Structure and behaviour of the sperm terminal filament

Light- and electron-microscopic observations of Ciona and Lytechinus spermatozoa show a thin terminal filament at the distal end. The terminal filament is 5-6 microns long and contains the two central microtubules and a variable number of A-tubule extensions of the peripheral doublet microtubules. The transition from the 9 + 2 region to the terminal filament is tapered more gradually in Lytechinus than in Ciona. Photographs of the movement of beating spermatozoa do not show any obvious discontinuity in curvature at the transition region. Bends are propagated smoothly off the end of the flagellum with no decrease in curvature. However, spermatozoa in which the terminal filament has been removed show a clear 'end effect'. This end effect involves a rapid unbending of bends that have reached the distal end of the flagellum. Computer simulations of flagellar models lacking a terminal filament show a similar end effect. Addition of a terminal filament to the end of the computer model can eliminate the end effect. Realistic bending behaviour of the model is obtained by using a terminal filament with a tapered elastic bending resistance in the basal portion of the terminal filament and a value of 0.03 x 10^(9) pN nm^2 in the remainder of the terminal filament. This leads to estimates of 0.01 x 10^(9) pN nm^2 for the elastic bending resistance of an individual microtubule, and 0.2 x 10^(9) pN nm^2 for the elastic bending resistance of the 9 + 2 region of the flagellum. An improvement in propulsive effectiveness by addition of a terminal filament remains to be demonstrated

Spontaneous Symmetry Breaking for Driven Interacting Particles on Triangular Substrates

For collectively interacting repulsive particles driven on triangular substrates, we show that for certain directions of drive a spontaneous symmetry breaking phenomena occurs where the particles can flow in one of two directions that are not aligned with the external drive, giving rise to a positive or negative Hall current. Along these directions, the particle flow is highly ordered, while in the direction of the drive the flow is disordered. We also find a number of dynamical phase transitions and unusual hysteretic properties that arise due to the symmetry breaking properties of the flows.Comment: 4 pages, 4 postscript figure

Are people really conformist-biased? An empirical test and a new mathematical model

According to an influential theory in cultural evolution, within-group similarity of culture is explained by a human 'conformist-bias', which is a hypothesized evolved predisposition to preferentially follow a member of the majority when acquiring ideas and behaviours. However, this notion has little support from social psychological research. In fact, a major theory in social psychology (LATANÉ and WOLF, 1981) argues for what is in effect a ‘nonconformist-bias’: by analogy to standard psychophysics they predict minority sources of influence to have relatively greater impact than majority sources. Here we present a new mathematical model and an experiment on social influence, both specifically designed to test these competing predictions. The results are in line with nonconformism. Finally, we discuss within-group similarity and suggest that it is not a general phenomenon but must be studied trait by trait

Counting Smooth Solutions to the Equation A+B=C

This paper studies integer solutions to the Diophantine equation A+B=C in which none of A, B, C have a large prime factor. We set H(A, B,C) = max(|A|, |B|, |C|), and consider primitive solutions (gcd}(A, B, C)=1) having no prime factor p larger than (log H(A, B,C))^K, for a given finite K. On the assumption that the Generalized Riemann hypothesis (GRH) holds, we show that for any K > 8 there are infinitely many such primitive solutions having no prime factor larger than (log H(A, B, C))^K. We obtain in this range an asymptotic formula for the number of such suitably weighted primitive solutions.Comment: 35 pages latex; v2 corrected misprint

On solutions to the non-Abelian Hirota-Miwa equation and its continuum limits

In this paper, we construct grammian-like quasideterminant solutions of a non-Abelian Hirota-Miwa equation. Through continuum limits of this non-Abelian Hirota-Miwa equation and its quasideterminant solutions, we construct a cascade of noncommutative differential-difference equations ending with the noncommutative KP equation. For each of these systems the quasideterminant solutions are constructed as well.Comment: 9 pages, 1 figur

Instability of three dimensional conformally dressed black hole

The three dimensional black hole solution of Einstein equations with negative cosmological constant coupled to a conformal scalar field is proved to be unstable against linear circularly symmetric perturbations.Comment: 5 pages, REVTe

The QCD String Spectrum and Conformal Field Theory

The low energy excitation spectrum of the critical Wilson surface is discussed between the roughening transition and the continuum limit of lattice QCD. The fine structure of the spectrum is interpreted within the framework of two-dimensional conformal field theory.Comment: Lattice2001 (confinement),3 pages,1 figure,uses espcrc2.st