Algorithms for group isomorphism via group extensions and cohomology

The isomorphism problem for finite groups of order n (GpI) has long been known to be solvable in $n^{\log n+O(1)}$ time, but only recently were polynomial-time algorithms designed for several interesting group classes. Inspired by recent progress, we revisit the strategy for GpI via the extension theory of groups. The extension theory describes how a normal subgroup N is related to G/N via G, and this naturally leads to a divide-and-conquer strategy that splits GpI into two subproblems: one regarding group actions on other groups, and one regarding group cohomology. When the normal subgroup N is abelian, this strategy is well-known. Our first contribution is to extend this strategy to handle the case when N is not necessarily abelian. This allows us to provide a unified explanation of all recent polynomial-time algorithms for special group classes. Guided by this strategy, to make further progress on GpI, we consider central-radical groups, proposed in Babai et al. (SODA 2011): the class of groups such that G mod its center has no abelian normal subgroups. This class is a natural extension of the group class considered by Babai et al. (ICALP 2012), namely those groups with no abelian normal subgroups. Following the above strategy, we solve GpI in $n^{O(\log \log n)}$ time for central-radical groups, and in polynomial time for several prominent subclasses of central-radical groups. We also solve GpI in $n^{O(\log\log n)}$ time for groups whose solvable normal subgroups are elementary abelian but not necessarily central. As far as we are aware, this is the first time there have been worst-case guarantees on a $n^{o(\log n)}$-time algorithm that tackles both aspects of GpI---actions and cohomology---simultaneously.Comment: 54 pages + 14-page appendix. Significantly improved presentation, with some new result

Accelerating charging dynamics in sub-nanometer pores

Having smaller energy density than batteries, supercapacitors have exceptional power density and cyclability. Their energy density can be increased using ionic liquids and electrodes with sub-nanometer pores, but this tends to reduce their power density and compromise the key advantage of supercapacitors. To help address this issue through material optimization, here we unravel the mechanisms of charging sub-nanometer pores with ionic liquids using molecular simulations, navigated by a phenomenological model. We show that charging of ionophilic pores is a diffusive process, often accompanied by overfilling followed by de-filling. In sharp contrast to conventional expectations, charging is fast because ion diffusion during charging can be an order of magnitude faster than in bulk, and charging itself is accelerated by the onset of collective modes. Further acceleration can be achieved using ionophobic pores by eliminating overfilling/de-filling and thus leading to charging behavior qualitatively different from that in conventional, ionophilic pores

Electrical properties of breast cancer cells from impedance measurement of cell suspensions

Impedance spectroscopy of biological cells has been used to monitor cell status, e.g. cell proliferation, viability, etc. It is also a fundamental method for the study of the electrical properties of cells which has been utilised for cell identification in investigations of cell behaviour in the presence of an applied electric field, e.g. electroporation. There are two standard methods for impedance measurement on cells. The use of microelectrodes for single cell impedance measurement is one method to realise the measurement, but the variations between individual cells introduce significant measurement errors. Another method to measure electrical properties is by the measurement of cell suspensions, i.e. a group of cells within a culture medium or buffer. This paper presents an investigation of the impedance of normal and cancerous breast cells in suspension using the Maxwell-Wagner mixture theory to analyse the results and extract the electrical parameters of a single cell. The results show that normal and different stages of cancer breast cells can be distinguished by the conductivity presented by each cell. © 2010 IOP Publishing Ltd

Studying top quark decay into the polarized W-boson in the TC2 model

We study the decay mode of top quark decaying into Wb in the TC2 model where the top quark is distinguished from other fermions by participating in a strong interaction. We find that the TC2 correction to the decay width $\Gamma (t \to b W)$ is generally several percent and maximum value can reach 8% for the currently allowed parameters. The magnitude of such correction is comparable with QCD correction and larger than that of minimal supersymmetric model. Such correction might be observable in the future colliders. We also study the TC2 correction to the branching ratio of top quark decay into the polarized W bosons and find the correction is below $1$. After considering the TC2 correction, we find that our theoretical predictions about the decay branching ratio are also consistent with the experimental data.Comment: 8 pages, 4 figure

Zero differential resistance state of two dimensional electron systems in strong magnetic fields

Zero differential resistance state is found in response to direct current applied to 2D electron systems at strong magnetic field and low temperatures. Transition to the state is accompanied by sharp dip of negative differential resistance, which occurs above threshold value $I_{th}$ of the direct current. The state depends significantly on the temperature and is not observable above several Kelvins. Additional analysis shows lack of the linear stability of the 2D electron systems at $I>I_{th}$ and inhomogeneous, non-stationary pattern of the electric current in the zero differential resistance state. We suggest that the dc bias induced redistribution of the 2D electrons in energy space is the dominant mechanism leading to the new electron state.Comment: 5 pages, 3 figure