Attenuated total reflectance fourier transform infrared spectroscopy: an analytical technique to understand therapeutic responses at the molecular level

Rapid monitoring of the response to treatment in cancer patients is essential to predict the outcome of the therapeutic regimen early in the course of the treatment. The conventional methods are laborious, time-consuming, subjective and lack the ability to study different biomolecules and their interactions, simultaneously. Since; mechanisms of cancer and its response to therapy is dependent on molecular interactions and not on single biomolecules, an assay capable of studying molecular interactions as a whole, is preferred. Fourier Transform Infrared (FTIR) spectroscopy has become a popular technique in the field of cancer therapy with an ability to elucidate molecular interactions. The aim of this study, was to explore the utility of the FTIR technique along with multivariate analysis to understand whether the method has the resolution to identify the differences in the mechanism of therapeutic response. Towards achieving the aim, we utilized the mouse xenograft model of retinoblastoma and nanoparticle mediated targeted therapy. The results indicate that the mechanism underlying the response differed between the treated and untreated group which can be elucidated by unique spectral signatures generated by each group. The study establishes the efficiency of non-invasive, label-free and rapid FTIR method in assessing the interactions of nanoparticles with cellular macromolecules towards monitoring the response to cancer therapeutics.

Fingerprint analysis using wavelet transform with application to compression and feature extraction

The main goal of this research is to design an efficient compression al~ gorithm for fingerprint images. The wavelet transform technique is the principal tool used to reduce interpixel redundancies and to obtain a parsimonious representation for these images. A specific fixed decomposition structure is designed to be used by the wavelet packet in order to save on the computation, transmission, and storage costs. This decomposition structure is based on analysis of information packing performance of several decompositions, two-dimensional power spectral density, effect of each frequency band on the reconstructed image, and the human visual sensitivities. This fixed structure is found to provide the "most" suitable representation for fingerprints, according to the chosen criteria. Different compression techniques are used for different subbands, based on their observed statistics. The decision is based on the effect of each subband on the reconstructed image according to the mean square criteria as well as the sensitivities in human vision. To design an efficient quantization algorithm, a precise model for distribution of the wavelet coefficients is developed. The model is based on the generalized Gaussian distribution. A least squares algorithm on a nonlinear function of the distribution model shape parameter is formulated to estimate the model parameters. A noise shaping bit allocation procedure is then used to assign the bit rate among subbands. To obtain high compression ratios, vector quantization is used. In this work, the lattice vector quantization (LVQ) is chosen because of its superior performance over other types of vector quantizers. The structure of a lattice quantizer is determined by its parameters known as truncation level and scaling factor. In lattice-based compression algorithms reported in the literature the lattice structure is commonly predetermined leading to a nonoptimized quantization approach. In this research, a new technique for determining the lattice parameters is proposed. In the lattice structure design, no assumption about the lattice parameters is made and no training and multi-quantizing is required. The design is based on minimizing the quantization distortion by adapting to the statistical characteristics of the source in each subimage. 11 Abstract Abstract Since LVQ is a multidimensional generalization of uniform quantizers, it produces minimum distortion for inputs with uniform distributions. In order to take advantage of the properties of LVQ and its fast implementation, while considering the i.i.d. nonuniform distribution of wavelet coefficients, the piecewise-uniform pyramid LVQ algorithm is proposed. The proposed algorithm quantizes almost all of source vectors without the need to project these on the lattice outermost shell, while it properly maintains a small codebook size. It also resolves the wedge region problem commonly encountered with sharply distributed random sources. These represent some of the drawbacks of the algorithm proposed by Barlaud [26). The proposed algorithm handles all types of lattices, not only the cubic lattices, as opposed to the algorithms developed by Fischer [29) and Jeong [42). Furthermore, no training and multiquantizing (to determine lattice parameters) is required, as opposed to Powell's algorithm [78). For coefficients with high-frequency content, the positive-negative mean algorithm is proposed to improve the resolution of reconstructed images. For coefficients with low-frequency content, a lossless predictive compression scheme is used to preserve the quality of reconstructed images. A method to reduce bit requirements of necessary side information is also introduced. Lossless entropy coding techniques are subsequently used to remove coding redundancy. The algorithms result in high quality reconstructed images with better compression ratios than other available algorithms. To evaluate the proposed algorithms their objective and subjective performance comparisons with other available techniques are presented. The quality of the reconstructed images is important for a reliable identification. Enhancement and feature extraction on the reconstructed images are also investigated in this research. A structural-based feature extraction algorithm is proposed in which the unique properties of fingerprint textures are used to enhance the images and improve the fidelity of their characteristic features. The ridges are extracted from enhanced grey-level foreground areas based on the local ridge dominant directions. The proposed ridge extraction algorithm, properly preserves the natural shape of grey-level ridges as well as precise locations of the features, as opposed to the ridge extraction algorithm in [81). Furthermore, it is fast and operates only on foreground regions, as opposed to the adaptive floating average thresholding process in [68). Spurious features are subsequently eliminated using the proposed post-processing scheme.

Fast fourier analysis of structural organization in decellularized cartilage-on-bone laminates

Denaturation of tissues can provide a unique biological environment for regenerative medicine application only if minimal disruption of their microarchitecture is achieved during the decellularization process. The goal is to keep the structural integrity of such a construct as functional as the tissues from which they were derived. In this work, cartilage-on-bone laminates were decellularized through enzymatic, non-ionic and ionic protocols. This work investigated the effects of decellularization process on the microarchitecture of cartiligous extracellular matrix; determining the extent of how each process deteriorated the structural organization of the network. High resolution microscopy was used to capture cross-sectional images of samples prior to and after treatment. The variation of the microarchitecture was then analysed using a well defined fast Fourier image processing algorithm. Statistical analysis of the results revealed how significant the alternations among aforementioned protocols were (p < 0.05). Ranking the treatments by their effectiveness in disrupting the ECM integrity, they were ordered as: Trypsin> SDS> Triton X-100.

Fourier Lucas-Kanade Algorithm

In this paper we propose a framework for both gradient descent image and object alignment in the Fourier domain. Our method centers upon the classical Lucas & Kanade (LK) algorithm where we represent the source and template/model in the complex 2D Fourier domain rather than in the spatial 2D domain. We refer to our approach as the Fourier LK (FLK) algorithm. The FLK formulation is advantageous when one pre-processes the source image and template/model with a bank of filters (e.g. oriented edges, Gabor, etc.) as: (i) it can handle substantial illumination variations, (ii) the inefficient pre-processing filter bank step can be subsumed within the FLK algorithm as a sparse diagonal weighting matrix, (iii) unlike traditional LK the computational cost is invariant to the number of filters and as a result far more efficient, and (iv) this approach can be extended to the inverse compositional form of the LK algorithm where nearly all steps (including Fourier transform and filter bank pre-processing) can be pre-computed leading to an extremely efficient and robust approach to gradient descent image matching. Further, these computational savings translate to non-rigid object alignment tasks that are considered extensions of the LK algorithm such as those found in Active Appearance Models (AAMs).

On the efficacy of Fourier series approximations for pricing European options

This paper investigates several competing procedures for computing the prices of vanilla European options, such as puts, calls and binaries, in which the underlying model has a characteristic function that is known in semi-closed form. The algorithms investigated here are the half-range Fourier cosine series, the half-range Fourier sine series and the full-range Fourier series. Their performance is assessed in simulation experiments in which an analytical solution is available and also for a simple affine model of stochastic volatility in which there is no closed-form solution. The results suggest that the half-range sine series approximation is the least effective of the three proposed algorithms. It is rather more difficult to distinguish between the performance of the halfrange cosine series and the full-range Fourier series. However there are two clear differences. First, when the interval over which the density is approximated is relatively large, the full-range Fourier series is at least as good as the half-range Fourier cosine series, and outperforms the latter in pricing out-of-the-money call options, in particular with maturities of three months or less. Second, the computational time required by the half-range Fourier cosine series is uniformly longer than that required by the full-range Fourier series for an interval of fixed length. Taken together,these two conclusions make a case for pricing options using a full-range range Fourier series as opposed to a half-range Fourier cosine series if a large number of options are to be priced in as short a time as possible.

On the Transform Method of Solution of an External Crack Problem

The breakdown of the usual method of Fourier transforms in the problem of an external line crack in a thin infinite elastic plate is discovered and the correct solution of this problem is derived using the concept of a generalised Fourier transform of a type discussed first by Golecki [1] in connection with Flamant's problem.

Segal-Bargmann transform and Paley-Wiener theorems on M(2)

We study the Segal-Bargmann transform on M(2). The range of this transform is characterized as a weighted Bergman space. In a similar fashion Poisson integrals are investigated. Using a Gutzmer's type formula we characterize the range as a class of functions extending holomorphically to an appropriate domain in the complexification of M(2). We also prove a Paley-Wiener theorem for the inverse Fourier transform.

Component wave delineation of ECG by filtering in the Fourier domain

A complete solution to the fundamental problem of delineation of an ECG signal into its component waves by filtering the discrete Fourier transform of the signal is presented. The set of samples in a component wave is transformed into a complex sequence with a distinct frequency band. The filter characteristics are determined from the time signal itself. Multiplication of the transformed signal with a complex sinusoidal function allows the use of a bank of low-pass filters for the delineation of all component waves. Data from about 300 beats have been analysed and the results are highly satisfactory both qualitatively and quantitatively.

Wavelet transform analysis of truncated fringe patterns in 3-D surface profilometry

Wavelet transform analysis of projected fringe pattern for phase recovery in 3-D shape measurement of objects is investigated. The present communication specifically outlines and evaluates the errors that creep in to the reconstructed profiles when fringe images do not satisfy periodicity. Three specific cases that give raise to non-periodicity of fringe image are simulated and leakage effects caused by each one of them are analyzed with continuous complex Morlet wavelet transform. Same images are analyzed with FFT method to make a comparison of the reconstructed profiles with both methods. Simulation results revealed a significant advantage of wavelet transform profilometry (WTP), that the distortions that arise due to leakage are confined to the locations of discontinuity and do not spread out over the entire projection as in the case of Fourier transform profilometry (FTP).

A transform approach to linear network coding for acyclic networks with delay

The algebraic formulation for linear network coding in acyclic networks with each link having an integer delay is well known. Based on this formulation, for a given set of connections over an arbitrary acyclic network with integer delay assumed for the links, the output symbols at the sink nodes at any given time instant is a Fq-linear combination of the input symbols across different generations, where Fq denotes the field over which the network operates. We use finite-field discrete Fourier transform (DFT) to convert the output symbols at the sink nodes at any given time instant into a Fq-linear combination of the input symbols generated during the same generation. We call this as transforming the acyclic network with delay into n-instantaneous networks (n is sufficiently large). We show that under certain conditions, there exists a network code satisfying sink demands in the usual (non-transform) approach if and only if there exists a network code satisfying sink demands in the transform approach. Furthermore, assuming time invariant local encoding kernels, we show that the transform method can be employed to achieve half the rate corresponding to the individual source-destination mincut (which are assumed to be equal to 1) for some classes of three-source three-destination multiple unicast network with delays using alignment strategies when the zero-interference condition is not satisfied.

Fractional Hilbert transform extensions and associated analytic signal construction

The analytic signal (AS) was proposed by Gabor as a complex signal corresponding to a given real signal. The AS has a one-sided spectrum and gives rise to meaningful spectral averages. The Hilbert transform (HT) is a key component in Gabor's AS construction. We generalize the construction methodology by employing the fractional Hilbert transform (FrHT), without going through the standard fractional Fourier transform (FrFT) route. We discuss some properties of the fractional Hilbert operator and show how decomposition of the operator in terms of the identity and the standard Hilbert operators enables the construction of a family of analytic signals. We show that these analytic signals also satisfy Bedrosian-type properties and that their time-frequency localization properties are unaltered. We also propose a generalized-phase AS (GPAS) using a generalized-phase Hilbert transform (GPHT). We show that the GPHT shares many properties of the FrHT, in particular, selective highlighting of singularities, and a connection with Lie groups. We also investigate the duality between analyticity and causality concepts to arrive at a representation of causal signals in terms of the FrHT and GPHT. On the application front, we develop a secure multi-key single-sideband (SSB) modulation scheme and analyze its performance in noise and sensitivity to security key perturbations. (C) 2013 Elsevier B.V. All rights reserved.

L-p-Integrability, Dimensions of Supports of Fourier Transforms and Applications

It is proved that there does not exist any non zero function in with if its Fourier transform is supported by a set of finite packing -measure where . It is shown that the assertion fails for . The result is applied to prove L-p Wiener Tauberian theorems for R-n and M(2).

Precoding-Based Network Alignment Using Transform Approach for Acyclic Networks With Delay

The algebraic formulation for linear network coding in acyclic networks with the links having integer delay is well known. Based on this formulation, for a given set of connections over an arbitrary acyclic network with integer delay assumed for the links, the output symbols at the sink nodes, at any given time instant, is a F(p)m-linear combination of the input symbols across different generations, where F(p)m denotes the field over which the network operates (p is prime and m is a positive integer). We use finite-field discrete Fourier transform to convert the output symbols at the sink nodes, at any given time instant, into a F(p)m-linear combination of the input symbols generated during the same generation without making use of memory at the intermediate nodes. We call this as transforming the acyclic network with delay into n-instantaneous networks (n is sufficiently large). We show that under certain conditions, there exists a network code satisfying sink demands in the usual (nontransform) approach if and only if there exists a network code satisfying sink demands in the transform approach. When the zero-interference conditions are not satisfied, we propose three precoding-based network alignment (PBNA) schemes for three-source three-destination multiple unicast network with delays (3-S 3-D MUN-D) termed as PBNA using transform approach and time-invariant local encoding coefficients (LECs), PBNA using time-varying LECs, and PBNA using transform approach and block time-varying LECs. We derive sets of necessary and sufficient conditions under which throughputs close to n' + 1/2n' + 1, n'/2n' + 1, and n'/2n' + 1 are achieved for the three source-destination pairs in a 3-S 3-D MUN-D employing PBNA using transform approach and time-invariant LECs, and PBNA using transform approach and block time-varying LECs, where n' is a positive integer. For PBNA using time-varying LECs, we obtain a sufficient condition under which a throughput demand of n(1)/n, n(2)/n, and n(3)/n can be met for the three source-destination pairs in a 3-S 3-D MUN-D, where n(1), n(2), and n(3) are positive integers less than or equal to the positive integer n. This condition is also necessary when n(1) + n(3) = n(1) + n(2) = n where n(1) >= n(2) >= n(3).

用Fourier变换莫尔法测量流体自由表面微幅波的振幅

采用一种非接触的光学方法——傅立叶变换莫尔法（Fourier transform method），结合数字图像处理技术，对微幅振荡的水表面波的振幅进行测量。它是对全场中每一个像素点进行测量，比接触测量法具有更高的灵敏度。它为微幅水表面波振幅的测量提供了一种手段。通过将计算机生成的周期性光栅图像经投影机直接投影到被测物体的参考平面，经CCD摄像头、图像板捕捉存储形成数字化的光栅图像，利用傅立叶变换莫尔法处理光栅图像，从而获得包含有水表面波的振幅的相位信息，再经适当的几何变换获得振幅信息。我们在生趣振荡装置上进行了不同激励频率和不同振幅的表面波的振幅测量。