A computational model for cancer growth by using complex networks

In this work we propose a computational model to investigate the proliferation of cancerous cell by using complex networks. In our model the network represents the structure of available space in the cancer propagation. The computational scheme considers a cancerous cell randomly included in the complex network. When the system evolves the cells can assume three states: proliferative, non-proliferative, and necrotic. Our results were compared with experimental data obtained from three human lung carcinoma cell lines. The computational simulations show that the cancerous cells have a Gompertzian growth. Also, our model simulates the formation of necrosis, increase of density, and resources diffusion to regions of lower nutrient concentration. We obtain that the cancer growth is very similar in random and small-world networks. On the other hand, the topological structure of the small-world network is more affected. The scale-free network has the largest rates of cancer growth due to hub formation. Finally, our results indicate that for different average degrees the rate of cancer growth is related to the available space in the network.     

Von Neumann’s growth model: Statistical mechanics and biological applications

We review recent work on the statistical mechanics of Von Neumann’s growth model and discuss its application to cellular metabolic networks. In this context, we present a detailed analysis of the physiological scenario underlying optimality à la Von Neumann in the metabolism of the bacterium E. coli, showing that optimal solutions are characterized by a considerable microscopic flexibility accompanied by a robust emergent picture for the key physiological functions. This suggests that the ideas behind optimal economic growth in Von Neumann’s model can be helpful in uncovering functional organization principles of cell energetics.     

On the security of K-tier heterogeneous cellular networks

Motivated by recent developments in heterogeneous cellular networks and physical-layer security, we aim to characterize the fundamental limits of secure communication in networks. Based on a general model in which both transmitters and receivers are randomly scattered in space, we model the locations of K-tier base stations, users, and potential eavesdroppers as independent two-dimensional Poisson point processes. Using the proposed model, we analyze the achievable secrecy rates for an arbitrarily located mobile user. Assuming that the cell selection is based on achievable-secrecy-rate threshold, we obtain approximations for: (a) secrecy coverage probability and (b) average secrecy load per tier. We also investigate how the network performance is affected by secrecy rate threshold, eavesdropper density, and different access strategies are analyzed, respectively. Finally, our theoretical claims are confirmed by the numerical results.     

Structurally constrained protein evolution: results from a lattice simulation

We simulate the evolution of a protein-like sequence subject to point mutations, imposing conservation of the ground state, thermodynamic stability and fast folding. Our model is aimed at describing neutral evolution of natural proteins. We use a cubic lattice model of the protein structure and test the neutrality conditions by extensive Monte Carlo simulations. We observe that sequence space is traversed by neutral networks, i.e. sets of sequences with the same fold connected by point mutations. Typical pairs of sequences on a neutral network are nearly as different as randomly chosen sequences. The fraction of neutral neighbors has strong sequence to sequence variations, which influence the rate of neutral evolution. In this paper we study the thermodynamic stability of different protein sequences. We relate the high variability of the fraction of neutral mutations to the complex energy landscape within a neutral network, arguing that valleys in this landscape are associated to high values of the neutral mutation rate. We find that when a point mutation produces a sequence with a new ground state, this is likely to have a low stability. Thus we tentatively conjecture that neutral networks of different structures are typically well separated in sequence space. This result indicates that changing significantly a protein structure through a biologically acceptable chain of point mutations is a rare, although possible, event. Received 8 July 1999     

Social power and opinion formation in complex networks

In this paper we investigate the effects of social power on the evolution of opinions in model networks as well as in a number of real social networks. A continuous opinion formation model is considered and the analysis is performed through numerical simulation. Social power is given to a proportion of agents selected either randomly or based on their degrees. As artificial network structures, we consider scale-free networks constructed through preferential attachment and Watts–Strogatz networks. Numerical simulations show that scale-free networks with degree-based social power on the hub nodes have an optimal case where the largest number of the nodes reaches a consensus. However, given power to a random selection of nodes could not improve consensus properties. Introducing social power in Watts–Strogatz networks could not significantly change the consensus profile.     

Efficient design method for cell allocation in hybrid CMOS/nanodevices using a cultural algorithm with chaotic behavior

The hybrid CMOS molecular (CMOL) circuit, which combines complementary metal–oxide–semiconductor (CMOS) components with nanoscale wires and switches, can exhibit significantly improved performance. In CMOL circuits, the nanodevices, which are called cells, should be placed appropriately and are connected by nanowires. The cells should be connected such that they follow the shortest path. This paper presents an efficient method of cell allocation in CMOL circuits with the hybrid CMOS/nanodevice structure; the method is based on a cultural algorithm with chaotic behavior. The optimal model of cell allocation is derived, and the coding of an individual representing a cell allocation is described. Then the cultural algorithm with chaotic behavior is designed to solve the optimal model. The cultural algorithm consists of a population space, a belief space, and a protocol that describes how knowledge is exchanged between the population and belief spaces. In this paper, the evolutionary processes of the population space employ a genetic algorithm in which three populations undergo parallel evolution. The evolutionary processes of the belief space use a chaotic ant colony algorithm. Extensive experiments on cell allocation in benchmark circuits showed that a low area usage can be obtained using the proposed method, and the computation time can be reduced greatly compared to that of a conventional genetic algorithm.     

基于休眠机理的三维小基站蜂窝网络能效优化

小基站通常部署在写字楼、商贸区等城市密集区域以弥补传统宏基站在覆盖和传输方面的不足.小基站的分布一般是根据高峰时的网络负荷设计的,这必然导致网络负荷较低时的资源浪费.讨论了在平均接入率和信道容量双重约束下基于休眠机理的三维小基站蜂窝网络的能效优化问题.借助泊松点过程理论推导了三维小基站网络下行信道容量和平均接入率的数学表达式.通过分析下行信道容量和平均接入率的单调性得出同时满足传输信道容量和接入率要求的最佳休眠概率.分析了小基站最大用户连接数的最佳值,通过对该参数的合理配置,可以在满足通信指标的前提下最大程度地降低网络能耗.仿真结果表明,设计的基站休眠机理可以使小基站网络的能耗下降约21%.     

简谐振子免疫优化算法求解异构无线网络垂直切换判决问题

本文设计了垂直切换判决方案问题的数学模型, 给出了一种基于简谐振子免疫优化算法的垂直切换判决方案, 并与文献方案进行了对比实验实验结果表明, 本文方案能够有效地平衡网络负载、增加终端电池的生存时间, 具有较好的应用价值.     

Migration-driven aggregate growth on scale-free networks

We study the kinetics of migration-driven aggregate growth on completely connected scale-free networks. A reversible migration system is considered with the size-dependent rate kernel K(k; l/i;j) approximately k(u)i(v)(lj)(v), at which an i-mer aggregate located on the node with j links gains one monomer from a k-mer aggregate on the node with l links. The results show that the evolution behavior of the aggregate size distribution is drastically different from that for the corresponding same system in normal space. This model can be used to mimic some phenomena such as the distribution of city populations. Moreover, we verify our analytic results in good agreement with the data of the population distributions of all U.S. counties.     

Self-regulation in infinite populations with fission-death dynamics

The evolution of an infinite population of interacting point entities placed in ${\mathbb{R}}^d$ is studied. The elementary evolutionary acts are death of an entity with rate that includes a competition term and independent fission into two entities. The population states are probability measures on the corresponding configuration space and the result is the construction of the evolution of states in the class of sub-Poissonian measures, that corresponds to the lack of clusters in such states. This is considered as a self-regulation in the population due to competition.     

Evolutionary construction of geographical networks with nearly optimal robustness and efficient routing properties

Robust and efficient design of networks on a realistic geographical space is one of the important issues for the realization of dependable communication systems. In this paper, based on a percolation theory and a geometric graph property, we investigate such a design from the following viewpoints: (1) network evolution according to a spatially heterogeneous population, (2) trimodal low degrees for the tolerant connectivity against both failures and attacks, and (3) decentralized routing within short paths. Furthermore, we point out the weakened tolerance by geographical constraints on local cycles, and propose a practical strategy by adding a small fraction of shortcut links between randomly chosen nodes in order to improve the robustness to a similar level to that of the optimal bimodal networks with a larger degree for the network size N. These properties will be useful for constructing future ad hoc networks in wide-area communications.     

Evolving complex dynamics in electronic models of genetic networks

Ordinary differential equations are often used to model the dynamics and interactions in genetic networks. In one particularly simple class of models, the model genes control the production rates of products of other genes by a logical function, resulting in piecewise linear differential equations. In this article, we construct and analyze an electronic circuit that models this class of piecewise linear equations. This circuit combines CMOS logic and RC circuits to model the logical control of the increase and decay of protein concentrations in genetic networks. We use these electronic networks to study the evolution of limit cycle dynamics. By mutating the truth tables giving the logical functions for these networks, we evolve the networks to obtain limit cycle oscillations of desired period. We also investigate the fitness landscapes of our networks to determine the optimal mutation rate for evolution.     

Steady States in SIRS Epidemical Model of Mobile Individuals

We consider an epidemical model within socially interacting mobile individuals to study the behaviors of steady states of epidemic propagation in 2D networks. Using mean-field approximation and large scale simulations, we recover the usual epidemic behavior with critical thresholds δ_c and p_c below which infectious disease dies out. For the population density δ far above δ_c, it is found that there is linear relationship between contact rate λ and the population density δ in the main. At the same time, the result obtained from mean-field approximation is compared with our numerical result, and it is found that these two results are similar by and large but not completely the same.     

Cell fates as high-dimensional attractor states of a complex gene regulatory network

Cells in multicellular organisms switch between distinct cell fates, such as proliferation or differentiation into specialized cell types. Genome-wide gene regulatory networks govern this behavior. Theoretical studies of complex networks suggest that they can exhibit ordered (stable) dynamics, raising the possibility that cell fates may represent high-dimensional attractor states. We used gene expression profiling to show that trajectories of neutrophil differentiation converge to a common state from different directions of a 2773-dimensional gene expression state space, providing the first experimental evidence for a high-dimensional stable attractor that represents a distinct cellular phenotype.     

Hybrid optimal scheduling for intermittent androgen suppression of prostate cancer

We propose a method for achieving an optimal protocol of intermittent androgen suppression for the treatment of prostate cancer. Since the model that reproduces the dynamical behavior of the surrogate tumor marker, prostate specific antigen, is piecewise linear, we can obtain an analytical solution for the model. Based on this, we derive conditions for either stopping or delaying recurrent disease. The solution also provides a design principle for the most favorable schedule of treatment that minimizes the rate of expansion of the malignant cell population.     

Kaleidoscope of life: A 24-neighbourhood outer-totalistic cellular automaton

One of the challenges of cellular automaton research is finding models with a low complexity and at the same time a rich dynamics. A measure of low complexity is the number of states in the model and the number of transition rules to switch between those states. In this paper, we propose a 2-dimensional 2-state cellular automaton that-though governed by a single simple transition rule-has a sufficiently rich dynamics to be computationally universal. According to the transition rule, a cell’s state is determined by the sum of the states of the cells at orthogonal or diagonal distances one or two from the cell (distance-2 Moore neighbourhood), but not by the previous state of the cell itself. Notwithstanding its simplicity, this model is able to generate a great variety of patterns, including several types of stable configurations, oscillators and patterns that move over cellular space (gliders). We prove the computational universality of the model by constructing a universal set of logic gates (NOT and AND) from these patterns. A key element in this proof is the shifting of phases and positions of signals such that they meet the input requirements of the logic gates. Similarities of the model with classical spin systems are also discussed.     

Scale-Free Properties in Traffic System

In this work, we propose a new model of evolution networks, which is based on the evolution of the traffic flow. In our method, the network growth does not take into account preferential attachment, and the attachment of new node is independent of the degree of nodes. Our aim is that employing the theory of evolution network, we give a further understanding about the dynamical evolution of the traffic flow. We investigate the probability distributions and scaling properties of the proposed model. The simulation results indicate that in the proposed model, the distribution of the output connections can be well described by scale-free distribution. Moreover, the distribution of the connections is largely related to the traffic flow states, such as the exponential distribution (i.e., the scale-free distribution) and random distribution etc.     

Scale-Free Properties in Traffic System

In this work, we propose a new model of evolution networks, which is based on the evolution of the traffic flow. In our method, the network growth does not take into account preferential attachment, and the attachment of new node is independent of the degree of nodes. Our aim is that employing the theory of evolution network, we give a further understanding about the dynamical evolution of the traffic flow. We investigate the probability distributions and scaling properties of the proposed model The simulation results indicate that in the proposed model, the distribution of the output connections can be well described by scale-free distribution. Moreover, the distribution of the connections is largely related to the traffic flow states, such as the exponential distribution （i.e., the scale-free distribution） and random distribution etc.     

Cell differentiation modeled via a coupled two-switch regulatory network

Mesenchymal stem cells can give rise to bone and other tissue cells, but their differentiation still escapes full control. In this paper we address this issue by mathematical modeling. We present a model for a genetic switch determining the cell fate of progenitor cells which can differentiate into osteoblasts (bone cells) or chondrocytes (cartilage cells). The model consists of two switch mechanisms and reproduces the experimentally observed three stable equilibrium states: a progenitor, an osteogenic, and a chondrogenic state. Conventionally, the loss of an intermediate (progenitor) state and the entailed attraction to one of two opposite (differentiated) states is modeled as a result of changing parameters. In our model in contrast, we achieve this by distributing the differentiation process to two functional switch parts acting in concert: one triggering differentiation and the other determining cell fate. Via stability and bifurcation analysis, we investigate the effects of biochemical stimuli associated with different system inputs. We employ our model to generate differentiation scenarios on the single cell as well as on the cell population level. The single cell scenarios allow to reconstruct the switching upon extrinsic signals, whereas the cell population scenarios provide a framework to identify the impact of intrinsic properties and the limiting factors for successful differentiation.