A Study of Biased and Unbiased Stochastic Algorithms for Solving Integral Equations

In this paper we propose and analyse a new unbiased stochastic method for solving a class of integral equations, namely the second kind Fredholm integral equations. We study and compare three possible approaches to compute linear functionals of the integral under consideration: i) biased Monte Carlo method based on evaluation of truncated Liouville-Neumann series, ii) transformation of this problem into the problem of computing a finite number of integrals, and iii) unbiased stochastic approach. Five Monte Carlo algorithms for numerical integration have been applied for approach (ii). Error balancing of both stochastic and systematic errors has been discussed and applied during the numerical implementation of the biased algorithms. Extensive numerical experiments have been performed to support the theoretical studies regarding the convergence rate of Monte Carlo methods for numerical integration done in our previous studies. We compare the results obtained by some of the best biased stochastic approaches with the results obtained by the proposed unbiased approach. Conclusions about the applicability and efficiency of the algorithms have been drawn

A New Walk on Equations Monte Carlo Method for Linear Algebraic Problems

International audienceA new Walk on Equations (WE) Monte Carlo algorithm for Linear Algebra (LA) problem is proposed and studied. This algorithm relies on a non-discounted sum of an absorbed random walk. It can be applied for either real or complex matrices. Several techniques like simultaneous scoring or the sequential Monte Carlo method are applied to improve the basic algorithm. Numerical tests are performed on examples with matrices of different size and on systems coming from various applications. Comparisons with standard deterministic or Monte Carlo algorithms are also done

Second harmonic optical coherence tomography

Second harmonic optical coherence tomography, which uses coherence gating of second-order nonlinear optical response of biological tissues for imaging, is described and demonstrated. Femtosecond laser pulses were used to excite second harmonic waves from collagen harvested from rat tail tendon and a reference nonlinear crystal. Second harmonic interference fringe signals were detected and used for image construction. Because of the strong dependence of second harmonic generation on molecular and tissue structures, this technique offers contrast and resolution enhancement to conventional optical coherence tomography.Comment: 3 pages, 5 figures. Submitted on November 8, 2003, this paper has recently been accepted by Optics Letter

Sexual maturation in adolescents from the region of Eastern Rodopi in connection with their social environment

The purpose of this paper is to characterize the influence of socio-economic environment on the processes of sexual maturation and the age of adolescent's menarche from the Eastern Rhodopi. Subjects of study are 1378 children and adolescents from local schools in Ivaylovgrad, Svilengrad and Lyubimets. These are 730 girls and 648 boys aged 8 to 17 years. In connection with studying the influence of environmental factors on the sexual maturation processes, interviews with parents were conducted . The survey contains 22 questions with parents' data, which were used to clarify the social, economic and professional status, living conditions of family life, etc. The results show that although genetically determinated, the processes of sexual maturation are significantly influenced by exogenous factors, and in a peculiar way they reflect the specific social and economic situation in a given geographical area at a randomly selected time period

Low Fatigue Dynamic Auxetic Lattices With 3D Printable, Multistable, and Tuneable Unit Cells

Stress distribution has led to the design of both tough and lightweight materials. Truss structures distribute stress well and are commonly used to design lightweight materials for applications experiencing low strains. In 3D lattices, however, few structures allow high elastic compression and tunable deformation. This is especially true for auxetic material designs, such as the prototypical re-entrant honeycomb with sharp corners, which are particularly susceptible to stress concentrations. There is a pressing need for lightweight lattice designs that are dynamic, as well as resistant to fatigue. Truss designs based on hinged structures exist in nature and delocalize stress rather than concentrating it in small areas. They have inspired us to develop s-hinge shaped elastic unit cell elements from which new classes of architected modular 2D and 3D lattices can be printed or assembled. These lattices feature locally tunable Poisson ratios (auxetic), large elastic deformations without fatigue, as well as mechanical switching between multistable states. We demonstrate 3D printed structures with stress delocalization that enables macroscopic 30% cyclable elastic strains, far exceeding those intrinsic to the materials that constitute them (6%). We also present a simple semi-analytical model of the deformations which is able to predict the mechanical properties of the structures within <5% error of experimental measurements from a few parameters such as dimensions and material properties. Using this model, we discovered and experimentally verified a critical angle of the s-hinge enabling bistable transformations between auxetic and normal materials. The dynamic modeling tools developed here could be used for complex 3D designs from any 3D printable material (metals, ceramics, and polymers). Locally tunable deformation and much higher elastic strains than the parent material would enable the next generation of compact, foldable and expandable structures. Mixing unit cells with different hinge angles, we designed gradient Poisson's ratio materials, as well as ones with multiple stable states where elastic energy can be stored in latching structures, offering prospects for multi-functional designs. Much like the energy efficient Venus flytrap, such structures can store elastic energy and release it on demand when appropriate stimuli are present

Large expert-curated database for benchmarking document similarity detection in biomedical literature search

Document recommendation systems for locating relevant literature have mostly relied on methods developed a decade ago. This is largely due to the lack of a large offline gold-standard benchmark of relevant documents that cover a variety of research fields such that newly developed literature search techniques can be compared, improved and translated into practice. To overcome this bottleneck, we have established the RElevant LIterature SearcH consortium consisting of more than 1500 scientists from 84 countries, who have collectively annotated the relevance of over 180 000 PubMed-listed articles with regard to their respective seed (input) article/s. The majority of annotations were contributed by highly experienced, original authors of the seed articles. The collected data cover 76% of all unique PubMed Medical Subject Headings descriptors. No systematic biases were observed across different experience levels, research fields or time spent on annotations. More importantly, annotations of the same document pairs contributed by different scientists were highly concordant. We further show that the three representative baseline methods used to generate recommended articles for evaluation (Okapi Best Matching 25, Term Frequency-Inverse Document Frequency and PubMed Related Articles) had similar overall performances. Additionally, we found that these methods each tend to produce distinct collections of recommended articles, suggesting that a hybrid method may be required to completely capture all relevant articles. The established database server located at https://relishdb.ict.griffith.edu.au is freely available for the downloading of annotation data and the blind testing of new methods. We expect that this benchmark will be useful for stimulating the development of new powerful techniques for title and title/abstract-based search engines for relevant articles in biomedical research.Peer reviewe

Second-harmonic optical coherence tomography.

Second-harmonic optical coherence tomography, which uses coherence gating of second-order nonlinear optical responses of biological tissues for imaging, is described and demonstrated. Femtosecond laser pulses were used to excite second-harmonic waves from collagen harvested from rat tail tendon and a reference non-linear crystal. Second-harmonic interference fringe signals were detected and used for image construction. Because of the strong dependence of second-harmonic generation on molecular and tissue structures, this technique imparts contrast and resolution enhancement to conventional optical coherence tomography

High-resolution frequency-domain second-harmonic optical coherence tomography.

We used continuum generated in an 8.5 cm long fiber by a femtosecond Yb fiber laser to improve threefold the axial resolution of frequency domain second-harmonic optical coherence tomography (SH-OCT) to 12 microm. The acquisition time was shortened by more than 2 orders of magnitude compared to the time-domain SH-OCT. The system was applied to image biological tissue of fish scales, pig leg tendon, and rabbit eye sclera. Highly organized collagen fibrils can be visualized in the recorded images. Polarization dependence on the SH has been used to obtain polarization resolved images

High-resolution frequency-domain second-harmonic optical coherence tomography.

We used continuum generated in an 8.5 cm long fiber by a femtosecond Yb fiber laser to improve threefold the axial resolution of frequency domain second-harmonic optical coherence tomography (SH-OCT) to 12 microm. The acquisition time was shortened by more than 2 orders of magnitude compared to the time-domain SH-OCT. The system was applied to image biological tissue of fish scales, pig leg tendon, and rabbit eye sclera. Highly organized collagen fibrils can be visualized in the recorded images. Polarization dependence on the SH has been used to obtain polarization resolved images

Scanning Еlectron Мicroscopy of Еnamel and Dentin of Тeeth with Hypocalcified Аmelogenesis Imperfecta

The histological features of teeth with hypocalcified amelogenesis imperfecta (AI) have been poorly studied, which calls into question the effectiveness of modern adhesive techniques used in the treatment of these noncarious defects