Statistical Signatures of Photon Localization

The realization that electron localization in disordered systems (Anderson localization) is ultimately a wave phenomenon has led to the suggestion that photons could be similarly localized by disorder. This conjecture attracted wide interest because the differences between photons and electrons - in their interactions, spin statistics, and methods of injection and detection - may open a new realm of optical and microwave phenomena, and allow a detailed study of the Anderson localization transition undisturbed by the Coulomb interaction. To date, claims of three-dimensional photon localization have been based on observations of the exponential decay of the electromagnetic wave as it propagates through the disordered medium. But these reports have come under close scrutiny because of the possibility that the decay observed may be due to residual absorption, and because absorption itself may suppress localization. Here we show that the extent of photon localization can be determined by a different approach - measurement of the relative size of fluctuations of certain transmission quantities. The variance of relative fluctuations accurately reflects the extent of localization, even in the presence of absorption. Using this approach, we demonstrate photon localization in both weakly and strongly scattering quasi-one-dimensional dielectric samples and in periodic metallic wire meshes containing metallic scatterers, while ruling it out in three-dimensional mixtures of aluminum spheres.Comment: 5 pages, including 4 figure

Down-Regulation of DNA Mismatch Repair Enhances Initiation and Growth of Neuroblastoma and Brain Tumour Multicellular Spheroids

Multicellular tumour spheroid (MCTS) cultures are excellent model systems for simulating the development and microenvironmental conditions of in vivo tumour growth. Many documented cell lines can generate differentiated MCTS when cultured in suspension or in a non-adhesive environment. While physiological and biochemical properties of MCTS have been extensively characterized, insight into the events and conditions responsible for initiation of these structures is lacking. MCTS are formed by only a small subpopulation of cells during surface-associated growth but the processes responsible for this differentiation are poorly understood and have not been previously studied experimentally. Analysis of gene expression within spheroids has provided clues but to date it is not known if the observed differences are a cause or consequence of MCTS growth. One mechanism linked to tumourigenesis in a number of cancers is genetic instability arising from impaired DNA mismatch repair (MMR). This study aimed to determine the role of MMR in MCTS initiation and development. Using surface-associated N2a and CHLA-02-ATRT culture systems we have investigated the impact of impaired MMR on MCTS growth. Analysis of the DNA MMR genes MLH1 and PMS2 revealed both to be significantly down-regulated at the mRNA level compared with non-spheroid-forming cells. By using small interfering RNA (siRNA) against these genes we show that silencing of MLH1 and PMS2 enhances both MCTS initiation and subsequent expansion. This effect was prolonged over several passages following siRNA transfection. Down-regulation of DNA MMR can contribute to tumour initiation and progression in N2a and CHLA-02-ATRT MCTS models. Studies of surface-associated MCTS differentiation may have broader applications in studying events in the initiation of cancer foci

On the simple random-walk models of ion-channel gate dynamics reflecting long-term memory

Several approaches to ion-channel gating modelling have been proposed. Although many models describe the dwell-time distributions correctly, they are incapable of predicting and explaining the long-term correlations between the lengths of adjacent openings and closings of a channel. In this paper we propose two simple random-walk models of the gating dynamics of voltage and Ca2+-activated potassium channels which qualitatively reproduce the dwell-time distributions, and describe the experimentally observed long-term memory quite well. Biological interpretation of both models is presented. In particular, the origin of the correlations is associated with fluctuations of channel mass density. The long-term memory effect, as measured by Hurst R/S analysis of experimental single-channel patch-clamp recordings, is close to the behaviour predicted by our models. The flexibility of the models enables their use as templates for other types of ion channel

Korteweg-de Vries solitons under additive stochastic perturbations

The evolution of solitonic solutions of the Korteweg-de Vries equation subject to additive noise is investigated using numerical techniques. Various types of additive white Gaussian noise are considered. The averaged solution amplitudes exhibit in all cases algebraic decay, verifying Wadati's universality conjecture. If the noise is time dependent, or position and time dependent, algebraic decay is obtained for intermediate times too. These intermediate-time results agree well with the outcome of an experiment on ion-acoustic soliton propagation in a noisy plasma. The distribution of soliton first passage times in a noisy medium is also discussed. [S1063-651X(98)10509-3]

Korteweg-de Vries solitons under additive stochastic perturbations

The evolution of solitonic solutions of the Korteweg-de Vries equation subject to additive noise is investigated using numerical techniques. Various types of additive white Gaussian noise are considered. The averaged solution amplitudes exhibit in all cases algebraic decay, verifying Wadati's universality conjecture. If the noise is time dependent, or position and time dependent, algebraic decay is obtained for intermediate times too. These intermediate-time results agree well with the outcome of an experiment on ion-acoustic soliton propagation in a noisy plasma. The distribution of soliton first passage times in a noisy medium is also discussed. [S1063-651X(98)10509-3]

Diffusion with evolving sources and competing sinks: Development of angiogenesis

Tumors ensure their long-time growth by emitting molecular messengers that induce cellular modifications in neighboring capillaries. These modifications are conducive to the enlargement of the vascular system feeding the tumor. This phenomenon, termed angiogenesis, is controlled by the diffusion and competitive trapping of nutrients and molecular messengers by several cell species. The number, location, and properties of these traps change continuously. The angiogenic process also implies that nutrient sources are time dependent. Starting from assumptions at the cellular level, we formulate a mathematical model that predicts the evolution of angiogenesis and the increase in the blood flow to the tumor. The model also predicts the emergence of directed growth and the possibility of therapeutical synergy. Simulations permit a careful analysis of the influence of the main parameters

Competition effects in the dynamics of tumor cords

A general feature of cancer growth is the cellular competition for available nutrients. This is also the case for tumor cords, neoplasms forming cylindrical structures around blood vessels. Experimental data show that, in their avascular phase, cords grow up to a limit radius of about 100 mum, reaching a quasi - steady-state characterized by a necrotized area separating the tumor from the surrounding healthy tissue. Here we use a set of rules to formulate a model that describes how the dynamics of cord growth is controlled by the competition of tumor cells among themselves and with healthy cells for the acquisition of essential nutrients. The model takes into account the mechanical effects resulting from the interaction between the multiplying cancer cells and the surrounding tissue. We explore the influence of the relevant parameters on the tumor growth and on its final state. The model is also applied to investigate cord deformation in a region containing multiple nutrient sources and to predict the further complex growth of the tumor

A model for diffusion and competition in cancer growth and metastasis

A master equation formalism is used to model the growth and metastasis of a tumor as a function of the diffusion and absorption of a nutrient. Healthy and cancerous (C-) cells compete to bind the nutrient, which is allowed to diffuse starting from a prescribed region. Two thresholds are defined for the quantity of nutrient bound by the C-cells. If this quantity falls below the lower threshold, the cell dies, while if it increases above the upper threshold, the cell divides according to a predefined stochastic mechanism. C-cells migrate when they record a low concentration of free nutrient in the local environment. The model is formulated in terms of a coupled system of equations for the cell populations and the free and bound nutrient. This system can be solved by using the Local Interaction Simulation Approach (LISA), a numerical procedure that permits an efficient and detailed solution and is easily adaptable to parallel processing. With suitable parameter variation, the model can describe multiple tumor configurations, ranging from the classical spheroid with a necrotic core favored by mathematicians to very anisotropic shapes with inhomogeneous concentrations of the various populations. This is important because the nature of the anisotropy may be crucial in determining whether and how the cancer metastasizes. The effects of stochasticity and the presence of additional nutrients or inhibitors can be easily incorporated