Mueller-matrix diagnostics of optical properties of polycrystalline networks of human blood plasma

The work is oriented toward a study of the possibilities of Mueller-matrix diagnostics of optical anisotropy of birefringent polycrystalline networks of human plasma amino acids. The interrelations between the statistical moments from the first to the fourth orders and fractal dimensionalities, which characterize the coordinate distributions of elements of the Mueller matrix for the blood plasma and the physiological state of the human organism, are determined.     

Complex polarization-phase and spatial-frequency selections of laser images of blood-plasma films in diagnostics of changes in their polycrystalline structure

We present a theoretical formalism of correlation phase analysis of laser images of human blood plasma with spatial-frequency selection of manifestations of mechanisms of linear and circular birefringence of albumin and globulin polycrystalline networks. Comparative results of the measurement of coordinate distributions of the correlation parameter—the modulus of the degree of local correlation of amplitudes—of laser images of blood plasma taken from patients of three groups—healthy patients (donors), rheumatoid-arthritis patients, and breast-cancer patients—are presented. We investigate values and ranges of change of statistical (the first to fourth statistical moments), correlation (excess of autocorrelation functions), and fractal (slopes of approximating curves and dispersion of extrema of logarithmic dependences of power spectra) parameters of coordinate distributions of the degree of local correlation of amplitudes. Objective criteria for diagnostics of occurrence and differentiation of inflammatory and oncological states are determined.     

Azimuth-invariant mueller-matrix differentiation of the optical anisotropy of biological tissues

A Mueller-matrix model is proposed for analysis of the optical anisotropy of protein networks of optically thin nondepolarizing layers of biological tissues with allowance for birefringence and dichroism. The model is used to construct algorithms for reconstruction of coordinate distributions of phase shifts and coefficient of linear dichroism. Objective criteria for differentiation of benign and malignant tissues of female genitals are formulated in the framework of the statistical analysis of such distributions. Approaches of evidence-based medicine are used to determine the working characteristics (sensitivity, specificity, and accuracy) of the Mueller-matrix method for the reconstruction of the parameters of optical anisotropy and show its efficiency in the differentiation of benign and malignant tumors.     

Wavelet analysis of polarization maps of polycrystalline biological fluids networks

The optical model of human joints synovial fluid is proposed. The statistic (statistic moments), correlation (autocorrelation function) and self-similar (Log-Log dependencies of power spectrum) structure of polarization two-dimensional distributions (polarization maps) of synovial fluid has been analyzed. It has been shown that differentiation of polarization maps of joint synovial fluid with different physiological state samples is expected of scale-discriminative analysis. To mark out of small-scale domain structure of synovial fluid polarization maps, the wavelet analysis has been used. The set of parameters, which characterize statistic, correlation and self-similar structure of wavelet coefficients’ distributions of different scales of polarization domains for diagnostics and differentiation of polycrystalline network transformation connected with the pathological processes, has been determined.     

Wavelet-analysis of polarization maps of human blood plasma

Possibilities of local wavelet-analysis of coordinate distributions of polarization azimuths and ellipticity of laser images of blood plasma in healthy and cancer patients are considered. The set of statistical, correlation, and fractal parameters of distributions of wavelet-coefficients characterizing different scales of geometric dimensions of amino acid polycrystalline networks is determined. The criteria for the differentiation of transformation processes of birefringence of optically anisotropic structures of blood plasma at different scales are established.     

Wavelet analysis of the polarization structure of biospeckle fields of statistical and multifractal phase-inhomogeneous layers

The mechanisms of formation of the polarization structure of biospeckle fields of statistical and multifractal phase-inhomogeneous layers are studied. Polarization maps of images are determined for biological tissues of various structures, namely, epidermis, muscular tissue, and myometrium. A relation between the polarization structure of biospeckles and the physiological conditions of phase-inhomogeneous layers is found. The distributions of wavelet coefficients of the polarization images of statistical and multifractal biological tissues are obtained. Criteria for the determination of the coordinate localization and scale of optical inhomogeneities of the architectonics of biological tissues are ascertained.     

Computer-generated holograms for producing fractal speckles

When a diffuser is illuminated by the coherent light with a negative power-law distribution, fractal speckles are produced in the far-field diffraction region. Fractal speckles have extremely long spatial correlation functions of the intensity distributions in comparison with ordinary speckles, which implies that they may extend measurement ranges in various metrological applications based on the spatial correlation of speckles. To have fractal speckles with satisfactory statistical properties, it is required to produce a power-law illumination profile with high quality. In this paper, we report on the computer-generated holograms for producing power-law intensities on the basis of the method of stationary phase, with the error-reduction algorithm combined with to suppress strong ringing of the intensity.     

Principles of statistical mechanics of uncorrelated random networks

We develop a statistical mechanics approach for random networks with uncorrelated vertices. We construct equilibrium statistical ensembles of such networks and obtain their partition functions and main characteristics. We find simple dynamical construction procedures that produce equilibrium uncorrelated random graphs with an arbitrary degree distribution. In particular, we show that in equilibrium uncorrelated networks, fat-tailed degree distributions may exist only starting from some critical average number of connections of a vertex, in a phase with a condensate of edges.     

Investigation of molecular complexes of blood serum by laser correlation spectroscopy and atomic-force microscopy

The progression of pathological processes in the human organism is accompanied by significant changes in a number of molecular parameters of biological fluids. An intensive search for methods appropriate for diagnosing homeostatic disturbances inherent in various pathologies in the preclinical stage has been performed all over the world. Macromolecular fractions of blood serum and blood plasma with typical sizes ranging from 1 to 1000 nm are of particular research interest from the viewpoint of the development of the methods intended for the early detection of oncological and cardiovascular diseases. Considerable possibilities for studying these objects are provided by a combined approach with the use of laser correlation spectroscopy and atomic-force microscopy. The results obtained within the proposed approach have been reported in the present paper. They have demonstrated that this approach holds much promise for composition analysis of blood serum and for further development of the methods employed in the early detection of serious diseases as a whole.     

Quantitative assessment of mobile protein levels in human knee synovial fluid: feasibility of chemical exchange saturation transfer (proteinCEST) MRI of osteoarthritis

Purpose

To establish the feasibility of chemical exchange saturation transfer (proteinCEST) MRI in the differentiation of osteoarthritis (OA) knee joints from non-OA joints by detecting mobile protein and peptide levels in synovial fluid by determining their relative distribution.

Materials and Methods

A total of 25 knees in 11 men and 12 women with knee injuries were imaged using whole knee joint proteinCEST MRI sequence at 3 T. The joint synovial fluid was segmented and the asymmetric magnetization transfer ratio at 3.5 ppm MTR_asym (3.5 ppm) was calculated to assess protein content in the synovial fluid. The 85th percentile of synovial fluid MTR_asym (3.5 ppm) distribution profile was compared using the independent Student's t test. The diagnostic performance of the 85th percentile of synovial fluid MTR_asym (3.5 ppm) in differentiating OA and non-OA knee joints was evaluated.

Results

The 85th percentile of synovial fluid MTR_asym (3.5 ppm) in knee joints with OA was 8.6%±3.4% and significantly higher than that in the knee joints without OA (6.3%±1.4%, P<.05). A knee joint with an 85th percentile of synovial fluid MTR_asym (3.5 ppm) greater than 7.7% was considered to be an OA knee joint. With the threshold, the sensitivity, specificity and overall accuracy for differentiating knee joints with OA from the joints without OA were 54% (7/13), 92% (11/12) and 72% (18/25), respectively.

Conclusion

proteinCEST MRI appears feasible as a quantitative methodology to determine mobile protein levels in synovial fluid and identify patterns characteristic for OA disease.     

Skeleton and fractal scaling in complex networks

We find that the fractal scaling in a class of scale-free networks originates from the underlying tree structure called a skeleton, a special type of spanning tree based on the edge betweenness centrality. The fractal skeleton has the property of the critical branching tree. The original fractal networks are viewed as a fractal skeleton dressed with local shortcuts. An in silico model with both the fractal scaling and the scale-invariance properties is also constructed. The framework of fractal networks is useful in understanding the utility and the redundancy in networked systems.     

Theoretical formulation of finite-dimensional discrete phase spaces: I. Algebraic structures and uncertainty principles

We propose a self-consistent theoretical framework for a wide class of physical systems characterized by a finite space of states which allows us, within several mathematical virtues, to construct a discrete version of the Weyl–Wigner–Moyal (WWM) formalism for finite-dimensional discrete phase spaces with toroidal topology. As a first and important application from this ab initio approach, we initially investigate the Robertson–Schrödinger (RS) uncertainty principle related to the discrete coordinate and momentum operators, as well as its implications for physical systems with periodic boundary conditions. The second interesting application is associated with a particular uncertainty principle inherent to the unitary operators, which is based on the Wiener–Khinchin theorem for signal processing. Furthermore, we also establish a modified discrete version for the well-known Heisenberg–Kennard–Robertson (HKR) uncertainty principle, which exhibits additional terms (or corrections) that resemble the generalized uncertainty principle (GUP) into the context of quantum gravity. The results obtained from this new algebraic approach touch on some fundamental questions inherent to quantum mechanics and certainly represent an object of future investigations in physics.     

Investigating the topology of interacting networks

Network theory provides various tools for investigating the structural or functional topology of many complex systems found in nature, technology and society. Nevertheless, it has recently been realised that a considerable number of systems of interest should be treated, more appropriately, as interacting networks or networks of networks. Here we introduce a novel graph-theoretical framework for studying the interaction structure between subnetworks embedded within a complex network of networks. This framework allows us to quantify the structural role of single vertices or whole subnetworks with respect to the interaction of a pair of subnetworks on local, mesoscopic and global topological scales. Climate networks have recently been shown to be a powerful tool for the analysis of climatological data. Applying the general framework for studying interacting networks, we introduce coupled climate subnetworks to represent and investigate the topology of statistical relationships between the fields of distinct climatological variables. Using coupled climate subnetworks to investigate the terrestrial atmosphere’s three-dimensional geopotential height field uncovers known as well as interesting novel features of the atmosphere’s vertical stratification and general circulation. Specifically, the new measure “cross-betweenness” identifies regions which are particularly important for mediating vertical wind field interactions. The promising results obtained by following the coupled climate subnetwork approach present a first step towards an improved understanding of the Earth system and its complex interacting components from a network perspective.     

Fractal characteristics of critical and localized states in incommensurate quantum systems

Incommensurate quantum systems with two competing periodicities exhibit metallic (with Bloch-type extended wave functions), insulating (with exponentially localized wave functions) as well ascritical (with fractal wave functions) phases. An exact renormalization method, which takes into account the inherent incommensurability, is used to obtain the phase diagram of various quantum models for the two-dimensional electron gas and for quantum spin chains in a magnetic field. In this approach, the scaling properties of the fractal eigenstates are characterized by a fixed point or a strange invariant set of the renormalization flow. One of our novel results is the existence of self-similar fluctuations in the localized states once the exponentially decaying envelope is factorized out. In almost all cases under investigation here, the universality classes can be broadly classified as those of the nearest-neighbor square or triangular lattices.     

Network analysis of time series under the constraint of fixed nearest neighbors

In this paper, we carried out network analysis for typical time series, such as periodic signals, chaotic maps, Gaussian white noise, and fractal Brownian motions. By reconstructing the phase space for a given time series, we can generate a network under the constraint of fixed nearest neighbors. The mapped networks are then analyzed from both the statistical properties, such as degree distribution, clustering coefficient, betweenness, etc, as well as the local topological structures, i.e., network motifs. It is shown that time series of different nature can be distinguished from these two aspects of the constructed networks.     

Fission studies of highly excited nuclei

The binary fission process in Bi, Au, W, Sb, Ag and Ni induced by 1 GeV protons has been investigated. The energies, time-of-flight and angular correlations of coincident fragments were measured by using a double arm spectrometer permitting a direct mass determination. Mass distributions are found to change their shape for nuclei lighterW. The interaction of protons with nuclei followed by fission is described in the framework of the cascade-evaporation model and the statistical approach. The observed mass distributions are in a good agreement with the results of the calculation. The experimental results present evidence for existence of an instability region with respect to the mass asymmetry coordinate in nuclear fission.     

Entropy, free energy and phase transitions in the lattice Lotka-Volterra model

A thermodynamic approach is developed for reactive dynamic models restricted to substrates of arbitrary dimensions, including fractal substrates. The thermodynamic formalism is successfully applied to the lattice Lotka-Volterra (LLV) model of autocatalytic reactions on various lattice substrates. Different regimes of reactions described as phases, and phase transitions, are obtained using this approach. The predictions of thermodynamic theory confirm extensive numerical kinetic Monte Carlo simulations on square and fractal lattices. Extensions of the formalism to multispecies LLV models are also presented. This article was submitted by the authors in English.     

Emergence of complex networks from diffusion on fractal lattices. A special case of the Sierpinski gasket and tetrahedron

A new approach to the assemblage of complex networks displaying the scale-free architecture is proposed. While the growth and the preferential attachment of incoming nodes assure an emergence of such networks according to the Barabási–Albert model, it is argued here that the preferential linking condition needs not to be a principal rule. To assert this statement a simple computer model based on random walks on fractal lattices is introduced. It is shown that the model successfully reproduces the degree distributions, the ultra-small-worldness and the high clustering arising from the topology of scale-free networks.     

Characterizing the topography of membrane receptors and signaling molecules from spatial patterns obtained using nanometer-scale electron-dense probes and electron microscopy

The flow of information through a cell requires the constant remodeling of cell signaling networks. Thus, spatially and temporally resolved microscopy of signaling components is needed to understand the behavior of normal cells as well as to uncover abnormal behavior leading to human disease. Nanoprobe labeling and transmission electron microscopy of cytoplasmic face-up sheets of cell membrane have been developed as a high-resolution approach to map the interactions of proteins and lipid during cell signaling. Membrane sheets are labeled with 3-15 nm electron-dense probes for receptors, signaling proteins and lipids and micrographs record the distributions of the probes relative to each other and to surface features. Here, we establish computational methods to extract spatial coordinates of probes from micrographs, to analyze and statistically validate the clustering and co-clustering of these probes and to integrate results between experiments in order to establish the relative spatial distributions of single and multiple probes. Our analyses, and the resulting programs for automating data collection and for carrying out statistical and clustering analyses provide toolboxes specialized for the spatiotemporal analysis and modeling of signal transduction pathways.