Amplifying single-photon nonlinearity using weak measurements

We show that weak measurement can be used to "amplify" optical nonlinearities at the single-photon level, such that the effect of one properly postselected photon on a classical beam may be as large as that of many unpostselected photons. We find that "weak-value amplification" offers a marked improvement in the signal-to-noise ratio in the presence of technical noise with long correlation times. Unlike previous weak-measurement experiments, our proposed scheme has no classical equivalent.     

Self-assembly of boehmite nanopetals to form 3D high surface area nanoarchitectures

A flower-like boehmite nanostructure was prepared through a template-free chemical route by the self-assembly process of nanosize petals 800–1000 nm long, 200–250 nm wide, 20–50 nm thick and having an average crystallite size of about 2.21 nm. X-ray diffraction analysis (XRD), transmission electron microscopy (TEM), scanning electron microscopy (SEM), DTA/TGA analyses and Brunauer–Emmet–Teller (BET-N₂) analyses were used in order to characterize the product obtained. XRD results exhibited that the obtained nanostructures composed of pure orthorhombic AlOOH phase. The effects of Cl⁻ ions and TEA on the growth of boehmite three-dimensional nanoarchitectures in the presence of NO₃^-\mathrm{NO}_{3}^{-} ions were investigated. BET analyses of as-prepared material demonstrate that this nanostructure material has a high specific surface area, as high as 123 m² g⁻¹.     

A CTRW-based model of time-resolved fluorescence lifetime imaging in a turbid medium

We develop an analytic model of time-resolved fluorescent imaging of photons migrating through a semi-infinite turbid medium bounded by an infinite plane in the presence of a single stationary point fluorophore embedded in the medium. In contrast to earlier models of fluorescent imaging in which photon motion is assumed to be some form of continuous diffusion process, the present analysis is based on a continuous-time random walk (CTRW) on a simple cubic lattice, the objective being to estimate the position and lifetime of the fluorophore. This can provide information related to local variations in pH and temperature with potential medical significance. Aspects of the theory were tested using time-resolved measurements of the fluorescence from small inclusions inside tissue-like phantoms. The experimental results were found to be in good agreement with theoretical predictions provided that the fluorophore was not located too close to the planar boundary, a common problem in many diffusive systems.     

Comparison of tumor histology to dynamic contrast enhanced magnetic resonance imaging-based physiological estimates

Purpose

The purpose of this study was to compare histologically determined cellularity and extracellular space to dynamic contrast-enhanced magnetic resonance imaging (DCE MRI)-based maps of a two-compartment model's parameters describing tumor contrast agent extravasation, specifically tumor extravascular extracellular space (EES) volume fraction (v_e), tumor plasma volume fraction (v_p) and volume-normalized contrast agent transfer rate between tumor plasma and interstitium (K_TRANS/V_T).

Materials and Methods

Obtained v_e, v_p and K_TRANS/V_T maps were estimated from gadolinium diethylenetriamine penta-acetic acid DCE T₁-weighted gradient-echo images at resolutions of 469, 938 and 2500 μm. These parameter maps were compared at each resolution to histologically determined tumor type, and the high-resolution 469-μm maps were compared with automated cell counting using Otsu's method and a color-thresholding method for estimated intracellular (V_{intracellular}) and extracellular (V_{extracellular}) space fractions.

Results

The top five K_TRANS/V_T values obtained from each tumor at 469 and 938 μm resolutions are significantly different from those obtained at 2500 μm (P<.0001) and from one another (P=.0014). Using these top five K_TRANS/V_T values and the corresponding tumor EES volume fractions v_e, we can statistically differentiate invasive ductal carcinomas from noninvasive papillary carcinomas for the 469- and 938-μm resolutions (P=.0017 and P=.0047, respectively), but not for the 2500-μm resolution (P=.9008). The color-thresholding method demonstrated that v_e measured by DCE MRI is statistically similar to histologically determined EES. The V_{extracellular} obtained from the color-thresholding method was statistically similar to the v_e measured with DCE MRI for the top 10 K_TRANS/V_T values (P>.05). DCE MRI-based K_TRANS/V_T estimates are not statistically correlated with histologically determined cellularity.

Conclusion

DCE MRI estimates of tumor physiology are a limited representation of tumor histological features. Extracellular spaces measured by both DCE MRI and microscopic analysis are statistically similar. Tumor typing by DCE MRI is spatial resolution dependent, as lower resolutions average out contributions to voxel-based estimates of K_TRANS/V_T. Thus, an appropriate resolution window is essential for DCE MRI tumor diagnosis. Within this resolution window, the top K_TRANS/V_T values with corresponding v_e are diagnostic for the tumor types analyzed in this study.     

Inplace 2D matching in compressed images

The compressed matching problem is the problem of finding all occurrences of a pattern in a compressed text. In this paper we discuss the 2-dimensional compressed matching problem in Lempel–Ziv compressed images. Given a pattern P of (uncompressed) size m×m, and a text T of (uncompressed) size n×n, both in 2D-LZ compressed form, our algorithm finds all occurrences of P in T. The algorithm is strongly inplace, that is, the amount of extra space used is proportional to the best possible compression of a pattern of size m². The best compression that the 2D-LZ technique can obtain for a file of size m² is O(m). The time for performing the search is O(n²) and the preprocessing time is O(m³). Our algorithm is general in the sense that it can be used for any 2D compression which can be sequentially decompressed in small space.     

Asynchronous and corrected-asynchronous finite difference solutions of PDEs on MIMD multiprocessors

A major problem in achieving significant speed-up on parallel machines is the overhead involved with synchronizing the concurrent processes. Removing the synchronization constraint has the potential of speeding up the computation, while maintaining greater computation flexibility (e.g. differences in processors speed; differences in the data input to processors). We construct asynchronous (AS) finite difference schemes for the solution of PDEs by removing the synchronization constraint. We analyze the numerical properties of these schemes. Based on the analysis, we develop corrected-asynchronous (CA) finite difference schemes which are specifically constructed for an asynchronous processing. We present asynchronous (AS) and corrected-asynchronous (CA) finite difference schemes for the multi-dimensional heat equation. Although our discussion concentrates on the Euler scheme it should serve only as a sample, as it can be extended to other schemes and other PDEs.These schemes are implemented on the shared-memory multi-userSequent Balance machine. Numerical results for one and two dimensional problems are presented. It is shown experimentally that synchronization penalty can be about 50% of run time: in most cases, the asynchronous scheme runs twice as fast as the parallel synchronous scheme. In general, the efficiency of the parallel schemes increases with processor load, with the time-level, and with the problem dimension. The efficiency of the AS may reach 90% and over, but it provides accurate results only for steady-state values. The CA, on the other hand, is less efficient but provides more accurate results for intermediate (non steady-state) values. The results show the potential of developing asynchronous finite deference schemes for steady-state as well as non steadystate problems.This research was partially supported by a grant from The Basic Research Foundation administrated by The Israel Academy of Sciences and Humanities.A reduced version of the paper was presented at the 4th SIAM Conference on Parallel Processing for Scientific Computing, Dec. 11–13, 1989, Chicago, USA.The work by this author was supported by research grant 337 of the Israeli National Council for Research and Development in the years 1990–1991.This research was supported by the National Aeronautics and Space Administration under NASA Contract No. NASI-18107 while the author was in residence at the Institute for Computer Applications in Sciences and Engineering (ICASE), NASA Langley Research Center, Hampton, VA 23665, USA.     

The complex networks approach for authorship attribution of books

Authorship analysis by means of textual features is an important task in linguistic studies. We employ complex networks theory to tackle this disputed problem. In this work, we focus on some measurable quantities of word co-occurrence network of each book for authorship characterization. Based on the network features, attribution probability is defined for authorship identification. Furthermore, two scaling exponents, q-parameter and α-exponent, are combined to classify personal writing style with acceptable high resolution power. The q-parameter, generally known as the nonextensivity measure, is calculated for degree distribution and the α-exponent comes from a power law relationship between number of links and number of nodes in the co-occurrence network constructed for different books written by each author. The applicability of the presented method is evaluated in an experiment with thirty six books of five Persian litterateurs. Our results show high accuracy rate in authorship attribution.     

Measuring persistence in a stationary time series using the complex network theory

A growing interest exists currently in the analysis of time series by the complex network theory. Here we present a simple and quick way for mapping time series to complex networks. Using a simple rule allows us to transform time series into a textual sequence then we divide it into words with fixed size. Distinct words are nodes of the network, and we have complete control on the network scale by adjusting the word size. Two nodes are linked if their associated words co-occur in sequence. We show that the network topological measures quantify the persistence and the long range correlations in fractional Brownian processes. For a particular word size we assume some relations between the topological measures and the Hurst exponent which characterised the persistence in fractional Brownian processes.     

Statistical isotropy of the cosmic microwave background

The breakdown of statistical homogeneity and isotropy of cosmic perturbations is a generic feature of ultra-large scale structure of the cosmos, in particular, of non-trivial cosmic topology. The statistical isotropy (SI) of the cosmic microwave background temperature fluctuations (CMB anisotropy) is sensitive to this breakdown on the largest scales comparable to, and even beyond the cosmic horizon. We propose a set of measures,K _l (l = 1, 2,3,...) which for non-zero values indicate and quantify statistical isotropy violations in a CMB map. We numerically compute the predictedK _l spectra for CMB anisotropy in flat torus universe models. Characteristic signatures of different models in theK _l spectrum are noted.     

A Study of Holographic Dark Energy Models in Chern-Simon Modified Gravity

This paper is devoted to study some holographic dark energy models in the context of Chern-Simon modified gravity by considering FRW universe. We analyze the equation of state parameter using Granda and Oliveros infrared cut-off proposal which describes the accelerated expansion of the universe under the restrictions on the parameter α. It is shown that for the accelerated expansion phase \( -1<\omega _{\Lambda }<-\frac {1}{3}\), the parameter α varies according as \(1<\alpha <\frac {3}{2}\). Furthermore, for 0<α<1, the holographic energy and pressure density illustrates phantom-like theory of the evolution when ω_Λ<?1. Also, we discuss the correspondence between the quintessence, K-essence, tachyon and dilaton field models and holographic dark energy models on similar fashion. To discuss the accelerated expansion of the universe, we explore the potential and the dynamics of quintessence, K-essence, tachyon and dilaton field models.