Two-dimensional Data Arrays Research Articles

Patch seriation to visualize data and model parameters

We developed a new seriation merit function for enhancing the visual information of data matrices. A local similarity matrix is calculated, where the average similarity of neighbouring objects is calculated in a limited variable space and a global function is constructed to maximize the local similarities and cluster them into patches by simple row and column ordering. The method identifies data clusters in a powerful way, if the similarity of objects is caused by some variables and these variables differ for the distinct clusters. The method can be used in the presence of missing data and also on more than two-dimensional data arrays. We show the feasibility of the method on different data sets: on QSAR, chemical, material science, food science, cheminformatics and environmental data in two- and three-dimensional cases. The method can be used during the development and the interpretation of artificial neural network models by seriating different features of the models. It helps to identify interpretable models by elucidating clusters of objects, variables and hidden layer neurons.Graphical

ОПТИМІЗАЦІЙНИЙ МЕТОД КОМРЕСІЇ БАГАТОСПЕКТРАЛЬНИХ ЦИФРОВИХ ЗОБРАЖЕНЬ ПРОЕКЦІЙНОЇ ПРИРОДИ

A method for compressing digital images of a projection nature obtained in an arbitrary amount of spectral radiation ranges - a carrier of specific information or under various positional conditions of formation, optimized according to the criteria for preserving the specified levels of signal image energy and their structural similarity, is proposed. The method uses the representation of a set of such images in the form of a single multidimensional geometric object, which is described by a two-dimensional data array ordered by raster and spectral intervals and includes preprocessing by means of singular decomposition of the specified array. Actual compression is carried out by means of decomposition the constituent images, represented by maximum singular numbers, according to discrete orthonormed functional bases, zeroing out part of the decomposition coefficients and subsequent reconstruction of the digital brightness codes of images. The determination of the thresholds for zeroing the decomposition coefficients of images digital levels is formulated in the form of a two-criteria optimization problem of obtaining the given ratios of signal energies of the compressed and initial images and indices of their structural similarity. The implementation of the proposed methods includes the following steps: pairwise orthogonalization of distributions of digital brightness codes of images in different spectral channels based on singular decompositions; preservation of the constituent distributions of brightness with maximum singular numbers; compression of orthogonalized representations according to the specified criteria; reconstructing the brightness codes of compressed images of spectral channels by a functional transformation reversed by the one used at the stage of decomposition of brightness distributions of directly recorded multispectral images. Comparison of various discretized functional bases as the basis for compression showed the greatest efficiency in the specified criteria of the discrete functional basis of Haar. Key words: multispectral image, orthogonalization, signal energy, structural similarity index, orthonormed basis.

Broadband Signal Digitization Based on Low-Speed Non-Uniform Photonic Sampling

A new non-uniform photonic sampling (NPS) strategy and its special signal reconstruction algorithm are proposed to achieve digital acquisition of broadband periodic signals at a low sampling rate. Compared with the existing schemes, the NPS strategy can largely reduce the sampling number to acquire identical signal information as that obtained by using its equivalent high-speed uniform photonic sampling, which is beneficial for reducing the sampling time and the data volume of the NPS-based analog-to-digital converter (ADC). In addition, the calculation time of the proposed algorithm is millions of times lower than that of the digital alias-free signal processing (DASP) algorithm used before, which benefits from the fast Fourier transform calculation of a one-dimensional data array instead of a two-dimensional data array calculation in the DASP algorithm. A simulation is performed to validate the feasibility of the proposed scheme. In the simulation, a single-channel NPS-based ADC with an average sampling rate of 1 GSa/s is demonstrated by using the proposed NPS strategy and signal reconstruction algorithm. The results indicate the reconstructed signal information for a single-tone microwave signal at 9.9 GHz and a linear frequency modulation signal in the frequency range of 1 GHz to 9 GHz are identical to those obtained by using its equivalent high-speed uniform photonic sampling-based ADC with a sampling rate of 20 GSa/s.

Static full-Stokes Fourier transform imaging spectropolarimeter capturing spectral, polarization, and spatial characteristics.

A static full-Stokes Fourier transform imaging spectropolarimeter incorporating a liquid-crystal polarization modulator (LPM) and birefringent shearing interferometer (BSI) is reported. It can decode the polarization information at each wavelength along the spatial dimension of a two-dimensional data array. The LPM has a high-speed time-division architecture and employs two ferroelectric liquid crystals and two wave plates to produce four polarization states, providing full-Stokes polarimetric information with a high signal-to-noise ratio. The BSI comprises two birefringent crystal plates and generates an optical path difference with good linear distribution for broadband interference, allowing a fast and high-precision spectral recovery. The optimized design of LPM and BSI are introduced in detail. Subsequently, the signal reconstruction is verified through simulations and experiments. The proposed scheme is highly efficient, exhibits a higher spectral resolution, and constitutes a compact technical approach to realize high-dimensional optical measurement.

The Combinatorial Expressions and Probability of Random Generation of Binary Palindromic Digit Combinations

The aim of this paper is to obtain three types of expressions for calculating the probability of implementing palindromic digit combinations on a finite equally possible combination of zeros and ones. When calculating the probability of implementation of palindromic digit combinations, the classical definition of probability is applied. The main results of the paper are formulated in the form of three theorems. Moreover, the consequences of these theorems and typical examples of calculating the probability of implementing palindromic digit combinations in a data string of binary code are considered. All formulated theorems and their consequences are accompanied by proofs. The obtained numerical results of the paper can be used in the analysis of numerical computer data written as a binary code string in BIN format files. It should also be noted that the combinatorial expressions described in the article for calculating the number of palindromic combinations of digits in the binary number system can be used in number theory and in various branches of computer science. The development of these results from the point of view of obtaining an expression for calculating the number of palindromic combinations of digits in the binary number system contained in two-dimensional data arrays is also of immediate theoretical and practical interest. However, these results are not presented in this work, but they can be considered in subsequent publications.

System for Measuring Emittance Characteristics of Ion Sources

The article presents the results of the development of a system for measuring emittance characteristics of ion sources studied at the IAP NAS of Ukraine with the aim of obtaining the ion beams with a high brightness. The emittance measurement system is based on the scheme of an electrostatic scanner and consists of two main parts: the scanner, which moves in the direction perpendicular to the beam axis using a stepper motor, and the electronic system of control, processing and data acquisition. The electronic system contains a Raspberry pi 3B microcomputer, precision DAC/ADCs, the high-voltage amplifier of a scanning voltage up to ±500 V on deflection plates of the scanner and a wide range current integrator. The determination of the emittance consists in measuring the ion beam intensity distribution when the scanner moves along the x-coordinate and the electrostatic scanning along the x´ angle. The obtained two-dimensional data array allows determining the main characteristics of ion beam: geometric 90% emittance, the root mean square (rms) emittance, the Twiss parameters and phase ellipse of rms emittance, the beam current profile and the angle current density distribution. To test the performance and functionality of the system, the emittance characteristics of the penning type ion source were measured. The working gas was helium, and the beam energy varied within 7–15 keV. At 13 keV of beam energy the following emittances of the He+ ions beam was obtained: 90% emittance is 30 π∙mm∙mrad, rms emittance is 8.4 mm∙mrad, and the normalized rms emittance is equal to 0.022 mm∙mrad. The developed system for measuring the emittance of the ion beams is characterized by a short measurement time of 10-15 minutes.

SVD and ASCII Character Encoding-Based Compression of Multiple Biosignals for Remote Healthcare Systems.

Advancements in electronics and miniaturized device fabrication technologies have enabled simultaneous acquisition of multiple biosignals (MBioSigs), but the area of compression of MBioSigs remains unexplored to date. This paper presents a robust singular value decomposition (SVD) and American standard code for information interchange (ASCII) character encoding-based algorithm for compression of MBioSigs for the first time to the best of our knowledge. At the preprocessing stage, MBioSigs are denoised, down sampled and then transformed to a two-dimensional (2-D) data array. SVD of the 2-D array is carried out and the dimensionality of the singular values is reduced. The resulting matrix is then compressed by a lossless ASCII character encoding-based technique. The proposed compression algorithm can be used in a variety of modes such as lossless, with or without using the down sampling operation. The compressed file is then uploaded to a hypertextpreprocessor (PHP)-based website for remote monitoring application. Evaluation results show that the proposed algorithm provides a good compression performance; in particular, the mean opinion score of the reconstructed signal falls under the category "very good" as per the gold standard subjective measure.

Analysis of fMRI images with bi-dimensional empirical mode decomposition based-on Green's functions

Abstract We present a new method for decomposing two-dimensional data arrays with empirical mode decomposition (EMD). It performs envelope surface interpolation based on Green's functions in tension (GiT) to extract bi-dimensional intrinsic mode functions (BIMFs). The new method is called GiT-BEMD and outperforms existing bi-dimensional ensemble EMD (BEEMD) variants in terms of computational costs and quality of extracted intrinsic modes. More specifically, it is easy to implement, much faster than BEEMD, very robust and free from processing artifacts. GiT-BEMD is applied to fMRI data recorded during a contour integration task. Features extracted from resulting volume intrinsic mode functions (VIMFs) achieve higher classification accuracy compared to the canonical BEEMD. The new method thus provides a valuable alternative to existing mode decomposition methods for analyzing images.

Optimizing two-dimensional DMA transfers for scratchpad Based MPSoCs platforms

Reducing the effects of off-chip memory access latency is a key factor in exploiting efficiently embedded multi-core platforms. We consider architectures that admit a multi-core computation fabric, having its own fast and small memory to which the data blocks to be processed are fetched from external memory using a DMA (direct memory access) engine, employing a double- or multiple-buffering scheme to avoid processor idling. In this paper we focus on application programs that process two-dimensional data arrays and we determine automatically the size and shape of the portions of the data array which are subject to a single DMA call, based on hardware and applications parameters. When the computation on different array elements are completely independent, the asymmetry of memory structure leads always to prefer one-dimensional horizontal pieces of memory, while when the computation of a data element shares some data with its neighbors, there is a pressure for more “square” shapes to reduce the amount of redundant data transfers. We provide an analytic model for this optimization problem and validate our results by running a mean filter application on the Cell simulator.

Setup and performance of a streak camera apparatus for transient absorption measurements in the ns to ms range

We describe the setup and performance of an apparatus for simultaneous time- and spectrally resolved measurements of transient absorption. The key component in this apparatus is a streak camera, yielding, for every excitation of the sample, a two-dimensional data array with 512 × 512 data points. The apparatus covers the spectral range 350–750 nm and time windows ranging from 500 ns up to 10 ms. Due to the large dynamic range of the streak camera of 10,000:1 we obtain a multiplex factor of more than 100 compared with sequential measurements at individual wavelengths. This makes it possible to extract the maximum amount of information from small amounts of sample, e.g. light-sensitive proteins. We show that already a single pump probe pulse sequence can yield useful spectra in a 20-μs time range, and that 10 pump-probe pulse sequences yield good time constants from a global lifetime analysis. An iterative method is presented for the treatment of artifacts due to scattered excitation laser light or strong fluorescence. As an alternative to a global lifetime analysis we propose a maximum entropy-based inverse Laplace transform for analysis of the data. This results in a wavelength-dependent distribution of amplitudes p(k, λ) for all rate constants k accessible with a given time window. This analysis is model free and yields a direct visual evaluation of the uncertainties in the rate constants.

A criterion for assessing homogeneity distribution in hyperspectral images. Part 2: Application of homogeneity indices to solid pharmaceutical dosage forms

This article is the second of a series of two articles detailing the application of mixing index to assess homogeneity distribution in oral pharmaceutical solid dosage forms by image analysis. Chemical imaging (CI) is an emerging technique integrating conventional imaging and spectroscopic techniques with a view to obtaining spatial and spectral information from a sample. Near infrared chemical imaging (NIR-CI) has proved an excellent analytical tool for extracting high-quality information from sample surfaces. The primary objective of this second part was to demonstrate that the approach developed in the first part could be successfully applied to near infrared hyperspectral images of oral pharmaceutical solid dosage forms such as coated, uncoated and effervescent tablets, as well as to powder blends. To this end, we assessed a new criterion for establishing mixing homogeneity by using four different methods based on a three-dimensional (M×N×λ) data array of hyperspectral images (spectral standard deviations and correlation coefficients) or a two-dimensional (M×N) data array (concentration maps and binary images). The four methods were used applying macropixel analysis to the Poole (M(P)) and homogeneity (H%(Poole)) indices. Both indices proved useful for assessing the degree of homogeneity of pharmaceutical samples. The results testify that the proposed approach can be effectively used in the pharmaceutical industry, in the finished products (e.g., tablets) and in mixing unit operations for example, as a process analytical technology tool for the blending monitoring (see part 1).

Diagnostic Nano-Analysis of Materials Properties by Multivariate Curve Resolution Applied to Spectrum Images by S/TEM-EELS

The data cube of spectrum imaging (SI) by scanning TEM (STEM) and electron energy-loss spectroscopy (EELS) or energy-filtering TEM (EF-TEM) can be treated as the two-dimensional data array, each row corresponding to the EELS spectrum at a specific position. A multivariate curve resolution (MCR) technique can then apply to the dataset, which decomposes the set of spectra into the product of the constituent pure spectral components and their corresponding relative composition matrices without any reference spectra. This method allows us to provide a two dimensional spatial distribution map of different chemical states incorporated even when the multiply spectra overlap with one another. Several application examples are presented.

PERFORMANCE EVALUATION OF BLAS ON THE TRIDENT PROCESSOR

Different subtasks of an application usually have different computational, memory, and I/O requirements that result in different needs for computer capabilities. Thus, the more appropriate approach for both high performance and simple programming model is designing a processor having multi-level instruction set architecture (ISA). This leads to high performance and minimum executable code size. Since the fundamental data structures for a wide variety of existing applications are scalar, vector, and matrix, our research Trident processor has three-level ISA executed on zero-, one-, and two-dimensional arrays of data. These levels are used to express a great amount of fine-grain data parallelism to a processor instead of the dynamical extraction by a complicated logic or statically with compilers. This reduces the design complexity and provides high-level programming interface to hardware. In this paper, the performance of Trident processor is evaluated on BLAS, which represent the kernel operations of many data parallel applications. We show that Trident processor proportionally reduces the number of clock cycles per floating-point operation by increasing the number of execution datapaths.

Comparison of Large-Eddy Simulation Data with Spatially Averaged Measurements Obtained by Acoustic Tomography – Presuppositions and First Results

An attempt is made to compare results oflarge-eddy simulation (LES) in a convective boundarylayer using the model PALM with experimental data obtained from acoustic travel time tomography.This method provides two-dimensional data arrays, which are considered as more suitable forLES-validation than classical local orline-integrated measurements, because the tomographic data are area- or volume-averaged.

Writing sequences on the plane

The problem of arranging two-dimensional arrays of data into one-dimensional sequences comes up in image processing, color quantization, and optical and magnetic data recording. A good arrangement should enable the one-dimensional sequences to be modeled as Markov chains or shifts of finite type. Since this is not possible in general, two-dimensional data is most commonly scanned by rows, columns, or diagonals. We look into three unusual ways to write a sequence,in the plane: by Penrose tilings, by space-filling curves, and by cylindrical and spiral lattices. We show how Penrose tilings can be used to record information and how some spiral lattices can be used for quantization of color spaces.

Generalized correlation NMR spectroscopy.

The use of generalized correlation analysis (Noda, I. Appl. Spectrosc. 1993, 47, 1329-1336) for processing two-dimensional arrays of NMR data is described. This analysis produces complex two-dimensional spectra whose cross-peak intensities are related to correlations in the responses of pairs of signals to systematically incremented perturbations. The technique extends and generalizes the applicability of two-dimensional NMR by allowing model-independent analysis of nonperiodic signals as well as model-dependent analysis of such signals. When applied to diffusion-ordered NMR data, the processing scheme produces two-dimensional output spectra having two frequency axes. Relative diffusion coefficients are encoded in the signs and intensities of the cross-peaks. Key properties of the resulting spectra are model-independent, so the approach provides an alternative to traditional DOSY processing and offers advantages for data sets that do not provide pure exponential or Gaussian response curves. When data do conform well to a known response function, the technique provides a method for extracting descriptors in a two-dimensional plot having one axis corresponding to the descriptor and the other axis corresponding to the usual chemical shift scale. Finally, the technique may be used to identify differences in the response functions of closely related samples, generating a one-dimensional spectrum with signals at frequencies whose response functions differ between two samples.

Simultaneous Determination of Zinc and Cadmium with 1-(2-Pyridylazo)-2-Naphthol in Aqueous Micellar Solutions Using Two-Dimensional Absorption Spectra

The simultaneous determination of zinc and cadmium with 1-(2-pyridylazo)-2-naphthol in aqueous micellar solutions using two-dimensional data arrays for the dependence of absorbance on the wavelength and pH was considered. Determination errors were minimized by optimal selection of analytical wavelengths in the spectrum and pH.

Secure optical storage that uses fully phase encryption

A secure holographic memory system that uses fully phase encryption is presented. Two-dimensional arrays of data are phase encoded. Each array is then transformed into a stationary white-noise-like pattern by use of a random-phase mask located at the input plane and another at the Fourier plane. This encrypted information is then stored holographically in a photorefractive LiNbO(3):Fe crystal. The original phase-encoded data can be recovered, by use of the two random-phase masks, with a phase-conjugate readout beam. This phase information can then be converted back to intensity information with an interferometer. Recording multiple images by use of angular multiplexing is demonstrated. The influence of a limited system bandwidth on the quality of reconstructed data is evaluated numerically. These computer simulation results show that a fully phase-based encryption system generally performs better than an amplitude-based encryption system when the system bandwidth is limited by a moderate amount.

Resolving and quantifying overlapped chromatographic bands by transmutation

A new chemometric technique called "transmutation" is developed for the purpose of sharpening overlapped chromatographic bands in order to quantify the components. The "transmutation function" is created from the chromatogram of the pure component of interest, obtained from the same instrument, operating under the same experimental conditions used to record the unresolved chromatogram of the sample mixture. The method is used to quantify mixtures containing toluene, ethylbenzene, m-xylene, naphthalene, and biphenyl from unresolved chromatograms previously reported. The results are compared to those obtained using window factor analysis, rank annihilation factor analysis, and matrix regression analysis. Unlike the latter methods, the transmutation method is not restricted to two-dimensional arrays of data, such as those obtained from HPLC/DAD, but is also applicable to chromatograms obtained from single detector experiments. Limitations of the method are discussed.

Evaluation of intrinsic chemical kinetics and transient product spectra from time-resolved spectroscopic data

This communication is devoted to the evaluation of true spectra and intrinsic (microscopic) rate constants from apparent kinetics measured in time-resolved spectroscopic experiments monitoring complex relaxation dynamics of multi-intermediate systems. Retinal proteins, cytochrom c oxidase, phytochrome, hemoglobin, and photoactive yellow protein are examples of natural systems in which several transient states (intermediates) overlap so strongly, both in time and spectral domains, that their isolation and full characterization by classical biochemical methods is impossible, and mathematical evaluation of their true spectra and microscopic kinetic constants is required. Most of the popular methods for analysis of kinetic data, global fitting (GF), singular value decomposition (SVD), principal component analysis (PCA) and factor analysis (FA), are applicable to two-dimensional (2D, in time and spectral domains) arrays of data. All these methods produce only a phenomenological description of data, that approximates the measured data only with apparent kinetics. A fundamental limitation, namely, insufficient information in 2D data, does not allow any of these methods to reach the final goal: to recalculate from apparent to intrinsic values in any but the most trivial cases. A strategy was proposed (J.F. Nagle, Biophys. J.. 59 (1991) 476–487) to include an additional (third) information-rich dimension, temperature, into the simultaneous computer analysis. A simultaneous direct fitting of 3D data arrays to systems of differential rate equations allows recalculation of apparent kinetics into true spectra and intrinsic rate constants. In spite of its evident theoretical advantages, this strategy has not been successful on real data. Here we describe another custom-built program, SCHEMEFIT, developed for the same purpose: to fit measured kinetics directly to the system of coupled differential rate equations describing the photochrome's relaxation dynamics. Though sharing the main strategy with the previous approach, SCHEMEFIT is based on a different set of numeric algorithms, and its application requires different tactics. Its performance is illustrated on synthetic data, and compared with GF and SVD. An example of applying SCHEMEFIT to the photocycle of halorhodopsin is also reported.