On the construction of a digital transfer function from its real part on unit circle

It is shown in this correspondence that the system function H(z) of a linear time invariant (LTI) causal digital filter with real impulse response coefficients can be obtained from the real part of its frequency response HR(ejω) given in the form of a rational trigonomentric function, using algebraic methods rather than complex contour integration techniques

Data mining in soft computing framework: a survey

The present article provides a survey of the available literature on data mining using soft computing. A categorization has been provided based on the different soft computing tools and their hybridizations used, the data mining function implemented, and the preference criterion selected by the model. The utility of the different soft computing methodologies is highlighted. Generally fuzzy sets are suitable for handling the issues related to understandability of patterns, incomplete/noisy data, mixed media information and human interaction, and can provide approximate solutions faster. Neural networks are nonparametric, robust, and exhibit good learning and generalization capabilities in data-rich environments. Genetic algorithms provide efficient search algorithms to select a model, from mixed media data, based on some preference criterion/objective function. Rough sets are suitable for handling different types of uncertainty in data. Some challenges to data mining and the application of soft computing methodologies are indicated. An extensive bibliography is also included

On arbitrary-level IIR and FIR filters

A recently published method for designing IIR (infinite-impulse-response) digital filters with multilevel magnitude responses is reinterpreted from a different viewpoint. On the basis of this interpretation, techniques for extending these results to the case of finite-impulse-response (FIR) filters are developed. An advantage of the authors' method is that, when the arbitrary-level filter is implemented, its power-complementary filter, which may be required in specific applications, is obtained simultaneously. Also, by means of a tuning factor (a parameter of the scaling matrix), it is possible to generate a whole family of arbitrary-level filters

Formation rates of Dark Matter Haloes

We derive an estimate of the rate of formation of dark matter halos per unit volume as a function of the halo mass and redshift of formation. Analytical estimates of the number density of dark matter halos are useful in modeling several cosmological phenomena. We use the excursion set formalism for computing the formation rate of dark matter halos. We use an approach that allows us to differentiate between major and minor mergers, as this is a pertinent issue for semi-analytic models of galaxy formation. We compute the formation rate for the Press-Schechter and the Sheth-Tormen mass function. We show that the formation rate computed in this manner is positive at all scales. We comment on the Sasaki formalism where negative halo formation rates are obtained. Our estimates compare very well with N-Body simulations for a variety of models. We also discuss the halo survival probability and the formation redshift distributions using our method.Comment: 30 pages, 9 figure

External leg amputation in conformal invariant three-point function

Amputation of external legs is carried out explicitly for the conformal invariant three-point function involving two spinors and one vector field. Our results are consistent with the general result that amputing an external leg in a conformal invariant Green function replaces a field by its conformal partner in the Green function. A new star-triangle relation, involving two spinors and one vector field, is derived and used for the calculation.Comment: 16 pages; last paragraph added in Sec. 10, presentation improved, to appear in Eur. Phys. J.

Fuzzy multi-layer perceptron, inferencing and rule generation

A connectionist expert system model, based on a fuzzy version of the multilayer perceptron developed by the authors, is proposed. It infers the output class membership value(s) of an input pattern and also generates a measure of certainty expressing confidence in the decision. The model is capable of querying the user for the more important input feature information, if and when required, in case of partial inputs. Justification for an inferred decision may be produced in rule form, when so desired by the user. The magnitudes of the connection weights of the trained neural network are utilized in every stage of the proposed inferencing procedure. The antecedent and consequent parts of the justificatory rules are provided in natural forms. The effectiveness of the algorithm is tested on the speech recognition problem, on some medical data and on artificially generated intractable (linearly nonseparable) pattern classes

The nature of simple random sampling

As an estimator of the population mean, the sample mean based only on the distinct units possesses a remarkable invariance property. Under three forms of simple random sampling, viz. simple random sampling without replacement (SRSWOR), simple random sampling with replacement (SRSWR), and fixed cost simple random sampling (SRSFC), it is admissible and unbiased; and asymptotically normally distributed if and only if the Erdos-Renyi-Hajek condition is satisfied. An important implication of this invariance is that for estimating the population mean, these forms of simple random sampling are asymptotically equally cost-efficient. However, from a practical point of view SRSFC does seem to provide greater flexibility in large surveys

The Fringe of the Atmosphere and the Ultraviolet Light Theory of Aurora and Magnetic Disturbances

An atmosphere in isothermal equilibrium has no natural limit , an atmosphere adiabatic equilibrium has, however, one. Beyond this “ inner” adiabatic atmosphere lies the outer atmosphere formed by molecules ” evaporated ” from the outer surface of the “ inner ” atmosphere. The fringe region lies at the farther limits of this outer atmosphere where the molecules moving without any collision describe orbits of enormous dimensions. Taking atomic oxygen and molecular nitrogen as the upper atmosphere constituents the height of the critical level or level of negligible collision is calculated by the authors and is found to be 770 km. Above 930 km. there is practically no collision between the atoms. Ionization of the atoms in the fringe region by solar ultra-violet radiation will diminish the rate of escape owing to their entanglement with the earth’s magnetic field. Critical velocities of escape of oxygen ions from different latitudes of the earth arc calculated. The increase with height of the viscous drag of the earth measured by kinematical viscosity n/p is taken into account and it is shown that the atmosphere rotates with the earth so long as there is appreciable collision between atoms. Molecular densities at different levels of the fringe region are estimated. The merging of the fringe region into interstellar space takes place between 2000 and 2500 km. above the earth’s surface. Existence of super-elastic collisions between an excited (metastable) atom and a neutral particle extends the fringe region. Of the various metastable states of the constituent particles only those of oxygen atoms are capable of producing any effect by super-elastic collisions. It is found that roughly about 104 atoms in the 15 state and 106 atoms in the 1D state suffer collisions per second with other atoms. The atoms in the 1S state can shoot a neutral oxygen atom to a height of about 14000km. above earth’s centre while an atom in the 1 D state can shoot it to a height of about 9,500 km. The density distribution in the fringe region and the merging with the interstellar space (which takes place at about 2500 km. above the earth surface) are found to be only slightly modified by the presence of these high speed particles. By considering the motion of ions in the earth’s magnetic and gravitational fields, taking into account the variations of g and H wdth altitude and also considering the rotation of the earth magnet it is found that an ion starting at the equator at 12 o’clock noon at 40,000 km. height and describing along the magnetic line of force with a velocity of 1 km /see will enter the earth's atmosphere at 12-54 local hair. Bearing of the above results on the Ultra-violet light theory of Aurorae and magnetic storms as suggested by Hulburt the essential feature of which is the distillation of speedy ionized particles from lower to higher latitudes by the earth’s magnetic field is discussed.If it is assumed that the high speed atoms are ionized ol a height of about 40,000 km the time of descent as calculated above by the authors agrees with that calculated by Hulburt. Analysis shows, however, that by no known imans particles from lower levels can reach 40,000 km level to which they must rise in order to reach the auroral latitude. Again according to Hulburt the particles driven upwards by super-clastic collisions will be ionized in three hours. Recent calculations on atomic absorption coefficient of oxygen shows, however, that the time required should he several orders higher than that assumed by Hulburt