Mathematical Biosciences Research Articles

Modeling and analysis of biodegradation of xenobiotic polymers based on experimental results

An endogenous depolymerization model based on uniform weight distribution is introduced. The time dependent model with temporal dependent degradation rate is reduced to a time independent model. The previously developed techniques were applied to an inverse problem to determine the degradation rate. The transition of weight distribution was simulated by solving an initial value problem. Those techniques are applied to degradation processes of polylactic acid. They are applicable to other polymers subject to endogenous depolymerization processes. References F. Kawai, Sphingomonads involved in the biodegradation of xenobiotic polymers, Journal of Industrial Microbiology and Biotechnology 23 (1999), 400--407. F. Kawai, M. Shibata, S. Yokoyama, S. Maeda, K. Tada, and S. Hayashi, Biodegradability of Scott--Gelead photodegradable polyethylene and polyethylene wax by microorganisms, Macromolecular Symposia 144 (1999), 73--84. F. Kawai, M. Watanabe, M. Shibata, S. Yokoyama, and Y. Sudate, Experimental analysis and numerical simulation for biodegradability of polyethylene, Polymer Degradation and Stability 76 (2002), 129--135. doi:10.1016/S0141-3910(02)00006-X F. Kawai, M. Watanabe, M. Shibata, S. Yokoyama, Y. Sudate, and S. Hayashi, Comparative Study on Biodegradability of Polyethylene Wax by Bacteria and Fungi, Polymer Degradation and Stability 86 (2004), 105--114. doi:10.1016/j.polymdegradstab.2004.03.015 J. D. Lambert, Computational Methods in Ordinary Differential Equations (John Wiley and Sons, Chichester, 1973). G. Madras and B. J. McCoy, Numerical and similarity solutions for reversible population balance equations with size-dependent rates, Journal of Colloid and Interface Science 246 (2002) 356--365. doi:10.1006/jcis.2001.8073 S. Matsumura, N. Tomizawa, A. Toki, K. Nishikawa and K. Toshima, Novel Poly(vinyl alcohol)-degrading enzyme and the degradation mechanism, Macromolecules 32 (1999), 7753--7761. B. J. McCoy and G. Madras, Evolution to similarity solutions for fragmentation and aggregation, Journal of Colloid and Interface Science 201 (1998) 200--209. doi:10.1006/jcis.1998.5434 B. J. McCoy, Distribution Kinetics for Temperature-Programmed Pyrolysis, Industrial and Engineering Chemistry Research 38 (1999) 4531--4537. B. J. McCoy and G. Madras, Discrete and continuous models for polymerization and depolymerization, Chemical Engineering Science 56 (2001) 2831--2836. doi:10.1016/S0009-2509(00)00516-9 J. E. J. Staggs, A continuous model for vaporization of linear polymers by random scission and recombination, Fire Safety Journal 40 (2005) 610--627. doi:10.1016/j.firesaf.2005.05.004 M. Watanabe and F. Kawai, Numerical simulation for enzymatic degradation of poly (vinyl alcohol), Polymer Degradation and Stability 81 (2003), 393--399. doi:10.1016/S0141-3910(03)00122-8 M. Watanabe and F. Kawai, Analysis of polymeric biodegradability based on experimental results and numerical simulation, Environmental Research and Control (in Japanese) 25 (2003), 25--32. M. Watanabe, F. Kawai, M. Shibata, S. Yokoyama, and Y. Sudate, Computational method for analysis of polyethylene biodegradation, Journal of Computational and Applied Mathematics 161 (2003), 133--144. doi:10.1016/S0377-0427(03)00551-X M. Watanabe, F. Kawai, M. Shibata, S. Yokoyama, Y. Sudate, and S. Hayashi, Analytical and computational techniques for exogenous depolymerization of xenobiotic polymers, Mathematical Biosciences 192 (2004) 19--37. doi:10.1016/j.mbs.2004.06.006 M. Watanabe and F. Kawai, Numerical simulation of microbial depolymerization process of exogenous type, R. May and A. J. Roberts (Eds.) Proc. of 12th Computational Techniques and Applications Conference, CTAC-2004, ANZIAM Journal, 46(E), pp. C1188--C1204, 2005. http://anziamj.austms.org.au/V46/CTAC2004/Wata M. Watanabe and F. Kawai, Mathematical modelling and computational analysis of enzymatic degradation of xenobiotic polymers, Applied Mathematical Modelling 30 (2006) 1497--1514. M. Watanabe, F. Kawai, S. Tsuboi, S Nakatsu, and H. Ohara, Study on enzymatic hydrolysis of polylactic acid by endogenous depolymerizaion model, Macromolecular Theory and Simulations 16 (2007) 619--626. doi:10.1002/mats.200700015 M. Watanabe and F. Kawai, Mathematical study of the biodegradation of xenobiotic polymers with experimental data introduced into analysis, Proceedings of the 7th Biennial Engineering Mathematics and Applications Conference, EMAC-2005, Melbourne, Editors: Andrew Stacey and Bill Blyth and John Shepherd and A. J. Roberts, ANZIAM J. 47 pp. C665--C681, 2007. http://anziamj.austms.org.au/V47EMAC2005/Watanabe

Application of Cathodoluminescence Imaging to the Study of Sedimentary Rocks. By Sam Boggs Jr. and David Krinsley. Cambridge: Cambridge University Press, 2006. 176 pages, 64 figures, 6 tables. $120.00 cloth.

Previous articleNext article No AccessReviewsApplication of Cathodoluminescence Imaging to the Study of Sedimentary Rocks. By Sam Boggs Jr. and David Krinsley. Cambridge: Cambridge University Press, 2006. 176 pages, 64 figures, 6 tables. $120.00 cloth.Roger MasonRoger MasonDepartment of Earth SciencesMemorial University of NewfoundlandSt. John's, Newfoundland and Labrador Search for more articles by this author Department of Earth SciencesMemorial University of NewfoundlandSt. John's, Newfoundland and LabradorPDFPDF PLUSFull Text Add to favoritesDownload CitationTrack CitationsPermissionsReprints Share onFacebookTwitterLinkedInRedditEmail SectionsMoreDetailsFiguresReferencesCited by The Journal of Geology Volume 115, Number 6November 2007 Article DOIhttps://doi.org/10.1086/522354 Views: 59Total views on this site Citations: 3Citations are reported from Crossref © 2007 by The University of Chicago. All rights reserved. For permission to reuse, please contact [email protected]PDF download Crossref reports the following articles citing this article:Ya-Hao Huang, You-Jun Tang, Mei-Jun Li, Hai-Tao Hong, Chang-Jiang Wu, Ji-Zhen Zhang, Xiao-Lin Lu, Xiao-Yong Yang Quantitative evaluation of geological fluid evolution and accumulated mechanism: in case of tight sandstone gas field in central Sichuan Basin, Petroleum Science 18, no.22 (Mar 2021): 416–429.https://doi.org/10.1007/s12182-021-00556-zWei Yang, Sheng He, Ao Su, Stefan Iglauer, Gangyi Zhai, Zhi Zhou, Tian Dong, Ze Tao, Sile Wei Paleo-Temperature and -Pressure Characteristics of Fluid Inclusions in Composite Veins of the Doushantuo Shale (Yichang Area, South China): Implications for the Preservation and Enrichment of Shale Gas, Energy & Fuels 35, no.55 (Feb 2021): 4091–4105.https://doi.org/10.1021/acs.energyfuels.1c00040Feng Wang, Shan Chang, Dashun Wei, , Prediction of conotoxin type based on long short-term memory network, Mathematical Biosciences and Engineering 18, no.55 (Jan 2021): 6700–6708.https://doi.org/10.3934/mbe.2021332

Allee effects in a discrete-time SIS epidemic model with infected newborns

We extend the framework of Rios-Soto et al. (Contemporary Mathematics, 2006, 410, 297) to include both compensatory (contest competition) and overcompensatory (scramble competition) population dynamics with and without the Allee effect. We compute the basic reproductive number ℛ0, and use it to predict the (uniform) persistence or extinction of the infective population, where the population dynamics are compensatory and the Allee effect is either present or absent. We also explore the relationship between the demographic equation and the epidemic process, where the total population dynamics are overcompensatory. In particular, we show that the demographic dynamics drive both the susceptible and infective dynamics. This is in contrast to the recent observations of Franke and Yakubu, that the demographic dynamics can be chaotic while the infective dynamics are oscillatory and non-chaotic in periodically-forced SIS epidemic models (Mathematical Biosciences, 2006, 204, 68).

From the Guest Editor

This Special Issue of <em>Mathematical Biosciences and Engineering</em> (MBE) contains a few of the papers presented at a special session in Mathematical Biology at the Regional Meeting of the American Mathematical Society, held in Lincoln, Nebraska, on October 21-23, 2005. The AMS meeting was preceded by a 2-day workshop on educational issues in mathematical biology, organized by Glenn Ledder. Many of the visitors attended both meetings, and therefore the five-day period was an enriching, double-barreled, math biology experience for nearly everyone. Near the end of the session the Editor-in-Chief of MBE, Yang Kuang, asked if we would be willing to collect together some of the papers from the special session for an issue of MBE. <br><br> For more information please click the “Full Text” button above.

Vascular Endothelial Growth Factor Signaling to Endothelial Nitric Oxide Synthase

See related article, pages 715–722 There is substantial evidence supporting the idea that the process of angiogenesis requires the synthesis of endothelium-derived nitric oxide (NO). NO, characterized as a major endothelial-derived relaxing factor, exerts paracrine and autocrine roles in maintaining cardiovascular homeostasis, vascular tone, and microvascular permeability. During the early steps of angiogenesis in which new blood vessels sprout from existing vascular beds, there is a persistence of vasodilation and increase in vascular permeability, suggesting that these hemodynamic changes in the existing vasculature are indispensable during an angiogenic process. A number of angiogenic factors can triggers the release of NO, synthesized by the endothelial isoform of NO synthase (eNOS). One such factor is the vascular endothelial growth factor (VEGF), which as its name implies, is a critical mitogenic, chemoattractant, and survival factor for endothelial cells1 in addition to being characterized as a potent vascular permeability factor.2 Early studies have demonstrated that VEGF can readily stimulate NO production in cultured cells and isolated blood vessels and that NO is essential in mediating the VEGF-induced endothelial cell proliferation and organization into tubes in 3D cultures.3,4 Subsequent in vivo studies have also demonstrated that eNOS knockout mice had significantly attenuated VEGF and ischemia induced angiogenesis and vascular permeability.5,6 These studies place eNOS derived NO as a key mediator of VEGF induced angiogenesis in postnatal mice. Since the discovery of VEGF, or VEGF-A, and subsequent members of the VEGF family (VEGF-B, -C, -D, -E, and placenta growth factor, PlGF), intense research has been performed to elucidate their modes of action. These growth factor ligands bind to 3 receptor tyrosine kinases (RTKs), namely VEGF receptor-1, -2, and -3 as well as to coreceptors such as heparan sulfate proteoglycans or neuropilins. Like many other RTKs, these receptors are able to form …

Letter to the editors

Dear Editors:<br> I request that <em>Mathematical Biosciences and Engineering</em> publish this Letter of Correction to an article published in the journal for which I was the corresponding author, "The Effect of Global Travel on the Spread of SARS'' (2006;3(1):205-218). The goal of this article was to study the effect of global travel on the geographic spread of SARS. A multiregional compartmental model was proposed, mathematically analyzed, and numerically simulated to study how SARS spread out from Guangdong, China. The article consists of six sections: (1) an introduction, (2) a background section on medical geography theory, (3) the mathematical model, (4) mathematical analysis and results, (5) numerical simulations, and (6) discussion. Sections 3, 4, and 5 are the main parts of the article which are all original work. <br><br> For more information please click the "Full Text” above

The S-system computation of non-central gamma distribution

The non-central gamma distribution can be regarded as a general form of non-central χ2 distributions whose computations were thoroughly investigated (Ruben, H., 1974, Non-central chi-square and gamma revisited. Communications in Statistics, 3(7), 607–633; Knüsel, L., 1986, Computation of the chi-square and Poisson distribution. SIAM Journal on Scientific and Statistical Computing, 7, 1022–1036; Voit, E.O. and Rust, P.F., 1987, Noncentral chi-square distributions computed by S-system differential equations. Proceedings of the Statistical Computing Section, ASA, pp. 118–121; Rust, P.F. and Voit, E.O., 1990, Statistical densities, cumulatives, quantiles, and power obtained by S-systems differential equations. Journal of the American Statistical Association, 85, 572–578; Chattamvelli, R., 1994, Another derivation of two algorithms for the noncentral χ2 and F distributions. Journal of Statistical Computation and Simulation, 49, 207–214; Johnson, N.J., Kotz, S. and Balakrishnan, N., 1995, Continuous Univariate Distributions, Vol. 2 (2nd edn) (New York: Wiley). Both distributional function forms are usually in terms of weighted infinite series of the central one. The ad hoc approximations to cumulative probabilities of non-central gamma were extended or discussed by Chattamvelli, Knüsel and Bablok (Knüsel, L. and Bablok, B., 1996, Computation of the noncentral gamma distribution. SIAM Journal on Scientific Computing, 17, 1224–1231), and Ruben (Ruben, H., 1974, Non-central chi-square and gamma revisited. Communications in Statistics, 3(7), 607–633). However, they did not implement and demonstrate proposed numerical procedures. Approximations to non-central densities and quantiles are not available. In addition, its S-system formulation has not been derived. Here, approximations to cumulative probabilities, density, and quantiles based on the method of Knüsel and Bablok are derived and implemented in R codes. Furthermore, two alternate S-system forms are recast on the basis of techniques of Savageau and Voit (Savageau, M.A. and Voit, E.O., 1987, Recasting nonlinear differential equations as S-systems: A canonical nonlinear form. Mathematical Biosciences, 87, 83–115) as well as Chen (Chen, Z.-Y., 2003, Computing the distribution of the squared sample multiple correlation coefficient with S-Systems. Communications in Statistics—Simulation and Computation, 32(3), 873–898.) and Chen and Chou (Chen, Z.-Y. and Chou, Y.-C., 2000, Computing the noncentral beta distribution with S-system. Computational Statistics and Data Analysis, 33, 343–360.). Statistical densities, cumulative probabilities, quantiles can be evaluated by only one numerical solver power low analysis and simulation (PLAS). With the newly derived S-systems of non-central gamma, the specialized non-central χ2 distributions are demonstrated under five cases in the same three situations studied by Rust and Voit. Both numerical values in pairs are almost equal. Based on these, nine cases in three similar situations are designed for demonstration and evaluation. In addition, exact values in finite significant digits are provided for comparison. Demonstrations are conducted by R package and PLAS solver in the same PC system. By doing these, very accurate and consistent numerical results are obtained by three methods in two groups. On the other hand, these three methods are performed competitively with respect to speed of computation. Numerical advantages of S-systems over the ad hoc approximation and related properties are also discussed.

Sufficient Conditions for Fast Switching Synchronization in Time-Varying Network Topologies

In previous work [J. D. Skufca and E. Bollt, Mathematical Biosciences and Engineering, 1 (2004), pp. 347-359], empirical evidence indicated that a time-varying network could propagate sufficient information to allow synchronization of the sometimes coupled oscillators, despite an instantaneously disconnected topology. We prove here that if the network of oscillators synchronizes for the static time-average of the topology, then the network will synchronize with the time-varying topology if the time-average is achieved sufficiently fast. Fast switching, fast on the time-scale of the coupled oscillators, overcomes the desynchronizing decoherence suggested by disconnected instantaneous networks. This result agrees in spirit with that of [J. D. Skufca and E. Bollt, Mathematical Biosciences and Engineering, 1 (2004), pp. 347-359] where empirical evidence suggested that a moving averaged graph Laplacian could be used in the master-stability function analysis [L. M. Pecora and T. L. Carroll, Phys. Rev. Lett., 80 (1998), pp. 2109-2112]. A new fast switching stability criterion herein gives sufficiency of a fast switching network leading to synchronization. Although this sufficient condition appears to be very conservative, it provides new insights about the requirements for synchronization when the network topology is time-varying. In particular, it can be shown that networks of oscillators can synchronize even if at every point in time the frozen-time network topology is insufficiently connected to achieve synchronization.

From the Guest Editors

The idea for this volume came from the session ''Control and Dynamics of Biomedical Systems,'' which we organized at the Fourth World Congress of Nonlinear Analysts held in Orlando, Florida, on June 30–July 7, 2004. We invited a number of speakers, and although not all could attend and give a talk in person, many expressed interest in contributing a paper. Following an invitation from Yang Kuang to put together a volume on the topic as a special issue of <em>Mathematical Biosciences and Engineering</em>, some papers presented at the session were submitted immediately, and others were contributed after the Congress. <br> <br> For the full paper, please click the "Full Text" button above.

From the Editors

It is easy to argue that we are entering a new golden era of science and engineering. The predominant approach of conducting timely and in-depth scienti c research is forever changed from cycles of simple experiment and theory to cycles that combine of experiment, theory, mathematical modeling, and analysis. The landscape of science is now clearly dominated by the peaks of biosciences. Integrative and interdisciplinary research in life sciences and engineering is no longer merely a slogan but aggressively and collectively pursued and practiced by researchers. This shift of paradigms greatly enhances the central importance of mathematical and computational modeling and analysis in scienti c and engineering endeavors. With this exciting backdrop in mind, the American Institute of Mathematical Sciences (AIMS) and Beihang University have decided to launch a joint international journal on mathematical biosciences and engineering. This journal will maximally serve the scienti c communities in both developed and developing countries. <br> <br> For more information, please click the "full text" above.

Why are dengue virus serotypes so distantly related? Enhancement and limiting serotype similarity between dengue virus strains.

Dengue virus, the causative agent of dengue fever, has four major serotypes characterized by large genetic and immunological distances. We propose that the unusually large distances between the serotypes can be explained in the light of a process of antibody-dependent enhancement (ADE) leading to increased mortality. Antibody-dependent enhancement results from a new infection with a particular serotype in an individual with acquired immunity to a different serotype. Classical dengue fever causes negligible mortality, but ADE leads to the risk of developing the significantly more dangerous dengue haemorrhagic fever (DHF) and dengue shock syndrome (DSS). A mathematical model is presented that describes the epidemiological dynamics of two serotypes of a pathogen where there is the possibility of co-infection and reinfection by a different serotype, along with increased mortality as a result of enhancement. We show that if there is no or slightly increased mortality after reinfection (enhancement), serotypes with a small immunological distance can stably coexist. This suggests that a cloud of serotypes with minor serological differences will constitute the viral population. By contrast, if enhancement is sufficiently great, a substantial immunological distance is necessary for two serotypes to stably coexist in the population. Therefore, high mortality owing to enhancement leads to an evolutionarily stable viral community comprising a set of distantly separated serotypes.

Transients and attractors in epidemics.

Historical records of childhood disease incidence reveal complex dynamics. For measles, a simple model has indicated that epidemic patterns represent attractors of a nonlinear dynamic system and that transitions between different attractors are driven by slow changes in birth rates and vaccination levels. The same analysis can explain the main features of chickenpox dynamics, but fails for rubella and whooping cough. We show that an additional (perturbative) analysis of the model, together with knowledge of the population size in question, can account for all the observed incidence patterns by predicting how stochastically sustained transient dynamics should be manifested in these systems.

Wavefronts and global stability in a time-delayed population model with stage structure

We formulate and study a one–dimensional single–species diffusive–delay population model. The time delay is the time taken from birth to maturity. Without diffusion, the delay differential model extends the well–known logistic differential equation by allowing delayed constant birth processes and instantaneous quadratically regulated death processes. This delayed model is known to have simple global dynamics similar to that of the logistic equation. Through the use of a sub/supersolution pair method, we show that the diffusive delay model continues to generate simple global dynamics. This has the important biological implication that quadratically regulated death processes dramatically simplify the growth dynamics. We also consider the possibility of travelling wavefront solutions of the scalar equation for the mature population, connecting the zero solution of that equation with the positive steady state. Our main finding here is that our fronts appear to be all monotone, regardless of the size of the delay. This is in sharp contrast to the frequently reported findings that delay causes a loss of monotonicity, with the front developing a prominent hump in some other delay models.

Computing the Distribution of the Squared Sample Multiple Correlation Coefficient with S-Systems

The multiple correlation coefficient is to measure the maximum correlation between one variable and the linear combination of other correlated variables. It is useful for studying the relationships among multiple covariate observations. The ad hoc approximation methods (Chen, Z.-Y. (2001). On the statistical computation of the sample multiple correlation coefficient. Journal of Statistical Computation and Simulation 70:299–324; Ding, C. G. (1996). On the computation of the distribution of the square of the sample multiple correlation coefficient. Computational Statistics and Data Analysis 22:345–350; Gurland, J., Asiribo, O. (1991). On the distribution of the multiple correlation coefficient and their kinked chi-squared random variable. Journal of Statistical Sinica 1:493–502; Lee, Y. S. (1972). Tables of upper percentage points of the multiple correlation coefficient. Biometrika 59:175–189.) for evaluating various distributional values of interest are represented by different forms and calculated in separate numerical procedures. Here, a unified approach of numerical methods using the S-system form for the squared sample multiple correlation coefficient is derived on the basis of recasting techniques of Rust and Voit (Rust, P. F., Voit, E. O. (1990). Statistical densities, cumulatives, quantiles, and power obtained by S-systems differential equations. Journal of the American Statistical Association. 85:572–578) and Sarageau and Voit (Savageau, M. A., Voit, E. O. (1987). Recasting nonlinear differential equations as S-systems: a canonical nonlinear form. Mathematical Biosciences 87:83–115). Its distributional function form in terms of an infinite weighted sum of the incomplete beta integral is closely related to that of noncentral beta distribution whose S-system form has been investigated by Chen and Chou (Chen, Z. -Y., Chou, Y. -C. (2000). Computing the noncentral beta distribution with S-system. Computational Statistics and Data Analysis 33:343–360). Following their derivations, the S-system formulations for this statistical distribution are studied and demonstrated. Statistical densities, cumulatives, quantiles, and related distributional values can be evaluated in only one S-system form by using its numerical solver PLAS. Compared with the ad hoc evaluations, the S-system demonstration produces more precise results under various situations for computing the statistical values of densities, cumulatives, and quantiles. In addition, this new formulation provides significant numerical advantages over its original form. Related properties are also discussed.

Causality in H -semiotic systems of ecosystems: Routes and tours

The influences (causes and effects) between the variables of an abstract system are considered from a theoretical point of view by authors such as Mesarovic and Takahara [(1989) Systems Theory (Springer, Berlin)], who employ two notions of causality--non-anticipation and past-determinancy--and by Caselles [(1993) Cybenetics and systems: An international Journal 24 , 305-323], who introduces the concepts of direct and indirect influence. From a practical point of view, in the context of the study of networks within an ecosystem, authors such as Patten et al. and Patten [(1982) Canadian Water Resource Journal 7 (1), 252-282; (1985) Contributions in Systems Ecology 65 , 271-284] have demonstrated that indirect effects between the variables of an ecosystem outweigh direct effects, while Higashi and Patten, Higashi and Burns and Higashi and Nakajima [(1989) The American Naturalist 133 , 288-302; (1991) Theoretical Studies of Ecosystems. The Network Perspective (Cambridge University Press, Oxford); (1995) Mathematical Biosciences 130 , 99-128] have studied indirect effects in ecological interaction networks by means of a chain rule, etc. Taking as a starting point the concept of system-linkage Lloret et al. [(1998) Cybernetics and systems: An international Journal 29 , 29-39] equivalent to Yang's definition [(1989) Cybernetics and Systems: An International Journal 20 , 67-76], the authors have developed a theory of the direct and indirect influences between variables with respect to paths and times in an H -semiotic systems or mathematical models of complex Reality.

A Scalable Model of Cerebellar Adaptive Timing and Sequencing: The Recurrent Slide and Latch (RSL) Model

From the dawn of modern neural network theory, the mammalian cerebellum has been a favored object of mathematical modeling studies. Early studies focused on the fanout, convergence, thresholding, and learned weighting of perceptual-motor signals within the cerebellar cortex. This led in the proposals of Albus (i>Mathematical Biosciences, vol. 10, pp. 25–61, 1971s i>Journal of Dynamic Systems, Measurement, and Control, vol. 97, pp. 220–227, 1975) and Marr (i>Journal of Physiology (London), vol. 202, no. 2, pp. 437–470, 1969) to the still viable idea that the granule cell stage in the cerebellar cortex performs a sparse expansive recoding of the time-varying input vector. This recoding reveals and emphasizes combinations (of input state variables) in a distributed representation that serves as a basis for the learned, state-dependent control actions engendered by cerebellar outputs to movement related centers. Although well-grounded as such, this perspective seriously underestimates the intelligence of the cerebellar cortex. Context and state information arises asynchronously due to the heterogeneity of sources that contribute signals to compose the cerebellar input vector. These sources include radically different sensory systems—vision, kinesthesia, touch, balance and audition—as well as many stages of the motor output channel. To make optimal use of available signals, the cerebellum must be able to sift the evolving state representation for the most reliable predictors of the need for control actions, and to use those predictors even if they appear only transiently and well in advance of the optimal time for initiating the control action. Such a i>cerebellar adaptive timing competence has recently been experimentally verified (Perrett, Ruiz, and Mauk, i>Journal of Neuroscience, vol. 13, no. 4, pp. 1708–1718, 1993). This paper proposes a modification to prior, population, models for cerebellar adaptive timing and sequencing. Since it replaces a population with a single element, the proposed Recurrent Slide and Latch (RSL) model is in one sense maximally efficient, and therefore optimal from the perspective of scalability.

HIV-1 dynamics revisited: biphasic decay by cytotoxic T lymphocyte killing?

The biphasic decay of blood viraemia in patients being treated for human immunodeficiency virus type 1 (HIV-1) infection has been explained as the decay of two distinct populations of cells: the rapid death of productively infected cells followed by the much slower elimination of a second population the identity of which remains unknown. Here we advance an alternative explanation based on the immune response against a single population of infected cells. We show that the biphasic decay can be explained simply, without invoking multiple compartments: viral load falls quickly while cytotoxic T lymphocytes (CTL) are still abundant, and more slowly as CTL disappear. We propose a method to test this idea, and develop a framework that is readily applicable to treatment of other infections.

Invasion thresholds for fungicide resistance: deterministic and stochastic analyses

Fungicide resistance is an important practical problem, but one that is poorly understood at the population level. Here we introduce a simple nonlinear model for fungicide resistance in botanical epidemics which includes the dynamics of the chemical control agent and the host population, while also allowing for demographic stochasticity in the host-parasite dynamics. This provides a mathematical framework for analysing the risk of fungicide resistance developing by including the parameters for the amount applied, longevity and application frequency of the fungicide. The model demonstrates the existence of thresholds for the invasion of the resistant strain in the parasite population which depend on two quantities: the relative fitness of the resistant strain and the effectiveness of control. This threshold marks a change from definite elimination of the resistant strain below the threshold to a finite probability of invasion which increases above the threshold. The fungicide decay rate, the amount of fungicide applied and the period between applications affect the effectiveness of control and, consequently, they influence whether or not resistance develops and the time taken to achieve a critical frequency of resistance. All three parameters are amenable to control by the grower or by coordinating the activity of a population of growers. Providing crude estimates of the effectiveness of control and relative fitness are available, the results can be used to predict the consequences of changing these parameters for the risk of invasion and the proportion of sites at which this might be expected to occur. Although motivated for fungicide resistance, the model has broader application to herbicide, antibiotic and antiviral resistance. The modelling approach and results are discussed in the context of resistance to chemical control in general.

Empirical determinants of measles metapopulation dynamics in England and Wales.

A key issue in metapopulation dynamics is the relative impact of internal patch dynamics and coupling between patches. This problem can be addressed by analysing large spatiotemporal data sets, recording the local and global dynamics of metapopulations. In this paper, we analyse the dynamics of measles meta-populations in a large spatiotemporal case notification data set, collected during the pre-vaccination era in England and Wales. Specifically, we use generalized linear statistical models to quantify the relative importance of local influences (birth rate and population size) and regional coupling on local epidemic dynamics. Apart from the proportional effect of local population size on case totals, the models indicate patterns of local and regional dynamic influences which depend on the current state of epidemics. Birth rate and geographic coupling are not associated with the size of major epidemics. By contrast, minor epidemics--and especially the incidence of local extinction of infection--are influenced both by birth rate and geographical coupling. Birth rate at a lag of four years provides the best fit, reflecting the delayed recruitment of susceptibles to school cohorts. A hierarchical index of spatial coupling to large centres provides the best spatial model. The model also indicates that minor epidemics and extinction patterns are more strongly influenced by this regional effect than the local impact of birth rate.

Schooling preferences for familiar fish vary with group size in a wild guppy population

The ability of fish to recognize and preferentially associate with familiar conspecifics has been well documented in a series of laboratory experiments. In this paper we investigate the schooling preferences of wild female guppies, Poecilia reticulata, in the Upper Tunapuna River in Trinidad and confirm that they do indeed prefer to associate with familiar individuals. The guppies in this river occur in a series of pools that become isolated during the dry season. These fish interact solely with other individuals in their pool for periods of several months at a time and thus have ample opportunity to become accustomed to one another. Our study also reveals that the tendency of female guppies to school with familiar fish declines as the group size in which they naturally live increases. Preferences are strong when there are small numbers of females in a pool, but diminish thereafter. This indicates that the expression of familiarity is constrained by group size. The basis of recognition and the consequences of schooling preferences for familiar individuals are discussed.