Transfer Function Distribution Research Articles

Characterizing short-term stability for Boolean networks over any distribution of transfer functions.

We present a characterization of short-term stability of Kauffman's NK (random) Boolean networks under arbitrary distributions of transfer functions. Given such a Boolean network where each transfer function is drawn from the same distribution, we present a formula that determines whether short-term chaos (damage spreading) will happen. Our main technical tool which enables the formal proof of this formula is the Fourier analysis of Boolean functions, which describes such functions as multilinear polynomials over the inputs. Numerical simulations on mixtures of threshold functions and nested canalyzing functions demonstrate the formula's correctness.

Axially and transversally super-resolved imaging and ranging with random aperture coding

In this paper we present a new approach allowing improved imaging capabilities while using imaging lenses with higher tolerances to fabrication errors. The idea is to attach a random phase to the aperture plane of the imaging lens, which generates a random phase in the optical transfer function distribution. This phase is a priori known and it is very much dependent on the range to the object. The randomness of this phase allows simultaneously increasing the depth of focus as well as estimating the range to the various objects in the field of view of the imager. In addition it allows increasing the geometrical resolution of the imager by orthogonal coding of the spatial spectral bands prior to their folding due to the under-sampling by the detector (aliased information).

Geomagnetic Transfer Functions in Japan Obtained by First Order Geomagnetic Survey.

Repeated measurements of the Earth's time varying magnetic field have been made across Japan by the Geographical Survey Institute. Such measurements are known as a first order geomagnetic survey. There are 105 geomagnetic stations located uniformly across the whole of Japan. Since 1987, triaxial fluxgate magnetometers have been used to obtain one-minute data at almost all stations. From the geomagnetic data, transfer functions were determined for each station. Traditional vertical field transfer functions of wide period range (from 4 min to 128 min) were obtained, making use of the interstation method. Additionally, we calculated transfer functions for the horizontal field. The distribution of the transfer functions can be used to form a reference map of geomagnetic induction in Japan. Moreover, the distribution of the horizontal transfer functions in Japan has been examined for the first time. After eliminating the effect of the sea water using thin-sheet models, large regional anomalies are found to remain. These anomalies are diagnostic of the resistivity structure and show patterns of current channeling in Japan.

Including uncertainty in the unit hydrograph method

The unit hydrograph method is reformulated into a stochastic integral equation for use in preparing probabilistic distributions of design criterion variable values (e.g., pipe size, basin volume, peak flow rate, etc.). By discretizing the ensemble of possible transfer functions (e.g., unit hydrographs) and weighting the resulting finite set of realizations, the stochastic integral equation can be more simply utilized in practical engineering problems. In this paper, a weighted set of mass curves are prepared for use in the Los Angeles, California, region. The weighted mass curves reflect the probabilistic weighting of the corresponding distribution of transfer functions used to convolute with effective rainfall (i.e., rainfall less losses) to produce runoff estimates.