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 image processing for the target centre detection in digital image

This thesis comprises of five chapters. Chapter one describes basic principles of the digital image, digital image construction and the present status of the digital photogrammetry system, named PHOENICS (PHOtogrammetric ENgineering and Industrial digital Camera System), as developed by H. Rüther (1989). The target's shape analysis in the digital image are presented in chapter two. Chapter three presents the algorithms to detect and locate target on the digital image. These are the least squares adjustment technique, moment method, moment-preserving for edge detection as well as test methods for the evaluation of the various alglorithms. The novel RG method is presented in chapter four. Chapter five introduces the theory of some image processing methods

Effects of surface wetness duration, temperature, and inoculum concentration on infection of winter barley by Rhynchosporium secalis

Nous avons étudié les effets de la durée d'humectation, de la température et de la concentration de l'inoculum sur le développement de la rhynchosporiose chez l'orge d'automne (Hordeum vulgare) inoculée avec la race SO1 du Rhynchosporium secalis du sud de l'Ontario (Canada). Sur la ignée d'orge GW8614 vaporisée avec une suspension de spores (2 X 105 conidies mL-1), des périodes d'humectation de 2-48 h et des températures de 0-25 °C pendant les périodes humides et sèches, de 10-25 °C pendant la période humide et de 20 °C pendant la période sèche, ou 20 °C pendant la période humide et 10-30 °C pendant la période sèche ont permis le développement de la rhynchosporiose 8,3-11,5 jours après l'inoculation. La maladie s'est développée plus rapidement et plus intensément quand la période humide après l'inoculation était de 48 h et quand la température de la période humide et de la période sèche subséquente était de 20 °C. La hynchosporiose ne s'est pas développée à l'intérieur de 14 jours suite à des yempératures de 30 °C pendant la période humide ou de 5 °C pendant les périodes humides ou sèches. À des concentrations d'inoculum de 102 - 106 conidies mL-1, l'indice de gravité (échelle de 0-100) a augmenté de 53 à 100 pour la lignée GW8614 et de 0 à 90 pour le cultivar OAC Acton et les périodes latentes ont diminué de 13,3 à 7,8 jours pour la lignée GW8614 et de plus de 14 à ,5 jours pour le cultivar OAC Acton. Ces renseignements devraient faciliter le criblage de cultivars d'orge résistants à la rhynchosporiose.The effects of surface wetness duration, temperature, and inoculum concentration on development of scald in winter barley (Hordeum vulgare) inoculated with race SOI of Rhynchosporium secalisfrom southern Ontario, Canada were examined. On barley line 'GW8614' sprayed with a spore suspension (2 x 105 conidia ml-1), wet periods of 2-48 h and constant temperatures of 10-25°C during the wet and dry periods, 10-25°C during the wet period and 20°C during the dry period, or 20°C during the wet period and 10-30°C during the dry period allowed scald to develop 8.3-11.5 d after inoculation. The disease developed most rapidly and most severely when the wet period after inoculation was 48 h and the temperature of the wet period and subsequent dry period was 20°C. Scald did not develop within 14 d following temperatures of 30°C during the wet period or of 5°C during the wet or dry periods. At inoculum densities of 102-106 conidia ml-1, the disease severity index values (0-100 scale) increased from 53 to 100 in line 'GW8614' and from 0 to 90 in cultivar OAC Acton and the latent periods decreased from 13.3 to 7.8 d in line 'GW8614' and from more than 14 to 8.5 d in cv. OAC Acton. This information should facilitate screening of barley for resistance to scald

The (11112) model on a 1+1 dimensional lattice

We study the chiral gauge model (11112) of four left-movers and one right-mover with strong interactions in the 1+1 dimensional lattice. Exact computations of relevant $S$-matrix elements demonstrate a loophole that so constructed model and its dynamics can possibly evade the ``no-go'' theorem of Nielsen and Ninomiya.Comment: 15 pages, 1 fig. to appear in Phys. Rev.

GRB970228 and the class of GRBs with an initial spikelike emission: do they follow the Amati relation?

On the basis of the recent understanding of GRB050315 and GRB060218, we return to GRB970228, the first Gamma-Ray Burst (GRB) with detected afterglow. We proposed it as the prototype for a new class of GRBs with "an occasional softer extended emission lasting tenths of seconds after an initial spikelike emission". Detailed theoretical computation of the GRB970228 light curves in selected energy bands for the prompt emission are presented and compared with observational BeppoSAX data. From our analysis we conclude that GRB970228 and likely the ones of the above mentioned new class of GRBs are "canonical GRBs" have only one peculiarity: they exploded in a galactic environment, possibly the halo, with a very low value of CBM density. Here we investigate how GRB970228 unveils another peculiarity of this class of GRBs: they do not fulfill the "Amati relation". We provide a theoretical explanation within the fireshell model for the apparent absence of such correlation for the GRBs belonging to this new class.Comment: 5 pages, 3 figures, in the Proceedings of the "4th Italian-Sino Workshop on Relativistic Astrophysics", held in Pescara, Italy, July 20-28, 2007, C.L. Bianco, S.-S. Xue, Editor

Testing the transition layer model of quasi-periodic oscillations in neutron star X-ray binarie

We compare the theoretical predictions of the transition layer model with some observational features of quasi-periodic oscillations (QPOs) in neutron star X-ray binaries. We found that the correlation between horizontal branch oscillation (HBO) frequencies and kilohertz (kHz) QPO frequencies, the difference between the low-frequency QPOs in atoll sources and HBOs in Z sources, and the correlation between the frequencies of low-frequency QPOs and break frequencies can be well explained by the transition layer model, provided the neutron star mass is around 1.4 solar mass and the angle between magnetosphere equator and accretion disk plane is around 6 degree. The observed decrease of peak separation between two kHz QPO frequencies with the increase of kHz QPO frequencies and the increase of QPO frequencies with the increase of inferred mass accretion rate are also consistent with the theoretical predictions of transition layer model. In addition, we derive a simple equation that can be adopted to estimate the angle ($\delta$) between magnetosphere equator and accretion disk plane by use of the simultaneously observed QPO frequency data. We estimate these angles, in the range of 4 to 8 degrees, for five Z sources and two atoll sources. The nearly constant $\delta$ value for each source, derived from the different sets of simultaneously observed QPO frequency data, provides a strong test of the theoretical model. Finally, we suggest that the similar transition layer oscillations may be also responsible for the observed QPOs in accretion-powered millisecond X-ray pulsar and Galactic black hole candidates.Comment: 10 pages, 5 figures, to appear in ApJ, Vol. 55

Improved Approximation Algorithms for Computing k Disjoint Paths Subject to Two Constraints

For a given graph $G$ with positive integral cost and delay on edges, distinct vertices $s$ and $t$, cost bound $C\in Z^{+}$ and delay bound $D\in Z^{+}$, the $k$ bi-constraint path ($k$BCP) problem is to compute $k$ disjoint $st$-paths subject to $C$ and $D$. This problem is known NP-hard, even when $k=1$ \cite{garey1979computers}. This paper first gives a simple approximation algorithm with factor-$(2,2)$, i.e. the algorithm computes a solution with delay and cost bounded by $2*D$ and $2*C$ respectively. Later, a novel improved approximation algorithm with ratio $(1+\beta,\,\max\{2,\,1+\ln\frac{1}{\beta}\})$ is developed by constructing interesting auxiliary graphs and employing the cycle cancellation method. As a consequence, we can obtain a factor-$(1.369,\,2)$ approximation algorithm by setting $1+\ln\frac{1}{\beta}=2$ and a factor-$(1.567,\,1.567)$ algorithm by setting $1+\beta=1+\ln\frac{1}{\beta}$. Besides, by setting $\beta=0$, an approximation algorithm with ratio $(1,\, O(\ln n))$, i.e. an algorithm with only a single factor ratio $O(\ln n)$ on cost, can be immediately obtained. To the best of our knowledge, this is the first non-trivial approximation algorithm for the $k$BCP problem that strictly obeys the delay constraint.Comment: 12 page

GRB 970228 Within the EMBH Model

We consider the gamma-ray burst of 1997 February 28 (GRB 970228) within the ElectroMagnetic Black Hole (EMBH) model. We first determine the value of the two free parameters that characterize energetically the GRB phenomenon in the EMBH model, that is to say the dyadosphere energy, $E_{dya}=5.1\times10^{52}$ ergs, and the baryonic remnant mass $M_{B}$ in units of $E_{dya}$, $B=M_{B}c^{2}/E_{dya}=3.0\times10^{-3}$. Having in this way estimated the energy emitted during the beam-target phase, we evaluate the role of the InterStellar Medium (ISM) number density (n$_{ISM}$) and of the ratio ${\cal R}$ between the effective emitting area and the total surface area of the GRB source, in reproducing the observed profiles of the GRB 970228 prompt emission and X-ray (2-10 keV energy band) afterglow. The importance of the ISM distribution three-dimensional treatment around the central black hole is also stressed in this analysis.Comment: 4 pages, 1 figure, to appear in the Proceedings of the Los Alamos "Gamma Ray Burst Symposium" in Santa Fe, New Mexico, September 8-12 2003 (AIP Conf. Ser.), CHAPTER: GRB Connection to Supernova

Theory for transport through a single magnetic molecule: Endohedral N@C60

We consider transport through a single N@C60 molecule, weakly coupled to metallic leads. Employing a density-matrix formalism we derive rate equations for the occupation probabilities of many-particle states of the molecule. We calculate the current-voltage characteristics and the differential conductance for N@C60 in a break junction. Our results reveal Coulomb-blockade behavior as well as a fine structure of the Coulomb-blockade peaks due to the exchange coupling of the C60 spin to the spin of the encapsulated nitrogen atom.Comment: 5 pages, 4 figures, v2: version as publishe