Fixed-lag blind equalization and sequence estimation in digital communications systems using sequential importance sampling

We present methods for fixed-lag smoothing using Sequential Importance sampling (SIS) on a discrete non-linear, non-Gaussian state space system with unknown parameters. Our particular application is in the field of digital communication systems. Each input data point is taken from a finite set of symbols. We represent transmission media as a fixed filter with a finite impulse response (FIR), hence a discrete state-space system is formed. Conventional Markov chain Monte Carlo (MCMC) techniques such as the Gibbs sampler are unsuitable for this task because they can only perform processing on a batch of data. Data arrives sequentially, so it would seem sensible to process it in this way. In addition, many communication systems are interactive, so there is a maximum level of latency that can be tolerated before a symbol is decoded. We will demonstrate this method by simulation and compare its performance to existing techniques.

Monte Carlo filtering and smoothing with application to time-varying spectral estimation

We develop methods for performing filtering and smoothing in non-linear non-Gaussian dynamical models. The methods rely on a particle cloud representation of the filtering distribution which evolves through time using importance sampling and resampling ideas. In particular, novel techniques are presented for generation of random realisations from the joint smoothing distribution and for MAP estimation of the state sequence. Realisations of the smoothing distribution are generated in a forward-backward procedure, while the MAP estimation procedure can be performed in a single forward pass of the Viterbi algorithm applied to a discretised version of the state space. An application to spectral estimation for time-varying autoregressions is described.

Forward Smoothing Using Sequential Monte Carlo

Sequential Monte Carlo (SMC) methods are a widely used set of computational tools for inference in non-linear non-Gaussian state-space models. We propose a new SMC algorithm to compute the expectation of additive functionals recursively. Essentially, it is an on-line or "forward only" implementation of a forward filtering backward smoothing SMC algorithm proposed by Doucet, Godsill and Andrieu (2000). Compared to the standard \emph{path space} SMC estimator whose asymptotic variance increases quadratically with time even under favorable mixing assumptions, the non asymptotic variance of the proposed SMC estimator only increases linearly with time. We show how this allows us to perform recursive parameter estimation using an SMC implementation of an on-line version of the Expectation-Maximization algorithm which does not suffer from the particle path degeneracy problem.

A backward particle interpretation of Feynman-Kac formulae

We design a particle interpretation of Feynman-Kac measures on path spaces based on a backward Markovian representation combined with a traditional mean field particle interpretation of the flow of their final time marginals. In contrast to traditional genealogical tree based models, these new particle algorithms can be used to compute normalized additive functionals "on-the-fly" as well as their limiting occupation measures with a given precision degree that does not depend on the final time horizon. We provide uniform convergence results with respect to the time horizon parameter as well as functional central limit theorems and exponential concentration estimates. Our results have important consequences for online parameter estimation for non-linear non-Gaussian state-space models. We show how the forward filtering backward smoothing estimates of additive functionals can be computed using a forward only recursion.

Sequential Monte Carlo computation of the score and observed information matrix in state-space models with application to parameter estimation

Sequential Monte Carlo (SMC) methods are popular computational tools for Bayesian inference in non-linear non-Gaussian state-space models. For this class of models, we propose SMC algorithms to compute the score vector and observed information matrix recursively in time. We propose two different SMC implementations, one with computational complexity $\mathcal{O}(N)$ and the other with complexity $\mathcal{O}(N^{2})$ where $N$ is the number of importance sampling draws. Although cheaper, the performance of the $\mathcal{O}(N)$ method degrades quickly in time as it inherently relies on the SMC approximation of a sequence of probability distributions whose dimension is increasing linearly with time. In particular, even under strong \textit{mixing} assumptions, the variance of the estimates computed with the $\mathcal{O}(N)$ method increases at least quadratically in time. The $\mathcal{O}(N^{2})$ is a non-standard SMC implementation that does not suffer from this rapid degrade. We then show how both methods can be used to perform batch and recursive parameter estimation.

Invariants, Lie-Bäcklund operators and Bäcklund transformations

This thesis is mainly concerned with the application of groups of transformations to differential equations and in particular with the connection between the group structure of a given equation and the existence of exact solutions and conservation laws. In this respect the Lie-Bäcklund groups of tangent transformations, particular cases of which are the Lie tangent and the Lie point groups, are extensively used.

In Chapter I we first review the classical results of Lie, Bäcklund and Bianchi as well as the more recent ones due mainly to Ovsjannikov. We then concentrate on the Lie-Bäcklund groups (or more precisely on the corresponding Lie-Bäcklund operators), as introduced by Ibragimov and Anderson, and prove some lemmas about them which are useful for the following chapters. Finally we introduce the concept of a conditionally admissible operator (as opposed to an admissible one) and show how this can be used to generate exact solutions.

In Chapter II we establish the group nature of all separable solutions and conserved quantities in classical mechanics by analyzing the group structure of the Hamilton-Jacobi equation. It is shown that consideration of only Lie point groups is insufficient. For this purpose a special type of Lie-Bäcklund groups, those equivalent to Lie tangent groups, is used. It is also shown how these generalized groups induce Lie point groups on Hamilton's equations. The generalization of the above results to any first order equation, where the dependent variable does not appear explicitly, is obvious. In the second part of this chapter we investigate admissible operators (or equivalently constants of motion) of the Hamilton-Jacobi equation with polynornial dependence on the momenta. The form of the most general constant of motion linear, quadratic and cubic in the momenta is explicitly found. Emphasis is given to the quadratic case, where the particular case of a fixed (say zero) energy state is also considered; it is shown that in the latter case additional symmetries may appear. Finally, some potentials of physical interest admitting higher symmetries are considered. These include potentials due to two centers and limiting cases thereof. The most general two-center potential admitting a quadratic constant of motion is obtained, as well as the corresponding invariant. Also some new cubic invariants are found.

In Chapter III we first establish the group nature of all separable solutions of any linear, homogeneous equation. We then concentrate on the Schrodinger equation and look for an algorithm which generates a quantum invariant from a classical one. The problem of an isomorphism between functions in classical observables and quantum observables is studied concretely and constructively. For functions at most quadratic in the momenta an isomorphism is possible which agrees with Weyl' s transform and which takes invariants into invariants. It is not possible to extend the isomorphism indefinitely. The requirement that an invariant goes into an invariant may necessitate variants of Weyl' s transform. This is illustrated for the case of cubic invariants. Finally, the case of a specific value of energy is considered; in this case Weyl's transform does not yield an isomorphism even for the quadratic case. However, for this case a correspondence mapping a classical invariant to a quantum orie is explicitly found.

Chapters IV and V are concerned with the general group structure of evolution equations. In Chapter IV we establish a one to one correspondence between admissible Lie-Bäcklund operators of evolution equations (derivable from a variational principle) and conservation laws of these equations. This correspondence takes the form of a simple algorithm.

In Chapter V we first establish the group nature of all Bäcklund transformations (BT) by proving that any solution generated by a BT is invariant under the action of some conditionally admissible operator. We then use an algorithm based on invariance criteria to rederive many known BT and to derive some new ones. Finally, we propose a generalization of BT which, among other advantages, clarifies the connection between the wave-train solution and a BT in the sense that, a BT may be thought of as a variation of parameters of some. special case of the wave-train solution (usually the solitary wave one). Some open problems are indicated.

Most of the material of Chapters II and III is contained in [I], [II], [III] and [IV] and the first part of Chapter V in [V].

Electromagnetically induced self-imaging

We study the self-imaging and image-transforming properties of a probe field in a cold atomic medium with electromagnetically induced transparency (EIT). Due to the similarities between the gradient-index medium and the inhomogeneous index distribution of an EIT medium under the conditions of a negative probe detuning and a Gaussian control field, we find based on analytical investigations that there exists a kind of electromagnetically induced self-imaging phenomenon in cold atomic media. Numerical simulations clearly show that electromagnetically induced self-imaging is observable and controllable. (c) 2007 Optical Society of America.

Chromosomal aberrations induced by C-12(6+) ions and Co-60 gamma-rays in mouse immature oocytes

The ovaries of Kun-Ming strain mice (3 weeks) were irradiated with different doses of C-12(6+) ion or Co-60 gamma-ray. Chromosomal aberrations were analyzed in metaphase II oocytes at 7 weeks after irradiation. The relative biological effectiveness (RBE) of C C-12(6+) ion was calculated with respect to Co-60 gamma-ray for the induction of chromosornal aberrations. The C-12(6+) ion and Co-60 gamma-ray dose-response relationships for chromosomal aberrations were plotted by linear quadratic models. The data showed that there was a dose-related increase in frequency of chromosomal aberrations in all the treated groups compared to controls. The RBE values for C-12(6+) ions relative to (CO)-C-60 gamma-rays were 2.49, 2.29, 1.57, 1.42 or 1.32 for the doses of 0.5, 1.0, 2.07 4.0 or 6.0 Gy, respectively. Moreover, a different distribution of the various types of aberrations has been found for C-12(6+) ion and Co-60 gamma-ray irradiations. The dose-response relationships for C-12(6+) ion and (CO)-C-60 gamma-ray exhibited positive correlations. The results from the present study may be helpful for assessing genetic damage following exposure of immature oocytes to ionizing radiation.

Biodosimetry estimate for high-LET irradiation

The purpose of this paper is to prepare for an easy and reliable biodosimeter protocol for radiation accidents involving high-linear energy transfer (LET) exposure. Human peripheral blood lymphocytes were irradiated using carbon ions (LET: 34.6 keV mu m(-1)), and the chromosome aberrations induced were analyzed using both a conventional colcemid block method and a calyculin A induced premature chromosome condensation (PCC) method. At a lower dose range (0-4 Gy), the measured dicentric (dics) and centric ring chromosomes (cRings) provided reasonable dose information. At higher doses (8 Gy), however, the frequency of dics and cRings was not suitable for dose estimation. Instead, we found that the number of Giemsa-stained drug-induced G2 prematurely condensed chromosomes (G2-PCC) can be used for dose estimation, since the total chromosome number (including fragments) was linearly correlated with radiation dose (r = 0.99). The ratio of the longest and the shortest chromosome length of the drug-induced G2-PCCs increased with radiation dose in a linear-quadratic manner (r = 0.96), which indicates that this ratio can also be used to estimate radiation doses. Obviously, it is easier to establish the dose response curve using the PCC technique than using the conventional metaphase chromosome method. It is assumed that combining the ratio of the longest and the shortest chromosome length with analysis of the total chromosome number might be a valuable tool for rapid and precise dose estimation for victims of radiation accidents.

A correlation between radiation sensitivity and initial chromatid breaks in cancer cell lines revealed by Calyculin A-induced premature condensation

Three human malignancy cell lines were irradiated with Co-60 gamma-rays. Initial chromatid breaks were measured by using the chemically induced premature chromosome condensation technique. Survival curves of cells exposed to gamma rays was linear-quadratic while the efficiency of Calyculin A in inducing PCC of G(2) PCC was about five times more than G(1) PCC. A dose-dependent increase in radiation-induced chromatid/isochromatid breaks was observed in G(1) and G(2) phase PCC and a nearly positive linear correlation was found between cell survival and chromatin breaks. This study implies that low LET radiation-induced chromatid/isochromatid breaks can potentially be used to predict the radiosensitivity of tumor cells either in in vitro experimentation or in in vivo clinical radiotherapy.

Comparison of clonogenic assay with premature chromosome condensation assay in prediction of human cell radiosensitivity

Aim: To determine whether the number of non-rejoining G2-chromatid breaks can predict the radiosensitivity of human cell lines. Methods: Cell lines of human ovary carcinoma cells (HO8910), human hepatoma cells (HepG2) and liver cells (L02) were irradiated with a range of doses and assessed both of cell survival and non-rejoining G2-chromatid breaks at 24 h after irradiation. Cell survival was documented by a colony assay. Non-rejoining G2-chromatid breaks were measured by counting the number of non-rejoining G2 chromatid breaks at 24 h after irradiation, detected by the prematurely chromosome condensed (PCC) technique. Results: A linear-quadratic survival curve was observed in three cell lines, and HepG2 was the most sensitive to gamma-radiation. A dose-dependent linear increase was observed in radiation-induced non-rejoining G2-PCC breaks measured at 24 h after irradiation in all cell lines, and HepG2 was the most susceptible to induction of non-rejoining G2-PCC breaks. A close correlation was found between the clonogenic radiosensitivity and the radiation-induced non-rejoining G2-PCC breaks (r=0.923). Furthermore, survival-aberration correlations for two or more than two doses lever were also significant. Conclusion: The number of non-rejoining G2 PCC breaks holds considerable promise for predicting the radiosensitivity of normal and tumor cells when two or more than two doses lever is tested.

HHT在电磁信号处理中的应用

In modem signal Processing，non－linear，non－Gaussian and non－stable signals are usually the analyzed and Processed objects，especially non－stable signals. The convention always to analyze and Process non－stable signals are： short time Fourier transform，Wigner－Ville distribution，wavelet Transform and so on. But the above three algorithms are all based on Fourier Transform，so they all have the shortcoming of Fourier Analysis and cannot get rid of the localization of it. Hilbert－Huang Transform is a new non－stable signal processing technology，proposed by N. E. Huang in 1998. It is composed of Empirical Mode Decomposition (referred to as EMD) and Hilbert Spectral Analysis (referred to as HSA). After EMD Processing，any non－stable signal will be decomposed to a series of data sequences with different scales. Each sequence is called an Intrinsic Mode Function (referred to as IMF). And then the energy distribution plots of the original non－stable signal can be found by summing all the Hilbert spectrums of each IMF. In essence，this algorithm makes the non－stable signals become stable and decomposes the fluctuations and tendencies of different scales by degrees and at last describes the frequency components with instantaneous frequency and energy instead of the total frequency and energy in Fourier Spectral Analysis. In this case，the shortcoming of using many fake harmonic waves to describe non－linear and non－stable signals in Fourier Transform can be avoided. This Paper researches in the following parts： Firstly，This paper introduce the history and development of HHT，subsequently the characters and main issues of HHT. This paper briefly introduced the basic realization principles and algorithms of Hilbert－Huang transformation and confirms its validity by simulations. Secondly, This paper discuss on some shortcoming of HHT. By using FFT interpolation, we solve the problem of IMF instability and instantaneous frequency undulate which are caused by the insufficiency of sampling rate. As to the bound effect caused by the limitation of envelop algorithm of HHT, we use the wave characteristic matching method, and have good result. Thirdly, This paper do some deeply research on the application of HHT in electromagnetism signals processing. Based on the analysis of actual data examples, we discussed its application in electromagnetism signals processing and noise suppression. Using empirical mode decomposition method and multi-scale filter characteristics can effectively analyze the noise distribution of electromagnetism signal and suppress interference processing and information interpretability. It has been founded that selecting electromagnetism signal sessions using Hilbert time-frequency energy spectrum is helpful to improve signal quality and enhance the quality of data.

Low-dose studies of bystander cell killing with targeted soft X rays

The Gray Cancer Institute ultrasoft X-ray microprobe was used to quantify the bystander response of individual V79 cells exposed to a focused carbon K-shell (278 eV) X-ray beam. The ultrasoft X-ray microprobe is designed to precisely assess the biological response of individual cells irradiated in vitro with a very fine beam of low-energy photons. Characteristic C-K X rays are generated by a focused beam of 10 keV electrons striking a graphite target. Circular diffraction gratings (i.e. zone plates) are then employed to focus the X-ray beam into a spot with a radius of 0.25 mum at the sample position. Using this microbeam technology, the correlation between the irradiated cells and their nonirradiated neighbors can be examined critically. The survival response of V79 cells irradiated with a C-K X-ray beam was measured in the 0-2-Gy dose range. The response when all cells were irradiated was compared to that obtained when only a single cell was exposed. The cell survival data exhibit a linear-quadratic response when all cells were targeted (with evidence for hyper-sensitivity at low doses). When only a single cell was targeted within the population, 10% cell killing was measured. In contrast to the binary bystander behavior reported by many other investigations, the effect detected was initially dependent on dose (200 mGy). In the low-dose region (

Out-of-field cell survival following exposure to intensity-modulated radiation fields

PURPOSE:
To determine the in-field and out-of-field cell survival of cells irradiated with either primary field or scattered radiation in the presence and absence of intercellular communication.
METHODS AND MATERIALS:
Cell survival was determined by clonogenic assay in human prostate cancer (DU145) and primary fibroblast (AGO1552) cells following exposure to different field configurations delivered using a 6-MV photon beam produced with a Varian linear accelerator.
RESULTS:
Nonuniform dose distributions were delivered using a multileaf collimator (MLC) in which half of the cell population was shielded. Clonogenic survival in the shielded region was significantly lower than that predicted from the linear quadratic model. In both cell lines, the out-of-field responses appeared to saturate at 40%-50% survival at a scattered dose of 0.70 Gy in DU-145 cells and 0.24 Gy in AGO1522 cells. There was an approximately eightfold difference in the initial slopes of the out-of-field response compared with the a-component of the uniform field response. In contrast, cells in the exposed part of the field showed increased survival. These observations were abrogated by direct physical inhibition of cellular communication and by the addition of the inducible nitric oxide synthase inhibitor aminoguanidine known to inhibit intercellular bystander effects. Additional studies showed the proportion of cells irradiated and dose delivered to the shielded and exposed regions of the field to impact on response.
CONCLUSIONS:
These data demonstrate out-of-field effects as important determinants of cell survival following exposure to modulated irradiation fields with cellular communication between differentially irradiated cell populations playing an important role. Validation of these observations in additional cell models may facilitate the refinement of existing radiobiological models and the observations considered important determinants of cell survival.

Cell survival responses after exposure to modulated radiation fields.

In the present study survival responses were determined in cells with differing radiosensitivity, specifically primary fibroblast (AG0-1522B), human breast cancer (MDA-MB-231), human prostate cancer (DU-145) and human glioma (T98G) cells, after exposure to modulated radiation fields delivered by shielding 50% of the tissue culture flask. A significant decrease (P < 0.05) in cell survival was observed in the shielded area, outside the primary treatment field (out-of-field), that was lower than predicted when compared to uniform exposures fitted to the linear-quadratic model. Cellular radiosensitivity was demonstrated to be an important factor in the level of response for both the in- and out-of-field regions. These responses were shown to be dependent on secretion-mediated intercellular communication, because inhibition of cellular secreted factors between the in- and out-of-field regions abrogated the response. Out-of-field cell survival was shown to increase after pretreatment of cells with agents known to inhibit factors involved in mediating radiation-induced bystander signaling (aminoguanidine, DMSO or cPTIO). These data illustrate a significant decrease in survival out-of-field, dependent upon intercellular communication, in several cell lines with varying radiosensitivity after exposure to a modulated radiation field. This study provides further evidence for the importance of intercellular signaling in modulated exposures, where dose gradients are present, and may inform the refinement of established radiobiological models to facilitate the optimization of advanced radiotherapy treatment plans.