Rumor Diffusion and Convergence during the 3.11 Earthquake: A Twitter Case Study

We focus on Internet rumors and present an empirical analysis and simulation results of their diffusion and convergence during emergencies. In particular, we study one rumor that appeared in the immediate aftermath of the Great East Japan Earthquake on March 11, 2011, which later turned out to be misinformation. By investigating whole Japanese tweets that were sent one week after the quake, we show that one correction tweet, which originated from a city hall account, diffused enormously. We also demonstrate a stochastic agent-based model, which is inspired by contagion model of epidemics SIR, can reproduce observed rumor dynamics. Our model can estimate the rumor infection rate as well as the number of people who still believe in the rumor that cannot be observed directly. For applications, rumor diffusion sizes can be estimated in various scenarios by combining our model with the real data.     

The Africanized honey bee dispersal: A mathematical zoom

A general mathematical model for population dispersal featuring long range taxis is presented and exemplified by the dispersal episode of the Africanized honey bees (Apis mellifera adansonii) throughout the American Continent. The mathematical model is a discrete-time and nonlocal model represented by an integrodifference recursion. A newtaxis concept is defined and introduced into the mathematical model by an appropriate modification of the redistribution kernel. The model is capable of predicting the natural barrier for the expansion of the Africanized honey bees in the southern part of the Continent due to low winter temperatures. It also describes a sensitive expansion velocity with respect to the quality of resources, which can explain the AHB’s astounding spread rate, by using two different kinds of population dynamics strategies, one for a resourceful environment and the other for poor regions. An erratum to this article is available at .     

Immunization against the Spread of Rumors in Homogenous Networks

Since most rumors are harmful, how to control the spread of such rumors is important. In this paper, we studied the process of "immunization" against rumors by modeling the process of rumor spreading and changing the termination mechanism for the spread of rumors to make the model more realistic. We derived mean-field equations to describe the dynamics of the rumor spread. By carrying out steady-state analysis, we derived the spreading threshold value that must be exceeded for the rumor to spread. We further discuss a possible strategy for immunization against rumors and obtain an immunization threshold value that represents the minimum level required to stop the rumor from spreading. Numerical simulations revealed that the average degree of the network and parameters of transformation probability significantly influence the spread of rumors. More importantly, the simulations revealed that immunizing a higher proportion of individuals is not necessarily better because of the waste of resources and the generation of unnecessary information. So the optimal immunization rate should be the immunization threshold.     

Neutral evolution in spatially continuous populations

We introduce a general recursion for the probability of identity in state of two individuals sampled from a population subject to mutation, migration, and random drift in a two-dimensional continuum. The recursion allows for the interactions induced by density-dependent regulation of the population, which are inevitable in a continuous population. We give explicit series expansions for large neighbourhood size and for low mutation rates respectively and investigate the accuracy of the classical Malécot formula for these general models. When neighbourhood size is small, this formula does not give the identity even over large scales. However, for large neighbourhood size, it is an accurate approximation which summarises the local population structure in terms of three quantities: the effective dispersal rate, sigma(e); the effective population density, rho(e); and a local scale, kappa, at which local interactions become significant. The results are illustrated by simulations.     

Plant–pollinator population dynamics

We formulate and analyze a multi-generation population dynamics model for pollinators’ mutualism with plants. The centerpiece of our model is an analytical expression for population-level plant–pollinator interactions extrapolated from a model of individual-level flowers and bees interactions. We also show that this analytical expression can be productively approximated by the Beddington–DeAngelis formula—a function used to model trophic interactions in mathematical ecology.     

Internet congestion control using nature population control tactics

In this paper we present a novel bio-inspired approach for congestion control in communication networks. This scheme is based on inspiration by natural population interactions: predator–prey and competition. We show that the relations of those Internet entities that are involved in congestion control mechanisms are similar to predator–prey and competition interactions. In order to apply these population control mechanisms to the Internet congestion control scheme, we combine the mathematical models of these interactions and obtain a hybrid mathematical model. The simulation results show that using appropriately defined parameters, this model leads to a scalable, stable, fair, and high-performance congestion control algorithm.     

Plant–pollinator population dynamics

We formulate and analyze a multi-generation population dynamics model for pollinators’ mutualism with plants. The centerpiece of our model is an analytical expression for population-level plant–pollinator interactions extrapolated from a model of individual-level flowers and bees interactions. We also show that this analytical expression can be productively approximated by the Beddington–DeAngelis formula—a function used to model trophic interactions in mathematical ecology.     

Sterilizing vaccines or the politics of the womb: retrospective study of a rumor in Cameroon

In 1990 a rumor that public health workers were administering a vaccine to sterilize girls and women spread throughout Cameroon. Schoolgirls leapt from windows to escape the vaccination teams, and the vaccination campaign (part of the Year of Universal Child Immunization) was aborted. This article traces the origin and development of this rumor. Theories of rumor and ambiguous cultural response to new technologies shed some light on its genesis and spread, but explain neither its timing nor its content. For this task we need to examine the historical context of Cameroonian experience with colonial vaccination campaigns and the contemporary contexts of the turmoil of democratization movements and economic crisis, concurrent changes in contraceptive policy, and regional mistrust of the state and its "hegemonic project." Drawing on Bayart's politique du ventre and White's thoughts on gossip, we explore this rumor as diagnostic of local response to global and national projects. This response, expressed in this case through the idiom of threats to local reproductive capacity, reveals a feminine side to local-global relations, a politics of the womb.     

Impacts of enemy-mediated effects and the additivity of interactions in an insect trophic system

In this study, we used data from both experiments and mathematical simulations to analyze the consequences of the interacting effects of intraguild predation (IGP), cannibalism and parasitism occurring in isolation and simultaneously in trophic interactions involving two blowfly species under shared parasitism. We conducted experiments to determine the short-term response of two blowfly species to these interactions with respect to their persistence. A mathematical model was employed to extend the results obtained from these experiments to the long-term consequences of these interactions for the persistence of the blowfly species. Our experimental results revealed that IGP attenuated the strength of the effects of cannibalism and parasitism between blowfly host species, increasing the probability of persistence of both populations. The simulations obtained from the mathematical model indicated that IGP is a key interaction for the long-term dynamics of this system. The presence of different species interacting in a tri-trophic system relaxed the severity of the effects of a particular interaction between two species, changing species abundances and promoting persistence through time. This pattern was related to indirect interactions with a third species, the parasitoid species included in this study.     

A mathematical synthesis of niche and neutral theories in community ecology

The debate between niche-based and neutral community theories centers around the question of which forces shape predominantly ecological communities. Niche theory attributes a central role to niche differences between species, which generate a difference between the strength of intra- and interspecific interactions. Neutral theory attributes a central role to migration processes and demographic stochasticity. One possibility to bridge these two theories is to combine them in a common mathematical framework. Here we propose a mathematical model that integrates the two perspectives. From a niche-based perspective, our model can be interpreted as a Lotka-Volterra model with symmetric interactions in which we introduce immigration and demographic stochasticity. From a neutral perspective, it can be interpreted as Hubbell's local community model in which we introduce a difference between intra- and interspecific interactions. We investigate the stationary species abundance distribution and other community properties as functions of the interaction coefficient, the immigration rate and the strength of demographic stochasticity.     

Modulation of acridine mutagen ICR191 intercalation to DNA by methylxanthines—Analysis with mathematical models

Caffeine (CAF) and other methylxanthines (MTX) may interact directly with several aromatic, intercalating ligands through mixed stacking aggregation. Formation of such stacking hetero-complexes may decrease their free form concentration and, in consequence, diminish their biological activity, which is often related to their direct interaction with DNA. In this paper interactions of acridine mutagen (ICR191) with DNA in the presence of three MTX: caffeine (CAF), pentoxifylline (PTX) and theophylline (TH) are investigated. Several mathematical models are used to calculate all association constant values and every component concentration in each analyzed mixture. Model McGhee–von Hippel is used to analyze ligand–DNA interaction, and model Zdunek et al.—to analyze ligand–MTX interactions. Finally, two distinct mathematical models are employed to analyze three-component mixture containing ligand, MTX and DNA molecules. The first model describes possible interactions of ligand with DNA and MTX, and rejects direct MTX interactions with DNA. The second model describes all interactions mentioned above and, additionally, allows MTX to interact directly with DNA. Results obtained using these models are similar. However, correspondence of theoretical results to experimental data is better for the first model than the second one. In this paper possible interactions of ICR191 with eukaryotic cell chromatin are also analyzed, showing that CAF reduces acridine mutagen potential to interact directly with cell chromatin. Additionally, it is demonstrated that MTX inhibit mutagenic activity of ICR191 in a dose-dependent manner. Furthermore, biological activity of ICR191–MTX mixtures corresponds with concentration of free mutagen form calculated using appropriate mathematical model.     

A formal model of an artificial immune system

The paper presents a mathematical model based on the features of antigen-antibody bindings in the immune system. In the natural immune system, local binding of immune cells and molecules to antigenic peptides is based generally on the behavior of surface proteins. In particular, immune cells contain proteins on their receptors, and apparently, these proteins play the key role both in immune response and recognition processes. In this work, we consider the immune cells in the form of formal B-cell and formal T-cell and develop a mathematical model of their interactions. We refer this model as the formal immune system (FIS). The paper provides an analysis of a network of bindings (or interactions) among the formal proteins of the FIS.     

Assembly systems in molecular biology: A graph theory of genetic complementation between two related species

In this report I discuss the interpretation of the data of genetic complementation in vivo of assembly systems between two related species, such as the complementation of structural proteins between related bacteriophages. It is suggested that such experiments reveal interactions between gene products that are overlooked in many other experiments. A mathematical model based on the graph theory is presented, assuming that the assembly system consists of gene products and interactions between them. The model shows that information from the complementation experiment is limited to those interactions which are mismatching if the interacting gene products are produced by different species. Moreover, it shows that the number and positions of mismatching interactions cannot always be determined uniquely by the data of complementation. However, there is a mathematical method by which one can calculate all the possible solutions for the number and positions of mismatching interactions from experimental data. Actual calculation is performed for a simple example. Thus, the model clarifies validity and limitation of complementation experimiments between related species.     

Towards a matrix mechanics framework for dynamic protein network

Protein–protein interaction networks are currently visualized by software generated interaction webs based upon static experimental data. Current state is limited to static, mostly non-compartmental network and non time resolved protein interactions. A satisfactory mathematical foundation for particle interactions within a viscous liquid state (situation within the cytoplasm) does not exist nor do current computer programs enable building dynamic interaction networks for time resolved interactions. Building mathematical foundation for intracellular protein interactions can be achieved in two increments (a) trigger and capture the dynamic molecular changes for a select subset of proteins using several model systems and high throughput time resolved proteomics and, (b) use this information to build the mathematical foundation and computational algorithm for a compartmentalized and dynamic protein interaction network. Such a foundation is expected to provide benefit in at least two spheres: (a) understanding physiology enabling explanation of phenomenon such as incomplete penetrance in genetic disorders and (b) enabling several fold increase in biopharmaceutical production using impure starting materials.     

Mathematical model for the control of ColE1 type plasmid replication

A mathematical model for the molecular events controlling replication of ColE1 type plasmids is described. All the model parameters can be evaluated independently. The model simulates plasmid replication and accurately predicts the copy-number of ColE1 plasmids carrying a variety of regulatory mutations. The model is used to test the plausibility of hypotheses concerning the interactions of regulatory elements involved in the replication apparatus. The model favorably supports the mechanism proposed by Tomizawa and co-workers concerning the nature of RNA-RNA interactions and that the Rom protein increases the binding between the two RNA species. The hypothesis that the interactions of RNA I-II increases the susceptibility of RNA II to the action of endonucleases is not a plausible mechanism.     

Efficient Simulation of Multivariate Binomial and Poisson Distributions

Power investigations, for example, in statistical procedures for the assessment of agreement among multiple raters often require the simultaneous simulation of several dependent binomial or Poisson distributions to appropriately model the stochastical dependencies between the raters' results. Regarding the rather large dimensions of the random vectors to be generated and the even larger number of interactions to be introduced into the simulation scenarios to determine all necessary information on their distributions' dependence stucture, one needs efficient and fast algorithms for the simulation of multivariate Poisson and binomial distributions. Therefore two equivalent models for the multivariate Poisson distribution are combined to obtain an algorithm for the quick implementation of its multivariate dependence structure. Simulation of the multivariate Poisson distribution then becomes feasible by first generating and then convoluting independent univariate Poisson variates with appropriate expectations. The latter can be computed via linear recursion formulae. Similar means for simulation are also considered for the binomial setting. In this scenario it turns out, however, that exact computation of the probability function is even easier to perform; therefore corresponding linear recursion formulae for the point probabilities of multivariate binomial distributions are presented, which only require information about the index parameter and the (simultaneous) success probabilities, that is the multivariate dependence structure among the binomial marginals.     

数学建模在生物化感及其赫米西斯(Hormesis)现象中的应用

简述了国内外对生物化感数学建模的研究近况,包括通过数学模型描述化感物质的赫米西斯(Hormesis)现象,化感作用在受体植物不同密度条件下的表达,植物残茬中化感物质的分解动态及受体植物的动态响应,环境中化感物质的动态变化规律及在植物-昆虫-天敌系统中的应用等。并对化感数学建模领域的先驱机理模型An-Hormesis模型,An-Liu-Johnson-Lovett模型,和An_Residue模型做了简介。     

The Mechanisms of Water Exchange: The Regulatory Roles of Multiple Interactions in Social Wasps

Evolutionary benefits of task fidelity and improving information acquisition via multiple transfers of materials between individuals in a task partitioned system have been shown before, but in this paper we provide a mechanistic explanation of these phenomena. Using a simple mathematical model describing the individual interactions of the wasps, we explain the functioning of the common stomach, an information center, which governs construction behavior and task change. Our central hypothesis is a symmetry between foragers who deposit water and foragers who withdraw water into and out of the common stomach. We combine this with a trade-off between acceptance and resistance to water transfer. We ultimately derive a mathematical function that relates the number of interactions that foragers complete with common stomach wasps during a foraging cycle. We use field data and additional model assumptions to calculate values of our model parameters, and we use these to explain why the fullness of the common stomach stabilizes just below 50 percent, why the average number of successful interactions between foragers and the wasps forming the common stomach is between 5 and 7, and why there is a variation in this number of interactions over time. Our explanation is that our proposed water exchange mechanism places natural bounds on the number of successful interactions possible, water exchange is set to optimize mediation of water through the common stomach, and the chance that foragers abort their task prematurely is very low.     

On the Question of Self-Organization of Population Dynamics on Earth

Biophysics - A new mathematical model based on the predator–prey interactions has been proposed. Strictly analytical solution has been found for a system of nonlinear differential equations...     

Time scale,geometrical constraints,and disulfide bond formation in the folding of small globular proteins

We hypothesize a model of protein folding based on the Poincaré recursion argument and a number of experimental results, including CD, nmr, and Raman spectra. Our model considers that protein folding in vivo proceeds through prefolded peptide segments consisting of 3 to 14 amino acid residues. Such segments may fold spontaneously into nativelike microdomains within a biologically feasible time, i.e., in the 10^?6–10^?1 s time scale. If, due to improper recognition and adjustment of their surfaces, these transiently formed secondary structures are not stabilized by long-range interactions, then the protein species occur within a time- and number-averaged spectrum of populations of transient conformational substates until the final, proper adjustment of the segments takes place. However, if, during protein folding, incorrect disulfide (S-S) bonds are formed, then such unique through-space contacts between the different parts of the polypeptide chain are usually restricted to a minimum. It is postulated that unfolding and refolding processes in vitro, and protein folding in vivo, proceed through variably populated quantized substates. The distribution of these substates depends on a number of molecular interactions between the phase and the hydration spheres surrounding the prefolded surfaces of peptide segments and long-range interactions between these prefolded surfaces.