The magniication exponents occuring in adaptive map formation algorithms like Kohonen's self-organizing feature map deviate for the information theoretically optimal value = 1 as well as from the values which optimize, e.g., the mean square distortion error (= 1=3 for one-dimensional maps). At the same time, models for categorical perception such as the \perceptual magnet" eeect which are based...

The self-organizing map is discussed as an unsupervised clustering method. Its ability to form clusters indicates similar features in a data set. Based on this property, it is demonstrated that a self-organizing map is capable of identifying features within software code by grouping procedures with similar properties together. This allows us to identify potential objects, abstract data types or...

In this paper, we study the consistency of the regularized least square regression in a general reproducing kernel Hilbert spaces. We characterized the compactness of the inclusion map from a reproducing kernel Hilbert space to the space of continuous functions and showed that the capacity based analysis by uniform covering numbers may fail in a very general setting. We prove the consistency an...

Ionospheric slab thickness is defined as the ratio of TEC to maximum electron density of the F-region (NmF2), proportional to the square of the F2-layer critical frequency (foF2). It is an important parameter in that it is linearly correlated with scale height of the ionosphere, which is related to electron density profile. It also reflects variation of the neutral temperature. Therefore, ionos...

We prove regularity (i.e., smoothness) of measures on R d satisfying the equation L = 0 where L is an operator of type Lu = tr(Au 00) + B ru. Here A is a Lipschitz continuous, uniformly elliptic matrix-valued map and B is merely-square integrable. We also treat a class of corresponding innnite dimensional cases where IR d is replaced by a locally convex topological vector space X. In this cases...

Figure 2 ADC map at 8h (a), T2WI image at 24h (c) of one mouse and MR spectra at 8 (c) and 24h (d). The spectra (SPECIAL, TE/TR=2.8/4000ms, NT=360) (5) was acquired from abnormal ADC region (yellow square, 1.4×1.2×1.6mm) at 8h (b) and T2-hyper-intensive regions (red square, 1.4×1.2×1.6mm) at 24h (d), and displayed with Gaussian adoptization (gf=0.15s). Diffusion tensor echo planar imaging of mo...

The first seven sections of the paper contain a version of localization for the normsquare of the moment map in equivariant de Rham theory. Similar results are proved by P.-E. Paradan in [30], [31], [32]; our statement and method of proof are somewhat different. The existence of such a formula was first suggested by Witten [39], see also Jeffrey and Kirwan [19]. A K-theory version is given by V...

We prove that the norm-square of a moment map associated to a linear action of a compact group on an affine variety satisfies a certain gradient inequality. This allows us to bound the gradient flow, even if we do not assume that the moment map is proper. We describe how this inequality can be extended to hyperkähler moment maps in some cases, and use Morse theory with the norm-squares of hyper...

We consider a map f from a locally compact metric space to itself, and use the discrete Conley index to study the difference between the local dynamics of f and f. In particular, we present a method, based on work by Mischaikow, Szymczak, et al., for detecting positive entropy symbolic dynamics by measuring the difference between Conley indices for f and f.

Consider the problem: given a real number x and an error bound ε, find an interval such that it contains √ x and its width is less than ε. One way to solve the problem is to start with an initial interval and repeatedly to update it by applying an interval refinement map on it until it becomes narrow enough. In this paper, we prove that the well known Secant-Newton map is the optimal among a ce...