From Individual to Collective Behavior of Unicellular Organisms: Recent Results and Open Problems

The collective movements of unicellular organisms such as bacteria or amoeboid (crawling) cells are often modeled by partial differential equations (PDEs) that describe the time evolution of cell density. In particular, chemotaxis equations have been used to model the movement towards various kinds of extracellular cues. Well-developed analytical and numerical methods for analyzing the time-dependent and time-independent properties of solutions make this approach attractive. However, these models are often based on phenomenological descriptions of cell fluxes with no direct correspondence to individual cell processes such signal transduction and cell movement. This leads to the question of how to justify these macroscopic PDEs from microscopic descriptions of cells, and how to relate the macroscopic quantities in these PDEs to individual-level parameters. Here we summarize recent progress on this question in the context of bacterial and amoeboid chemotaxis, and formulate several open problems

The corotating variation of the north-south anisotropy of cosmic rays

Correlation analysis on the relation of the north-south (N-S) anisotropy of cosmic rays, observed by the Nagoya multidirectional meson telescope, with the interplanetary magnetic field (IMP) as well the solar wind velocity within solar Carrington rotation for the period 1971 to 1976 is discussed. It is found that the N-S anisotropy of cosmic rays correlates quite well with the Bx component of the IMF. The correlation coefficient is nearly equal to 0.8

Distinguishing RBL-like objects and XBL-like objects with the peak emission frequency of the overall energy spectrum

We investigate quantitatively how the peak emission frequency of the overall energy spectrum is at work in distinguishing RBL-like and XBL-like objects. We employ the sample of Giommi et al. (1995) to study the distribution of BL Lacertae objects with various locations of the cutoff of the overall energy spectrum. We find that the sources with the cutoff located at lower frequency are indeed sited in the RBL region of the $\alpha_{ro}-\alpha_{ox}$ plane, while those with the cutoff located at higher frequency are distributed in the XBL region. For a more quantitative study, we employ the BL Lacertae samples presented by Sambruna et al. (1996), where, the peak emission frequency, $\nu _p$, of each source is estimated by fitting the data with a parabolic function. In the plot of $\alpha_{rx}-\log \nu_p$ we find that, in the four different regions divided by the $\alpha_{rx}=0.75$ line and the $\log \nu_p=14.7$ line, all the RBL-like objects are inside the upper left region, while most XBL-like objects are within the lower right region. A few sources are located in the lower left region. No sources are in the upper right region. This result is rather quantitative. It provides an evidence supporting what Giommi et al. (1995) suggested: RBL-like and XBL-like objects can be distinguished by the difference of the peak emission frequency of the overall energy spectrum.Comment: 7 pages, 2 figure