Approximation capabilities of single non-linear layer networks, that feature a single global minimum of the error function are addressed. Bases of different transfer functions are tested (Gaussian, sigmoidal, multiquadratics). These functions are orthogonalised in an incremental manner for training and restored back to the original basis for network deployment. Approximation results are given f...

A state space version of the skew Toeplitz theory for (distributed) H" optimization theory is presented. The approach combines this theory with the realization theory for pseudorational transfer functions. 1 Time-Domain Interpretation of Sarason Space In [15], we established a strong link between the skew Toeplitz H" theory of 12, 4, 5, 6, 9, 121 and its realization in the time domain. The fund...

We consider the Hypothesis Transfer Learning (HTL) problem where one incorporates a hypothesis trained on the source domain into the learning procedure of the target domain. Existing theoretical analysis either only studies specific algorithms or only presents upper bounds on the generalization error but not on the excess risk. In this paper, we propose a unified algorithm-dependent framework f...

Transmission characteristics of layers that contain fractal aggregates are investigated. In particular, the modulation transfer functions of these layers are studied in comparison with the case of uniformly dispersed particles. The effects of aggregation type (fractal dimension) and aggregate size are discussed.

Transfer functions with finite zeros giving the minimum product of the impulse response duration and the frequency bandwidth are considered. The impulse response spread is characterized by the higher order moments. For the frequency spread measure, the second order moment is used. Minimizing products of the moments, causal systems with the largest energy concentration in time for a given bandwi...

We present a new type of neural network (NN) where the data for the input layer are the value x in R, the vector y in R(m ) associated to an initial value problem (IVP) with y'(x)= f(y(x)) and a steplength h. Then the stages of a Runge-Kutta (RK) method with trainable coefficients are used as hidden layers for the integration of the IVP using f as transfer function. We take as output two estima...

Using current techniques it is usually impractical to measure head-related transfer functions (HRTFs) at a spatial resolution that does not exceed the minimum audible angle, i.e. 1-2° for a source directly in front, by a considerable amount. As a result, measured HRTFs must be interpolated to generate a display in which auditory space is rendered smoothly. The spatial resolution at which it is ...

In this paper we prove the fundamental lemma for Deligne–Lusztig functions. Namely, for every Deligne–Lusztig function φ on a p-adic group G we write down an explicit linear combination φ of Deligne–Lusztig functions on an endoscopic group H such that φ and φ have “matching orbital integrals”. In particular, we prove a conjecture of Kottwitz [Ko4]. More precisely, we do it under some mild restr...

In the design of a signal processing network, control system, or other analog system, it is usually necessary to work with frequency-dependent transfer functions and impedances, and to construct Bode diagrams. The Bode diagram is a log-log plot of the magnitude and phase of an impedance, transfer function, or other frequency-dependent complex-valued quantity, as a function of the frequency of a...

Coprimeness conditions play important roles in various aspects of system/control theory: realization, controllability, stabilization, just to name a few. While the issue is now well understood for finite-dimensional systems, it is far from being settled for infinite-dimensional systems. This is due to a wide variety of situations in which this issue occurs, and several variants of coprimeness n...