New doubly periodic waves of the (2+1)-dimensional double sine-Gordon equation

New exact solutions of the (2 + 1)-dimensional double sine-Gordon equation are studied by introducing the modified mapping relations between the cubic nonlinear Klein-Gordon system and double sine-Gordon equation. Two arbitrary functions are included into the Jacobi elliptic function solutions. New doubly periodic wave solutions are obtained and displayed graphically by proper selections of the arbitrary functions.

Differential activity of GSK-3 isoforms regulates NF-kappa B and TRAIL- or TNF alpha induced apoptosis in pancreatic cancer cells

While TRAIL is a promising anticancer agent due to its ability to selectively induce apoptosis in neoplastic cells, many tumors, including pancreatic ductal adenocarcinoma (PDA), display intrinsic resistance, highlighting the need for TRAIL-sensitizing agents. Here we report that TRAIL-induced apoptosis in PDA cell lines is enhanced by pharmacological inhibition of glycogen synthase kinase-3 (GSK-3) or by shRNA-mediated depletion of either GSK-3 alpha or GSK-3 beta. In contrast, depletion of GSK-3 beta, but not GSK-3 alpha, sensitized PDA cell lines to TNF alpha-induced cell death. Further experiments demonstrated that TNF alpha-stimulated I kappa B alpha phosphorylation and degradation as well as p65 nuclear translocation were normal in GSK-3 beta-deficient MEFs. Nonetheless, inhibition of GSK-3 beta function in MEFs or PDA cell lines impaired the expression of the NF-kappa B target genes Bcl-xL and cIAP2, but not I kappa B alpha. Significantly, the expression of Bcl-xL and cIAP2 could be reestablished by expression of GSK-3 beta targeted to the nucleus but not GSK-3 beta targeted to the cytoplasm, suggesting that GSK-3 beta regulates NF-kappa B function within the nucleus. Consistent with this notion, chromatin immunoprecipitation demonstrated that GSK-3 inhibition resulted in either decreased p65 binding to the promoter of BIR3, which encodes cIAP2, or increased p50 binding as well as recruitment of SIRT1 and HDAC3 to the promoter of BCL2L1, which encodes Bcl-xL. Importantly, depletion of Bcl-xL but not cIAP2, mimicked the sensitizing effect of GSK-3 inhibition on TRAIL-induced apoptosis, whereas Bcl-xL overexpression ameliorated the sensitization by GSK-3 inhibition. These results not only suggest that GSK-3 beta overexpression and nuclear localization contribute to TNF alpha and TRAIL resistance via anti-apoptotic NF-kappa B genes such as Bcl-xL, but also provide a rationale for further exploration of GSK-3 inhibitors combined with TRAIL for the treatment of PDA.

An allometric smoothing function to describe the relation between otolith and somatic growth over the lifespan of walleye pollock (Theragra chalcogramma)

We propose a new equation to describe the relation between otolith length (OL) and somatic length (fork length [FL]) of fish for the entire lifespan of the fish. The equation was developed by applying a mathematical smoothing method based on an allometric equation with a constant term for walleye pollock (Theragra chalcogramma) —a species that shows an extended longevity (>20 years). The most appropriate equation for defining the relation between OL and FL was a four-phase allometric smoothing function with three inflection points. The inflection points correspond to the timing of settlement of walleye pollock, changes in sexual maturity, and direction of otolith growth. Allometric smoothing functions describing the relation between short otolith radius and FL, long otolith radius and FL, and FL and body weight were also developed. The proposed allometric smoothing functions cover the entire lifespan of walleye pollock. We term these equations “allometric smoothing functions for otolith and somatic growth over the lifespan of walleye pollock.”

Distribution theory and fundamental solutions of differential operators

The objective of this dissertation is to study the theory of distributions and some of its applications. Certain concepts which we would include in the theory of distributions nowadays have been widely used in several fields of mathematics and physics. It was Dirac who first introduced the delta function as we know it, in an attempt to keep a convenient notation in his works in quantum mechanics. Their work contributed to open a new path in mathematics, as new objects, similar to functions but not of their same nature, were being used systematically. Distributions are believed to have been first formally introduced by the Soviet mathematician Sergei Sobolev and by Laurent Schwartz. The aim of this project is to show how distribution theory can be used to obtain what we call fundamental solutions of partial differential equations.

Posicionamento aproximado do estado final para sistemas térmicos descritos pela equação do calor.

Neste trabalho, será considerado um problema de controle ótimo quadrático para a equação do calor em domínios retangulares com condição de fronteira do tipo Dirichlet é nos quais, a função de controle (dependente apenas no tempo) constitui um termo de fonte. Uma caracterização da solução ótima é obtida na forma de uma equação linear em um espaço de funções reais definidas no intervalo de tempo considerado. Em seguida, utiliza-se uma sequência de projeções em subespaços de dimensão finita para obter aproximações para o controle ótimo, o cada uma das quais pode ser gerada por um sistema linear de dimensão finita. A sequência de soluções aproximadas assim obtidas converge para a solução ótima do problema original. Finalmente, são apresentados resultados numéricos para domínios espaciais de dimensão 1.

Differential Dynamic Microscopy: a High-Throughput Method for Characterizing the Motility of Microorganism

We present a fast, high-throughput method for characterizing the motility of microorganisms in 3D based on standard imaging microscopy. Instead of tracking individual cells, we analyse the spatio-temporal fluctuations of the intensity in the sample from time-lapse images and obtain the intermediate scattering function (ISF) of the system. We demonstrate our method on two different types of microorganisms: bacteria, both smooth swimming (run only) and wild type (run and tumble) Escherichia coli, and the bi-flagellate alga Chlamydomonas reinhardtii. We validate the methodology using computer simulations and particle tracking. From the ISF, we are able to extract (i) for E. coli: the swimming speed distribution, the fraction of motile cells and the diffusivity, and (ii) for C. reinhardtii: the swimming speed distribution, the amplitude and frequency of the oscillatory dynamics. In both cases, the motility parameters are averaged over \approx 10^4 cells and obtained in a few minutes.

Novel applications of BEM based Poisson level set approach

Accurate and efficient computation of the distance function d for a given domain is important for many areas of numerical modeling. Partial differential (e.g. HamiltonJacobi type) equation based distance function algorithms have desirable computational efficiency and accuracy. In this study, as an alternative, a Poisson equation based level set (distance function) is considered and solved using the meshless boundary element method (BEM). The application of this for shape topology analysis, including the medial axis for domain decomposition, geometric de-featuring and other aspects of numerical modeling is assessed. © 2011 Elsevier Ltd. All rights reserved.

Reconstruction of arbitrary biochemical reaction networks: A compressive sensing approach

Reconstruction of biochemical reaction networks (BRN) and genetic regulatory networks (GRN) in particular is a central topic in systems biology which raises crucial theoretical challenges in system identification. Nonlinear Ordinary Differential Equations (ODEs) that involve polynomial and rational functions are typically used to model biochemical reaction networks. Such nonlinear models make the problem of determining the connectivity of biochemical networks from time-series experimental data quite difficult. In this paper, we present a network reconstruction algorithm that can deal with ODE model descriptions containing polynomial and rational functions. Rather than identifying the parameters of linear or nonlinear ODEs characterised by pre-defined equation structures, our methodology allows us to determine the nonlinear ODEs structure together with their associated parameters. To solve the network reconstruction problem, we cast it as a compressive sensing (CS) problem and use sparse Bayesian learning (SBL) algorithms as a computationally efficient and robust way to obtain its solution. © 2012 IEEE.

The acoustic analogy in an annular duct with swirling mean flow

This paper is concerned with modelling the effects of swirling flow on turbomachinery noise. We develop an acoustic analogy to predict sound generation in a swirling and sheared base flow in an annular duct, including the presence of moving solid surfaces to account for blade rows. In so doing we have extended a number of classical earlier results, including Ffowcs Williams & Hawkings' equation in a medium at rest with moving surfaces, and Lilley's equation for a sheared but non-swirling jet. By rearranging the Navier-Stokes equations we find a single equation, in the form of a sixth-order differential operator acting on the fluctuating pressure field on the left-hand side and a series of volume and surface source terms on the right-hand side; the form of these source terms depends strongly on the presence of swirl and radial shear. The integral form of this equation is then derived, using the Green's function tailored to the base flow in the (rigid) duct. As is often the case in duct acoustics, it is then convenient to move into temporal, axial and azimuthal Fourier space, where the Green's function is computed numerically. This formulation can then be applied to a number of turbomachinery noise sources. For definiteness here we consider the noise produced downstream when a steady distortion flow is incident on the fan from upstream, and compare our results with those obtained using a simplistic but commonly used Doppler correction method. We show that in all but the simplest case the full inclusion of swirl within an acoustic analogy, as described in this paper, is required. © 2013 Cambridge University Press.

Identification of differential transcript profiles between mutual crossbred embryos of zebrafish (Danio rerio) and Chinese rare minnow (Gobiocypris rarus) by cDNA-AFLP

The crosstalk between naive nucleus and maternal factors deposited in egg cytoplasm before zygotic genome activation is crucial for early development. In this study, we utilized two laboratory fishes, zebrafish (Danio rerio) and Chinese rare minnow and Chinese rare minnow (Gobiocypris rarus), to obtain mutual crossbred embroys and examine the interaction between nucleus and egg cytoplasm from different species. Although these two types of crossbred embryos originated from common nuclei, various developmental capacities were gained due to different origins of the egg cytoplasm. Using cDNA amplified fragment length polymorphism (cDNA-AFLP), We Compared transcript profiles between the mutual crossbred embryos at two developmental stages (50%- and 90%-epiholy). Three thousand cDNA fragments were generated in four cDNA pools with 64 primer combinations. All differently displayed transcript-derived fragments (TDFs) were screened by (lot blot hybridization, and the selected sequences were further analyzed by semi-quantitative RT-PCR and quantitative real-time RT-PCR. Compared with ZR embryos, 12 genes were up-regulated and 12 were down-regulated in RZ embryos. The gene fragments were sequenced and subjected to BLASTN analysis. The sequences encoded various proteins which functioned at various levels of proliferation, growth, and development. One gene (ZR6), dramatically down-regulated in RZ embryos, was chosen for loss-of-function study; the knockdown of ZR6 gave rise to the phenotype resembling that of RZ embryos. (c) 2008 Elsevier Inc. All rights reserved.

A differential lyapunov framework for contraction analysis

Lyapunov's second theorem is an essential tool for stability analysis of differential equations. The paper provides an analog theorem for incremental stability analysis by lifting the Lyapunov function to the tangent bundle. The Lyapunov function endows the state-space with a Finsler structure. Incremental stability is inferred from infinitesimal contraction of the Finsler metrics through integration along solutions curves. © 2013 IEEE.

Unified form language: A domain-specific language for weak formulations of partial differential equations

We present the Unified Form Language (UFL), which is a domain-specific language for representing weak formulations of partial differential equations with a view to numerical approximation. Features of UFL include support for variational forms and functionals, automatic differentiation of forms and expressions, arbitrary function space hierarchies formultifield problems, general differential operators and flexible tensor algebra. With these features, UFL has been used to effortlessly express finite element methods for complex systems of partial differential equations in near-mathematical notation, resulting in compact, intuitive and readable programs. We present in this work the language and its construction. An implementation of UFL is freely available as an open-source software library. The library generates abstract syntax tree representations of variational problems, which are used by other software libraries to generate concrete low-level implementations. Some application examples are presented and libraries that support UFL are highlighted. © 2014 ACM.

Investigation of gain recovery for InAs/GaAs quantum dot semiconductor optical amplifiers by rate equation simulation

The gain recoveries in quantum dot semiconductor optical amplifiers (QD SOAs) are numerically studied by rate equation simulation. Similar to the optical pump-probe experiment, the injection of double 150 fs optical pulses is used to simulate the gain recovery of a weak continuous signal under different injection levels, inhomogeneous broadenings, detuning wavelengths, and pulse signal energies for the QD SOAs. The obtained gain recoveries are then fitted by a response function with multiple exponential terms to determine the response times. The gain recovery can be described by three exponential terms with the time constants, which can be explained as carrier relaxation from the excited state to the ground state, carrier captured by the excited state from the wetting layer, and the supply of the wetting layer carriers. The fitted lifetimes decrease with the increase of the injection currents under gain unsaturation, slightly decrease with the decrease of inhomogeneous broadening of QDs, and increase with the increase of detuning wavelength between continuous signal and pulse signal and the increase of the pulse energy.

Spectral properties of a double-quantum-dot structure: A causal Green's function approach

Spectral properties of a double quantum dot (QD) structure are studied by a causal Green's function (GF) approach. The double QD system is modeled by an Anderson-type Hamiltonian in which both the intra- and interdot Coulomb interactions are taken into account. The GF's are derived by an equation-of-motion method and the real-space renormalization-group technique. The numerical results show that the average occupation number of electrons in the QD exhibits staircase features and the local density of states depends appreciably on the electron occupation of the dot.