some insights into how task correlations in multi-task Gaussian process (GP) regression affect the generalization error and the learning curve. We analyze the asymmetric two-tasks case, where a secondary task is to help the learning of a primary task. Within this setting, we give bounds on the generalization error and the learning curve of the primary task. Our approach admits intuit...

Roe and Woodroofe (RW) have suggested that certain conditional probabilities be incorporated into the “unified approach” for constructing confidence intervals, previously described by Feldman and Cousins (FC). RW illustrated this conditioning technique using one of the two prototype problems in the FC paper, that of Poisson processes with background. The main effect was on the upper curve in th...

In the Pseudo-Multiple-Exposure-Based Tone Fusion with Local Region Adjustment [1], it introduces a framework for inverse tone mapping which uses only one Low Dynamic Range (LDR) image to evaluate High Dynamic Range (HDR) image. First, map LDR image to HDR images using S curve. By changing the parameters of S curve, we can get different EV scenes. Then, segment the image into four different lum...