A Dynamical Model of Lipoprotein Metabolism

We present a dynamical model of lipoprotein metabolism derived by combining a cascading process in the blood stream and cellular level regulatory dynamics. We analyse the existence and stability of equilibria and show that this low-dimensional, nonlinear model exhibits bistability between a low and a high cholesterol state. A sensitivity analysis indicates that the intracellular concentration of cholesterol is robust to parametric variations while the plasma cholesterol can vary widely. We show how the dynamical response to time-dependent inputs can be used to diagnose the state of the system. We also establish the connection between parameters in the system and medical and genetic conditions.     

A Dynamical Model of Fast Cortical Reorganization

In this work we study the connection between some dynamic effects at the synaptic level and fast reorganization of cortical sensory maps. By using a biologically plausible computational model of the primary somatosensory system we obtained simulation results that can be used to relate the dynamics of the interactions of excitatory and inhibitory neurons to the process of somatotopic map reorganization immediately after peripheral lesion. The model consists of three regions integrated into a single structure: tactile receptors representing the glabrous surface of the hand, ventral posterior lateral nucleus of the thalamus and area 3b of the primary somatosensory cortex, reproducing the main aspects of the connectivity of these regions. By applying informational measures to the simulation results of the dynamic behavior of AMPA, NMDA and GABA synaptic conductances we draw some conjectures about how the several neuronal synaptic elements are related to the initial stage of the digit-induced reorganization of the hand map in the somatosensory cortex.     

A Neuro-Mechanical Model for Interpersonal Coordination

The present study investigates the coordination between two people oscillating handheld pendulums, with a special emphasis on the influence of the mechanical properties of the effector systems involved. The first part of the study is an experiment in which eight pairs of participants are asked to coordinate the oscillation of their pendulum with the other participant’s in an in-phase or antiphase fashion. Two types of pendulums, A and B, having different resonance frequencies (Freq A=0.98 Hz and Freq B=0.64 Hz), were used in different experimental combinations. Results confirm that the preferred frequencies produced by participants while manipulating each pendulum individually were close to the resonance frequencies of the pendulums. In their attempt to synchronize with one another, participants met at common frequencies that were influenced by the mechanical properties of the two pendulums involved. In agreement with previous studies, both the variability of the behavior and the shift in the intended relative phase were found to depend on the task-effector asymmetry, i.e., the difference between the mechanical properties of the effector systems involved. In the second part of the study, we propose a model to account for these results. The model consists of two cross-coupled neuro-mechanical units, each composed of a neural oscillator driving a wrist-pendulum system. Taken individually, each unit reproduced the natural tendency of the participants to freely oscillate a pendulum close to its resonance frequency. When cross-coupled through the vision of the pendulum of the other unit, the two units entrain each other and meet at a common frequency influenced by the mechanical properties of the two pendulums involved. The ability of the proposed model to address the other effects observed as a function of the different conditions of the pendulum and intended mode of coordination is discussed.     

A Stochastic Spatial Dynamical Model for Aedes Aegypti

We develop a stochastic spatial model for Aedes aegypti populations based on the life cycle of the mosquito and its dispersal. Our validation corresponds to a monitoring study performed in Buenos Aires. Lacking information with regard to the number of breeding sites per block, the corresponding parameter (BS) was adjusted to the data. The model is able to produce numerical data in very good agreement with field results during most of the year, the exception being the fall season. Possible causes of the disagreement are discussed. We analyzed the mosquito dispersal as an advantageous strategy of persistence in the city and simulated the dispersal of females from a source to the surroundings along a 3-year period observing that several processes occur simultaneously: local extinctions, recolonization processes (resulting from flight and the oviposition performed by flyers), and colonization processes resulting from the persistence of eggs during the winter season. In view of this process, we suggest that eradication campaigns in temperate climates should be performed during the winter time for higher efficiency.     

A Stochastic Model for Detecting Overlapping and Hierarchical Community Structure

Community detection is a fundamental problem in the analysis of complex networks. Recently, many researchers have concentrated on the detection of overlapping communities, where a vertex may belong to more than one community. However, most current methods require the number (or the size) of the communities as a priori information, which is usually unavailable in real-world networks. Thus, a practical algorithm should not only find the overlapping community structure, but also automatically determine the number of communities. Furthermore, it is preferable if this method is able to reveal the hierarchical structure of networks as well. In this work, we firstly propose a generative model that employs a nonnegative matrix factorization (NMF) formulization with a l_2,1 norm regularization term, balanced by a resolution parameter. The NMF has the nature that provides overlapping community structure by assigning soft membership variables to each vertex; the l_2,1 regularization term is a technique of group sparsity which can automatically determine the number of communities by penalizing too many nonempty communities; and hence the resolution parameter enables us to explore the hierarchical structure of networks. Thereafter, we derive the multiplicative update rule to learn the model parameters, and offer the proof of its correctness. Finally, we test our approach on a variety of synthetic and real-world networks, and compare it with some state-of-the-art algorithms. The results validate the superior performance of our new method.     

病毒感染的动态模型

以SARS病毒为例,从病毒在宿主细胞内的复制和在细胞间的传播两个方面建立了数学模型,对模型平衡点的稳定性和分岔类型做出了初步分析,同时讨论了不同个体的免疫力和病毒感染能力之间的关系.由此可定性地认识病毒在宿主体内的动态特征,以了解病毒的致病机理.本文还对模型提出进一步研究的方向.     

A Dynamical Phyllotaxis Model to Determine Floral Organ Number

How organisms determine particular organ numbers is a fundamental key to the development of precise body structures; however, the developmental mechanisms underlying organ-number determination are unclear. In many eudicot plants, the primordia of sepals and petals (the floral organs) first arise sequentially at the edge of a circular, undifferentiated region called the floral meristem, and later transition into a concentric arrangement called a whorl, which includes four or five organs. The properties controlling the transition to whorls comprising particular numbers of organs is little explored. We propose a development-based model of floral organ-number determination, improving upon earlier models of plant phyllotaxis that assumed two developmental processes: the sequential initiation of primordia in the least crowded space around the meristem and the constant growth of the tip of the stem. By introducing mutual repulsion among primordia into the growth process, we numerically and analytically show that the whorled arrangement emerges spontaneously from the sequential initiation of primordia. Moreover, by allowing the strength of the inhibition exerted by each primordium to decrease as the primordium ages, we show that pentamerous whorls, in which the angular and radial positions of the primordia are consistent with those observed in sepal and petal primordia in Silene coeli-rosa, Caryophyllaceae, become the dominant arrangement. The organ number within the outmost whorl, corresponding to the sepals, takes a value of four or five in a much wider parameter space than that in which it takes a value of six or seven. These results suggest that mutual repulsion among primordia during growth and a temporal decrease in the strength of the inhibition during initiation are required for the development of the tetramerous and pentamerous whorls common in eudicots.     

Development of a Serial Order in Speech Constrained by Articulatory Coordination

Universal linguistic constraints seem to govern the organization of sound sequences in words. However, our understanding of the origin and development of these constraints is incomplete. One possibility is that the development of neuromuscular control of articulators acts as a constraint for the emergence of sequences in words. Repetitions of the same consonant observed in early infancy and an increase in variation of consonantal sequences over months of age have been interpreted as a consequence of the development of neuromuscular control. Yet, it is not clear how sequential coordination of articulators such as lips, tongue apex and tongue dorsum constrains sequences of labial, coronal and dorsal consonants in words over the course of development. We examined longitudinal development of consonant-vowel-consonant(-vowel) sequences produced by Japanese children between 7 and 60 months of age. The sequences were classified according to places of articulation for corresponding consonants. The analyses of individual and group data show that infants prefer repetitive and fronting articulations, as shown in previous studies. Furthermore, we reveal that serial order of different places of articulations within the same organ appears earlier and then gradually develops, whereas serial order of different articulatory organs appears later and then rapidly develops. In the same way, we also analyzed the sequences produced by English children and obtained similar developmental trends. These results suggest that the development of intra- and inter-articulator coordination constrains the acquisition of serial orders in speech with the complexity that characterizes adult language.     

A Population Genetics Model of Marker-Assisted Selection

A deterministic two-loci model was developed to predict genetic response to marker-assisted selection (MAS) in one generation and in multiple generations. Formulas were derived to relate linkage disequilibrium in a population to the proportion of additive genetic variance used by MAS, and in turn to an extra improvement in genetic response over phenotypic selection. Predictions of the response were compared to those predicted by using an infinite-loci model and the factors affecting efficiency of MAS were examined. Theoretical analyses of the present study revealed the nonlinearity between the selection intensity and genetic response in MAS. In addition to the heritability of the trait and the proportion of the marker-associated genetic variance, the frequencies of the selectively favorable alleles at the two loci, one marker and one quantitative trait locus, were found to play an important role in determining both the short- and long-term efficiencies of MAS. The evolution of linkage disequilibrium and thus the genetic response over several generations were predicted theoretically and examined by simulation. MAS dissipated the disequilibrium more quickly than drift alone. In some cases studied, the rate of dissipation was as large as that to be expected in the circumstance where the true recombination fraction was increased by three times and selection was absent.     

A Coordination Model of Whole-plant Carbon Allocation in Relation to Water Stress

Although water is an important determinant of the allocationof material between roots and shoots during growth, and oftenparallels the effects of nitrogen, few models have explicitlyconsidered allocation in relation to water supply. We use coordinationtheory to develop a simple exponential model that considersallocation of dry matter between shoots and roots during growthin relation to carbon and watersupplies, and accounts for theeffects of water stress on growth. We compare coordinationvs.optimization(global and local) versions of the exponential model by examiningsimilarities and differences in model behaviour obtained underconstant and variable environmental conditions, and with drasticallychanging conditions (mild, moderate and severe water stress).The greatest differences between coordination and optimizationexist in the drastically changing conditions. In a second versionof the model, we remove the restriction of exponential growthand show how coordination principles can be extended to a morecomplicated structure. The non-exponential model is used toanalyse experimental data on the effects of different pot sizes(and hence water availability) on root restriction and plantgrowth as reported by Thomas and Strain (Plant Physiology96:627–634, 1991). With further refinements, the coordinationmodel has potential as a tool to model plant growth in relationto water supply under various environmental conditions. Optimization; functional balance; root: shoot ratio; root restriction     

When Feeling Skillful Impairs Coordination in a Lottery Selection Task

Choosing a major field of study to secure a good job after graduation is a tacit coordination problem that requires considering others’ choices. We examine how feeling skillful, either induced (Experiment 1) or measured (Experiment 2), affects coordination in this type of task. In both experiments participants chose between two lotteries, one offering a larger prize than the other. Participants’ entry into the chosen lottery was either related or unrelated to their skill, with the final prize allocated randomly to one of the entrants in each lottery. Importantly, across conditions skill was irrelevant to choosing between lotteries. Notwithstanding, when skill was related to determining lottery entrants, participants who felt highly skillful chose the high prize lottery excessively. Results further suggest that this stems from high confidence in self skill, rather than incorrect expectations regarding others.     

A Dynamical Model of Biological Population Under the Variation of Resource and Its Numerical Analysis

1IntroductionTheLogisticequationofpopulationgroanisaclassicalmodeld~bingthePOPulationdy~cs,itisconSiderasthefundamentalthaiofPOPulationd~cs(May,1974).Inthebeisticmodel,thegrowth~ourofpopulationdependsonthebiolodedspeCies'intrinsicrateofincreaseandthe~lugCapaCityofenvironxnent.Therearetwoqueshonswoadinvestigatingfabler.First,dasapopulationreachitSintrinsicrateonlywhenthePOPulatonsizeisequaltozero?hand,isthe~lugcapadtyofenvironmentaconStantwhichcanbedet~nedinadvance?Infact,anypopulationc…     

A Model of Two-Way Selection System for Human Behavior

Two-way selection is a common phenomenon in nature and society. It appears in the processes like choosing a mate between men and women, making contracts between job hunters and recruiters, and trading between buyers and sellers. In this paper, we propose a model of two-way selection system, and present its analytical solution for the expectation of successful matching total and the regular pattern that the matching rate trends toward an inverse proportion to either the ratio between the two sides or the ratio of the state total to the smaller group''s people number. The proposed model is verified by empirical data of the matchmaking fairs. Results indicate that the model well predicts this typical real-world two-way selection behavior to the bounded error extent, thus it is helpful for understanding the dynamics mechanism of the real-world two-way selection system.     

A Model for Selection of Eyespots on Butterfly Wings

Unsolved Problem

The development of eyespots on the wing surface of butterflies of the family Nympalidae is one of the most studied examples of biological pattern formation.However, little is known about the mechanism that determines the number and precise locations of eyespots on the wing. Eyespots develop around signaling centers, called foci, that are located equidistant from wing veins along the midline of a wing cell (an area bounded by veins). A fundamental question that remains unsolved is, why a certain wing cell develops an eyespot, while other wing cells do not.

Key Idea and Model

We illustrate that the key to understanding focus point selection may be in the venation system of the wing disc. Our main hypothesis is that changes in morphogen concentration along the proximal boundary veins of wing cells govern focus point selection. Based on previous studies, we focus on a spatially two-dimensional reaction-diffusion system model posed in the interior of each wing cell that describes the formation of focus points. Using finite element based numerical simulations, we demonstrate that variation in the proximal boundary condition is sufficient to robustly select whether an eyespot focus point forms in otherwise identical wing cells. We also illustrate that this behavior is robust to small perturbations in the parameters and geometry and moderate levels of noise. Hence, we suggest that an anterior-posterior pattern of morphogen concentration along the proximal vein may be the main determinant of the distribution of focus points on the wing surface. In order to complete our model, we propose a two stage reaction-diffusion system model, in which an one-dimensional surface reaction-diffusion system, posed on the proximal vein, generates the morphogen concentrations that act as non-homogeneous Dirichlet (i.e., fixed) boundary conditions for the two-dimensional reaction-diffusion model posed in the wing cells. The two-stage model appears capable of generating focus point distributions observed in nature.

Result

We therefore conclude that changes in the proximal boundary conditions are sufficient to explain the empirically observed distribution of eyespot focus points on the entire wing surface. The model predicts, subject to experimental verification, that the source strength of the activator at the proximal boundary should be lower in wing cells in which focus points form than in those that lack focus points. The model suggests that the number and locations of eyespot foci on the wing disc could be largely controlled by two kinds of gradients along two different directions, that is, the first one is the gradient in spatially varying parameters such as the reaction rate along the anterior-posterior direction on the proximal boundary of the wing cells, and the second one is the gradient in source values of the activator along the veins in the proximal-distal direction of the wing cell.     

A Hierarchical Bayesian Model to Predict Self-Thinning Line for Chinese Fir in Southern China

Self-thinning is a dynamic equilibrium between forest growth and mortality at full site occupancy. Parameters of the self-thinning lines are often confounded by differences across various stand and site conditions. For overcoming the problem of hierarchical and repeated measures, we used hierarchical Bayesian method to estimate the self-thinning line. The results showed that the self-thinning line for Chinese fir (Cunninghamia lanceolata (Lamb.)Hook.) plantations was not sensitive to the initial planting density. The uncertainty of model predictions was mostly due to within-subject variability. The simulation precision of hierarchical Bayesian method was better than that of stochastic frontier function (SFF). Hierarchical Bayesian method provided a reasonable explanation of the impact of other variables (site quality, soil type, aspect, etc.) on self-thinning line, which gave us the posterior distribution of parameters of self-thinning line. The research of self-thinning relationship could be benefit from the use of hierarchical Bayesian method.     

F(st) in a Hierarchical Island Model

It is shown that in a hierarchical island model, in which demes within a neighborhood exchange migrants at a much higher rate than do demes in different neighborhoods, hierarchical F statistics introduced by S. Wright can indicate the extent of gene flow within and between neighborhoods. At equilibrium, the within-neighborhood inbreeding coefficient, FSN, is approximately 1/(1 + 4Nm1) where N is the deme size and m1 is the migration rate among demes in the same neighborhood. The between-neighborhood inbreeding coefficient, FNT, is approximately 1/(1 + 4Ndm2) where d is the number of demes in a neighborhood and m2 is the migration rate among demes in different neighborhoods.