About the fastest growth of Order Parameter in Models of Percolation

Can there be a `Litmus test' for determining the nature of transition in models of percolation? In this paper we argue that the answer is in the affirmative. All one needs to do is to measure the `growth exponent' $\chi$ of the largest component at the percolation threshold; $\chi < 1$ or $\chi = 1$ determines if the transition is continuous or discontinuous. We show that a related exponent $\eta = 1 - \chi$ which describes how the average maximal jump sizes in the Order Parameter decays on increasing the system size, is the single exponent that describes the finite-size scaling of a number of distributions related to the fastest growth of the Order Parameter in these problems. Excellent quality scaling analysis are presented for the two single peak distributions corresponding to the Order Parameters at the two ends of the maximal jump, the bimodal distribution constructed by interpolation of these distributions and for the distribution of the maximal jump in the Order Parameter.Comment: 8 pages, 9 figure

Weak Radiative Decays of Beauty Baryons

Weak radiative decays of beauty baryons into strange baryons, induced by the electroweak penguin, are estimated by using a quark model approach. Relations between formfactors in the semileptonic and in the weak radiative decays are derived within the heavy quark effective theory. The partial decay widths are found to be of the order of $10^{-15}{\rm MeV}$ for $\Lambda_b\rightarrow\Lambda\gamma$ and $\Xi_b\rightarrow\Xi\gamma$ and of the oder of $10^{-13}{\rm MeV}$ for $\Omega_b\rightarrow\Omega\gamma$. The $\Omega_b$ radiative decay is thus expected at the sizable branching ratio of approximately $10^{-4}$.Comment: 10 pages, latex, no figure

Distributed Computation with Continual Population Growth

Computing with synthetically engineered bacteria is a vibrant and active field with numerous applications in bio-production, bio-sensing, and medicine. Motivated by the lack of robustness and by resource limitation inside single cells, distributed approaches with communication among bacteria have recently gained in interest. In this paper, we focus on the problem of population growth happening concurrently, and possibly interfering, with the desired bio-computation. Specifically, we present a fast protocol in systems with continuous population growth for the majority consensus problem and prove that it correctly identifies the initial majority among two inputs with high probability if the initial difference is ?(?{nlog n}) where n is the total initial population. We also present a fast protocol that correctly computes the NAND of two inputs with high probability. We demonstrate that combining the NAND gate protocol with the continuous-growth majority consensus protocol, using the latter as an amplifier, it is possible to implement circuits computing arbitrary Boolean functions

Cell sorting in a Petri dish controlled by computer vision.

Fluorescence-activated cell sorting (FACS) applying flow cytometry to separate cells on a molecular basis is a widespread method. We demonstrate that both fluorescent and unlabeled live cells in a Petri dish observed with a microscope can be automatically recognized by computer vision and picked up by a computer-controlled micropipette. This method can be routinely applied as a FACS down to the single cell level with a very high selectivity. Sorting resolution, i.e., the minimum distance between two cells from which one could be selectively removed was 50-70 micrometers. Survival rate with a low number of 3T3 mouse fibroblasts and NE-4C neuroectodermal mouse stem cells was 66 +/- 12% and 88 +/- 16%, respectively. Purity of sorted cultures and rate of survival using NE-4C/NE-GFP-4C co-cultures were 95 +/- 2% and 62 +/- 7%, respectively. Hydrodynamic simulations confirmed the experimental sorting efficiency and a cell damage risk similar to that of normal FACS

Theoretical Update on Two Non-Resonant Three-Body Channels in Charmed Meson Decays

Predictions of two channels in the three-bod decays of the charmed mesons are made within the heavy hadron chiral perturbation theory. There still exists the problem that the theoretical expectation is too small compared to the experimental data.Comment: 13 pages with 2 figures included. To be publishe