Rapid evaluation of integer-order Bessel functions using an FFTalgorithm

A rapid, accurate, and stable method for computing integer-order Bessel functions is presented. In contrast to the iterative procedures normally used in the numerical evaluation of Bessel functions, this approach requires little more than a commonly available fast Fourier transform algorithm, and yet, for a given argument, can provide many J_ns in a single pass     

Comments ``Rapid evaluation of integer-order Bessel functions usingan FFT algorithm' [and reply]

The commenter disagrees with a statement by J. Nachamkin and D.C. Hoffman (see ibid., vol.33, no.6, p.33-5, Dec. 1991) that complicated procedures are needed to find the initial terms in the recursion relation when backward-recursion techniques are used, and points out that the initial terms required to start backward recursion need not be calculated at J. Nachamkin agrees that in many cases using recursions is better than all the other methods     

Motor nerve terminal degeneration provides a potential mechanism for rapid recovery in acute motor axonal neuropathy after Campylobacter infection

We investigated the possible mechanisms of paralysis and recovery in a patient with the acute motor axonal neuropathy (AMAN) pattern of the Guillain-Barré syndrome. The AMAN pattern of GBS is characterized clinically by acute paralysis without sensory involvement and electrodiagnostically by low compound motor action potential amplitudes, suggesting axonal damage, without evidence of demyelination. Many AMAN patients have serologic or culture evidence of recent Campylobacter jejuni infection. Pathologically, the most severe cases are characterized by wallerian-like degeneration of motor axons affecting the ventral roots as well as peripheral nerves, but some fatal cases have only minor changes in the roots and peripheral nerves, and some paralyzed patients with the characteristic electrodiagnostic findings of AMAN recover rapidly. The mechanism of paralysis and recovery in such cases has been uncertain. A 64-year-old woman with culture-proven Campylobacter upsaliensis diarrhea developed typical features of AMAN. She improved quickly following plasmapheresis. Her serum contained IgG anti-GM1 antibodies. The lipopolysaccharide of the organism bound peanut agglutinin. This binding was blocked by cholera toxin, suggesting that the organism contained the Gal(beta1-3)GalNAc epitope of GM1 in its lipopolysaccharide. Motor-point biopsy showed denervated neuromuscular junctions and reduced fiber numbers in intramuscular nerves. In contrast, the sural nerve biopsy was normal and skin biopsy showed normal dermal and epidermal innervation. In AMAN the paralysis may reflect degeneration of motor nerve terminals and intramuscular axons. In addition, the anti-GM1 antibodies, which can bind at nodes of Ranvier, might produce failure of conduction. These processes are potentially reversible and likely to underlie the capacity for rapid recovery that characterizes some cases of AMAN.     

Some fun with Bessel functions

A theoretical investigation of generating functions is pursued using the theory of the Z-transform. Bessel functions are viewed as outputs from infinite impulse response (IIR) filters. It is shown that a single second-order linear ordinary differential equation with nonconstant coefficients defines a family of generating functions for all the Bessel functions of integral order. A numerical method that directly makes use of the three-term recurrence relation, as a tri-diagonal set of equations solved by Gaussian elimination, is proposed for their evaluation. What results is that both J_n and Y_n, for each n, are derived at the cost of one floating-point division and four floating-point multiplications, after initial set up, using an algorithm that has possibilities for parallelization     

Integrating the dyadic Green's function near sources

Formulas are derived which allow the dyadic Green's function to be integrated for well-behaved currents in the source region. The result is that the electric field due to a current distribution local to an observer can be expressed as a function of the current and its spatial derivatives at the point of observation plus a nonsingular integral over a surface containing the local currents. Although a spherical principal volume is used to derive the theory, the field due to this principal volume is exactly canceled by other terms. The exact form for pulse currents is derived. The theory is extended to nonpulse currents in an appendix     

Production of chemoattractant by Helicobacter pylori

Helicobacter pylori is present in the antral region of the stomach in a majority of patients with gastritis type B. The specific mechanism whereby the organism participates in the development of disease remains uncertain. Since the organism is not invasive, we postulate that H. pylori produces a chemoattractant that recruits inflammatory cells to the antral region of the stomach. H. pylori was grown under microaerophilic conditions at 37 degrees C for 72 hr in Brucella broth containing 1% fetal bovine serum. Culture supernates were harvested after removal of organisms by centrifugation and filtration. The putative chemoattractant in culture supernates as well as that which might be present endogenously in the growth medium (negative control) was assayed against human neutrophils (PMN) in modified Boyden blind-well chambers using 3.0-microns membranes. We found that H. pylori supernates are chemotactic and showed up to 130% activity when compared to the positive chemoattractant control (zymosan-activated serum, a source of C5a). Minimal activity was observed with virgin growth medium. The chemoattractant activity is proportional to the number of colony forming units (CFU) of H. pylori. Preliminary characterization of the activity shows that the chemoattractant is stable in a boiling water bath for 15 min, activity is lost within 1 hr in acid or alkali, and the chemotactic factor has an approximate molecular weight of 8500 daltons. The factor has no amino-sugar and is negative for the lipid A portion of lipopolysaccharide.(ABSTRACT TRUNCATED AT 250 WORDS)