Models of collective cell behaviour with crowding effects : comparing lattice-based and lattice-free approaches

Individual-based models describing the migration and proliferation of a population of cells frequently restrict the cells to a predefined lattice. An implicit assumption of this type of lattice based model is that a proliferative population will always eventually fill the lattice. Here we develop a new lattice-free individual-based model that incorporates cell-to-cell crowding effects. We also derive approximate mean-field descriptions for the lattice-free model in two special cases motivated by commonly used experimental setups. Lattice-free simulation results are compared to these mean-field descriptions and to a corresponding lattice-based model. Data from a proliferation experiment is used to estimate the parameters for the new model, including the cell proliferation rate, showing that the model fits the data well. An important aspect of the lattice-free model is that the confluent cell density is not predefined, as with lattice-based models, but an emergent model property. As a consequence of the more realistic, irregular configuration of cells in the lattice-free model, the population growth rate is much slower at high cell densities and the population cannot reach the same confluent density as an equivalent lattice-based model.

Lattice-free models of cell invasion : discrete simulations and travelling waves

Invasion waves of cells play an important role in development, disease and repair. Standard discrete models of such processes typically involve simulating cell motility, cell proliferation and cell-to-cell crowding effects in a lattice-based framework. The continuum-limit description is often given by a reaction–diffusion equation that is related to the Fisher–Kolmogorov equation. One of the limitations of a standard lattice-based approach is that real cells move and proliferate in continuous space and are not restricted to a predefined lattice structure. We present a lattice-free model of cell motility and proliferation, with cell-to-cell crowding effects, and we use the model to replicate invasion wave-type behaviour. The continuum-limit description of the discrete model is a reaction–diffusion equation with a proliferation term that is different from lattice-based models. Comparing lattice based and lattice-free simulations indicates that both models lead to invasion fronts that are similar at the leading edge, where the cell density is low. Conversely, the two models make different predictions in the high density region of the domain, well behind the leading edge. We analyse the continuum-limit description of the lattice based and lattice-free models to show that both give rise to invasion wave type solutions that move with the same speed but have very different shapes. We explore the significance of these differences by calibrating the parameters in the standard Fisher–Kolmogorov equation using data from the lattice-free model. We conclude that estimating parameters using this kind of standard procedure can produce misleading results.

Lattice-free descriptions of collective motion with crowding and adhesion

Cell-to-cell adhesion is an important aspect of malignant spreading that is often observed in images from the experimental cell biology literature. Since cell-to-cell adhesion plays an important role in controlling the movement of individual malignant cells, it is likely that cell-to-cell adhesion also influences the spatial spreading of populations of such cells. Therefore, it is important for us to develop biologically realistic simulation tools that can mimic the key features of such collective spreading processes to improve our understanding of how cell-to-cell adhesion influences the spreading of cell populations. Previous models of collective cell spreading with adhesion have used lattice-based random walk frameworks which may lead to unrealistic results, since the agents in the random walk simulations always move across an artificial underlying lattice structure. This is particularly problematic in high-density regions where it is clear that agents in the random walk align along the underlying lattice, whereas no such regular alignment is ever observed experimentally. To address these limitations, we present a lattice-free model of collective cell migration that explicitly incorporates crowding and adhesion. We derive a partial differential equation description of the discrete process and show that averaged simulation results compare very well with numerical solutions of the partial differential equation.

Interacting motile agents : taking a mean-field approach beyond monomers and nearest-neighbor steps

We consider a discrete agent-based model on a one-dimensional lattice, where each agent occupies L sites and attempts movements over a distance of d lattice sites. Agents obey a strict simple exclusion rule. A discrete-time master equation is derived using a mean-field approximation and careful probability arguments. In the continuum limit, nonlinear diffusion equations that describe the average agent occupancy are obtained. Averaged discrete simulation data are generated and shown to compare very well with the solution to the derived nonlinear diffusion equations. This framework allows us to approach a lattice-free result using all the advantages of lattice methods. Since different cell types have different shapes and speeds of movement, this work offers insight into population-level behavior of collective cellular motion.

Doping dependence of fluctuation diamagnetism in high T-c superconductors

Using a recently proposed Ginzburg-Landau-like lattice free energy functional due to Banerjee et al. (2011) we calculate the fluctuation diamagnetism of high -T-c superconductors as a function of doping, magnetic field and temperature. We analyse the pairing fluctuations above the superconducting transition temperature in the cuprates, ranging from the strong phase fluctuation dominated underdoped limit to the more conventional amplitude fluctuation dominated overdoped regime. We show that a model where the pairing scale increases and the superfluid density decreases with underdoping produces features of the observed magnetization in the pseudogap region, in good qualitative and reasonable quantitative agreement with the experimental data. In particular, we explicitly show that even when the pseudogap has a pairing origin the magnetization actually tracks the superconducting dome instead of the pseudogap temperature, as seen in experiment. We discuss the doping dependence of the `onset' temperature for fluctuation diamagnetism and comment on the role of vortex core -energy jn our model. (C) 2015 Elsevier Inc. All rights reserved.

Enhanced Mixed Integer Programming Techniques and Routing Problems

Mixed integer programming is up today one of the most widely used techniques for dealing with hard optimization problems. On the one side, many practical optimization problems arising from real-world applications (such as, e.g., scheduling, project planning, transportation, telecommunications, economics and finance, timetabling, etc) can be easily and effectively formulated as Mixed Integer linear Programs (MIPs). On the other hand, 50 and more years of intensive research has dramatically improved on the capability of the current generation of MIP solvers to tackle hard problems in practice. However, many questions are still open and not fully understood, and the mixed integer programming community is still more than active in trying to answer some of these questions. As a consequence, a huge number of papers are continuously developed and new intriguing questions arise every year. When dealing with MIPs, we have to distinguish between two different scenarios. The first one happens when we are asked to handle a general MIP and we cannot assume any special structure for the given problem. In this case, a Linear Programming (LP) relaxation and some integrality requirements are all we have for tackling the problem, and we are ``forced" to use some general purpose techniques. The second one happens when mixed integer programming is used to address a somehow structured problem. In this context, polyhedral analysis and other theoretical and practical considerations are typically exploited to devise some special purpose techniques. This thesis tries to give some insights in both the above mentioned situations. The first part of the work is focused on general purpose cutting planes, which are probably the key ingredient behind the success of the current generation of MIP solvers. Chapter 1 presents a quick overview of the main ingredients of a branch-and-cut algorithm, while Chapter 2 recalls some results from the literature in the context of disjunctive cuts and their connections with Gomory mixed integer cuts. Chapter 3 presents a theoretical and computational investigation of disjunctive cuts. In particular, we analyze the connections between different normalization conditions (i.e., conditions to truncate the cone associated with disjunctive cutting planes) and other crucial aspects as cut rank, cut density and cut strength. We give a theoretical characterization of weak rays of the disjunctive cone that lead to dominated cuts, and propose a practical method to possibly strengthen those cuts arising from such weak extremal solution. Further, we point out how redundant constraints can affect the quality of the generated disjunctive cuts, and discuss possible ways to cope with them. Finally, Chapter 4 presents some preliminary ideas in the context of multiple-row cuts. Very recently, a series of papers have brought the attention to the possibility of generating cuts using more than one row of the simplex tableau at a time. Several interesting theoretical results have been presented in this direction, often revisiting and recalling other important results discovered more than 40 years ago. However, is not clear at all how these results can be exploited in practice. As stated, the chapter is a still work-in-progress and simply presents a possible way for generating two-row cuts from the simplex tableau arising from lattice-free triangles and some preliminary computational results. The second part of the thesis is instead focused on the heuristic and exact exploitation of integer programming techniques for hard combinatorial optimization problems in the context of routing applications. Chapters 5 and 6 present an integer linear programming local search algorithm for Vehicle Routing Problems (VRPs). The overall procedure follows a general destroy-and-repair paradigm (i.e., the current solution is first randomly destroyed and then repaired in the attempt of finding a new improved solution) where a class of exponential neighborhoods are iteratively explored by heuristically solving an integer programming formulation through a general purpose MIP solver. Chapters 7 and 8 deal with exact branch-and-cut methods. Chapter 7 presents an extended formulation for the Traveling Salesman Problem with Time Windows (TSPTW), a generalization of the well known TSP where each node must be visited within a given time window. The polyhedral approaches proposed for this problem in the literature typically follow the one which has been proven to be extremely effective in the classical TSP context. Here we present an overall (quite) general idea which is based on a relaxed discretization of time windows. Such an idea leads to a stronger formulation and to stronger valid inequalities which are then separated within the classical branch-and-cut framework. Finally, Chapter 8 addresses the branch-and-cut in the context of Generalized Minimum Spanning Tree Problems (GMSTPs) (i.e., a class of NP-hard generalizations of the classical minimum spanning tree problem). In this chapter, we show how some basic ideas (and, in particular, the usage of general purpose cutting planes) can be useful to improve on branch-and-cut methods proposed in the literature.

Impact of Stone-Wales and lattice vacancy defects on the electro-thermal transport of the free standing structure of metallic ZGNR

We report the effect of topological as well as lattice vacancy defects on the electro-thermal transport properties of the metallic zigzag graphene nano ribbons at their ballistic limit. We employ the density function theory-Non equilibrium green's function combination to calculate the transmission details. We then present an elaborated study considering the variation in the electrical current and the heat current transport with the change in temperature as well as the voltage gradient across the nano ribbons. The comparative analysis shows, that in the case of topological defects, such as the Stone-Wales defect, the electrical current transport is minimum. Besides, for the voltage gradient of 0.5 Volt and the temperature gradient of 300 K, the heat current transport reduces by similar to 62 % and similar to 50% for the cases of Stones-Wales defect and lattice vacancy defect respectively, compared to that of the perfect one.

Flux line lattice structure and behavior in antiphase boundary free vicinal YBa2Cu3O7-delta thin films

Field angle dependent critical current, magneto-optical microscopy and high resolution electron microscopy studies have been performed on YBa2Cu3O7-delta thin films grown on miscut substrates. High resolution electron microscopy images show that the films studied exhibited clean epitaxial growth with a low density of antiphase boundaries and stacking faults. Any antiphase boundaries (APBs) formed near the film substrate interface rapidly healed rather than extending through the thickness of the film. Unlike vicinal films grown on annealed substrates, which contain a high density of antiphase boundaries, magneto-optical imaging showed no filamentary flux penetration in the films studied. The flux penetration is, however, asymmetric. This is associated with intrinsic pinning of flux strings by the tilted a-b planes and the dependence of the pinning force on the angle between the local field and the a-b planes. Field angle dependent critical current measurements exhibited the striking vortex channeling effect previously reported in vicinal films. By combining the results of three complementary characterization techniques it is shown that extended APB free films exhibit markedly different critical current behavior compared to APB rich films. This is attributed to the role of APB sites as strong pinning centers for Josephson string vortices between the a-b planes. (C) 2003 American Institute of Physics.

Study of surface free energy on a lattice-gas model applied to Liquid bridge

The pulmonary crackling and the formation of liquid bridges are problems that for centuries have been attracting the attention of scientists. In order to study these phenomena, it was developed a canonical cubic lattice-gas­ like model to explain the rupture of liquid bridges in lung airways [A. Alencar et al., 2006, PRE]. Here, we further develop this model and add entropy analysis to study thermodynamic properties, such as free energy and force. The simulations were performed using the Monte Carlo method with Metropolis algorithm. The exchange between gas and liquid particles were performed randomly according to the Kawasaki dynamics and weighted by the Boltzmann factor. Each particle, which can be solid (s), liquid (l) or gas (g), has 26 neighbors: 6 + 12 + 8, with distances 1, √2 and √3, respectively. The energy of a lattice's site m is calculated by the following expression: Em = ∑k=126 Ji(m)j(k) in witch (i, j) = g, l or s. Specifically, it was studied the surface free energy of the liquid bridge, trapped between two planes, when its height is changed. For that, was considered two methods. First, just the internal energy was calculated. Then was considered the entropy. It was fond no difference in the surface free energy between this two methods. We calculate the liquid bridge force between the two planes using the numerical surface free energy. This force is strong for small height, and decreases as the distance between the two planes, height, is increased. The liquid-gas system was also characterized studying the variation of internal energy and heat capacity with the temperature. For that, was performed simulation with the same proportion of liquid and gas particle, but different lattice size. The scale of the liquid-gas system was also studied, for low temperature, using different values to the interaction Jij.

Optimization of a label-free biosensor vertically characterized based on a periodic lattice of high aspect ratio SU-8 nano-pillars with a simplified 2D theoretical model

We have recently demonstrated a biosensor based on a lattice of SU8 pillars on a 1 μm SiO2/Si wafer by measuring vertically reflectivity as a function of wavelength. The biodetection has been proven with the combination of Bovine Serum Albumin (BSA) protein and its antibody (antiBSA). A BSA layer is attached to the pillars; the biorecognition of antiBSA involves a shift in the reflectivity curve, related with the concentration of antiBSA. A detection limit in the order of 2 ng/ml is achieved for a rhombic lattice of pillars with a lattice parameter (a) of 800 nm, a height (h) of 420 nm and a diameter(d) of 200 nm. These results correlate with calculations using 3D-finite difference time domain method. A 2D simplified model is proposed, consisting of a multilayer model where the pillars are turned into a 420 nm layer with an effective refractive index obtained by using Beam Propagation Method (BPM) algorithm. Results provided by this model are in good correlation with experimental data, reaching a reduction in time from one day to 15 minutes, giving a fast but accurate tool to optimize the design and maximizing sensitivity, and allows analyzing the influence of different variables (diameter, height and lattice parameter). Sensitivity is obtained for a variety of configurations, reaching a limit of detection under 1 ng/ml. Optimum design is not only chosen because of its sensitivity but also its feasibility, both from fabrication (limited by aspect ratio and proximity of the pillars) and fluidic point of view. (© 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Development of a Coupling Model for Fluid-Structure Interaction using the Mesh-free Finite Element Method and the Lattice Boltzmann Method

In the presented thesis work, the meshfree method with distance fields was coupled with the lattice Boltzmann method to obtain solutions of fluid-structure interaction problems. The thesis work involved development and implementation of numerical algorithms, data structure, and software. Numerical and computational properties of the coupling algorithm combining the meshfree method with distance fields and the lattice Boltzmann method were investigated. Convergence and accuracy of the methodology was validated by analytical solutions. The research was focused on fluid-structure interaction solutions in complex, mesh-resistant domains as both the lattice Boltzmann method and the meshfree method with distance fields are particularly adept in these situations. Furthermore, the fluid solution provided by the lattice Boltzmann method is massively scalable, allowing extensive use of cutting edge parallel computing resources to accelerate this phase of the solution process. The meshfree method with distance fields allows for exact satisfaction of boundary conditions making it possible to exactly capture the effects of the fluid field on the solid structure.

Lattice-based certificateless public-key encryption in the standard model

The notion of certificateless public-key encryption (CL-PKE) was introduced by Al-Riyami and Paterson in 2003 that avoids the drawbacks of both traditional PKI-based public-key encryption (i.e., establishing public-key infrastructure) and identity-based encryption (i.e., key escrow). So CL-PKE like identity-based encryption is certificate-free, and unlike identity-based encryption is key escrow-free. In this paper, we introduce simple and efficient CCA-secure CL-PKE based on (hierarchical) identity-based encryption. Our construction has both theoretical and practical interests. First, our generic transformation gives a new way of constructing CCA-secure CL-PKE. Second, instantiating our transformation using lattice-based primitives results in a more efficient CCA-secure CL-PKE than its counterpart introduced by Dent in 2008.