1.1. Linear Algebra. Let F = R or F = C and let V be a vector space over F. A finite dimensional vector space over R (C) is isomorphic to Rn (Cn) for some n, where Rn = {x = (x1, . . . , xn)} for xi ∈ R and Cn = {z = (z1, . . . , zn)} for zi ∈ Cn. On Rn, the standard Euclidean inner product is given by 〈x, y〉 = ∑ xiyi and the Euclidean norm is given by ||x|| = 〈x, x〉 2 . On Cn the standard Herm...

The Hinton network (Hinton, 2001, personal communication) is a deterministic mapping from an observable space x to an energy function E(x;w), parameterized by parameters w. The energy defines a probability P (x|w) = exp(−E(x;w))/Z(w). A maximum likelihood learning algorithm for this density model takes steps ∆w ∝ −〈g〉0+ 〈g〉∞ where 〈g〉0 is the average of the gradient g = ∂E/∂w evaluated at point...

This paper consists of three parts. In the first part we prove a general theorem on the image of a language K under a substitution, in the second we apply this to the special case when K is the language of balanced words and in the third part we deal with recurrent Z-words of minimal block growth. Definitions and notation In this paper a word is a mapping w : I → {a, b} where I is a subinterval...

The standard trace-driven cache simulation evaluates the miss rate of cache C on an address trace T for program P running on input data I with object-code address map M for P. We note that the measured miss rate depends significantly on the address mapping M set arbitrarily by the compiler and linker. In this paper, we remove the effect of the address-mapping on the miss rate by analyzing a sym...

This paper examines contemporary attempts to explicate the explanatory role of mathematics in the physical sciences. Most such approaches involve developing so-called mapping accounts of the relationships between the physical world and mathematical structures. The paper argues that the use of idealizations in physical theorizing poses serious difficulties for such mapping accounts. An new appro...

We prove that planar homeomorphisms can be approximated by diffeomorphisms in the Sobolev space W 1,2 and in the Royden algebra. As an application, we show that every discrete and open planar mapping with a holomorphic Hopf differential is harmonic.

In 4 experiments, the authors investigated the reversal of spatial congruency effects when participants concurrently practiced incompatible mapping rules (J. G. Marble & R. W. Proctor, 2000). The authors observed an effect of an explicit spatially incompatible mapping rule on the way numerical information was associated with spatial responses. The authors also observed an effect of an incompati...

C. ZHU*{{§, W. SHI{, M. PESARESI", L. LIU{, X. CHEN** and B. KING{ {Institute of Geodesy and Geophysics, Chinese Academy of Science, Wuhan, 430077, China {Advanced Research Centre for Spatial Information Technology, Department of Land Surveying and Geo-Informatics, The Hong Kong Polytechnic University, Hong Kong §Zhengzhou Institute of Surveying and Mapping, Zhengzhou, 450052, China "Inform S.r...

Despite the significant number of existing tools, incorporating data from multiple sources and different formats into the Linked Open Data cloud remains complicated. No mapping formalisation exists to define how to map such heterogeneous sources into rdf in an integrated and interoperable fashion. This paper introduces the rml mapping language, a generic language based on an extension over rrm...

The network autocorrelation model has been a workhorse for modeling network influences on individual behavior. The standard network approaches to mapping social influence using network measures, however, are limited to specifying an influence weight matrix (W) based on a single mode network. Additionally, it has been demonstrated that the estimate of the autocorrelation parameter of the network...