In this contribution we provide an application of the technique of F–transform. We demonstrate that by using a simple density-based preprocessing, the applicability of F–transform in data analysis can be significantly improved. Despite of the fact that our procedure is demonstrated by a well-known DBSCAN algorithm and the technique of F–transform, the ideas are general enough to be applied for ...

Radiological images are gradually more being used in healthcare and medical research. There is, accordingly, widespread interest in accurately relating information in the different images for diagnosis, treatment and basic science. In this paper we formulate feature registration problems by using F-transform (Fuzzy-Transform) to extract the salient edges and extracted control points (CP) of med...

This paper continues the development of the innovative method for time series analysis and forecasting using special soft-computing techniques: fuzzy (F-) transform and Fuzzy Natural Logic. We will demonstrate that the F-transform is a proper technique for extraction of the trend-cycle of time series. Furthermore, we will elaborate in more detail automatic generation of linguistic evaluation of...

For functions defined on Cn or Rn+ we construct a dequantization transform f 7→ f̂ ; this transform is closely related to the Maslov dequantization. If f is a polynomial, then the subdifferential ∂f̂ of f̂ coincides with the Newton polytope of f . For the semiring of polynomials with nonnegative coefficients, the dequantization transform is a homomorphism of this semiring to the idempotent semirin...

For functions defined on C or R+ we construct a dequantization transform f 7→ f̂ ; this transform is closely related to the Maslov dequantization. If f is a polynomial, then the subdifferential ∂f̂ of f̂ at the origin coincides with the Newton polytope of f . For the semiring of polynomials with nonnegative coefficients, the dequantization transform is a homomorphism of this semiring to the idempo...

1 Review 1.1 Setup In the previous lecture, we considered an apparatus consisting of three planes: • an aperture plane. Coordinates on the aperture plane are denoted by x and y. • a transform plane. Coordinates on the transform plane are denoted by X and Y. • an image plane. Coordinates on the image plane are denoted by x and y. We defined the spatial frequencies, µ = k f X ν = k f Y where f is...

Let G be a locally compact abelian group with dual group Ĝ. The Hausdorff–Young theorem states that if f ∈ Lp(G), where 1 ≤ p ≤ 2, then its Fourier transform Fp(f) belongs to Lq(Ĝ) (where 1 p + 1 q = 1) and ||Fp(f)||q ≤ ||f ||p. Kunze and Terp extended this to unimodular and locally compact groups, respectively. We further generalize this result to an arbitrary locally compact quantum group G b...

This paper shows that binary decision diagrams (BDDs) and their generalizations are not only representations of switching and integer-valued functions, but also Fourier-like series expansions of them. Furthermore, it shows that edge-valued binary decision diagrams (EVBDDs) are related to arithmetic transform decision diagrams (ACDDs), which are the integer counterparts of the functional decisio...

Let f : M → G(m, n) be a harmonic map from surface into complex Grassmann manifold. In this paper, some sufficient conditions for the harmonic sequence generated by f to have degenerate ∂-transform or ∂-transform are given.

Both the Walsh system and the trigonometric system are systems of characters on a compact abelian group. This explains that many of the results in the theory of those systems are parallel. However, those similarities do usually not extend to the case when the systems are compared directly. So it is known that the Walsh system in the Walsh-Paley order and the trigonometric system are not equival...