Discrete breathers in a two-dimensional Fermi-Pasta-Ulam lattice

Using asymptotic methods, we investigate whether discrete breathers are supported by a two-dimensional Fermi-Pasta-Ulam lattice. A scalar (one-component) two-dimensional Fermi-Pasta-Ulam lattice is shown to model the charge stored within an electrical transmission lattice. A third-order multiple-scale analysis in the semi-discrete limit fails, since at this order, the lattice equations reduce to the (2+1)-dimensional cubic nonlinear Schrödinger (NLS) equation which does not support stable soliton solutions for the breather envelope. We therefore extend the analysis to higher order and find a generalised $(2+1)$-dimensional NLS equation which incorporates higher order dispersive and nonlinear terms as perturbations. We find an ellipticity criterion for the wave numbers of the carrier wave. Numerical simulations suggest that both stationary and moving breathers are supported by the system. Calculations of the energy show the expected threshold behaviour whereby the energy of breathers does {\em not} go to zero with the amplitude; we find that the energy threshold is maximised by stationary breathers, and becomes arbitrarily small as the boundary of the domain of ellipticity is approached

Asymptotic analysis of combined breather-kink modes in a Fermi-Pasta-Ulam chain

We find approximations to travelling breather solutions of the one-dimensional Fermi-Pasta-Ulam (FPU) lattice. Both bright breather and dark breather solutions are found. We find that the existence of localised (bright) solutions depends upon the coefficients of cubic and quartic terms of the potential energy, generalising an earlier inequality derived by James [CR Acad Sci Paris 332, 581, (2001)]. We use the method of multiple scales to reduce the equations of motion for the lattice to a nonlinear Schr{\"o}dinger equation at leading order and hence construct an asymptotic form for the breather. We show that in the absence of a cubic potential energy term, the lattice supports combined breathing-kink waveforms. The amplitude of breathing-kinks can be arbitrarily small, as opposed to traditional monotone kinks, which have a nonzero minimum amplitude in such systems. We also present numerical simulations of the lattice, verifying the shape and velocity of the travelling waveforms, and confirming the long-lived nature of all such modes

Asymptotic analysis of combined breather-kink modes in a Fermi-Pasta-Ulam chain

We find approximations to travelling breather solutions of the one-dimensional Fermi-Pasta-Ulam (FPU) lattice. Both bright breather and dark breather solutions are found. We find that the existence of localised (bright) solutions depends upon the coefficients of cubic and quartic terms of the potential energy, generalising an earlier inequality derived by James [CR Acad Sci Paris 332, 581, (2001)]. We use the method of multiple scales to reduce the equations of motion for the lattice to a nonlinear Schr{\"o}dinger equation at leading order and hence construct an asymptotic form for the breather. We show that in the absence of a cubic potential energy term, the lattice supports combined breathing-kink waveforms. The amplitude of breathing-kinks can be arbitrarily small, as opposed to traditional monotone kinks, which have a nonzero minimum amplitude in such systems. We also present numerical simulations of the lattice, verifying the shape and velocity of the travelling waveforms, and confirming the long-lived nature of all such modes

A synchronous multimedia annotation system for secure collaboratories

In this paper, we describe the Vannotea system - an application designed to enable collaborating groups to discuss and annotate collections of high quality images, video, audio or 3D objects. The system has been designed specifically to capture and share scholarly discourse and annotations about multimedia research data by teams of trusted colleagues within a research or academic environment. As such, it provides: authenticated access to a web browser search interface for discovering and retrieving media objects; a media replay window that can incorporate a variety of embedded plug-ins to render different scientific media formats; an annotation authoring, editing, searching and browsing tool; and session logging and replay capabilities. Annotations are personal remarks, interpretations, questions or references that can be attached to whole files, segments or regions. Vannotea enables annotations to be attached either synchronously (using jabber message passing and audio/video conferencing) or asynchronously and stand-alone. The annotations are stored on an Annotea server, extended for multimedia content. Their access, retrieval and re-use is controlled via Shibboleth identity management and XACML access policies

Image-Based Quantification of Benzoporphyrin Derivative Uptake, Localization, and Photobleaching in 3D Tumor Models, for Optimization of PDT Parameters

Photodynamic therapy (PDT) is a light-based treatment modality in which wavelength specific activation of a photosensitizer (PS) generates cytotoxic response in the irradiated region. PDT response is critically dependent on several parameters including light dose, PS dose, uptake time, fluence rate, and the mode of light delivery. While the systematic optimization of these treatment parameters can be complex, it also provides multiple avenues for en- hancement of PDT efficacy under diverse treatment conditions, provided that a rational framework is established to quantify the impact of parameter selection upon treatment re- sponse. Here we present a theranostic technique, combining the inherent ability of the PS to serve simultaneously as a therapeutic and imaging agent, with the use of image-based treatment assessment in three dimensional (3D) in vitro tumor models, to comprise a platform to evaluate the impact of PDT parameters on treatment outcomes. We use this approach to visualize and quantify the uptake, localization, and photobleaching of the PS benzoporphyrin derivative monoacid ring-A (BPD) in a range of treatment conditions with varying uptake times as well as continuous and fractionated light delivery regimens in 3D cultures of AsPC-1 and PANC-1 cells. Informed by photobleaching patterns and correlation with cytotoxic re- sponse, asymmetric fractionated light delivery at 4 hours BPD uptake was found to be the most effective regimen assessed. Quantification of the spatial profile of cell killing within multicellular nodules revealed that these conditions also achieve the highest depth of cyto- toxicity along the radial axis of 3D nodules. The framework introduced here provides a means for systematic assessment of PDT treatment parameters in biologically relevant 3D tumor models with potential for broader application to other systems

Impact of Treatment Response Metrics on Photodynamic Therapy Planning and Outcomes in a Three-Dimensional Model of Ovarian Cancer

Common methods to characterize treatment efficacy based on morphological imaging may misrepresent outcomes and exclude effective therapies. Using a three-dimensional model of ovarian cancer, two functional treatment response metrics are used to evaluate photodynamic therapy (PDT) efficacy: total volume, calculated from viable and nonviable cells, and live volume, calculated from viable cells. The utility of these volume-based metrics is corroborated using independent reporters of photodynamic activity: viability, a common fluorescence-based ratiometric analysis, and photosensitizer photobleaching, which is characterized by a loss of fluorescence due in part to the production of reactive species during PDT. Live volume correlated with both photobleaching and viability, suggesting that it was a better reporter of PDT efficacy than total volume, which did not correlate with either metric. Based on these findings, live volume and viability are used to probe the susceptibilities of tumor populations to a range of PDT dose parameters administered using 0.25, 1, and 10 μM benzoporphyrin derivative (BPD). PDT with 0.25 μM BPD produces the most significant reduction in live volume and viability and mediates a substantial shift toward small nodules. Increasingly sophisticated bioengineered models may complement current treatment planning approaches and provide unique opportunities to critically evaluate key parameters including metrics of therapeutic response

Discrete breathers in a two-dimensional Fermi-Pasta-Ulam lattice

Using asymptotic methods, we investigate whether discretebreathers are supported by a two-dimensional Fermi-Pasta-Ulam lattice. A scalar (one-component) two-dimensionalFermi-Pasta-Ulam lattice is shown to model the charge storedwithin an electrical transmission lattice. A third-order multiple-scale analysis in the semi-discrete limit fails, since at this order, the lattice equations reduce to the (2+1)-dimensional cubic nonlinear Schrödinger (NLS) equation which does not support stable soliton solutions for the breather envelope. We therefore extendthe analysis to higher order and find a generalised$(2+1)$-dimensional NLS equation which incorporates higher order dispersive and nonlinear terms as perturbations. We find an ellipticity criterion for the wave numbers of the carrier wave. Numerical simulations suggest that both stationary and moving breathers are supported by the system. Calculations of the energy show the expected threshold behaviour whereby the energy of breathers does {\em not} go to zero with the amplitude; we findthat the energy threshold is maximised by stationary breathers, and becomes arbitrarily small as the boundary of the domain of ellipticity is approached

Discrete breathers in a two-dimensional hexagonal Fermi-Pasta-Ulam lattice

We consider a two-dimensional Fermi-Pasta-Ulam (FPU) latticewith hexagonal symmetry. Using asymptotic methods based onsmall amplitude ansatz, at third order we obtain a eduction to a cubic nonlinear Schr{\"o}dinger equation (NLS) for the breather envelope. However, this does not support stable soliton solutions, so we pursue a higher-order analysis yielding a generalised NLS, which includes known stabilising terms. We present numerical results which suggest that long-lived stationary and moving breathersare supported by the lattice. We find breather solutions which move in an arbitrary direction, an ellipticity criterion for the wavenumbers of the carrier wave, symptotic estimates for the breather energy,and a minimum threshold energy below which breathers cannot be found. This energy threshold is maximised for stationary breathers, and becomes vanishingly small near the boundary of the elliptic domain where breathers attain a maximum speed. Several of the results obtained are similar to those obtained for the square FPU lattice (Butt \& Wattis, {\em J Phys A}, {\bf 39}, 4955, (2006)), though we find that the square and hexagonal lattices exhibit different properties in regard to the generation of harmonics, and the isotropy of the generalised NLS equation

Oleyl Conjugated Histidine-Arginine Cell-Penetrating Peptides as Promising Agents for siRNA Delivery

Recent approvals of siRNA-based products motivated the scientific community to explore siRNA as a treatment option for several intractable ailments, especially cancer. The success of approved siRNA therapy requires a suitable and safer drug delivery agent. Herein, we report a series of oleyl conjugated histidine–arginine peptides as a promising nonviral siRNA delivery tool. The conjugated peptides were found to bind with the siRNA at N/P ratio ≥ 2 and demonstrated complete protection for the siRNA from early enzymatic degradation at N/P ratio ≥ 20. Oleyl-conjugated peptide -siRNA complexes were found to be noncytotoxic in breast cancer cells (MCF-7 and MDA-MB-231) and normal breast epithelial cells (MCF 10A) at N/P ratio of ~40. The oleyl-R3-(HR)4 and oleyl-R4-(HR)4 showed ~80-fold increased cellular uptake in MDA-MB-231 cells at N/P 40. Moreover, the conjugated peptides-siRNA complexes form nanocomplexes (~115 nm in size) and have an appropriate surface charge to interact with the cell membrane and cause cellular internalization. Furthermore, this study provides a proof-of-concept that oleyl-R5-(HR)4 can efficiently silence STAT-3 gene (~80% inhibition) in MDA-MB-231 cells with similar effectiveness to Lipofectamine. Further exploration of this approach holds a great promise in discovering a successful in vivo siRNA delivery agent with a favorable pharmacokinetic profile

Asymptotic analysis of combined breather-kink modes in a Fermi-Pasta-Ulam chain

We find approximations to travelling breather solutions of theone-dimensional Fermi-Pasta-Ulam (FPU) lattice. Both brightbreather and dark breather solutions are found. We find that theexistence of localised (bright) solutions depends upon thecoefficients of cubic and quartic terms of the potential energy,generalising an earlier inequality derived by James [CR Acad SciParis 332, 581, (2001)]. We use the method of multiple scales toreduce the equations of motion for the lattice to a nonlinearSchr{\"o}dinger equation at leading order and hence construct anasymptotic form for the breather. We show that in the absence ofa cubic potential energy term, the lattice supports combinedbreathing-kink waveforms. The amplitude of breathing-kinks can bearbitrarily small, as opposed to traditional monotone kinks, whichhave a nonzero minimum amplitude in such systems. We also presentnumerical simulations of the lattice, verifying the shape andvelocity of the travelling waveforms, and confirming thelong-lived nature of all such modes