Pseudo orthogonal bases are a certain type of frames proposed in the engineering field, whose concept is equivalent to a normalized tight frame in the frame terminology. This paper shows that pseudo orthogonal bases play an essential role in neural network learning. One of the most important issues in neural network learning is “what training data provides the optimal generalization capability?...

Pseudo orthogonal bases are a certain type of frames proposed in the engineering field, whose concept is equivalent to a tight frame with frame bound 1 in the frame terminology. This paper shows that pseudo orthogonal bases play an essential role in neural network learning. One of the most important issues in neural network learning is “what training data provides the optimal generalization cap...

These notes have a dual goal. On the one hand we shall give an overview of the recently introduced class of scalable frames. These are (finite) frames with the property that each frame vector can be rescaled in such a way that the resulting frames are tight. This process can be viewed as a preconditioning method for finite frames. In particular, we shall: (1) describe the class of scalable fram...

In a previous paper we introduce the concept of full d-stability, in this work several types of generalizations were introduced ; minimal (maximal) d-stable; fully pseudo d-stable and afd-stable module. A dual to the notion of terse module is, also, introduced namely d-terse and it is shown that it is coincide with fully pseudo d-stable.

In this paper, we show that the shifts of a pseudo-spline are linearly independent. This is stronger than the (more obvious) statement that the shifts of a pseudo-spline form a Riesz system. In fact, the linear independence of a compactly supported (refinable) function and its shifts has been studied in several areas of approximation and wavelet theory (see e.g. [4], [9], [10], [13], [14], [16]...

The Pseudo Primal-Dual Algorithm solves the pure integer programming problem in two stages, systematically violating and restoring dual feasibility while maintaining an all-integer matrix. The algorithm is related to Gomory AlI-fnteger Algorithm and the Young Primal Integer Programming Algorithm, differing from the former in the dual feasible stage by the choice of cuts and pivot variable, and ...

We show that Derksen-Weyman-Zelevinsky’s mutations of quivers with potential yield equivalences of suitable 3-Calabi-Yau triangulated categories. Our approach is related to that of Iyama-Reiten and ‘Koszul dual’ to that of Kontsevich-Soibelman. It improves on previous work by Vitória. In the appendix, the first-named author studies pseudo-compact derived categories of certain pseudo-compact dg ...

Pseudo-Goldstone bosons in 4D strongly coupled theories have a dual description in terms of 5D gauge theories in warped backgrounds. We introduce systematic methods of computing the pseudo-Goldstone potential for an arbitrary warp factor in 5D. When applied to electroweak symmetry breaking, our approach clarifies the relation of physical observables to geometrical quantities in five dimensions....

Regular Gabor frames for L2(Rd) are obtained by applying time-frequency shifts from a lattice in Λ Rd× R̂d to some decent so-called Gabor atom g, which typically is something like a summability kernel in classical analysis, or a Schwartz function, or more generally some g∈ S0(R). There is always a canonical dual frame, generated by the dual Gabor atom g̃. The paper promotes a numerical approach f...

We analyse the relation between innnite-dimensional frame theory and nite-dimensional models for frames as they are used for numerical algorithms. Special emphasis in this paper is on perfect reconstruction oversampled lter banks, also known as shift-invariant frames. For certain nite-dimensional models it is shown that the corresponding nite dual frame provides indeed an approximation of the d...