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PubMed2001

Periodic and quasi-periodic behavior in resource-dependent age structured population models.

To describe the dynamics of a resource-dependent age structured population, a general non-linear Leslie type model is derived. The dependence on the resources is introduced through the death rates of the reproductive age classes. The conditions assumed in the derivation of the model are regularity and plausible limiting behaviors of the functions in the model. It is shown that the model dynamics restricted to its omega-limit sets is a diffeomorphism of a compact set, and the period-1 fixed points of the model are structurally stable. The loss of stability of the non-zero steady state occurs by a discrete Hopf bifurcation. Under general conditions, and after the loss of stability of the structurally stable steady states, the time evolution of population numbers is periodic or quasi-periodic. Numerical analysis with prototype functions has been performed, and the conditions leading to chaotic behavior in time are discussed.

Age Distribution↗

PubMedDate not supplied

Making sense of sparse rating data in collaborative filtering via topographic organization of user preference patterns.

We introduce topographic versions of two latent class models (LCM) for collaborative filtering. Latent classes are topologically organized on a square grid. Topographic organization of latent classes makes orientation in rating/preference patterns captured by the latent classes easier and more systematic. The variation in film rating patterns is modelled by multinomial and binomial distributions with varying independence assumptions. In the first stage of topographic LCM construction, self-organizing maps with neural field organized according to the LCM topology are employed. We apply our system to a large collection of user ratings for films. The system can provide useful visualization plots unveiling user preference patterns buried in the data, without loosing potential to be a good recommender model. It appears that multinomial distribution is most adequate if the model is regularized by tight grid topologies. Since we deal with probabilistic models of the data, we can readily use tools from probability and information theories to interpret and visualize information extracted by our system.

Behavior↗

PubMed2001

Best harmony, unified RPCL and automated model selection for unsupervised and supervised learning on Gaussian mixtures, three-layer nets and ME-RBF-SVM models.

After introducing the fundamentals of BYY system and harmony learning, which has been developed in past several years as a unified statistical framework for parameter learning, regularization and model selection, we systematically discuss this BYY harmony learning on systems with discrete inner-representations. First, we shown that one special case leads to unsupervised learning on Gaussian mixture. We show how harmony learning not only leads us to the EM algorithm for maximum likelihood (ML) learning and the corresponding extended KMEAN algorithms for Mahalanobis clustering with criteria for selecting the number of Gaussians or clusters, but also provides us two new regularization techniques and a unified scheme that includes the previous rival penalized competitive learning (RPCL) as well as its various variants and extensions that performs model selection automatically during parameter learning. Moreover, as a by-product, we also get a new approach for determining a set of 'supporting vectors' for Parzen window density estimation. Second, we shown that other special cases lead to three typical supervised learning models with several new results. On three layer net, we get (i) a new regularized ML learning, (ii) a new criterion for selecting the number of hidden units, and (iii) a family of EM-like algorithms that combines harmony learning with new techniques of regularization. On the original and alternative models of mixture-of-expert (ME) as well as radial basis function (RBF) nets, we get not only a new type of criteria for selecting the number of experts or basis functions but also a new type of the EM-like algorithms that combines regularization techniques and RPCL learning for parameter learning with either least complexity nature on the original ME model or automated model selection on the alternative ME model and RBF nets. Moreover, all the results for the alternative ME model are also applied to other two popular nonparametric statistical approaches, namely kernel regression and supporting vector machine. Particularly, not only we get an easily implemented approach for determining the smoothing parameter in kernel regression, but also we get an alternative approach for deciding the set of supporting vectors in supporting vector machine.

Algorithms↗

PubMed2003

Regular exercise is beneficial to a mouse model of amyotrophic lateral sclerosis.

We tested whether a regular exercise regimen was associated with a change in the life span of G93A-SOD1 transgenic mice, a model of familial ALS. Regular treadmill running for 10 weeks led to a significant increase in the life span of G93A-SOD1 mice. The effect was stronger in male mice, whereas there was only a trend between exercised and sedentary female G93A-SOD1 mice. The data suggest that regular exercise has a beneficial effect on the progression of ALS.

Amyotrophic Lateral Sclerosis↗

PubMed2003

Defining and measuring trophic role similarity in food webs using regular equivalence.

We present a graph theoretic model of analysing food web structure called regular equivalence. Regular equivalence is a method for partitioning the species in a food web into "isotrophic classes" that play the same structural roles, even if they are not directly consuming the same prey or if they do not share the same predators. We contrast regular equivalence models, in which two species are members of the same trophic group if they have trophic links to the same set of other trophic groups, with structural equivalence models, in which species are equivalent if they are connected to the exact same other species. Here, the regular equivalence approach is applied to two published food webs: (1) a topological web (Malaysian pitcher plant insect food web) and (2) a carbon-flow web (St. Marks, Florida seagrass ecosystem food web). Regular equivalence produced a more satisfactory set of classes than did the structural approach, grouping basal taxa with other basal taxa and not with top predators. Regular equivalence models provide a way to mathematically formalize trophic position, trophic group and trophic niche. These models are part of a family of models that includes structural models used extensively by ecologists now. Regular equivalence models uncover similarities in trophic roles at a higher level of organization than do the structural models. The approach outlined is useful for measuring the trophic roles of species in food web models, measuring similarity in trophic relations of two or more species, comparing food webs over time and across geographic regions, and aggregating taxa into trophic groups that reduce the complexity of ecosystem feeding relations without obscuring network relationships. In addition, we hope the approach will prove useful in predicting the outcome of predator-prey interactions in experimental studies.

Animals↗

PubMed2005

A hierarchical Bayesian model for learning nonlinear statistical regularities in nonstationary natural signals.

Capturing statistical regularities in complex, high-dimensional data is an important problem in machine learning and signal processing. Models such as principal component analysis (PCA) and independent component analysis (ICA) make few assumptions about the structure in the data and have good scaling properties, but they are limited to representing linear statistical regularities and assume that the distribution of the data is stationary. For many natural, complex signals, the latent variables often exhibit residual dependencies as well as nonstationary statistics. Here we present a hierarchical Bayesian model that is able to capture higher-order nonlinear structure and represent nonstationary data distributions. The model is a generalization of ICA in which the basis function coefficients are no longer assumed to be independent; instead, the dependencies in their magnitudes are captured by a set of density components. Each density component describes a common pattern of deviation from the marginal density of the pattern ensemble; in different combinations, they can describe nonstationary distributions. Adapting the model to image or audio data yields a nonlinear, distributed code for higher-order statistical regularities that reflect more abstract, invariant properties of the signal.

Bayes Theorem↗

PubMed1997

Predicting the conformational class of short and medium size loops connecting regular secondary structures: application to comparative modelling.

Loops are regions of non-repetitive conformation connecting regular secondary structures. They are both the most difficult and error prone regions of a protein to solve by X-ray crystallography and the hardest regions to model using comparative procedures. Although a loop can sometimes be modelled from a homologue, very often it must be selected from outside the family. The loop prediction procedure, SLoop, attempts to identify the conformational class of the loop rather than to select a specific loop from a set of fragments extracted from known structures or generated ab initio. Templates are constructed for each of the 161 loop conformational classes that have been identified from the clustering of the structures of some 2024 loops of one to eight residues in length. A class template describes both sequence preferences and relative disposition of bounding secondary structures. During comparative modelling, the conformation of a loop can be predicted by identifying a loop class with which its sequence and disposition of bounding secondary structures are compatible. The procedure is tested on an unrelated non-redundant set of 1785 loops under stringent and lax evaluation schemes. Optimal sequence score cut-offs are identified such that the prediction rate is equal to the percentage of loops assigned to acceptable classes. Under the stringent evaluation, at the optimal sequence score cut-off, a conformation is predicted for 50% of loops of which 47% are correct, while under the lax evaluation a conformation is predicted for 63% of loops of which 54% are correct. Sequence score is shown to be a good indicator of the probability of a prediction being correct. Loop length also has a strong affect on prediction outcomes. Considering only loops of two to five residues in length, under the stringent evaluation 62% of loops are predicted with 52% of these predictions being correct while under the lax evaluation predictions are provided for 75% of loops of which 57% are correct.

Computer Simulation↗

PubMed1992

X-ray scattering study of the shape of the DNA region in nucleosome core particle with synchrotron radiation.

The structure of the DNA region in rat thymus nucleosome core particle has been studied by synchrotron X-ray scattering analysis and the contrast-variation technique has been applied to determine the contribution of the DNA to the total scatterings. Small-angle contrast-matching measurements show that the entire core particle and isolated histone octamers are contrast-matched by solvents containing 64 and 54% (w/w) sucrose, respectively. At a contrast of 54% sucrose, where the scattering of the DNA dominates, the scattering data extending to higher angle of about 0.05 A-1 have been collected from relatively concentrated solutions (10 mg/ml) of core particles and interpreted on the basis of the regular helical model for the DNA region. The model calculations show that the shape of the DNA around the histone core is approximately by 1.8 turns of regular helix of 42 A radius and 28 A pitch. These values for helical parameters of our model are in good agreement with those of the structure of DNA in crystallized nucleosome cores shown by earlier diffraction studies.

Algorithms↗

PubMed1992

A comparison of some statistical techniques for road accident analysis.

At the TRRL/SWOV Workshop on Accident Analysis Methodology, held in Amsterdam in 1988, the need to establish a methodology for the analysis of road accidents was firmly stated by all participants. Data from different countries cannot be compared because there is no agreement on research methodology, data collection, and analysis. Linear and log-linear models are regularly used for the analysis of such data. This paper discusses the background of these models and the model assumptions. It is stated that two relevant and fundamentally different classes of models exist. However, in most cases the difference between these classes remains implicit. These classes of models are called design oriented and object oriented models. Within the context of linear models, the basic assumptions deal with this distinction and the generalization of linear to log-linear models. It is argued that there are advantages and disadvantages for each choice and that a check on the tenability of a particular model is to be recommended. Two different types of generalized linear models, both object-oriented, are used by SWOV and TRRL for the analysis of accidents of road users or on particular road locations. The qualitative data analysis (QDA) models used at SWOV are primarily descriptive and useful for model exploration. The generalized linear interactive modeling (GLIM) technique used at TRRL has stricter assumptions, but is better suited for model testing. In order to compare these models, a number of analyses has been carried out on roundabout data from TRRL. The outcomes are consistent and highly comparable. The results show that for this kind of data these two types of models are to be preferred over classical multiple linear regression analysis (MLR) and log-linear analysis of contingency tables (LLA). QDA turned out to be the most powerful in data exploration. A QDA analysis showed that the dominant accident type of entering and circulating accidents had a different relation with the road and traffic characteristics of the roundabouts than the other accident types and should be analyzed separately. Furthermore, it was shown by a QDA analysis that the choice of a log-link function was preferable over an identity relation as used in MLR. This log-link function in combination with the choice of a Poisson error distribution results in a GLIM model with parameter estimates and errorbounds for these estimates. The errorbounds can be used as an indication of the reliability of the parameters. It is stated that the combination of QDA and GLIM is most powerful for the analysis of this type of problems.

Accidents, Traffic↗

PubMed2006

Stochastic approaches to understanding dissociations in inflectional morphology.

Computer modelling research has undermined the view that double dissociations in behaviour are sufficient to infer separability in the cognitive mechanisms underlying those behaviours. However, all these models employ multi-modal representational schemes, where functional specialisation of processing emerges from the training process. Targeted lesioning of different regions of functional specialisation leads to varied but predictable deficits in model performance. We argue that multi-modal representational schemes are not a necessary condition for the observation of double dissociations in an information processing system that shares resources across multiple tasks. Using a uni-modal representational system, we demonstrate that double dissociations may also result from stochastic processes. Lesioning experiments on a single-route, uni-modal connectionist model of regular and irregular noun and verb morphology confirm and extend earlier work demonstrating that selective impairment across tasks can result from damage to a distributed information processing system. A systematic investigation of the degree to which performance deteriorates across different inflectional classes reveals that simple and double dissociations can occur in this single-route, uni-modal model. An important prediction of the model is that double dissociations between regular and irregular inflection, resulting from stochastic processes should be extremely rare. However, they are particularly likely to occur when the researcher uses test batteries consisting of a small number of items. Given that cognitive neuropsychologists rarely provide details about the distribution of performance in a disordered population, it is concluded that a stochastic interpretation of double dissociations may have wider applicability than is normally supposed.

Alzheimer Disease↗

PubMed1996

Conformational analysis and clustering of short and medium size loops connecting regular secondary structures: a database for modeling and prediction.

Loops are regions of nonrepetitive conformation connecting regular secondary structures. We identified 2,024 loops of one to eight residues in length, with acceptable main-chain bond lengths and peptide bond angles, from a database of 223 protein and protein-domain structures. Each loop is characterized by its sequence, main-chain conformation, and relative disposition of its bounding secondary structures as described by the separation between the tips of their axes and the angle between them. Loops, grouped according to their length and type of their bounding secondary structures, were superposed and clustered into 161 conformational classes, corresponding to 63% of all loops. Of these, 109 (51% of the loops) were populated by at least four nonhomologous loops or four loops sharing a low sequence identity. Another 52 classes, including 12% of the loops, were populated by at least three loops of low sequence similarity from three or fewer nonhomologous groups. Loop class suprafamilies resulting from variations in the termini of secondary structures are discussed in this article. Most previously described loop conformations were found among the classes. New classes included a 2:4 type IV hairpin, a helix-capping loop, and a loop that mediates dinucleotide-binding. The relative disposition of bounding secondary structures varies among loop classes, with some classes such as beta-hairpins being very restrictive. For each class, sequence preferences as key residues were identified; those most frequently at these conserved positions than in proteins were Gly, Asp, Pro, Phe, and Cys. Most of these residues are involved in stabilizing loop conformation, often through a positive phi conformation or secondary structure capping. Identification of helix-capping residues and beta-breakers among the highly conserved positions supported our decision to group loops according to their bounding secondary structures. Several of the identified loop classes were associated with specific functions, and all of the member loops had the same function; key residues were conserved for this purpose, as is the case for the parvalbumin-like calcium-binding loops. A significant number, but not all, of the member loops of other loop classes had the same function, as is the case for the helix-turn-helix DNA-binding loops. This article provides a systematic and coherent conformational classification of loops, covering a broad range of lengths and all four combinations of bounding secondary structure types, and supplies a useful basis for modelling of loop conformations where the bounding secondary structures are known or reliably predicted.

Databases, Factual↗

PubMed2004

Large liver tumors: protocol for radiofrequency ablation and its clinical application in 110 patients--mathematic model, overlapping mode, and electrode placement process.

PURPOSE: To establish a preoperative protocol for ultrasonographically guided percutaneous radiofrequency (RF) ablation of large liver tumors that is based on mathematic models and clinical experience and to evaluate the role of this protocol in RF ablation. MATERIALS AND METHODS: A regular prism and a regular polyhedron model were used to develop a preoperative protocol for liver tumor ablation. This protocol enabled the authors to minimize the number of ablation spheres, optimize the overlapping mode, and determine the electrode placement process. One hundred ten patients with 121 liver tumors were treated by using this protocol. Sixty-nine patients had 74 hepatocellular carcinomas (HCCs), and 41 had 47 metastases to the liver (ie, metastatic liver carcinomas [MLCs]). Patients underwent follow-up helical computed tomography (CT) 1 month and every 2-3 months after RF ablation. Ablation was considered a success if no contrast enhancement was detected in the treated area on the CT scan obtained at 1 month. RESULTS: A total of 536 ablations were performed in the 121 tumors. The ablation success rate was 87.6% (106 of 121 tumors); the local recurrence rate, 24.0% (29 of 121 tumors); and the estimated mean recurrence-free survival, 17.1 months. Twenty-five patients underwent 38 re-treatments for local tumor recurrence. Major complications occurred in seven patients. Of these patients, only one, who had a tumor close to the colon, had a colon perforation 1 week after RF and required surgical intervention. CONCLUSION: The described protocol for treatment of large tumors had a success rate of 87.6% and a local recurrence rate of 24.0%.

Adult↗

PubMed2006

Discrete solitons and vortices in the two-dimensional Salerno model with competing nonlinearities.

An anisotropic lattice model in two spatial dimensions, with on-site and intersite cubic nonlinearities (the Salerno model), is introduced, with emphasis on the case in which the intersite nonlinearity is self-defocusing, competing with on-site self-focusing. The model applies, for example, to a dipolar Bose-Einstein condensate trapped in a deep two-dimensional (2D) optical lattice. Soliton families of two kinds are found in the model: ordinary ones and cuspons, with peakons at the border between them. Stability borders for the ordinary solitons are found, while all cuspons (and peakons) are stable. The Vakhitov-Kolokolov criterion does not apply to cuspons, but for the ordinary solitons it correctly identifies the stability limits. In direct simulations, unstable solitons evolve into localized pulsons. Varying the anisotropy parameter, we trace a transition between the solitons in 1D and 2D versions of the model. In the isotropic model, we also construct discrete vortices of two types, on-site and intersite centered (vortex crosses and squares, respectively), and identify their stability regions. In simulations, unstable vortices in the noncompeting model transform into regular solitons, while in the model with the competing nonlinearities they evolve into localized vortical pulsons, which maintain their topological character. Bound states of regular solitons and vortices are constructed too, and their stability is identified.

Journal Article↗

PubMed1992

Factors affecting survival of hemodialysis patients utilizing urea kinetic modeling. A critical appraisal of shortening dialysis times.

The objective of this study was to analyze risk factors affecting mortality rates (MR) in hemodialysis patients undergoing shortened dialysis time who were regularly kinetically modeled. Over a 14-month period, 180 in-center hemodialysis patients, 54% male, 46% female, 57% Black, 39% Caucasian, and 4% Hispanic, treated with rapid high efficiency dialysis (RHED = 2-3 h, 3 times/week) and conventional dialysis (3-4 h, 3 times/week) were studied. Median patient age was 56.7 years (16-84 years) and dialysis care ranged from 6 months to 18 years (mean +/- SD = 4.0 +/- 4.2 years). The patients underwent monthly urea kinetic modeling. The dialysis prescription was based upon normalizing Kt/V between 0.8 and 1.2 and the protein catabolic rate (PCRn) between 0.9 and 1.1. Thirty-three percent of the patients received recombinant human erythropoietin (r-HuEPO). The effects of various covariates, including primary diagnosis, post/predialysis BUN ratios, creatinine, albumin, calcium, phosphate, cholesterol, hemoglobin, r-HuEPO, Kt/V, and PCRn were analyzed using analysis of variance, chi 2 and linear discriminant function (DF) statistical methods. Several significant factors emerged as influencing outcome. The DF analysis produced a highly statistically significant (p < 0.0001) model to predict mortality based upon certain laboratory and dialysis parameters. Further, the linear DF correctly predicted mortality rate in 86% of cases. The results of the analysis revealed an overall mortality rate of 15.6%; hospitalization rates (HR) were 1.4 +/- 1.8 times/year. Length of dialysis time, i.e., dialysis times between 2 and 4 h, when adjusted for Kt/V has no correlation with MR or HR. Variables associated with survival were higher post/predialysis BUN ratios, normal Kt/V (0.8-1.2), normal albumin levels (> 3.5 g/dl), higher postdialysis BUN, creatinine, and cholesterol levels, and use of r-HuEPO. The use of r-HuEPO when analyzed by DF significantly improved MR, 8.3% as opposed to 19.2%. It is concluded that urea kinetic modeling permits shortening dialysis times without affecting mortality or hospitalization rates, and that low postdialysis BUN, post/predialysis BUN ratios, creatinine, and albumin values are correlated with a lower chance of survival.

Analysis of Variance↗

PubMedDate not supplied

Ground water model calibration using pilot points and regularization.

Use of nonlinear parameter estimation techniques is now commonplace in ground water model calibration. However, there is still ample room for further development of these techniques in order to enable them to extract more information from calibration datasets, to more thoroughly explore the uncertainty associated with model predictions, and to make them easier to implement in various modeling contexts. This paper describes the use of "pilot points" as a methodology for spatial hydraulic property characterization. When used in conjunction with nonlinear parameter estimation software that incorporates advanced regularization functionality (such as PEST), use of pilot points can add a great deal of flexibility to the calibration process at the same time as it makes this process easier to implement. Pilot points can be used either as a substitute for zones of piecewise parameter uniformity, or in conjunction with such zones. In either case, they allow the disposition of areas of high and low hydraulic property value to be inferred through the calibration process, without the need for the modeler to guess the geometry of such areas prior to estimating the parameters that pertain to them. Pilot points and regularization can also be used as an adjunct to geostatistically based stochastic parameterization methods. Using the techniques described herein, a series of hydraulic property fields can be generated, all of which recognize the stochastic characterization of an area at the same time that they satisfy the constraints imposed on hydraulic property values by the need to ensure that model outputs match field measurements. Model predictions can then be made using all of these fields as a mechanism for exploring predictive uncertainty.

Calibration↗

PubMed2004

A modeling approach for burn scar assessment using natural features and elastic property.

A modeling approach is presented for quantitative burn scar assessment. Emphases are given to: 1) constructing a finite-element model from natural image features with an adaptive mesh and 2) quantifying the Young's modulus of scars using the finite-element model and regularization method. A set of natural point features is extracted from the images of burn patients. A Delaunay triangle mesh is then generated that adapts to the point features. A three-dimensional finite-element model is built on top of the mesh with the aid of range images providing the depth information. The Young's modulus of scars is quantified with a simplified regularization functional, assuming that the knowledge of the scar's geometry is available. The consistency between the relative elasticity index and the physician's rating based on the Vancouver scale (a relative scale used to rate burn scars) indicates that the proposed modeling approach has high potential for image-based quantitative burn scar assessment.

Algorithms↗

PubMed2004

Power, selection bias and predictive performance of the Population Pharmacokinetic Covariate Model.

Identification and quantification of covariate relations is often an important part of population pharmacokinetic/pharmacodynamic (PK/PD) modelling. The covariate model is regularly built in a stepwise manner. With such methods, selection bias may be a problem if only statistically significant covariates are accepted into the model. Competition between multiple covariates may further increase selection bias, especially when there is a moderate to high correlation between the covariates. This can also result in a loss of power to find the true covariates. The aim of this simulation study was to investigate the effect on power, selection bias and predictive performance of the covariate model, when altering study design and system-related quantities. Data sets with 20-1000 subjects were investigated. Five covariates were created by sampling from a multivariate standard normal distribution. The true covariate was set up to have no, low, moderate and high correlation to the other four covariates, respectively. Data sets, in which each individual had two or three PK observations, were simulated using a one-compartment i.v. bolus model. The true covariate influenced clearance according to one of several magnitudes. Different magnitudes of residual error and inter-individual variability in the structural model parameters were also introduced to the simulation model. A total of 7400 replicate data sets were simulated independently for each combination of the above conditions. Models with one of the five simulated covariates influencing clearance and the model without any covariate were fitted to the data. The probability of selecting (according to a pre-specified P-value) the different covariates, along with the estimated covariate coefficient, was recorded. The results show that selection bias is very high for small data sets (< or = 50 subjects) simulated with a weak covariate effect. If selected under these circumstances, the covariate coefficient is on average estimated to be more than twice its true value, making the covariate model useless for predictive purposes. Surprisingly, even though competition from false covariates caused substantial loss in the power of selecting the true covariate, the already high selection bias increased only marginally. This means that the bias due to competition is negligible if statistical significance is also required for covariate selection. Bias and predictive performance are direct functions of power, only indirectly affected by study design and system-related quantities. Mainly because of selection bias, low-powered covariates can be expected to harm the predictive performance when selected. For the same reason these low-powered covariates may falsely appear to be clinically relevant when selected. If the aim of an analysis is predictive modelling, we do not recommend stepwise selection or significance testing of covariates to be performed on small or moderately sized data sets (<50-100 subjects).

Computer Simulation↗

PubMed2005

Diffuse interface approach to brittle fracture.

We present a continuum model for the propagation of cracks and fractures in brittle materials. The components of the strain tensor epsilon are the fundamental variables. The evolution equations are based on a free energy that reduces to that of linear elasticity for small epsilon, and accounts for cracks through energy saturation at large values of epsilon. We regularize the model by including terms dependent on gradients of epsilon in the free energy. No additional fields are introduced, and then the whole dynamics is perfectly defined. We show that the model is able to reproduce basic facts in fracture physics, like the Griffith's dependence of the critical stress as a minus one-half power of the crack length. In addition, regularization makes the results insensitive to the numerical mesh used, something not at all trivial in crack modeling. We present an example of the application of the model to predict the growth and curving of cracks in a nontrivial geometrical configuration.

Journal Article↗