Related papers: Generalized Householder transformations
We present an intuitive and scalable algorithm for the diagonalization of complex symmetric matrices, which arise from the projection of pseudo--Hermitian and complex scaled Hamiltonians onto a suitable basis set of "trial" states. The…
This paper presents in detail the generalized pignistic transformation (GPT) succinctly developed in the Dezert-Smarandache Theory (DSmT) framework as a tool for decision process. The GPT allows to provide a subjective probability measure…
A general deformation of the Heisenberg algebra is introduced with two deformed operators instead of just one. This is generalised to many variables, and permits the simultaneous existence of coherent states, and the transposition of…
This paper considers Darboux transformations of a bispectral operator which preserve its bispectrality. A sufficient condition for this to occur is given, and applied to the case of generalized Airy operators of arbitrary order $r>1$. As a…
The general notion of a Hausdorff-type operator with a kernel depending on an external variable is introduced and generalizations and analogs of classical results on the regularity of various summation methods are proved for the case of…
Compositional generalization is the ability to generalize systematically to a new data distribution by combining known components. Although humans seem to have a great ability to generalize compositionally, state-of-the-art neural models…
We study the properties of different type of transforms by means of operational methods and discuss the relevant interplay with many families of special functions. We consider in particular the binomial transform and its generalizations. A…
We consider the transformation of Hamilton operators under various sets of quantum operations acting simultaneously on all adjacent pairs of particles. We find mappings between Hamilton operators analogous to duality transformations as well…
Classical Stieltjes Transform is modified in a way to generalize both Stieltjes and Fourier transforms. This transform allows to intro- duce new classes of commutative and non-commutative generalized convolutions. Key words: Stieltjes…
Kendall transformation is a conversion of an ordered feature into a vector of pairwise order relations between individual values. This way, it preserves ranking of observations and represents it in a categorical form. Such transformation…
Using a probabilistic approach, we derive some interesting combinatorial identities involving gamma and beta functions. These results generalize certain well-known combinatorial identities involving binomial coefficients and special…
Generalized translation operators for orthogonal expansions with respect to families of weight functions on the unit ball and on the standard simplex are studied. They are used to define convolution structures and modulus of smoothness for…
Generalized eigenfunctions may be regarded as vectors of a basis in a particular direct integral of Hilbert spaces or as elements of the antidual space $\Phi^\times$ in a convenient Gelfand triplet…
We study a generalization of conditional probability for arbitrary ordered vector spaces. A related problem is that of assigning a numerical value to one vector relative to another. We characterize the groups for which these generalized…
This investigation pertains to the construction of a class of generalised deformed derivative operators which furnish the familiar finite difference and the q-derivatives as special cases. The procedure involves the introduction of a linear…
The inference of deep hierarchical models is problematic due to strong dependencies between the hierarchies. We investigate a specific transformation of the model parameters based on the multivariate distributional transform. This…
The classical Fourier transform is, in essence, a way to take data and extract components (in the form of complex exponentials) which are invariant under cyclic shifts. We consider a case in which the components must instead be invariant…
The context transformation and generalized context transformation methods, we introduced recently, were able to reduce zero order entropy by exchanging digrams, and as a consequence, they were removing mutual information between consecutive…
It is well known that, when defining Householder transformations, the correct choice of sign in the standard formula is important to avoid cancellation and hence numerical instability. In this note we point out that when the "wrong" choice…
This paper is devoted to linear space representations of contextual probabilities - in generalized Fock space. This gives the possibility to use the calculus of creation and annihilation operators to express probabilistic dynamics in the…