Topological Heterogeneity Research Articles

Simulating contact angle hysteresis using pseudo-line tensions

Abstract

A protocol of field-based phenotyping procedure for no-till wheat root system architecture based on data-driven model-assist

Field-based phenotyping (FBP) of crop root system architecture (RSA) provides a way to quantify the root growth and distribution in field with a smaller scale. Studies on a better understanding of the interrelations between field crop root physiological traits, root developmental phases and environmental changes are hindered due to deficiency of in situ root system architecture testing and quantitative methods for field crop. The present study aimed to propose a protocol for field-based wheat root system architecture with technical details of key operational procedures. Phenotyping of RSA traits from root spatial coordinate data acquisition and visualization software presented scaled illustrations of wheat RSA dynamics and root developmental phases which also revealed the root topological heterogeneities, either within a plant or among individuals. Percentage of horizontal and vertical soil coverage by root showed that root foraging capability along soil depth was better than within the horizontal dimension. In brief, our data indicated that FBP of wheat RSA could be achieved using the protocol of data-driven model-assisted phenotyping procedure. The proposed protocol was demonstrated useful for FBP of RSAs. It was proved effective to illustrate the topological structures of the wheat root system and to quantify RSA-derived parameters, this could be a useful tool for characterizing and analyzing the structural distortion, heterogeneous distribution and the soil space exploration characteristics of wheat root.

Topological characteristics of metro networks based on transfer constraint

Based on graph theory, this paper presents a topological heterogeneity and vulnerability analysis of metro networks where transfer constraint is taken into account. The statistical measurements based on minimal transfer times are defined, such as betweenness, the shortest path and the average transfer times. Based on above, on the one hand, heterogeneity of network is analyzed by adopting entropy theory; on the other hand, travel efficiency and connectivity based on effective paths are proposed to measure the topological vulnerability of metro network. The feasibility and rationality of the methods described above are verified through the Beijing metro network. The results show that the topological analysis neglecting transfer constraint would underestimate the heterogeneity and vulnerability of the metro network: the topological heterogeneity and vulnerability of Beijing metro network with considering transfer constraint are smaller than without considering transfer constraint; in the case of considering transfer constraint, with the scale expansion of network, travel efficiency and convenience increase, and topological heterogeneity and vulnerability of network decrease, but the connectivity of metro network is more vulnerable to node-based attack.

The perils of intralocus recombination for inferences of molecular convergence.

Accurate inferences of convergence require that the appropriate tree topology be used. If there is a mismatch between the tree a trait has evolved along and the tree used for analysis, then false inferences of convergence ('hemiplasy') can occur. To avoid problems of hemiplasy when there are high levels of gene tree discordance with the species tree, researchers have begun to construct tree topologies from individual loci. However, due to intralocus recombination, even locus-specific trees may contain multiple topologies within them. This implies that the use of individual tree topologies discordant with the species tree can still lead to incorrect inferences about molecular convergence. Here, we examine the frequency with which single exons and single protein-coding genes contain multiple underlying tree topologies, in primates and Drosophila, and quantify the effects of hemiplasy when using trees inferred from individual loci. In both clades, we find that there are most often multiple diagnosable topologies within single exons and whole genes, with 91% of Drosophila protein-coding genes containing multiple topologies. Because of this underlying topological heterogeneity, even using trees inferred from individual protein-coding genes results in 25% and 38% of substitutions falsely labelled as convergent in primates and Drosophila, respectively. While constructing local trees can reduce the problem of hemiplasy, our results suggest that it will be difficult to completely avoid false inferences of convergence. We conclude by suggesting several ways forward in the analysis of convergent evolution, for both molecular and morphological characters. This article is part of the theme issue 'Convergent evolution in the genomics era: new insights and directions'.

Effects of correlated morphological and topological heterogeneity of pore network on effective transport and reaction parameters

The effective diffusivity and the effective Thiele modulus of reactive porous matrices are determined by using a hybrid discrete and continuum model. The model describes static heterogeneity with weak noise on both morphology and topology of the matrix. Variations in diffusivity with respect to pore size (radius and length) and network connectivity up to second order are analyzed to assess the effect of stochastic media on catalytic reaction and transition of a single species. The porous medium is simulated by several building blocks (BB) which are regular in topology and morphology. A methodology is presented to construct a BB such that it fits the true matrix. Permutation of several regular pore networks in series constructs the porous media. Local mass balances over each BB yields model equations for reaction and transport in the matrix. Correlated random walk theory is used in each BB in order to relate the diffusivity to the coordination number.The Gaussian correlation function is assumed to model the autocorrelation of independent variables which are used to characterize the correlated porous media. The contribution of the fluctuating parameters in the mass conservation of the matrix yields a new closure equation in which ensemble average concentration of the reactant depends on different cross-correlations. The model is stable as long as the Thiele modulus at the correlation length scale is small. It predicts that geometrical heterogeneities lead to correction in effective diffusivity while the reaction rate is unaffected due to small Thiele modulus at correlation length scale. The model is verified by assessing the Thiele modulus of a pore network under Knudsen regime during a first order catalytic reaction; a good agreement was found especially for moderate Thiele modulus of correlated network. However, it fails to simulate random networks. Our systematic study revealed that the pore radius statistics impact significantly the diffusivity and the Thiele modulus while the topological parameters are important in weakly connected networks. The model predictions show that the diffusion constant decreases sharply as pore radius variance increases but increases smoothly with Thiele modulus.

Impact of perception models on friendship paradox and opinion formation

Topological heterogeneities of social networks have a strong impact on the individuals embedded in those networks. One of the interesting phenomena driven by such heterogeneities is the friendship paradox (FP), stating that the mean degree of one's neighbors is larger than the degree of oneself. Alternatively, one can use the median degree of neighbors as well as the fraction of neighbors having a higher degree than oneself. Each of these reflects on how people perceive their neighborhoods, i.e., their perception models, hence how they feel peer pressure. In our paper, we study the impact of perception models on the FP by comparing three versions of the perception model in networks generated with a given degree distribution and a tunable degree-degree correlation or assortativity. The increasing assortativity is expected to decrease network-level peer pressure, while we find a nontrivial behavior only for the mean-based perception model. By simulating opinion formation, in which the opinion adoption probability of an individual is given as a function of individual peer pressure, we find that it takes the longest time to reach consensus when individuals adopt the median-based perception model compared to other versions. Our findings suggest that one needs to consider the proper perception model for better modeling human behaviors and social dynamics.

Structural and temporal heterogeneities on networks

A heterogeneous continuous time random walk is an analytical formalism for studying and modeling diffusion processes in heterogeneous structures on microscopic and macroscopic scales. In this paper we study both analytically and numerically the effects of structural and temporal heterogeneities onto the diffusive dynamics on different types of networks. For this purpose we investigate how the distribution of the first passage time is affected by the global topological network properties and heterogeneities in the distributions of the travel times. In particular, we analyze transport properties of random networks and define network measures based on the first-passage characteristics. The heterogeneous continuous time random walk framework, presented in the paper, has potential applications in biology, social and urban science, search of optimal transport properties, analysis of the effects of heterogeneities or bursts in transportation networks.

Tuning Correlative Heterogeneity and Related Properties in Ni-Nb-Tm (Tm=Zr, Y, Gd) Metallic Glasses

Herein, we systematically investigated how to tailor correlative heterogeneity and related properties in Ni-Nb-(Zr, Y, Gd) metallic glasses (MGs). The Ni60Nb40-xZrx MGs (x=0-20 at.%) with Nb-Zr atomic pair (〖∆H〗mix=+4 kJ/mol) exhibited correlative atomic scale chemical and topological heterogeneities upon Zr addition, which can be evaluated by EXAFS analysis. Interestingly, a statistical analysis of strain burst sizes along with in situ bending test showed that the easier nucleation of chaotic shear bands is promoted with the aid of stress localization induced by the heterogeneities. The bulk specimens (d=1 mm) for 8 and 10 at.% of Zr with increased glass-forming ability (GFA) exhibited enhanced plasticity without the reduction of fracture strength, implying cooling rate effect on heterogeneity-induced plasticity. Contrastively, the Ni60Nb40-y(Y, Gd)y MGs with Nb-Y or Nb-Gd atomic pair (〖∆H〗mix=+30 kJ/mol) showed hierarchically correlative nanoscale phase separated microstructures, which can be carefully interpreted by construction of metastable miscibility gap. The microstructures rely on four different variables (the composition, the symmetry of a miscibility gap, the critical temperature and the GFA of each phase) and provide a weak interface resulting in extreme brittleness as well as drastically decreased GFA. We believe that the results of this study would provide an effective guideline for tuning correlative heterogeneity and related properties in MGs via manipulation of enthalpy relationship and cooling rate.

Multispecies coalescent analysis confirms standing phylogenetic instability in Hexapoda.

The multispecies coalescent (MSC) has been increasingly used in phylogenomic analyses due to the accommodation of gene tree topological heterogeneity by taking into account population-level processes, such as incomplete lineage sorting. In this sense, the phylogeny of insect species, which are characterized by their large effective population sizes, is suitable for a coalescent-based analysis. Furthermore, studies so far recovered short internal branches at early divergences of the insect tree of life, indicating fast evolutionary radiations that increase the probability of incomplete lineage sorting in deep time. Here, we investigated the performance of the MSC for a phylogenomic data set of hexapods compiled by Misof etal. (2014, Science 346:763). Our analysis recovered the monophyly of most insect orders, and major phylogenetic relationships were in agreement with current insect systematics. We identified, however, some evolutionary associations that were consistently problematic. Most noticeable, Hexapod monophyly was disrupted by the sister group relationship between the remiped crustacean and Insecta. Additionally, the interordinal relationships within Polyneoptera and Neuropteroidea were found to be phylogenetically unstable. We show that these controversial phylogenetic arrangements were also poorly supported by previous analyses, and therefore, we evaluated their robustness to stochastic errors from sampling sites and terminals, confirming standing problems in hexapod phylogeny in the genomics age.

(Keynote) Preparation and Structural Investigation of Linear and 4-Arm Poly(ethylene glycol) (2 x 4 PEG) Gels

Gel is a 3D polymer network holding solvent molecules inside its network. There are two major heterogeneities in gels. One is spatial heterogeneity, and the other is topological heterogeneity. The spatial heterogeneity is introduced by random cross-linking, so the network structure has both sparse and dense region. The spatial heterogeneity is observed as excess scattering in a light, X-ray, or neutron scattering experiment. On the other hand, the topological heterogeneity is related to the presence of dangling chains, loop structure, and entanglements inside the network, and is investigated by viscoelasticity and/or swelling experiments, or by other means, such as NMR. Because of these inhomogeneities, gels have seldom been applied to structural materials because of their poor mechanical properties. Hence, realization of ideal model networks free from heterogeneities has been strongly anticipated. Sakai et al. succeeded in fabrication of near ideal polymer networks called “Tetra-PEG gel”.[1] A Tetra-PEG gel is synthesized from two complementary end-functionalized poly(ethylene glycol) (PEG) which is able to react each other. It is pointed out that the Tetra-PEG gel has insignificant small spatial homogeneity and negligible topological heterogeneity, respectively by small angle scattering[2] and mechanical test.[3] Recently, we extended the above-mentioned method and succeeded in fabrication of multiple model network gels consisting of alternating tetra-functional poly(ethylene glycol)s (PEGs) and bis-functional linear PEGs (2 x 4 gels), where the molecular weight of linear PEG was varied from 200 Da to 20000 Da while that of tetra-functional PEG component was fixed to be 20000 Da.[4] The same level of homogeneities in the network structure as those of Tetra-PEG gels has been confirmed by dynamic light scattering (DLS) and dynamic viscoelastic measurements. Advantages of 2 x 4 gels are that one can independently tune the cross-link density (by the concentration of tetra-functional PEG) and the total polymer concentration. By using a series of 2 x 4 gels, we examined the concentration/cross-link density dependence of the correlation blob, the elastic blob, and geometric blob. We will discuss the scaling rules of these blob sizes as a function of polymer/cross-linker concentrations. Sakai, T. et al, Macromolecules 2008, 41, 5379.Matsunaga, T. et al, Macromolecules 2009, 42, 1344.Akagi, Y. et al, Macromolecules 2010, 43, 488.Tsuji, Y. et al., Gels 2018, 4, 50.

Quantitative Evaluation of Homogeneous Hydrogel Surface Wettability

A hydrogel is constructed of polymers that are crosslinked to form a three-dimensional network structure with water absorbed within. When using hydrogel as a biomaterial, wettability is one of the important physical properties as it largely affects how protein and cells can adhere on its surface. In previous studies aiming to evaluate the wettability of hydrogel, the affect was evaluated by changing the composition and side chain of the polymer chain constituting the network structure for existing hydrogels such as agarose and gelatin. However, the existing network structure of hydrogel has spatial heterogeneity and topological heterogeneity, and therefore it has been said to be difficult to independently determine which parameter of the network structure was truly affecting wettability. In this research, in order to solve this problem, we aimed to independently and quantitatively evaluate the effect of each parameter on wettability by using the Tetra-PEG gel.Tetra-PEG gel is a type of gel that is composed of two symmetrical tetra-branched structure of Tetra-amine-terminated PEG (Tetra-PEG-NH2) and Tetra-OSu-terminated PEG (Tetra-PEG-OSu). Gelation is done simply by mixing equal amounts of these polymer solutions. As our first attempt, we controlled the polymer volume fraction of the hydrogel and the molecular weight between the crosslinking points by adjusting the concentration of the polymer solution and the molecular weight of the polymer, respectively. To evaluate the effect of charged groups, p-tuned Tetra-PEG gel having ion pairs of positive and negative charged groups was prepared. On the other hand, r-tuned Tetra - PEG gel was prepared to evaluate the effect of the presence of ionic pairs on wettability. Positive or negative charged groups were introduced into the system by changing the mixing ratio of Tetra-PEG-NH2 and Tetra-PEG-Osu, and by so causing either polymer to excessively exist within the hydrogel.Wettability was evaluated through static contact angle measurement. 2 uL of water droplets were dropped onto the surface of the hydrogel, and the contact angle immediately after the dropping was measured. The contact angle measurement results for 5k, 10k, 20k, and 40k Tetra-PEG gel are shown in Fig. 1. For 5k Tetra - PEG gel, contact angle showed values less than 30 degrees, and contact angle showed a decrease with increase in volume fraction. However, contact angle for 5k polymer suddenlyd increase at volume fraction of 0.11.To give a logical and consistent explanation to this result, we introduced the idea of mobility of the polymer chains into the discussion of how the wettability of the hydrogel was determined. When the polymer molecular weight is large, the polymer chain is largely movable, so the PEG chain is bound in the bulk due to the intermolecular force with the water molecules in the gel . As a result, the surface exhibited a hydrophobic property. On the other hand, when the polymer molecular weight is small like 5k Tetra-PEG gel, it is considered that the surface was kept relatively hydrophilic because the polymer chain was bound near the surface and pulled the droplet inwards. Furthermore, in the region of low polymer molecular weight such as 5k Tetra-PEG gel, it is considered that if the volume fraction increases, the polymer chain becomes difficult to move and the hydrophilicity also increases. Fig. 2 shows the results of contact angle measurement when the charged group concentration was changed. At polymer volume fractions 0.066, 0.081, and 0.096, the contact angle decreased with an increase in the charged group concentration, but decrease in contact angle could not be confirmed at polymer volume fraction of 0.50. In addition, it was confirmed from Fig. 3 that the contact angle of r-tuned Tetra-PEG gel was lower than that of p-tuned Tetra-PEG gel.These results are thought to be because the charged group acted as a hydrophilic group for water molecules which are polar molecules. Wettability did not decrease with p-tuned Tetra-PEG gel with a volume fraction of 0.050, because there were too few charged groups (5 mol/m3) per volume and was not sufficient to visibly affect the surface characteristics. In addition, since the p-tuned Tetra-PEG gel in which the ion pair exists exhibits lower wettability than the r-tuned Tetra-PEG gel, the affinity between the polymer and water decreases due to the presence of the ion pair. As a conclusion, it was revealed that polymer molecular weight greatly affects the mobility of the polymer chain and the wettability, and the wettability is increased by the introduction of the charged group, and when the ion pair is present, wettability decreases. Figure 1

So many genes, so little time: A practical approach to divergence-time estimation in the genomic era.

Phylogenomic datasets have been successfully used to address questions involving evolutionary relationships, patterns of genome structure, signatures of selection, and gene and genome duplications. However, despite the recent explosion in genomic and transcriptomic data, the utility of these data sources for efficient divergence-time inference remains unexamined. Phylogenomic datasets pose two distinct problems for divergence-time estimation: (i) the volume of data makes inference of the entire dataset intractable, and (ii) the extent of underlying topological and rate heterogeneity across genes makes model mis-specification a real concern. “Gene shopping”, wherein a phylogenomic dataset is winnowed to a set of genes with desirable properties, represents an alternative approach that holds promise in alleviating these issues. We implemented an approach for phylogenomic datasets (available in SortaDate) that filters genes by three criteria: (i) clock-likeness, (ii) reasonable tree length (i.e., discernible information content), and (iii) least topological conflict with a focal species tree (presumed to have already been inferred). Such a winnowing procedure ensures that errors associated with model (both clock and topology) mis-specification are minimized, therefore reducing error in divergence-time estimation. We demonstrated the efficacy of this approach through simulation and applied it to published animal (Aves, Diplopoda, and Hymenoptera) and plant (carnivorous Caryophyllales, broad Caryophyllales, and Vitales) phylogenomic datasets. By quantifying rate heterogeneity across both genes and lineages we found that every empirical dataset examined included genes with clock-like, or nearly clock-like, behavior. Moreover, many datasets had genes that were clock-like, exhibited reasonable evolutionary rates, and were mostly compatible with the species tree. We identified overlap in age estimates when analyzing these filtered genes under strict clock and uncorrelated lognormal (UCLN) models. However, this overlap was often due to imprecise estimates from the UCLN model. We find that “gene shopping” can be an efficient approach to divergence-time inference for phylogenomic datasets that may otherwise be characterized by extensive gene tree heterogeneity.

Dispersion and Mixing in Three‐Dimensional Discrete Fracture Networks: Nonlinear Interplay Between Structural and Hydraulic Heterogeneity

AbstractWe investigate the relative impact of topological, geometric, and hydraulic heterogeneity on transport processes in three‐dimensional fracture networks. Focusing on the two largest scales of heterogeneity in these systems, individual fracture and network structure, we compare transport through analogous structured and disordered three‐dimensional fracture networks with varying degrees of hydraulic heterogeneity. For the moderate levels of hydraulic heterogeneity we consider, network structure is the dominant control of transport through the networks. Less dispersion, both longitudinal and transverse, is observed in structured networks than in disordered networks, due in part to the higher connectivity in the former, independent of the level of hydraulic heterogeneity. However, increases in dispersion with higher hydraulic heterogeneity are larger in the disordered networks than in the structured networks, thereby indicating that the interplay between structural and hydraulic heterogeneity is nonlinear. We propose a measure of disorder in fracture networks by computing the Shannon entropy of the spectrum of the Laplacian of a weighted graph representation of the networks, where the weights are given by a combination of topological, geometric, and hydraulic properties. This metric, as a relative indicator by comparison between two networks, is a first approach to the dispersion potential and “mixing capacity” of a fracture network.

Crowd motion segmentation and behavior recognition fusing streak flow and collectiveness

Crowd motion segmentation and crowd behavior recognition are two hot issues in computer vision. A number of methods have been proposed to tackle these two problems. Among the methods, flow dynamics is utilized to model the crowd motion, with little consideration of collective property. Moreover, the traditional crowd behavior recognition methods treat the local feature and dynamic feature separately and overlook the interconnection of topological and dynamical heterogeneity in complex crowd processes. A crowd motion segmentation method and a crowd behavior recognition method are proposed based on streak flow and crowd collectiveness. The streak flow is adopted to reveal the dynamical property of crowd motion, and the collectiveness is incorporated to reveal the structure property. Experimental results show that the proposed methods improve the crowd motion segmentation accuracy and the crowd recognition rates compared with the state-of-the-art methods.

Targeting Ligand Specificity Linked to Tumor Tissue Topological Heterogeneity via Single-Cell Micro-Pharmacological Modeling

Targeted therapy has held promise to be a successful anticancer treatment due to its specificity towards tumor cells that express the target receptors. However, not all targeting drugs used in the clinic are equally effective in tumor eradication. To examine which biochemical and biophysical properties of targeted agents are pivotal for their effective distribution inside the tumor and their efficient cellular uptake, we combine mathematical micro-pharmacological modeling with in vivo imaging of targeted human xenograft tumors in SCID mice. The mathematical model calibrated to experimental data was used to explore properties of the targeting ligand (diffusion and affinity) and ligand release schemes (rates and concentrations) with a goal to identify the properties of cells and ligands that enable high receptor saturation. By accounting for heterogeneities typical of in vivo tumors, our model was able to identify cell- and tissue-level barriers to efficient drug uptake. This work provides a base for utilizing experimentally measurable properties of a ligand-targeted agent and patient-specific attributes of the tumor tissue to support the development of novel targeted imaging agents and for improvement in their delivery to individual tumor cells.

Suggested Mechanisms of Tracheal Occlusion Mediated Accelerated Fetal Lung Growth: A Case for Heterogeneous Topological Zones.

In this article, we report an up-to-date summary on tracheal occlusion (TO) as an approach to drive accelerated lung growth and strive to review the different maternal- and fetal-derived local and systemic signals and mechanisms that may play a significant biological role in lung growth and formation of heterogeneous topological zones following TO. Pulmonary hypoplasia is a condition whereby branching morphogenesis and embryonic pulmonary vascular development are globally affected and is classically seen in congenital diaphragmatic hernia. TO is an innovative approach aimed at driving accelerated lung growth in the most severe forms of diaphragmatic hernia and has been shown to result in improved neonatal outcomes. Currently, most research on mechanisms of TO-induced lung growth is focused on mechanical forces and is viewed from the perspective of homogeneous changes within the lung. We suggest that the key principle in understanding changes in fetal lungs after TO is taking into account formation of unique variable topological zones. Following TO, fetal lungs might temporarily look like a dynamically changing topologic mosaic with varying proliferation rates, dissimilar scale of vasculogenesis, diverse patterns of lung tissue damage, variable metabolic landscape, and different structures. The reasons for this dynamic topological mosaic pattern may include distinct degree of increased hydrostatic pressure in different parts of the lung, dissimilar degree of tissue stress/damage and responses to this damage, and incomparable patterns of altered lung zones with variable response to systemic maternal and fetal factors, among others. The local interaction between these factors and their accompanying processes in addition to the potential role of other systemic factors might lead to formation of a common vector of biological response unique to each zone. The study of the interaction between various networks formed after TO (action of mechanical forces, activation of mucosal mast cells, production and secretion of damage-associated molecular pattern substances, low-grade local pulmonary inflammation, and cardiac contraction-induced periodic agitation of lung tissue, among others) will bring us closer to an appreciation of the biological phenomenon of topological heterogeneity within the fetal lungs.

Quantum materials discovery from a synthesis perspective

The synthesis of bulk crystals, thin films and nanostructures plays a seminal role in expanding the frontiers of quantum materials. Crystal growers accomplish this by creating materials aimed at harnessing the complex interplay between quantum wavefunctions and various factors such as dimensionality, topology, Coulomb interactions and symmetry. This Review provides a synthesis perspective on how this discovery of quantum materials takes place. After introducing the general paradigms that arise in this context, we provide a few examples to illustrate how thin-film growers in particular exploit quantum confinement, topology, disorder and interfacial heterogeneity to realize new quantum materials.

Structural Characterization of the Amyloid Precursor Protein Transmembrane Domain and Its γ-Cleavage Site.

Alzheimer’s disease is the most common form of dementia that affects about 50 million of sufferers worldwide. A major role for the initiation and progression of Alzheimer’s disease has been associated with the amyloid β-peptide (Aβ), which is a protease cleavage product of the amyloid precursor protein. The amyloid precursor protein is an integral membrane protein with a single transmembrane domain. Here, we assessed the structural integrity of the transmembrane domain within oriented phosphatidylcholine lipid bilayers and determined the tilt angle distribution and dynamics of various subdomains using solid-state NMR and attenuated total reflectance Fourier transform infrared spectroscopies. Although the overall secondary structure of the transmembrane domain is α-helical, pronounced conformational and topological heterogeneities were observed for the γ- and, to a lesser extent, the ζ-cleavage site, with pronounced implications for the production of Aβ and related peptides, the development of the disease, and pharmaceutical innovation.

Macro and micro collapse mechanisms of closed-cell aluminium foams during quasi-static compression

The pore collapse mechanisms of closed-cell aluminium foams during quasi-static compression have been investigated. A suite of experiments and numerical simulations were carried out to elucidate the deformation pathways of individual pores during quasi-static compressive loading. X-ray computed tomography was utilized to generate 3D views of the foams before and after deformation. The tomography based foam geometry was imported into the finite element software ABAQUS/Explicit for simulations. The results showed that the simulations accurately reproduced the experimentally observed yielding and post yielding behaviour of the foams. As expected, pores with thin cell-walls were observed to deform at faster rates both experimentally and in simulations. The simulations aided to reveal the complex deformation evolution of cell-walls and junctions (plateau borders) during compression. While the cell-walls experienced bending, buckling and rotation by forming hinges; the plateau borders experienced considerably less deformation. The thickness/strength of cell-walls and topological foams' heterogeneities are observed as the governing factors for collapse. Significant lateral strain is observed at the cell level, although the bulk lateral strain was negligible. Finally, it was also observed that the micro-pores and cracks present within the cell-walls contribute to their deformation.

Critical dynamics on a large human Open Connectome network.

Extended numerical simulations of threshold models have been performed on a human brain network with N=836733 connected nodes available from the Open Connectome Project. While in the case of simple threshold models a sharp discontinuous phase transition without any critical dynamics arises, variable threshold models exhibit extended power-law scaling regions. This is attributed to fact that Griffiths effects, stemming from the topological or interaction heterogeneity of the network, can become relevant if the input sensitivity of nodes is equalized. I have studied the effects of link directness, as well as the consequence of inhibitory connections. Nonuniversal power-law avalanche size and time distributions have been found with exponents agreeing with the values obtained in electrode experiments of the human brain. The dynamical critical region occurs in an extended control parameter space without the assumption of self-organized criticality.