Tuning the intensity statistics of random speckle patterns

Speckle patterns are a fundamental tool in a variety of physical and optical applications. Here, we investigate a method of precisely tuning the intensity statistics of random speckle patterns into a desirable pattern that possesses the same spatial correlation length and similar statistics distribution. This tuning mechanism relies on the derivation of the transform function and transmission matrix, which achieves different contrasts while maintaining the same average value or energy level. The statistics properties of the generated speckle patterns are further investigated by analyzing the standard deviation under different fitting parameters. Precisely tuning the intensity statistics of random speckle patterns could be useful for both fundamental research and practical applications, such as microscopy, imaging, and optical manipulation.     

Recent developments in fiber optics in the United States

This paper reviews recent developments of fiber optics technology and applications in the United States. The major application of fiber optics in the world is in telecommunications, and the United States represents 40% of this world market. In 1986, U.S. telecommunications companies, mainly telephone companies, will invest $24 billion dollars in new telephone plants. Of this, approximately 4% will be invested in fiber optics. These telephony applications represent approximately 80–90% of the total fiber optics equipment market. The remaining market is divided among a number of applications such as local area networks (LAN), military data links, CATV, and process control. Each of these applications is discussed and factors affecting the use of fiber optics are analyzed.     

Polarimetric target detection in the presence of spatially fluctuating Mueller matrices

In polarimetric imaging systems, the main source of perturbations may not be detection noise but fluctuations of the Mueller matrices in the scene. In this case, we propose a method for determining the illumination and analysis polarization states that allow reaching the highest target detection performance. We show with simulations and real-world images that, in practical applications, the statistics of Mueller matrix fluctuations have to be taken into account to optimize polarimetric imagery.     

Statistical analysis and accuracy of PIV data

In an assessment of PIV measurement accuracy under practical experimental circumstances, grid-generated turbulence in its early decay (x/M=13.6–15.2,Re _λ≈25) has been studied. Since a real-time processor was used, it was practical to acquire a statistically significant sample size of 3000 vector maps so that accurate turbulence statistics could be calculated. Results include moments of velocity components and spatial structures in terms of auto-correlations, turbulence scales and spectra. Data fall within limits of standard error estimates. This study demonstrates the need for large sample sizes, particularly for higher order statistics.     

Valuation and dynamic replication of contingent claims in the framework of the beliefs-preferences gauge symmetry

Although symmetries play a major role in physics, their use in finance is relatively new and, to the best of our knowledge, can be traced to 1995 when Kholodnyi introduced the beliefs-preferences gauge symmetry. One of the main outcomes of the beliefs-preferences gauge symmetry is that it allows for the valuation and dynamic replication of contingent claims in a general market environment, that is, in the case of a general, not necessarily diffusion Markov process for the prices of underlying securities. This valuation and dynamic replication is based on the novel ideas of symmetry in contrast to the standard approach which uses stochastic analysis. The practical applications of the beliefs-preferences gauge symmetry range from the detection of a new type of true arbitrage to the beliefs-preferences-independent valuation and dynamic replication of contingent claims in a general market environment. Received 31 December 2001     

Noise analysis of grating-based x-ray differential phase-contrast imaging with angular signal radiography

X-ray phase-contrast imaging is one of the novel techniques,and has potential to enhance image quality and provide the details of inner structures nondestructively.In this work,we investigate quantitatively signal-to-noise ratio(SNR) of grating-based x-ray phase contrast imaging(GBPCI) system by employing angular signal radiography(ASR).Moreover,photon statistics and mechanical error that is a major source of noise are investigated in detail.Results show the dependence of SNR on the system parameters and the effects on the extracted absorption,refraction and scattering images.Our conclusions can be used to optimize the system design for upcoming practical applications in the areas such as material science and biomedical imaging.     

Noise properties of multi-combination information in x-ray grating-based phase-contrast imaging

Grating-based x-ray phase contrast imaging has attracted increasing interest in recent decades as multimodal and laboratory source usable method. Specific efforts have been focused on establishing a new extraction method to perform practical applications. In this work, noise properties of multi-combination information of newly established information extraction method, so-called angular signal radiography method, are investigated to provide guidelines for targeted and specific applications. The results show that how multi-combination of images can be used in targeted practical applications to obtain a high-quality image in terms of signal-to-noise ratio. Our conclusions can also hold true for upcoming targeted practical applications such as biomedical imaging, non-destructive imaging, and materials science.     

A first-principles investigation on the effect of the divacancy defect on the band structures of boron nitride (BN) nanoribbons

On the basis of the comprehensive first-principles computations, we investigated the geometries, electronic and magnetic properties of zigzag and armchair boron nitride nanoribbons (BNNRs) with the divacancy defect of 5–8–5 ring fusions formed by removing B–N pair, where the defect orientation and position are considered. Our computed results reveal that all of the defective BNNRs systems can uniformly exhibit nonmagnetic semiconducting behavior, and the formation of the divacancy 5–8–5 defect can significantly impact the band structures of BNNRs with not only the zigzag but also armchair edges, where their wide band gaps are reduced and the defect orientation and position play an important role. Clearly, introducing divacancy defect can be a promising and effective approach to engineer the band structures of BNNRs, and the present computed results can provide some valuable insights for promoting the practical applications of excellent BN-based nanomaterials in the nanodevices.     

Seeing small

This paper reviews a number of used and/or proposed ideas for optical detection of small particles including single-molecules. Different techniques (direct absorption and scattering, interferometry, use of sub Poissonian statistics, cavity enhancement, and thermal lens detection) are compared in terms of signal-to-noise (SNR) ratio. It is shown that scattering (resonance and non-resonance) remains the method of choice for most practical applications. Thermal lens detection can do potentially better, but its performance critically depends on the thermal properties of the particle surroundings.     

Persistent scale free fluctuation in market recovery and recession

A counting procedure is introduced to track the persistent trending feature in the market fluctuation based on the second order statistics of the fluctuation. The method is applied to the daily number of the market index in different economic times of the recession and recovery. Similar characteristics with the discrete lattice cascade were found. It suggests the market index fluctuation over a wide range of scales can be modeled as a state of persistent “coordination”. Specific time scales of the persistent trending feature are extracted and differences in the recovery and recession are compared.     

On the effect of fractional statistics on quantum ion acoustic waves

In this paper, I study the effect of a small deviation from the Fermi–Dirac statistics on the quantum ion acoustic waves. For this purpose, a quantum hydrodynamic model is developed based on the Polychronakos statistics, which allows for a smooth interpolation between the Fermi and Bose limits, passing through the case of classical particles. The model includes the effect of pressure as well as quantum diffraction effects through the Bohm potential. The equation of state for electrons obeying fractional statistics is obtained and the effect of fractional statistics on the kinetic energy and the coupling parameter is analyzed. Through the model, the effect of fractional statistics on the quantum ion acoustic waves is highlighted, exploring both linear and weakly nonlinear regimes. It is found that fractional statistics enhance the amplitude and diminish the width of the quantum ion acoustic waves. Furthermore, it is shown that a small deviation from the Fermi–Dirac statistics can modify the type structures, from bright to dark soliton. All known results of fully degenerate and non-degenerate cases are reproduced in the proper limits.     

Exotic statistics of leapfrogging vortex rings

The leapfrogging motion of vortex rings is a three-dimensional version of the motion that in two dimensions leads to exotic exchange statistics. The statistical phase factor can be computed using the hydrodynamical Euler equation, which suggests that three-dimensional exotic exchange statistics is a common property of vortex rings in a variety of quantum liquids and gases. Potential applications range from helium superfluids to Bose-Einstein condensed alkali gases, metallic hydrogen in its liquid phases, and maybe even nuclear matter in extreme conditions.     

Manifestations of topological effects in graphene

Graphene is a monoatomic layer of graphite with carbon atoms arranged in a two-dimensional honeycomb lattice configuration. It has been known for more than 60 years that the electronic structure of graphene can be modelled by two-dimensional massless relativistic fermions. This property gives rise to numerous applications, both in applied sciences and in theoretical physics. Electronic circuits made out of graphene could take advantage of its high electron mobility that is witnessed even at room temperature. In the theoretical domain the Dirac-like behaviour of graphene can simulate high energy effects, such as the relativistic Klein paradox. Even more surprisingly, topological effects can be encoded in graphene such as the generation of vortices, charge fractionalisation and the emergence of anyons. The impact of the topological effects on graphene's electronic properties can be elegantly described by the Atiyah–Singer index theorem. Here we present a pedagogical encounter of this theorem and review its various applications to graphene. A direct consequence of the index theorem is charge fractionalisation that is usually known from the fractional quantum Hall effect. The charge fractionalisation gives rise to the exciting possibility of realising graphene based anyons that unlike bosons or fermions exhibit fractional statistics. Besides being of theoretical interest, anyons are a strong candidate for performing error free quantum information processing.     

The quantum geometry of spin and statistics

Both, spin and statistics of a quantum system can be seen to arise from underlying (quantum) group symmetries. We show that the spin–statistics theorem is equivalent to a unification of these symmetries. Besides covering the Bose–Fermi case we classify the corresponding possibilities for anyonic spin and statistics. We incorporate the underlying extended concept of symmetry into quantum field theory in a generalised path integral formulation capable of handling general braid statistics. For bosons and fermions the different path integrals and Feynman rules naturally emerge without introducing Grassmann variables. We also consider the anyonic example of quons and obtain the path integral counterpart to the usual canonical approach.     

Biconical-taper-assisted fiber interferometer with modes coupling enhancement for high-sensitive curvature measurement

A modal interferometer based on multimode–singlemode–multimode fiber structure built with a biconical taper for fiber curvature measurement is proposed and experimentally demonstrated. Due to the tapered singlemode fiber acting as a high-efficient mode power converter to enhance the modes coupling, curvature sensor with improved sensitivity is achieved by monitoring the defined fringe visibility of the interference spectrum. The measuring range can be tuned by changing the waist diameter of the fiber taper. Meanwhile, the sensor shows an intrinsic ability to overcome the influence of temperature cross-sensitivity and the power fluctuation of light source. The advantages of easy fabrication, high-quality spectrum with improved sensitivity, and small hysteresis will provide great potential for practical applications of the sensor.     

First-principle study of energy band structure of armchair graphene nanoribbons

First-principle calculation is carried out to study the energy band structure of armchair graphene nanoribbons (AGNRs). Hydrogen passivation is found to be crucial to convert the indirect band gaps into direct ones as a result of enhanced interactions between electrons and nuclei at the edge boundaries, as evidenced from the shortened bond length as well as the increased differential charge density. Ribbon width usually leads to the oscillatory variation of band gaps due to quantum confinement no matter hydrogen passivated or not. Mechanical strain may change the crystal symmetry, reduce the overlapping integral of C–C atoms, and hence modify the band gap further, which depends on the specific ribbon width sensitively. In practical applications, those effects will be hybridized to determine the energy band structure and subsequently the electronic properties of graphene. The results can provide insights into the design of carbon-based devices.     

Exponential smoothing weighted correlations

In many practical applications, correlation matrices might be affected by the ??curse of dimensionality?? and by an excessive sensitiveness to outliers and remote observations. These shortcomings can cause problems of statistical robustness especially accentuated when a system of dynamic correlations over a running window is concerned. These drawbacks can be partially mitigated by assigning a structure of weights to observational events. In this paper, we discuss Pearson??s ?? and Kendall??s ?? correlation matrices, weighted with an exponential smoothing, computed on moving windows using a data-set of daily returns for 300 NYSE highly capitalized companies in the period between 2001 and 2003. Criteria for jointly determining optimal weights together with the optimal length of the running window are proposed. We find that the exponential smoothing can provide more robust and reliable dynamic measures and we discuss that a careful choice of the parameters can reduce the autocorrelation of dynamic correlations whilst keeping significance and robustness of the measure. Weighted correlations are found to be smoother and recovering faster from market turbulence than their unweighted counterparts, helping also to discriminate more effectively genuine from spurious correlations.     

Look-up table and Gaussian filter-based inverse halftoning method excellent in gray-scale reproducibility of details and flat regions

Halftoning is a technique in which gray-scale images are converted into binary ones, and has been used widely in many practical image processing applications. On the other hand, inverse halftoning is a technique of reproducing a grayscale image from a binary one. One of the sophisticated inverse halftoning methods which can yield a high quality grayscale image is that based on a look-up table (LUT). In this paper, a new inverse halftoning method based on a combination of this LUT method and a Gaussian filter is discussed. Here, the output gray-scale image is reproduced by blending the output of the LUT-based inverse halftoning and that of the Gaussian filtering appropriately in accordance with local statistics of the image. The effectiveness and the validity of the described method are verified through experiments.     

Long-term memory: a natural mechanism for the clustering of extreme events and anomalous residual times in climate records

We study the statistics of the return intervals between extreme events above a certain threshold in long-term persistent records. We find that the long-term memory leads (i) to a stretched exponential distribution of the return intervals, (ii) to a pronounced clustering of extreme events, and (iii) to an anomalous behavior of the mean residual time to the next event that depends on the history and increases with the elapsed time in a counterintuitive way. We present an analytical scaling approach and demonstrate that all these features can be seen in long climate records. The phenomena should also occur in heartbeat records, Internet traffic, and stock market volatility and have to be taken into account for an efficient risk evaluation.