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The power-law random banded matrices and the ultrametric random matrices are investigated numerically in the regime where eigenstates are extended but all integer matrix moments remain finite in the limit of large matrix dimensions. Though in this case standard analytical tools are inapplicable, we found that in all considered cases eigenvector distributions are extremely well described by the generalised hyperbolic distribution which differs considerably from the usual Porter-Thomas distribution but shares with it certain universal properties., 20 pages, 12 figures

The statistical distribution of eigenfunctions for the Rosenzweig-Porter model is derived for the region where eigenfunctions have fractal behaviour. The result is based on simple physical ideas and leads to transparent explicit formulas which agree very well with numerical calculations. It constitutes a rare case where a non-trivial eigenfunction distribution is obtained in a closed form., 5 pages, 4 figures

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 the authors of [PRL \textbf{115}, 052501 (2015)] 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 the paper is to solve this model analytically and to find explicitly the modifications of the PT distribution due to such interaction. Resulting formulae are simple, in a good agreement with numerics, and could explain experimental results., 17 pages, 4 figures

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, canceroustissues, 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).

Light-induced fluorescence (LIF) spectroscopy has demonstrated ability as a novel, noninvasive and sensitive technology for early detection of cancer. The goal of the present study is to examine the potential of this spectroscopic method for early detection and characterization of premalignant changes. As a model we used both cell lines and primary cells, which were transformed to malignant by retrovirus. Fluorescence measurements and morphological observations of the infected cells were performed at various postinfection times. Our results showed gradual attenuation of fluorescence intensities due to cancer progression which corresponds to aromatic amino acids and nicotinamide adenine dinucleotide (NADH) molecules. In order to obtain grading and supervised classifications of the spectral premalignant changes we used approaches of linear discriminant analysis. The classifications based on Mahalanobis distances allowed us to demonstrate that the accuracy of identification of premalignant stages varied between 83.1% and 96.4%. In summary, we conclude that LIF in tandem with proper statistical tools may be a promising technique for early detection of malignant progression.

Recently it was conjectured that nodal domains of random wave functions are adequately described by critical percolation theory. In this paper we strengthen this conjecture in two respects. First, we show that, though wave function correlations decay slowly, a careful use of Harris' criterion confirms that these correlations are unessential and nodal domains of random wave functions belong to the same universality class as non critical percolation. Second, we argue that level domains of random wave functions are described by the non-critical percolation model., Comment: 13 pages

Accurate characterization of submicron particles within biological fluids presents a major challenge for a wide range of biomedical research. Detection, characterization and classification are difficult due to the presence of particles and debris ranging from single molecules up to particles slightly smaller than cells. Especial interest arises from extracellular vesicles (EVs) which are known to play a pivotal role in cell-signaling in multicellular organisms. Tunable resistive pulse sensing (TRPS) is increasingly proving to be a useful tool for high throughput particle-by-particle analysis of EVs and other submicron particles. This study examines the capability of TRPS for characterization of EVs derived from bacteria, also called outer membrane vesicles (OMVs). Measurement of a size distribution (124 ± 3 nm modal diameter) and concentration (lower bound 7.4 x 10 9 mL -1 ) are demonstrated using OMVs derived from uropathogenic Escherichia coli . Important aspects of measurement are discussed, including sample preparation and size selection. Application of TRPS to study EVs could assist the development of these particles in clinical diagnostics and therapeutics.

The computation of the two-point correlation form factor K(t) is performed for a rectangular billiard with a small size impurity inside for both periodic or Dirichlet boundary conditions. It is demonstrated that all terms of perturbation expansion of this form factor in powers of t can be computed directly by semiclassical trace formula. The main part of the calculation is the summation of non-diagonal terms in the cross product of classical orbits. When the diffraction coefficient is a constant our results coincide with expansion of exact expressions ontained by a different method., Comment: 42 pages, 10 figures, Latex

Tunable resistive pulse sensing (TRPS) has been implemented alongside dynamic light scattering (DLS) and scanning electron microscopy (SEM) to characterise a particle size distribution between 400 nm and 1 μm effective diameter. The carboxylate polystyrene particles studied were synthesised by dispersion polymerisation, and overall the data suggest that there are two modal peaks in the distribution. TRPS data indicated that the primary mode was near 630 nm, with a lesser peak near 830 nm. Two pores of different sizes were used for TRPS, and the lower size measurement threshold was apparent for both pores. High throughput particle-by-particle size measurement techniques such as TRPS are of interest for measuring synthetic particles, with potential roles including quality control and compliance, in addition to fundamental studies.

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., Comment: 20 pages, 13 figures, 3 tables

Accurate monitoring of microbial viability plays an essential role in pharmacodynamic studies such as in estimating the efficiency of antimicrobial agents. Traditionally, bacterial viability is determined by their ability to form colonies on solid growth medium or to proliferate in liquid nutrient broths but, with these culture-based methods, the live bacterial population can only be estimated retrospectively. To address this challenge, we have employed differential fluorescence staining and an all-fiber optical system developed by our group. The detection is based on the collection of the fluorescence from commercial dyes that produce a substantially increased signal upon binding with bacterial nucleic acids. The dyes allow discrimination between alive and dead cells through differential membrane permeability and fluorescence wavelength. The respective fluorescence signal is correlated to the number of bacterial cells present in the sample. Our setup uses DPSS lasers and a sensitive CCD-based spectrometer over the 400-800 nm wavelength range. A laser shutter allows the sample exposure time and acquisition time to be synchronized to minimize the effect of photobleaching. As a model, bacteria (Escherichia coli or Staphylococcus aureus) killed with isopropyl alcohol were mixed with live cells at different ratios. The population ratios of alive and dead cells were accurately quantified by our optical setup providing a rapid method for the estimation of bactericidal treatments. In summary, our optical system may offer a robust, accurate and fast alternative for detection of dead/alive bacteria in turbid solution opening the new avenues for pharmacodynamic studies.

It was demonstrated in [Phys. Rev. E 86, 021104, (2012)], that the ground-state wave functions for a large variety of one-dimensional spin-1/2 models are multifractals in the natural spin-z basis. We present here the details of analytical derivations and numerical confirmations of these results., Comment: 25 pages

Enumeration of microorganisms is an essential microbiological task for many industrial sectors and research fields. To address this challenge, we have tested an all-fibre fluorescence spectroscopic system to enumerate bacteria in industrial samples.

Based on numerical results it is conjectured that the spectral statistics of certain pseudointegrable billiards have a special form similar to that of the Anderson model at the transition point. A simple theoretical model where such statistics can be obtained analytically is briefly discussed. A few models with similar behavior are considered. In particular, we analytically found the eigenvalue statistics of a Poisson-distributed matrix perturbed by a rank one matrix, which is a good model for spectral statistics of a singular billiard.

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., 6 pages, 5 figures, 1 table

Enumeration of microorganisms is an essential microbiological task for many industrial sectors and research fields. Various tests for detection and counting of microorganisms are used today. However most of the current methods to enumerate bacteria require either long incubation time for limited accuracy, or use complicated protocols along with bulky equipment. We have developed an accurate, all-fibre spectroscopic system to measure fluorescence signal in-situ. In this paper, we examine the potential of this setup for near real time bacteria enumeration in aquatic environment. The concept is based on a well-known phenomenon that the fluorescence quantum yields of some nucleic acid stains significantly increase upon binding with nucleic acids of microorganisms. In addition we have used GFP labeled organisms. The fluorescence signal increase can be correlated to the amount of nucleic acid present in the sample. In addition we have used GFP labeled organisms. Our results show that we are able to detect a wide range of bacteria concentrations without dilution or filtration (1-108 CFU/ml) using different optical probes we designed. This high sensitivity is due to efficient light delivery with an appropriate collection volume and in situ fluorescence detection as well as the use of a sensitive CCD spectrometer. By monitoring the laser power, we can account for laser fluctuations while measuring the fluorescence signal which improves as well the system accuracy. A synchronized laser shutter allows us to achieve a high SNR with minimal integration time, thereby reducing the photobleaching effect. In summary, we conclude that our optical setup may offer a robust method for near real time bacterial detection in aquatic environment.

We developed a computerized optical probe for near real time bacterial detection in water. This microorganism detection technique, based on fluorescence enhanced by nucleic acids staining, shows promising results compared to conventional methods.

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.

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., 5 pages, 4 figures

For random matrices with tree-like structure there exists a recursive relation for the local Green functions whose solution permits to find directly many important quantities in the limit of infinite matrix dimensions. The purpose of this note 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., 23 pages

We calculate analytically, for finite-size matrices, joint probability densities of ratios of level spacings in ensembles of random matrices characterized by their associated confining potential. We focus on the ratios of two spacings between three consecutive real eigenvalues, as well as certain generalizations such as the overlapping ratios. The resulting formulas are further analyzed in detail in two specific cases: the beta-Hermite and the beta-Laguerre cases, for which we offer explicit calculations for small N. The analytical results are in excellent agreement with numerical simulations of usual random matrix ensembles, and with the level statistics of a quantum many-body lattice model and zeros of the Riemann zeta function., Comment: 20 pages

The problem of two Aharonov–Bohm (AB) vortices for the Helmholtz equation is examined in detail. It is demonstrated that the method proposed by Myers (1963 J. Math. Phys. 6 1839) for slit diffraction can be generalised to obtain an explicit solution for AB vortices. Due to the singular nature of AB interaction the Green function and scattering amplitude for two AB vortices obey a series of partial differential equations. Coefficients entering these equations, fulfil ordinary non-linear differential equations whose solutions can be obtained by solving the Painleve III equation. The asymptotics of necessary functions for very large and very small vortex separations are calculated explicitly. Taken together, this means that the problem of two AB vortices is exactly solvable.

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

We investigate different one-dimensional quantum spin-$\frac{1}{2}$ 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.

We construct perturbation series for the q-th 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, 12 pages, 12 figures

The construction of the semiclassical trace formula for the resonances with the transverse electric (TE) 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 obtained formulas agree well with numerical calculations for dielectric cavities of different shapes., Comment: 12 pages, 6 figures

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.

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., Comment: 13 pages, 12 figures, 1 table

We propose new classes of random matrix ensembles whose statistical properties are intermediate between statistics of Wigner-Dyson random matrices and Poisson statistics. The construction is based on integrable N-body classical systems with a random distribution of momenta and coordinates of the particles. The Lax matrices of these systems yield random matrix ensembles whose joint distribution of eigenvalues can be calculated analytically thanks to integrability of the underlying system. Formulas for spacing distributions and level compressibility are obtained for various instances of such ensembles., 32 pages, 8 figures

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.

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 et al. [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., 14 pages, 12 figures, 1 table

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.

One of the major public health hazards is colon cancer. There is a great necessity to develop new methods for early detection of cancer. If colon cancer is detected and treated early, cure rate of more than 90% can be achieved. In this study we used FTIR microscopy (MSP), which has shown a good potential in the last 20 years in the fields of medical diagnostic and early detection of abnormal tissues. Large database of FTIR microscopic spectra was acquired from 230 human colonic biopsies. Five different subgroups were included in our database, normal and cancer tissues as well as three stages of benign colonic polyps, namely, mild, moderate and severe polyps which are precursors of carcinoma. In this study we applied advanced mathematical and statistical techniques including principal component analysis (PCA) and linear discriminant analysis (LDA), on human colonic FTIR spectra in order to differentiate among the mentioned subgroups' tissues. Good classification accuracy between normal, polyps and cancer groups was achieved with approximately 85% success rate. Our results showed that there is a great potential of developing FTIR-micro spectroscopy as a simple, reagent-free viable tool for early detection of colon cancer in particular the early stages of premalignancy among the benign colonic polyps.

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.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.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.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).

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 chi are related by the simple equation chi+D_1/d=1, where d is the system dimensionality., Comment: 4 pages, 3 figures

International audience; The scattering of an incident plane wave on two Aharonov-Bohm vortices with opposite fluxes is considered in detail. The presence of the vortices imposes non-trivial boundary conditions for the partial waves on a cut joining the two vortices. These conditions result in an infinite system of equations for scattering amplitudes between incoming and outgoing partial waves, which can be solved numerically. The main focus of the paper is the analytic determination of the scattering amplitude in two limits, the small flux limit and the limit of small vortex separation. In the latter limit the dominant contribution comes from the S-wave amplitude. Calculating it, however, still requires solving an infinite system of equations, which is achieved by the Riemann-Hilbert method. The results agree well with the numerical calculations.

International audience; A method to generate new classes of random matrix ensembles is proposed. Random matrices from these ensembles are Lax matrices of classically integrable systems with a certain distribution of momenta and coordinates. The existence of an integrable structure permits to calculate the joint distribution of eigenvalues for these matrices analytically. Spectral statistics of these ensembles are quite unusual and in many cases give rigorously new examples of intermediate statistics.

It is well established numerically that spectral statistics of pseudo-integrable models differs considerably from the reference statistics of integrable and chaotic systems. In Bogomolny and Schmit (2004 Phys. Rev. Lett. 93 254102) statistical properties of a certain quantized pseudo-integrable map had been calculated analytically but only for a special sequence of matrix dimensions. The purpose of this paper is to obtain the spectral statistics of the same quantum map for all matrix dimensions.

There is currently a great deal of interest in flat dielectric micro-cavities due to their numerous practical applications and their ability to address fundamental physics issues. But apart from circular cavity, exact expressions of wave-functions and spectrum are still unknown for all other cavity shapes. The difficulty originates from two separated factors: non-linearities induced by the boundary shape and diffraction at the corners. Here we propose an analytical perturbation method for nearly circular cavities and give general formulae up to the second order in the perturbation parameter for the wave-functions, the spectrum, and the far-field pattern. This approach is confirmed with the example of the cut-disk (a chaotic cavity shape with corners) by numerical simulations based on the Boundary Element Method and experiments with organic micro-lasers. This analytical method can be extended to a broad diversity of cavity shapes. We discuss its range of validity in length scale and the limit of the effective refractive index approximation which underlies the two-dimensional approximation.

There is currently a great deal of interest in dielectric micro-cavities due to their numerous practical applications and their use to test fundamental physics issues. A systematic way of identifying dominating periodic orbits is presented including a comparison of cavities with singular or smooth edges.

Fourier transform infrared microspectroscopy (FTIR-MSP) is an analytical method with a promising potential for detecting the spectral changes due to cancerous changes in cells. The purpose of the present study is monitoring biochemical spectral changes accompanying viral cancer progression in cells and tissues using FTIR-MSP. As a model system, we used cells in culture which were transformed to malignant cells by infection with murine sarcoma virus (MuSV) and cervical tissues at different neoplastic stages. In order to devise a systematic follow-up of the cancer progression, it was essential first to determine and validate consistent and significant spectral biomarkers, which can evidently discriminate between normal and cancerous cells/tissues. Then these biomarkers were used for the characterization and classification of early stages of malignant transformation utilizing discriminant classification function techniques. Our study points out that malignancy progression can be eminently graded for both cell lines and tissues. For example, using the array of four biomarkers: A 2958 A 2852 + A 2923 , A 1121 / A 1015 , A 1171 / A 1152 and | A 1082 − A 1056 | A 1028 , we attained that the classification accuracies of different premalignant stages of cell lines and tissues were varied between 89.5 and 97.4%. These results strongly support the potential of developing FTIR microspectroscopy as a simple, reagent free method for early detection and accurate differentiation of premalignant stages.

The construction of perturbation series for slightly deformed dielectric circular cavity is discussed in details. The obtained formulae are checked on the example of cut disks. A good agreement is found with direct numerical simulations and far-field experiments., Comment: 17 pages, 12 figures

The construction of the trace formula for open dielectric cavities is examined in detail. Using the Krein formula it is shown that the sum over cavity resonances can be written as a sum over classical periodic orbits for the motion inside the cavity. The contribution of each periodic orbit is the product of the two factors. The first is the same as in the standard trace formula and the second is connected with the product of reflection coefficients for all points of reflection with the cavity boundary. Two asymptotic terms of the smooth resonance counting function related with the area and the perimeter of the cavity are derived. The coefficient of the perimeter term differs from the one for closed cavities due to unusual high-energy asymptotics of the $\mathbf{S}$-matrix for the scattering on the cavity. Corrections to the leading semi-classical formula are briefly discussed. Obtained formulas agree well with numerical calculations for circular dielectric cavities., 13 pages, 10 figures

Fourier transform infrared microspectroscopy (FTIR-MSP) is potentially a powerful analytical method for identifying the spectral properties of biological activity in cells. The goal of the present research is the implementation of FTIR-MSP to study early spectral changes accompanying malignant transformation of cells. As a model system, cells in culture are infected by the murine sarcoma virus (MuSV), which induces malignant transformation. The spectral measurements are taken at various postinfection time intervals. To follow up systematically the progress of the spectral changes at early stages of cell transformation, it is essential first to determine and validate consistent and significant spectral parameters (biomarkers), which can evidently discriminate between normal and cancerous cells. Early stages of cell transformation are classified by an array of spectral biomarkers utilizing cluster analysis and discriminant classification function techniques. The classifications indicate that the first spectral changes are detectable much earlier than the first morphological signs of cell transformation. Our results point out that the first spectral signs of malignant transformation are observed on the first and third day of postinfection (PI) (for NIH/3T3 and MEF cell cultures, respectively), while the first visible morphological alterations are observed only on the third and seventh day, respectively. These results strongly support the potential of developing FTIR microspectroscopy as a simple, reagent-free method for early detection of malignancy.

Dielectric micro-cavities are widely used as laser resonators and characterizations of their spectra are of interest for various applications. We experimentally investigate micro-lasers of simple shapes (Fabry-Perot, square, pentagon, and disk). Their lasing spectra consist mainly of almost equidistant peaks and the distance between peaks reveals the length of a quantized periodic orbit. To measure this length with a good precision, it is necessary to take into account different sources of refractive index dispersion. Our experimental and numerical results agree with the superscar model describing the formation of long-lived states in polygonal cavities. The limitations of the two-dimensional approximation are briefly discussed in connection with micro-disks., Comment: 13 pages, 19 figures, accepted for publication in Physical Review A

The far-field emission of two dimensional (2D) stadium-shaped dielectric cavities is investigated. Micro-lasers with such shape present a highly directional emission. We provide experimental evidence of the dependance of the emission directionality on the shape of the stadium, in good agreement with ray numerical simulations. We develop a simple geometrical optics model which permits to explain analytically main observed features. Wave numerical calculations confirm the results., 4 pages, 8 figures

It has been conjectured that the statistical properties of zeros of the Riemann zeta function near $z = 1/2 + \ui E$ tend, as $E \to \infty$, to the distribution of eigenvalues of large random matrices from the Unitary Ensemble. At finite $E$ numerical results show that the nearest-neighbour spacing distribution presents deviations with respect to the conjectured asymptotic form. We give here arguments indicating that to leading order these deviations are the same as those of unitary random matrices of finite dimension $N_{\rm eff}=\log(E/2\pi)/\sqrt{12 \Lambda}$, where $\Lambda=1.57314 ...$ is a well defined constant., Comment: 9 pages, 3 figures

Wave functions of pseudointegrable plane polygonal billiards are investigated. It is demonstrated that they have clear structures (superscars) related with families of classical periodic orbits which do not disappear at large energy.

Curious spectral properties of an ensemble of random unitary matrices appearing in the quantization of a map p -> p+alpha, q -> q+f(p+alpha) in [Giraud et al. nlin.CD/0403033] are investigated. When alpha=m/n with integer co-prime m,n and matrix dimension N -> infinity is such that mN = 1 or -1 mod n, local spectral statistics of this ensemble tends to the semi-Poisson distribution [Bogomolny et al. Eur. Phys. J. B 19, 121 (2001)] with arbitrary integer or half-integer level repulsion at small distances: R(s)-> s^{beta} when s -> 0 and beta=n-1 or n/2-1 depending on time-reversal symmetry of the map., 4 pages, 3 figures