We consider the scattering transform for the first order system in the plane, ( ∂x̄ 0 0 ∂x ) ψ − ( 0 q1 q2 0 ) ψ = 0. We show that the scattering map is Lipschitz continuous on a neighborhood of zero in L2. This paper gives an estimate for the scattering map associated to a first-order system Dψ −Qψ = 0 (1) in the plane. Here, D and Q are defined by D = ( ∂x̄ 0 0 ∂x ) and Q = ( 0 q q 0 ) and ∂x̄ a...

Consider an i.i.d. sequence of random variables whose distribution f lies in one of a nested family of models (Mq)q∈N, Mq ⊂ Mq+1. The smallest index q such that Mq⋆ contains f is called the model order. We establish strong consistency of the penalized likelihood order estimator in a general setting with penalties of order η(q) log log n, where η(q) is a dimensional quantity. Moreover, such pena...

the aij and bij being real or complex. This vector field is a deformation of the vector field x∂y −y∂x whose trajectories are concentric circles around 0. We prove in this paper a precise version of the following assertion: for any compact K in the space of the (aij ,bij ), there exist a number p(q) and a neighborhood U(q,K) of 0 such that for (a,b) ∈ K , either 0 is again a center of Wa,b (i.e...

In this paper, we show the second part of Schur-Weyl duality for mixed tensor space. The quantum group U = U(gln) of the general linear group and a q-deformation Br,s(q) of the walled Brauer algebra act on V ⊗r ⊗V ∗⊗s where V = R is the natural U-module. We show that EndBnr,s(q)(V ⊗r ⊗ V ∗) is the image of the representation of U, which we call the rational q-Schur algebra. As a byproduct, we o...

The traditional way to model the visual appearance of the image is to define the spatial interactions of the image voxels in terms of their neighboring voxels. A new spatial interaction model was developed for the 3D lung data by extracting new spatial features based on NMF. Let GNx,y,z ∈ QIx×Iy×Iz be the image signals of the neighborhood of the voxel (x, y, z). By including the image signals o...

Chain Form Reinforcement Learning (CFRL) was proposed for a reinforcement learning agent using low memory. In this paper, we introduce Sneak Form Reinforcement Learning (SFRL). SFRL is the method where we improve CFRL in terms of Contextual Learning. If a sequence of state-action pairs has a shortest path, a SFRL agent cuts and saves the path. To improve the performance of SFRL, we introduce Ma...

We give a precise statement of KAM theorem for a Hamiltonian system in a neighborhood of an elliptic equilibrium point If the frequencies of the elliptic point satisfy a Diophantine condition with exponent and a nondegeneracy condition is ful lled we show that in a neighborhood of radius r the measure of the complement of the KAM tori is exponentially small in r This result is obtained by putti...

(a) X is said to be a Loeb space i® the family of all non-empty, closed subsets of X has a choice function. (b) X is said to be selective i® the family of all non-empty, open subsets of X has a choice function. (c) X is said to be locally compact i® each point in X has a neighborhood base consisting of compact sets. (d) X is called second countable if it has a countable base for T . (e) X is ca...

The design of an ensemble guarantees success, only when its base classifiers make both limited errors as well as high accuracy. We address the problem of achieving the possible enhancement of accuracy of the learning models for diabetes data set.In this paper we design an ensemble by four types of Meta level classifiers for this purpose. The base classifiers for feeding the ensemble we have pro...