Parallel algorithm with spectral convergence for nonlinear integro-differential equations

We discuss a numerical algorithm for solving nonlinear integro-differential equations, and illustrate our findings for the particular case of Volterra type equations. The algorithm combines a perturbation approach meant to render a linearized version of the problem and a spectral method where unknown functions are expanded in terms of Chebyshev polynomials (El-gendi's method). This approach is shown to be suitable for the calculation of two-point Green functions required in next to leading order studies of time-dependent quantum field theory.Comment: 15 pages, 9 figure

Robustly Learning Mixtures of kk Arbitrary Gaussians

We give a polynomial-time algorithm for the problem of robustly estimating a mixture of $k$ arbitrary Gaussians in $\mathbb{R}^d$, for any fixed $k$, in the presence of a constant fraction of arbitrary corruptions. This resolves the main open problem in several previous works on algorithmic robust statistics, which addressed the special cases of robustly estimating (a) a single Gaussian, (b) a mixture of TV-distance separated Gaussians, and (c) a uniform mixture of two Gaussians. Our main tools are an efficient \emph{partial clustering} algorithm that relies on the sum-of-squares method, and a novel \emph{tensor decomposition} algorithm that allows errors in both Frobenius norm and low-rank terms.Comment: This version extends the previous one to yield 1) robust proper learning algorithm with poly(eps) error and 2) an information theoretic argument proving that the same algorithms in fact also yield parameter recovery guarantees. The updates are included in Sections 7,8, and 9 and the main result from the previous version (Thm 1.4) is presented and proved in Section

WRKY6 restricts Piriformospora indica-stimulated and phosphate-induced root development in Arabidopsis

BACKGROUND: Arabidopsis root growth is stimulated by Piriformospora indica, phosphate limitation and inactivation of the WRKY6 transcription factor. Combinations of these factors induce unexpected alterations in root and shoot growth, root architecture and root gene expression profiles. RESULTS: The results demonstrate that P. indica promotes phosphate uptake and root development under Pi limitation in wrky6 mutant. This is associated with the stimulation of PHOSPHATE1 expression and ethylene production. Expression profiles from the roots of wrky6 seedlings identified genes involved in hormone metabolism, transport, meristem, cell and plastid proliferation, and growth regulation. 25 miRNAs were also up-regulated in these roots. We generated and discuss here a list of common genes which are regulated in growing roots and which are common to all three growth stimuli investigated in this study. CONCLUSION: Since root development of wrky6 plants exposed to P. indica under phosphate limitation is strongly promoted, we propose that common genes which respond to all three growth stimuli are central for the control of root growth and architecture. They can be tested for optimizing root growth in model and agricultural plants. ELECTRONIC SUPPLEMENTARY MATERIAL: The online version of this article (doi:10.1186/s12870-015-0673-4) contains supplementary material, which is available to authorized users

Time evolution of the chiral phase transition during a spherical expansion

We examine the non-equilibrium time evolution of the hadronic plasma produced in a relativistic heavy ion collision, assuming a spherical expansion into the vacuum. We study the $O(4)$ linear sigma model to leading order in a large-$N$ expansion. Starting at a temperature above the phase transition, the system expands and cools, finally settling into the broken symmetry vacuum state. We consider the proper time evolution of the effective pion mass, the order parameter $\langle \sigma \rangle$, and the particle number distribution. We examine several different initial conditions and look for instabilities (exponentially growing long wavelength modes) which can lead to the formation of disoriented chiral condensates (DCCs). We find that instabilities exist for proper times which are less than 3 fm/c. We also show that an experimental signature of domain growth is an increase in the low momentum spectrum of outgoing pions when compared to an expansion in thermal equilibrium. In comparison to particle production during a longitudinal expansion, we find that in a spherical expansion the system reaches the ``out'' regime much faster and more particles get produced. However the size of the unstable region, which is related to the domain size of DCCs, is not enhanced.Comment: REVTex, 20 pages, 8 postscript figures embedded with eps

Gravitational Charged Perfect Fluid Collapse in Friedmann Universe Models

This paper is devoted to study the gravitational charged perfect fluid collapse in the Friedmann universe models with cosmological constant. For this purpose, we assume that the electromagnetic field is so weak that it does not introduce any distortion into the geometry of the spacetime. The results obtained from the junction conditions between the Friedmann and the Reissner-Nordstr$\ddot{o}$m de-Sitter spacetimes are used to solve the field equations. Further, the singularity structure and mass effects of the collapsing system on time difference between the formation of apparent horizons and singularity have been studied. This analysis provides the validity of Cosmic Censorship Hypothesis. It is found that the electric field affects the area of apparent horizons and their time of formation.Comment: 17 pages, accepted for publication in Astrophys. Space Sc

Antibacterial and antioxidant potential of biosynthesized copper nanoparticles mediated through Cissus arnotiana plant extract

© 2019 Elsevier B.V. Environment friendly methods for the synthesis of copper nanoparticles have become a valuable trend in the current scenario. The utilization of phytochemicals from plant extracts has become a unique technology for the synthesis of nanoparticles, as they possess dual nature of reducing and capping agents to the nanoparticles. In the present investigation we have synthesized copper nanoparticles (CuNPs) using a rare medicinal plant Cissus arnotiana and evaluated their antibacterial activity against gram negative and gram positive bacteria. The morphology and characterization of the synthesized CuNPs were studied and done using UV-Visible spectroscopy at a wavelength range of 350–380 nm. XRD studies were performed for analyzing the crystalline nature; SEM and TEM for evaluating the spherical shape within the size range of 60–90 nm and AFM was performed to check the surface roughness. The biosynthesized CuNPs showed better antibacterial activity against the gram-negative bacteria, E. coli with an inhibition zone of 22.20 ± 0.16 mm at 75 μg/ml. The antioxidant property observed was comparatively equal with the standard antioxidant agent ascorbic acid at a maximum concentration of 40 μg/ ml. This is the first study reported on C. arnotiana mediated biosynthesis of copper nanoparticles, where we believe that the findings can pave way for a new direction in the field of nanotechnology and nanomedicine where there is a significant potential for antibacterial and antioxidant activities. We predict that, these could lead to an exponential increase in the field of biomedical applications, with the utilization of green synthesized CuNPs, due to its remarkable properties. The highest antibacterial property was observed with gram-negative strains mainly, E. coli, due to its thin peptidoglycan layer and electrostatic interactions between the bacterial cell wall and CuNPs surfaces. Hence, CuNPs can be potent therapeutic agents in several biomedical applications, which are yet to be explored in the near future

Ion emission measurements and mirror erosion studies for extreme ultraviolet lithography

Mirror erosion by high energy ion emission from extreme UV light sources is one of the main factors contributing to EUVL collector mirror reflectivity degradation. We are measuring ion energy distributions at the mirror distance from the plasma utilizing three different ion diagnostics for the case of tin-doped microscopic droplet laser plasmas. Typical ion energy distributions measured by an electrostatic spectrorneter are described. From the ion energy distributions, an estimate of mirror erosion is obtained. The effectiveness of electrostatic field mitigation is evaluated for the EUVL source requirement. (c) 2005 American Vacuum Society

Emerging trends in the novel drug delivery approaches for the treatment of lung cancer

© 2019 Elsevier B.V. Cancer is one of the major diseases that cause a high number of deaths globally. Of the major types of cancers, lung cancer is known to be the most chronic form of cancer in the world. The conventional management of lung cancer includes different medical interventions like chemotherapy, surgical removal, and radiation therapy. However, this type of approach lacks specificity and also harms the adjacent normal cells. Lately, nanotechnology has emerged as a promising intervention in the management and treatment of lung cancers. Nanotechnology has revolutionized the existing modalities and focuses primarily on reducing toxicity and improving the bioavailability of anticancer drugs to the target tumor cells. Nanocarrier systems are being currently used extensively to exploit and to overcome the obstructions induced by cancers in the lungs. The nano-carrier-loaded therapeutic drug delivery methods have shown promising potential in treating lung cancer as its target is to control the growth of tumor cells. In this review, various modes of nano drug delivery options like liposomes, dendrimers, quantum dots, carbon nanotubes and metallic nanoparticles have been discussed. Nano-carrier drug delivery systems emerge as a promising approach and thus is expected to provide newer and advanced avenues in cancer therapeutics

Numerical Approximations Using Chebyshev Polynomial Expansions

We present numerical solutions for differential equations by expanding the unknown function in terms of Chebyshev polynomials and solving a system of linear equations directly for the values of the function at the extrema (or zeros) of the Chebyshev polynomial of order N (El-gendi's method). The solutions are exact at these points, apart from round-off computer errors and the convergence of other numerical methods used in connection to solving the linear system of equations. Applications to initial value problems in time-dependent quantum field theory, and second order boundary value problems in fluid dynamics are presented.Comment: minor wording changes, some typos have been eliminate

Structural Instability in Polyacene : A Projector Quantum Monte Carlo Study

We have studied polyacene within the Hubbard model to explore the effect of electron correlations on the Peierls' instability in a system marginally away from one-dimension. We employ the projector quantum Monte Carlo method to obtain ground state estimates of the energy and various correlation functions. We find strong similarities between polyacene and polyacetylene which can be rationalized from the real-space valence-bond arguments of Mazumdar and Dixit. Electron correlations tend to enhance the Peierls' instability in polyacene. This enhancement appears to attain a maximum at $U/t \sim 3.0$ and the maximum shifts to larger values when the alternation parameter is increased. The system shows no tendency to destroy the imposed bond-alternation pattern, as evidenced by the bond-bond correlations. The cis- distortion is seen to be favoured over the trans- distortion. The spin-spin correlations show that undistorted polyacene is susceptible to a SDW distortion for large interaction strength. The charge-charge correlations indicate the absence of a CDW distortion for the parameters studied.Comment: 13 pages, 10 figures available on reques