Multifactor authentication reinforces optical security

A new optical method to obtain multifactor image encoding and authentication is proposed. The encoded complex-amplitude image function fulfills the general requirements of invisible content, extreme difficulty in copying or counterfeiting, and real-time automatic verification. This optical technique is attractive for high-security purposes that require multifactor reliable authentication. A demonstration using a combination of biometric images and key codes is provided. Retina images, which are very effective for authentication, are used as biometric signals. To the best of our knowledge, this is the first report on combined multiple signal encoding and simultaneous AND authentications for optical security reinforcement.     

Partial least squares-based multivariate spectral calibration method for simultaneous determination of beta-carboline derivatives in Peganum harmala seed extracts

The partial least squares regression method has been applied for simultaneous spectrophotometric determination of harmine, harmane, harmalol and harmaline in Peganum harmala L. (Zygophyllaceae) seeds. The effect of pH was optimized employing multivariate definition of selectivity and sensitivity and best results were obtained in basic media (pH > 9). The calibration models were optimized for number of latent variables by the cross-validation procedure. Determinations were made over the concentration range of 0.15-10 μg mL⁻¹. The proposed method was validated by applying it to the analysis of the β-carbolines in synthetic quaternary mixtures of media at pH 9 and 11. The relative standard errors of prediction were less than 4% in most cases. Analysis of P. harmala seeds by the proposed models for contents of the β-carboline derivatives resulted in 1.84%, 0.16%, 0.25% and 3.90% for harmine, harmane, harmaline and harmalol, respectively. The results were validated against an existing HPLC method and it no significant differences were observed between the results of two methods.     

SAYD Modules over Lie-Hopf Algebras

In this paper a general van Est type isomorphism is proved. The isomorphism is between the Lie algebra cohomology of a bicrossed sum Lie algebra and the Hopf cyclic cohomology of its Hopf algebra. We first prove a one to one correspondence between stable-anti-Yetter-Drinfeld (SAYD) modules over the total Lie algebra and those modules over the associated Hopf algebra. In contrast to the non-general case done in our previous work, here the van Est isomorphism is proved at the first level of a natural spectral sequence, rather than at the level of complexes. It is proved that the Connes-Moscovici Hopf algebras do not admit any finite dimensional SAYD modules except the unique one-dimensional one found by Connes-Moscovici in 1998. This is done by extending our techniques to work with the infinite dimensional Lie algebra of formal vector fields. At the end, the one to one correspondence is applied to construct a highly nontrivial four dimensional SAYD module over the Schwarzian Hopf algebra. We then illustrate the whole theory on this example. Finally explicit representative cocycles of the cohomology classes for this example are calculated.     

Generalization of three-dimensional N-ocular imaging systems under fixed resource constraints

The performance of multiview three-dimensional imaging systems depends on several factors, including the number of sensors, sensor pixel size, relative sensor configuration, imaging optics, and computational reconstruction algorithm. Therefore, it is important to compare the performance of such systems under equally constrained resources. In this Letter, we develop a unifying framework to evaluate the lateral and axial resolution of N-ocular imaging systems ranging from stereo (two cameras) to multiple sensors (integral imaging) under fixed resource constraints. The proposed framework enables one to evaluate the system performance as a function of sensing parameters such as the number of cameras, the number of pixels, parallax, pixel size, lens aperture, and focal length. We carry out Monte Carlo simulations based on this framework to evaluate system performance as a function of sensing parameters. To the best of our knowledge, this is the first report on quantitative analysis of N-ocular imaging systems under common resource constraints.     

Superresolved and field-of-view extended digital holography with particle encoding

We present a new configuration for superresolution (SR) as well as for field-of-view (FOV) extension in a digital holography concept based on random movement of sparse metallic particles. In the SR configuration, the particles are in proximity to the recorded object, while in the FOV configuration, the particles are in proximity to the hologram plane. The particles' movement encodes the high spatial features in the plane of their movement. This high-resolution information can later be decoded by proper numerical postprocessing that either remedies the resolution limitations in the object plane (or the limited NA of the lens) or extends the FOV in the object plane.     

Three-dimensional imaging and visualization of partially occluded objects using axially distributed stereo image sensing

In this Letter, we propose a multiperspective three-dimensional (3D) imaging system using axially distributed stereo image sensing. In this proposed method, the stereo camera is translated along its optical axis and multiple axial elemental image pairs for a 3D scene are collected. The captured elemental images are reconstructed in 3D using a computational reconstruction algorithm based on ray back-projection. The proposed method is applied to partially occluded object visualization. Optical experiments are performed to verify the approach.     

Construction of stable multivariate calibration models using unsupervised segmented principal component regression

In multivariate spectral calibration by principal component regression (PCR), the principal components (PCs) are calculated from the response data measured at all employed instrument channels; however some channels are redundant and their responses do not possess useful information. Thus, the extracted PCs possess mixed information from both useful and redundant channels. In this work, we propose a segmentation approach based on unsupervised pattern recognition to identify the most informative spectral region and then to construct a stable multivariate calibration model by PCR. In this method, the instrument channels are clustered into different segments via Kohonen self‐organization map. The spectral data of each segment are then subjected to PCA and the derived PCs are used as input variables for an inverse least square (ILS) regression model employing stepwise selection of the informative PCs. The proposed method was evaluated by the analysis of four simulated and six experimental data sets. It was found that our proposed method can model the above data sets with prediction errors lower than conventional partial least squares (PLS) and PCR methods. In addition, the prediction ability of our method was better than the previously reported models for these data sets. Copyright © 2011 John Wiley & Sons, Ltd.     

Langevin Equation Involving Three Fractional Orders

In this paper, the existence and uniqueness of initial value problems for nonlinear Langevin equation involving three fractional orders are discussed. We use a new norm that is convenient for the fractional and singular differential equations. This norm and the contraction mapping principles are the main tools for investigating the existence and uniqueness of the desired issue. The fractional derivatives are described in Caputo sense.