A sandpile model for proportionate growth

An interesting feature of growth in animals is that different parts of the body grow at approximately the same rate. This property is called proportionate growth. In this paper, we review our recent work on patterns formed by adding $N$ grains at a single site in the abelian sandpile model. These simple models show very intricate patterns, show proportionate growth, and sometimes having a striking resemblance to natural forms. We give several examples of such patterns. We discuss the special cases where the asymptotic pattern can be determined exactly. The effect of noise in the background or in the rules on the patterns is also discussed.Comment: 18 pages, 14 figures, to appear in a special issue of JSTAT dedicated to Statphys2

Statistical Physics of Vehicular Traffic and Some Related Systems

In the so-called "microscopic" models of vehicular traffic, attention is paid explicitly to each individual vehicle each of which is represented by a "particle"; the nature of the "interactions" among these particles is determined by the way the vehicles influence each others' movement. Therefore, vehicular traffic, modeled as a system of interacting "particles" driven far from equilibrium, offers the possibility to study various fundamental aspects of truly nonequilibrium systems which are of current interest in statistical physics. Analytical as well as numerical techniques of statistical physics are being used to study these models to understand rich variety of physical phenomena exhibited by vehicular traffic. Some of these phenomena, observed in vehicular traffic under different circumstances, include transitions from one dynamical phase to another, criticality and self-organized criticality, metastability and hysteresis, phase-segregation, etc. In this critical review, written from the perspective of statistical physics, we explain the guiding principles behind all the main theoretical approaches. But we present detailed discussions on the results obtained mainly from the so-called "particle-hopping" models, particularly emphasizing those which have been formulated in recent years using the language of cellular automata.Comment: 170 pages, Latex, figures include

Autonomous Robot Navigation through a Crowded and Dynamic Environment: Using A Novel form of Path Planning to Demonstrate Consideration towards Pedestrians and other Robots

This thesis presents a novel path planning algorithm for robotic crowd navigation through a pedestrian environment. The robot is designed to negotiate its way through the crowd using considerate movements. Unlike many other path planning algorithms, which assume cooperation with other pedestrians, this algorithm is completely independent and requires only observation. A considerate navigation strategy has been developed in this thesis, which utilises consideration as an directs an autonomous mobile robot. Using simple methods of predicting pedestrian movements, as well as simple relative distance and trajectory measurements between the robot and pedestrians, the robot can navigate through a crowd without causing disruption to pedestrian trajectories. Dynamic pedestrian positions are predicted using uncertainty ellipses. A novel Voronoi diagram-visibility graph hybrid roadmap is implemented so that the path planner can exploit any available gaps in between pedestrians, and plan considerate paths. The aim of the considerate path planner is to have the robot behave in specific ways when moving through the crowd. By predicting pedestrian trajectories, the robot can avoid interfering with them. Following preferences to move behind pedestrians, when cutting across their trajectories; to move in the same direction of the crowd when possible; and to slow down in crowded areas, will prevent any interference to individual pedestrians, as well as preventing an increase in congestion to the crowd as a whole. The effectiveness of the considerate navigation strategy is evaluated using simulated pedestrians, multiple mobile robots loaded with the path planning algorithm, as well as a real-life pedestrian dataset. The algorithm will highlight its ability to move with the aforementioned consideration towards each individual dynamic agent

Models in molecular evolution: the case of toyLIFE

Mención Internacional en el título de doctorThis thesis set out to contribute to the growing body of knowledge pertaining models of the genotype-phenotype map. In the process, we proposed and studied a new computational model, toyLIFE, and a new metaphor for molecular evolution —adaptive multiscapes. We also studied functional promiscuity and the evolutionary dynamics of shifting environments. The first result of this thesis was the definition of toyLIFE, a simplified model of cellular biology that incorporated toy versions of genes, proteins and regulation as well as metabolic laws. Molecules in toyLIFE interact between each other following the laws of the HP protein folding model, which endows toyLIFE with a simplified chemistry. From these laws, we saw how something reminiscent of cell-like behavior emerged, with complex regulatory and metabolic networks that grew in complexity as the genome increased. toyLIFE is, to our knowledge, the first multi-level model of the genotype- phenotype map, compared to previous models studied in the literature, such as RNA, proteins, gene regulatory networks (GRNs) or metabolic networks. All of these models either disregarded cellular context when assigning phenotype and function (RNA and proteins) or omitted genome dynamics, by defining their genotypes from high-level abstractions (GRNs and metabolic networks). toyLIFE shares the same features exhibited by all genotype-phenotype maps studied so far. There is strong degeneracy in the map, with many genotypes mapping into the same phenotype. This degeneracy translates into the existence of neutral networks, that span genotype space as soon as the genotype contains more than two genes. There is also a strong asymmetry in the size distribution of phenotypes: most phenotypes were rare, while a few of them covered most genotypes. Moreover, most common phenotypes are easily accessed from each other. We also studied the prevalence of functional promiscuity (the ability to perform more than one function) in computational models of the genotypephenotype map. In particular, we studied RNA, Boolean GRNs and toy- LIFE. Our results suggest that promiscuity is the norm, rather than the exception. These results prompt us to rethink our understanding of biology as a neatly functioning machine. One of the most interesting results of this thesis came from studying the evolutionary dynamics of shifting environments in populations showing functional promiscuity: our results show that there is an optimal frequency of change that minimizes the time to extinction of the population. Finally, we presented a new metaphor for molecular evolution: adaptive multiscapes. This framework intends to update the fitness landscape metaphor proposed by Sewall Wright in the 1930s. Adaptive multiscapes include many features that we have learned from computational studies of the genotype-phenotype map, and that have been discussed throughout the thesis. The existence of neutral networks, the asymmetry in phenotype sizes -and the concomitant asymmetry in phenotype accessibility- and the presence of functional promiscuity all alter the original fitness landscape picture.Programa Oficial de Doctorado en Ingeniería MatemáticaPresidente: Joshua Levy Payne.- Secretario: Saúl Arés García.- Vocal: Jacobo Aguirre Arauj

Overcoming conventional modeling limitations using image- driven lattice-boltzmann method simulations for biophysical applications

The challenges involved in modeling biological systems are significant and push the boundaries of conventional modeling. This is because biological systems are distinctly complex, and their emergent properties are results of the interplay of numerous components/processes. Unfortunately, conventional modeling approaches are often limited by their inability to capture all these complexities. By using in vivo data derived from biomedical imaging, image-based modeling is able to overcome this limitation. In this work, a combination of imaging data with the Lattice-Boltzmann Method for computational fluid dynamics (CFD) is applied to tissue engineering and thrombogenesis. Using this approach, some of the unanswered questions in both application areas are resolved. In the first application, numerical differences between two types of boundary conditions: “wall boundary condition” (WBC) and “periodic boundary condition” (PBC), which are commonly utilized for approximating shear stresses in tissue engineering scaffold simulations is investigated. Surface stresses in 3D scaffold reconstructions, obtained from high resolution microcomputed tomography images are calculated for both boundary condition types and compared with the actual whole scaffold values via image-based CFD simulations. It is found that, both boundary conditions follow the same spatial surface stress patterns as the whole scaffold simulations. However, they under-predict the absolute stress values approximately by a factor of two. Moreover, it is found that the error grows with higher scaffold porosity. Additionally, it is found that the PBC always resulted in a lower error than the WBC. In a second tissue engineering study, the dependence of culture time on the distribution and magnitude of fluid shear in tissue scaffolds cultured under flow perfusion is investigated. In the study, constructs are destructively evaluated with assays for cellularity and calcium deposition, imaged using µCT and reconstructed for CFD simulations. It is found that both the shear stress distributions within scaffolds consistently increase with culture time and correlate with increasing levels of mineralized tissues within the scaffold constructs as seen in calcium deposition data and µCT reconstructions. In the thrombogenesis application, detailed analysis of time lapse microscopy images showing yielding of thrombi in live mouse microvasculature is performed. Using these images, image-based CFD modeling is performed to calculate the fluid-induced shear stresses imposed on the thrombi’s surfaces by the surrounding blood flow. From the results, estimates of the yield stress (A critical parameter for quantifying the extent to which thrombi material can resist deformation and breakage) are obtained for different blood vessels. Further, it is shown that the yielding observed in thrombi occurs mostly in the outer shell region while the inner core remains intact. This suggests that the core material is different from the shell. To that end, we propose an alternative mechanism of thrombogenesis which could help explain this difference. Overall, the findings from this work reveal that image-based modeling is a versatile approach which can be applied to different biomedical application areas while overcoming the difficulties associated with conventional modeling

Dynamic and static charging processes of single molecules - A scanning probe study

This thesis describes the investigation of fundamental properties of molecules in the tunnelling junction using combined scanning tunneling (STM) and atomic force microscopy (AFM). In this work, five different experimental topics are addressed. A reduction of the single-particle level spacing of two frontier orbitals enables the manifestation of strong electron-correlation effects in single molecules. In this regime conduction exhibits a spatial signature fundamentally different from what a single particle picture would predict. Individual molecules at the edges of self-assembled islands temporarily change their charge state due to the presence of the electric field from a scanning-probe tip. Close to the threshold voltage for a charge state transition, periodic switching of the charge is directly driven by the cantilever motion in frequency-modulated AFM. A novel concept for the realization of molecular quantum cellular automata is demonstrated. The solution lies in the combination of the creation of perfectly aligned inactive cells by self-assembly as a first and their selective and controlled activation as a second step. A real space investigation of a singly charged molecules adsorbed on an ultrathin insulating film reveals a two-level system that can reversibly change between configurations, resembling the motion of a rocker switch. Selective intermolecular aryl-aryl coupling via dehydrogenative C-H activation occurs on the surface upon thermal annealing. A full atomistic description of the different reaction products based on an unambiguous discrimination between pyrazine and pyridine moieties is presented

Hierarchical multiscale modeling of materials: an application to microporous systems

Computer modeling techniques have now established as a standard method for the study of chemical and physical phenomena in complex systems. The origin of their success is twofold: from one side, the continuous increase in the computational power, along with the spread of parallel architectures, has made accessible to a wide audience the most accurate methodologies, while, on the other side, the refinement of the techniques themselves has improved the reliability of the results. Nevertheless, when dealing with multiscale systems it is not possible to effectively use just one single simulation technique. This problem is largely due to inherent limitations of the methods, and it depends only slightly on the finite nature of computing resources. The extension of space and time scales can be achieved through two different approaches: one consists in connecting different levels in the hierarchy by a coarse-graining of the information coming from highly detailed levels, and the other consists in overcoming the intrinsic limitations of the single techniques. In this thesis, the possibility of using both approaches for large scale simulations has been investigated. The methods here developed have been applied to the study of microporous systems, being particularly well suited for a multiscale approach. Nonetheless, such methods are completely general, and can be employed for the simulation of a wide class of materials without too much effort.</br