Modification of the Porter-Thomas Distribution by Rank-One Interaction.

The Porter-Thomas (PT) distribution of resonance widths is one of the oldest and simplest applications of statistical ideas in nuclear physics. Previous experimental data confirmed it quite well, but recent and more careful investigations show clear deviations from this distribution. To explain these discrepancies, Volya, Weidenmüller, and Zelevinsky [Phys. Rev. Lett. 115, 052501 (2015)PRLTAO0031-900710.1103/PhysRevLett.115.052501] argued that to get a realistic model of nuclear resonances is not enough to consider one of the standard random matrix ensembles which leads immediately to the PT distribution, but it is necessary to add a rank-one interaction which couples resonances to decay channels. The purpose of this Letter is to solve this model analytically and to find explicitly the modifications of the PT distribution due to such an interaction. Resulting formulas are simple, in good agreement with numerics, and could explain experimental results.

Correction: Total viable bacterial count using a real time all-fibre spectroscopic system.

Correction for 'Total viable bacterial count using a real time all-fibre spectroscopic system' by E. Bogomolny et al., Analyst, 2013, 138, 4112-4119.

Dielectric square resonator investigated with microwave experiments.

We present a detailed experimental study of the symmetry properties and the momentum space representation of the field distributions of a dielectric square resonator as well as the comparison with a semiclassical model. The experiments have been performed with a flat ceramic microwave resonator. Both the resonance spectra and the field distributions were measured. The momentum space representations of the latter evidenced that the resonant states are each related to a specific classical torus, leading to the regular structure of the spectrum. Furthermore, they allow for a precise determination of the refractive index. Measurements with different arrangements of the emitting and the receiving antennas were performed and their influence on the symmetry properties of the field distributions was investigated in detail, showing that resonances with specific symmetries can be selected purposefully. In addition, the length spectrum deduced from the measured resonance spectra and the trace formula for the dielectric square resonator are discussed in the framework of the semiclassical model.

Calculation of multi-fractal dimensions in spin chains.

It was demonstrated in Atas & Bogomolny (2012 Phys. Rev. E 86, 021104) that the ground-state wave functions for a large variety of one-dimensional spin- models are multi-fractals in the natural spin-z basis. We present here the details of analytical derivations and numerical confirmations of this statement.

Total viable bacterial count using a real time all-fibre spectroscopic system.

Rapid, accurate and sensitive enumeration of bacterial populations in the natural environment is an essential task for many research fields. Widely used standard methods for counting bacteria such as heterotrophic plate count require 1 to 8 days of incubation time for limited accuracy, while more accurate and rapid techniques are often expensive and may require bulky equipment. In the present study, we have developed a computerized optical prototype for bacterial detection. The goal of this research was to estimate the potential of this optical system for Total Viable Bacterial Count in water. For this purpose, we tested water batches with different microbiological content. Bacterial detection was based on fluorescence enhanced by nucleic acid staining. High sensitivity was achieved by a stable diode pumped solid state laser, sensitive CCD spectrometer and in situ excitation and signal collection. The results have shown that the bacterial count from different water origins using our optical setup along with multivariate analysis presents a higher accuracy and a shorter detection time compared to standard methods. For example, in a case where the fluorescence signal is calibrated to the water batch regression line, the relative standard deviation of the optical system enumeration varies between 21 and 36%, while that of the heterotropic plate count counterpart varies between 41 and 59%. In summary, we conclude that the all-fibre optical system may offer the following advantages over conventional methods: near real time examinations, portability, sensitivity, accuracy and ability to detect 10(2) to 10(8) CFU per ml bacterial concentrations.

Distribution of the ratio of consecutive level spacings in random matrix ensembles.

We derive expressions for the probability distribution of the ratio of two consecutive level spacings for the classical ensembles of random matrices. This ratio distribution was recently introduced to study spectral properties of many-body problems, as, contrary to the standard level spacing distributions, it does not depend on the local density of states. Our Wigner-like surmises are shown to be very accurate when compared to numerics and exact calculations in the large matrix size limit. Quantitative improvements are found through a polynomial expansion. Examples from a quantum many-body lattice model and from zeros of the Riemann zeta function are presented.

Calculation of mean spectral density for statistically uniform treelike random models.

For random matrices with treelike structure there exists a recursive relation for the local Green functions whose solution permits us to find directly many important quantities in the limit of infinite matrix dimensions. The purpose of this article is to investigate and compare expressions for the spectral density of random regular graphs, based on easy approximations for real solutions of the recursive relation valid for trees with large coordination number. The obtained formulas are in a good agreement with the results of numerical calculations even for small coordination number.

Experimental observation of localized modes in a dielectric square resonator.

We investigated the frequency spectra and field distributions of a dielectric square resonator in a microwave experiment. Since such systems cannot be treated analytically, the experimental studies of their properties are indispensable. The momentum representation of the measured field distributions shows that all resonant modes are localized on specific classical tori of the square billiard. Based on these observations a semiclassical model was developed. It shows excellent agreement with all but a single class of measured field distributions that will be treated separately.

Multifractality of eigenfunctions in spin chains.

We investigate different one-dimensional quantum spin-1/2 chain models, and by combining analytical and numerical calculations we prove that their ground state wave functions in the natural spin basis are multifractals with, in general, nontrivial fractal dimensions.

Trace formula for dielectric cavities. III. TE modes.

The construction of the semiclassical trace formula for resonances with transverse electric polarization for two-dimensional dielectric cavities is discussed. Special attention is given to the derivation of the two first terms of Weyl's series for the average number of such resonances. The formulas obtained agree well with numerical calculations for dielectric cavities of different shapes.

Multifractal dimensions for all moments for certain critical random-matrix ensembles in the strong multifractality regime.

We construct perturbation series for the qth moment of eigenfunctions of various critical random-matrix ensembles in the strong multifractality regime close to localization. Contrary to previous investigations, our results are valid in the region q<1/2. Our findings allow one to verify, at first leading orders in the strong multifractality limit, the symmetry relation for anomalous fractal dimensions Δ(q)=Δ(1-q), recently conjectured for critical models where an analog of the metal-insulator transition takes place. It is known that this relation is verified at leading order in the weak multifractality regime. Our results thus indicate that this symmetry holds in both limits of small and large coupling constant. For general values of the coupling constant we present careful numerical verifications of this symmetry relation for different critical random-matrix ensembles. We also present an example of a system closely related to one of these critical ensembles, but where the symmetry relation, at least numerically, is not fulfilled.

Application of a trace formula to the spectra of flat three-dimensional dielectric resonators.

The length spectra of flat three-dimensional dielectric resonators of circular shape were determined from a microwave experiment. They were compared to a semiclassical trace formula obtained within a two-dimensional model based on the effective index of refraction approximation and a good agreement was found. It was necessary to take into account the dispersion of the effective index of refraction for the two-dimensional approximation. Furthermore, small deviations between the experimental length spectrum and the trace formula prediction were attributed to the systematic error of the effective index of refraction approximation. In summary, the methods developed in this article enable the application of the trace formula for two-dimensional dielectric resonators also to realistic, flat three-dimensional dielectric microcavities and -lasers, allowing for the interpretation of their spectra in terms of classical periodic orbits.

Perturbation approach to multifractal dimensions for certain critical random-matrix ensembles.

Fractal dimensions of eigenfunctions for various critical random matrix ensembles are investigated in perturbation series in the regimes of strong and weak multifractality. In both regimes, we obtain expressions similar to those of the critical banded random matrix ensemble extensively discussed in the literature. For certain ensembles, the leading-order term for weak multifractality can be calculated within standard perturbation theory. For other models, such a direct approach requires modifications, which are briefly discussed. Our analytical formulas are in good agreement with numerical calculations.

Infrared spectral changes identified during different stages of herpes viruses infection in vitro.

Microscopic Fourier transform infrared spectroscopy (FTIR) which is based on the characteristic molecular vibrational spectra of cells was previously applied for the identification of various biological samples. In the present study, FTIR spectroscopy was used for the characterization of different stages during the development of herpes viruses infection. Vero cells in culture were infected with high and low doses of different herpes viruses [herpes simplex virus types 1 and 2 (HSV-1, -2) or varicella-zoster virus (VZV)], and cellular changes were observed by optical and electron microscopy and analyzed by FTIR microscopy at different periods of time post-infection. Specific different spectral changes were observed at various stages of the viral infection development. The spectral intensity in the 1220-1260 cm(-1) region (mainly attributed to phosphate levels) was considerably increased in all infected cells compared to normal uninfected cells during the early stages of the viral infection development. However, at the late stages of the viral infection development (when all the cells in the infected culture lost their spindle shape and became circular) the spectral intensities in this region significantly decreased in the infected compared to the control cells. In addition, the peak at 1023 cm(-1), attributed to carbohydrates, almost fully disappeared at early stages of the viral infection development, whereas at late stages of the infection it raised to an equivalent or higher level than that of the uninfected control cells. These results support the potential of developing FTIR microspectroscopy as a simple, reagent free method for the early detection and accurate differentiation of different stages during the development of herpes virus infection.

Grading of intrinsic and acquired cisplatin-resistant human melanoma cell lines: an infrared ATR study.

Attenuated total reflection (ATR) spectroscopy is used as an in vitro optical approach for the diagnosis and characterization of cell and tissue pathology. In comparison with the more conventional FTIR microspectroscopy that relies on transmission of IR radiation, ATR spectroscopy uses the evanescent wave technique, which is a step forward toward in vivo research. The aim of the present investigation was to examine the potential of ATR spectroscopy to differentiate between drug-resistant and drug-sensitive melanoma cell lines. We studied two human melanoma parental cell lines, GA and BG, and their cisplatin-resistant counterparts, GAC and BGC, respectively, which were derived by survival selection with this anticancer drug. Cisplatin cytotoxicity was measured on the four cell lines, and their relative resistance to cisplatin was established: BGC > BG > GAC > GA. Different resistance mechanisms were noticed between the two parental groups in accordance with their spectrum. ATR spectra-based cluster analysis of the selective biomarkers, such as phosphate and RNA/DNA, were found useful in differentiating sensitive from resistant cells. Normalized and absolute values of the differences between spectra were employed to compare between the two parental groups. It was possible to predict the relative cisplatin resistance between the cell lines using the discriminant classifying function. The success rates in predicting cisplatin resistance in these cells was 88 and 81% for GA versus GAC and BG versus BGC, respectively. These results support the further development of the ATR technique as a simple, in vitro, reagent-free method to identify drug resistance in cancer cells.

Trace formula for dielectric cavities. II. Regular, pseudointegrable, and chaotic examples.

Dielectric resonators are open systems particularly interesting due to their wide range of applications in optics and photonics. In a recent paper [Phys. Rev. E 78, 056202 (2008)] the trace formula for both the smooth and the oscillating parts of the resonance density was proposed and checked for the circular cavity. The present paper deals with numerous shapes which would be integrable (square, rectangle, and ellipse), pseudointegrable (pentagon), and chaotic (stadium), if the cavities were closed (billiard case). A good agreement is found between the theoretical predictions, the numerical simulations, and experiments based on organic microlasers.

Eigenfunction entropy and spectral compressibility for critical random matrix ensembles.

Based on numerical and perturbation series arguments we conjecture that for certain critical random matrix models the information dimension of eigenfunctions D(1) and the spectral compressibility χ are related by the simple equation χ+D(1)/d=1, where d is system dimensionality.

Experimental test of a trace formula for two-dimensional dielectric resonators.

Resonance spectra of two-dimensional dielectric microwave resonators of circular and square shapes have been measured. The deduced length spectra of periodic orbits were analyzed and a trace formula for dielectric resonators recently proposed by Bogomolny [Phys. Rev. E 78, 056202 (2008)] was tested. The observed deviations between the experimental length spectra and the predictions of the trace formula are attributed to a large number of missing resonances in the measured spectra. We show that by taking into account the systematics of observed and missing resonances the experimental length spectra are fully understood. In particular, a connection between the most long-lived resonances and certain periodic orbits is established experimentally.

Attenuated total reflectance spectroscopy: a promising technique for early detection of premalignancy.

In last decades infrared spectroscopy has demonstrated potential as a novel technology for early cancer diagnosis. Among the various IR spectroscopic techniques special interest has arisen from methods based on evanescent wave absorbance due to the possibility for in situ and in vivo implementation. The goal of the present study is to examine the potential of Attenuated Total Reflectance (ATR) spectroscopy for early detection of premalignant changes. As a model we used both cell lines and primary cells, which were transformed to be malignant by a retrovirus. Spectral measurements were performed at various post infection stages in parallel with morphological observations. Our results showed gradual and consistent spectral alterations in both cell cultures due to carcinogenesis, which were outlined using Principal Component Analysis (PCA). The main spectral differences appeared in three spectral ranges: at 3000-2800 cm(-1) (attributed to stretching vibrational modes of lipids and proteins), at 1470-1300 cm(-1)(attributed to bending overlapping modes of lipids and proteins) and also at the highly overlapping spectral range at 1000-1200 cm(-1) (attributed to bending and starching vibrational modes corresponding to all types of biological macromolecules). In order to obtain robust unsupervised classifications of the malignant progression we applied approaches of Linear Discriminant Analysis (LDA). The classifications based on Mahalanobis distances allowed us to discern that the accuracy of successful identification of premalignant stages varied between 86.5-97.2%. Our results show that ATR spectroscopy in tandem with proper statistical tools may provide a promising technique for early detectable signals of malignant progression.

Advanced statistical techniques applied to comprehensive FTIR spectra on human colonic tissues.

PURPOSE: Colon cancer is a major public health problem due to its high disease rate and death toll worldwide. The use of FTIR microscopy in the field of cancer diagnosis has become attractive over the past 20 years. In the present study, the authors investigated the potential of FTIR microscopy to define spectral changes among normal, polyp, and cancer human colonic biopsied tissues. METHODS: A large database of FTIR microscopic spectra was compiled from 230 human colonic biopsies. The database was divided into five subgroups: Normal, cancerous tissues, and three stages of benign colonic polyps, namely, mild, moderate, and severe polyps, which are precursors of carcinoma. All biopsied tissue sections were classified concurrently by an expert pathologist. The authors applied the principal components analysis (PCA) model to reduce the dimension of the original data size to 13 principal components. RESULTS: While PCA analysis shows only partial success in distinguishing among cancer, polyp, and the normal tissues, multivariate analysis (e.g., LDA) shows a promising distinction even within the polyp subgroups. CONCLUSIONS: Good classification accuracy among normal, polyp, and cancer groups was achieved with a success rate of approximately 85%. These results strongly support the potential of developing FTIR microscopy as a simple, reagent-free tool for early detection of colon cancer and, in particular, for discriminating among the benign premalignant colonic polyps having increasing degrees of dysplasia severity (mild, moderate, and severe).