of the Correlation Matrix Memory (CMM), which is useful to work with binary memories. A novel Boolean Orthonormalization Process (BOP) is presented to convert a non-orthonormal Boolean basis, i.e., a set of non-orthonormal binary vectors (in a Boolean sense) to an orthonormal Boolean basis, i.e., a set of orthonormal binary vectors (in a Boolean sense). This work shows that it is possible to im...

The paper deals with structural properties of a class of strictly causal systems. It is shown that a special physically correct internal structure of a given system representation caled dissipation normal form can be derived as a natural consequence of strict causality, dissipativity, minimality and asymptotic stability requirements. A generalization of classic Tellegen’s theorem together with ...

Recently an upsurge in research relating to Laguerre filters for use in system optimization [1], system identification [2] and reduced-order modeling [3] has been noticed. The main reason for the good performance of Laguerre filters is that they form a uniformly bounded orthonormal basis in Hardy space [1]. Another reason, and this represents the novelty of the work carried out in this paper, i...

Let {Φn}n∈N0 and {Φ̃n}n∈N0 be such systems of orthonormal polynomials on the unit circle that the recurrence coefficients of the perturbed polynomials Φ̃n behave asymptotically like those of Φn. We give, under weak assumptions on the system {Φn}n∈N0 and the perturbations, comparative asymptotics as for Φ̃n(z)/Φ ∗ n(z) etc., Φ ∗ n(z) := z Φ̄n( 1 z ), on the open unit disk and on the circumference ma...

The general form of non-entangling unitary maps for measurement schemes is determined. It is shown that any POVM admits a non-entangling measurement. We prove the following. Proposition 1 Let H1,H2 be complex separable Hilbert spaces, φ0 a unit vector in H2. Assume U : H1 ⊗ H2 → H1 ⊗ H2 is a unitary map such that for all φ ∈ H1, U(φ ⊗ φ0) = φ′ ⊗ φ′ for some unit vectors φ′ ∈ H1, φ′ ∈ H2. Then U...

The aim of this paper is to present a new class of learning models for linear as well as non-linear neural layers called Orthonormal StronglyConstrained (SOC or Stiefel). They allow to solve orthonormal problems where orthonormal matrices are involved. After general properties of the learning rules belonging to this new class are shown, examples derived independently or by reviewing learning th...