33,650 research outputs found
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.
Theories and Varying Fine Structure Constant
In analogy to theory, recently a new modified gravity theory, namely
the so-called 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 theories with the varying fine
structure "constant", . We find that the constraints
on theories from the observational data are very
severe. In fact, they make theories almost indistinguishable from
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
High moment partial sum processes of residuals in GARCH models and their applications
In this paper we construct high moment partial sum processes based on
residuals of a GARCH model when the mean is known to be 0. We consider partial
sums of th powers of residuals, CUSUM processes and self-normalized partial
sum processes. The th power partial sum process converges to a Brownian
process plus a correction term, where the correction term depends on the th
moment of the innovation sequence. If , then the correction
term is 0 and, thus, the th power partial sum process converges weakly to
the same Gaussian process as does the th power partial sum of the i.i.d.
innovations sequence. In particular, since , this holds for the first
moment partial sum process, but fails for the second moment partial sum
process. We also consider the CUSUM and the self-normalized processes, that is,
standardized by the residual sample variance. These behave as if the residuals
were asymptotically i.i.d. We also study the joint distribution of the th
and st self-normalized partial sum processes. Applications to
change-point problems and goodness-of-fit are considered, in particular, CUSUM
statistics for testing GARCH model structure change and the Jarque--Bera
omnibus statistic for testing normality of the unobservable innovation
distribution of a GARCH model. The use of residuals for constructing a kernel
density function estimation of the innovation distribution is discussed.Comment: Published at http://dx.doi.org/10.1214/009053605000000534 in the
Annals of Statistics (http://www.imstat.org/aos/) by the Institute of
Mathematical Statistics (http://www.imstat.org
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