On a new geometric homology theory

In this note we present a new homology theory, we call it geometric homology theory (or GHT for brevity). We prove that the homology groups of GHT are isomorphic to the singular homology groups, which solves a Conjecture of Voronov. GHT has several nice properties compared with singular homology, which makes itself more suitable than singular homology in some situations, especially in chain-level theories. We will develop further of this theory in our sequel paper.Comment: Comments are appreciated !. arXiv admin note: text overlap with arXiv:0709.3874 by other author

Hierarchical equilibria of branching populations

In this paper we study high moment partial sum processes based on residuals of a stationary ARMA model with or without a unknown mean parameter. We show that they can be approximated in probability by the analogous processes which are obtained from the independent and identically distributed (iid) errors of the ARMA model. However, if a unknown mean parameter is used, there will be an additional term that depends on model parameters and a mean estimator. But, when properly normalized, this additional term will be cancelled out. Thus they converge weakly to the same Gaussian processes as if the residuals were iid. Applications to changepoint problems and goodness-of-fit are considered, in particular CUSUM statistics for testing ARMA model structure changes and the Jarque-Bera omnibus statistic for testing normality of the unobservable error distribution of an ARMA model.ARMA, residuals, high moment partial sum process, weak convergence, CUSUM, omnibus, skewness, kurtosis, (sqare root)n consistency.

f(T)f(T) Theories and Varying Fine Structure Constant

In analogy to $f(R)$ theory, recently a new modified gravity theory, namely the so-called $f(T)$ theory, has been proposed to drive the current accelerated expansion without invoking dark energy. In the present work, by extending Bisabr's idea, we try to constrain $f(T)$ theories with the varying fine structure "constant", $\alpha\equiv e^2/\hbar c$. We find that the constraints on $f(T)$ theories from the observational $\Delta\alpha/\alpha$ data are very severe. In fact, they make $f(T)$ theories almost indistinguishable from $\Lambda$CDM model.Comment: 12 pages, 4 figures, 1 table, revtex4; v2: discussions added, Phys. Lett. B in press; v3: published versio

Quantification of propidium iodide delivery with millisecond electric pulses: A model study

A model study of propidium iodide delivery with millisecond electric pulses is presented; this work is a companion of the experimental efforts by Sadik et al. [1]. Both membrane permeabilization and delivery are examined with respect to six extra-cellular conductivities. The transmembrane potential of the permeabilized regions exhibits a consistent value, which corresponds to a bifurcation point in the pore-radius-potential relation. Both the pore area density and membrane conductance increase with an increasing extra-cellular conductivity. On the other hand, the inverse correlation between propidium iodide delivery and extra-cellular conductivity as observed in the experiments is quantitatively captured by the model. This agreement confirms that this behavior is primarily mediated by electrophoretic transport during the pulse. The results suggest that electrophoresis is important even for the delivery of small molecules such as propidium iodide. The direct comparison between model prediction and experimental data presented in this work helps validate the former as a robust predictive tool for the study of electroporation