We present a new algorithm for nonlinear blind source separation, which is based on the geometry of the mixture space. This space is decomposed in a set of concentric rings, in which we perform ordinary linear ICA after central transformation; we show that this transformation can be left out if we use linear geometric ICA. In any case, we get a set of images of ring points under the original mi...

We present three functional interpretations of intuitionistic linear logic and show how these correspond to well-known functional interpretations of intuitionistic logic via embeddings of IL into ILL. The main difference from previous work of the second author is that in intuitionistic linear logic the interpretations of !A are simpler (at the cost of an asymmetric interpretation of pure ILL) a...

There is a variety ofapplications thatcan benefit from the ability oautomatically find optimal orgood routes from real maps. There have been therefore several efforts ocreate and use real maps in computer applications. However, for the purpose ofroute planning, maps cannot beseen as static and complete, as there are dynamic factors and missing information that affect the selection of good route...

Although many solution methods are available for the linear programming problem, the simplex method is undoubtedly the most widely used one for its simplicity. In this paper, we propose an implementation of the simplex method on freed-size hypercubes. A partitioning technique and a mapping technique are presented to fit largo~sL~ problem instances into relatively small-size hypercubes. Two case...

(a) Define a linear mapping R2h h : R 5 → R3 according to the full weighting scheme (see Lecture slides). Setup the respective matrix R2h h . (b) Define a linear mapping Ph 2h : R 3 → R5 which prolongates a solution vector from the coarse to the fine grid using linear interpolation (see Lecture slides). Setup the respective matrix Ph 2h. (c) Based on the matrices R2h h , P h 2h and Ah, compute ...

Decomposable mappings from the space of symmetric k-fold tensors over E, ⊗ s,k E, to the space of k-fold tensors over F , ⊗ s,k F , are those linear operators which map nonzero decomposable elements to nonzero decomposable elements. We prove that any decomposable mapping is induced by an injective linear operator between the spaces on which the tensors are defined. Moreover, if the decomposable...