Complementary variational principles for the steady-state finite cable model of nerve membranes

Maximum and minimum principles for the steady-state finite cable model of nerve membranes are derived from the canonical theory of complementary variational principles. An accurate variational solution is obtained in an illustrative calculation.     

Extremum principles and the elastic and fluid mechanical behaviour of the human eye

Complementary variational principles are derived for the pressure boundary value problems in Weinbaum's (1965) model of the human eye. These principles can be used to obtain accurate solutions for the pressure.     

Complementary variational principles for diffusion problems with Michaelis-Menten kinetics

The theory of complementary variational principles is used to obtain maximum and minimum principles for diffusion problems with Michaelis-Menten kinetics. In an illustrative calculation we obtain an extremely accurate variational solution in good agreement with the numerical solution of McElwain (1978).     

A Neuro-Muscular Elasto-Dynamic Model of the Human Arm Part 1: Model Development

In this paper we develop an elasto-dynamic model of the human arm for use in neuro-muscular control and dynamic interactionstudies.The motivation for this work is to present a case for developing and using non-quasistatic models of humanmusculo-skeletal biomechanics.The model is based on hybrid parameter multiple body system(HPMBS)variational projectionprinciples.In this paper,we present an overview of the HPMBS variational principle applied to the full elasto-dynamic model ofthe arm.The generality of the model allows one to incorporate muscle effects as either loads transmitted through the tendon atpoints of origin and insertion or as an effective torque at a joint.Though the technique is suitable for detailed bone and jointmodeling,we present in this initial effort only simple geometry with the bones discretized as Rayleigh beams with elongation,while allowing for large deflections.Simulations demonstrate the viability of the mcthod for use in the companion paper and infuture studies.     

Variational Principles in the Mechanics of Conformational Motions of Macromolecules in a Viscous Medium

The mechanics of the conformational motions of macromolecules due to rotations around the valence bonds in a viscous medium have been considered. The variational principles for the energy-dissipation rate during conformational motions in a viscous medium and the rate of the potential energy decrease of a macromolecule during conformational relaxation have been analyzed. The seeming contradiction between this principle and the principle of the minimum energy-dissipation rate is resolved. It is shown that the energy-dissipation rate must be optimal and minimal in order to simultaneously satisfy the conservation laws and fulfill the deterministic nature of classical trajectories. The generalization and analysis of the influence of thermal fluctuations and external forces on the variational principles for the conformational relaxation of macromolecules is carried out. A visual graphical geometric depiction has been developed using hyperspheres in the space of the velocities of chain nodes to describe conformational movements along many degrees of freedom in a viscous medium. The equipartition of the energy-dissipation rates (and the rates of potential energy decrease) among the conformational degrees of freedom is discussed.     

Development of a variational scheme for model inversion of multi-area model of brain. Part II: VBEM method

In Part I and Part II of these two companion papers (henceforth called Part I and Part II), we develop and evaluate a variational Bayesian expectation maximization (VBEM) method for model inversion of our multi-area extended neural mass model (MEN). In this paper, we develop the VBEM method to estimate posterior distributions of parameters of MEN. We choose suitable prior distributions for the model parameters in order to use properties of a conjugate-exponential model in implementing VBEM. Consequently, VBEM leads to analytically tractable forms. The proposed VBEM algorithm starts with initialization and consists of repeated iterations of a variational Bayesian expectation step (VB E-step) and a variational Bayesian maximization step (VB M-step). Posterior distributions of the model parameters are updated in the VB M-step. Distribution of the hidden state is updated in the VB E-step. We develop a variational extended Kalman smoother (VEKS) to infer the distribution of the hidden state in the VB E-step and derive the forward and backward passes of VEKS, analogous to the Kalman smoother. In Part I, we evaluate and validate the VBEM method using simulation studies.     

A Neuro-Muscular Elasto-Dynamic Model of the Human Arm Part 2: Musculotendon Dynamics and Related Stress Effects

In this paper we develop an elasto-dynamic model of the human arm that includes effects of neuro-muscular control uponelastic deformation in the limb.The elasto-dynamic model of the arm is based on hybrid parameter multiple body systemvariational projection principles presented in the companion paper.Though the technique is suitable for detailed bone and jointmodeling,we present simulations for simplified geometry of the bones,discretized as Rayleigh beams with elongation,whileallowing for large deflections.Motion of the upper extremity is simulated by incorporating muscle forces derived from aHill-type model of musculotendon dynamics.The effects of muscle force are modeled in two ways.In one approach,aneffective joint torque is calculated by multiplying the muscle force by a joint moment ann.A second approach models themuscle as acting along a straight line between the origin and insertion sites of the tendon.Simple arm motion is simulated byutilizing neural feedback and feedforward control.Simulations illustrate the combined effects of neural control strategies,models of muscle force inclusion,and elastic assumptions on joint trajectories and stress and strain development in the bone andtendon.     

Efficient approximations for learning phylogenetic HMM models from data

MOTIVATION: We consider models useful for learning an evolutionary or phylogenetic tree from data consisting of DNA sequences corresponding to the leaves of the tree. In particular, we consider a general probabilistic model described in Siepel and Haussler that we call the phylogenetic-HMM model which generalizes the classical probabilistic models of Neyman and Felsenstein. Unfortunately, computing the likelihood of phylogenetic-HMM models is intractable. We consider several approximations for computing the likelihood of such models including an approximation introduced in Siepel and Haussler, loopy belief propagation and several variational methods. RESULTS: We demonstrate that, unlike the other approximations, variational methods are accurate and are guaranteed to lower bound the likelihood. In addition, we identify a particular variational approximation to be best-one in which the posterior distribution is variationally approximated using the classic Neyman-Felsenstein model. The application of our best approximation to data from the cystic fibrosis transmembrane conductance regulator gene region across nine eutherian mammals reveals a CpG effect.     

Quantitative patterns of development of community of <Emphasis Type="Italic">Pseudomonas aeruginosa</Emphasis> dissociants

The stationary phase of batch culture of Pseudomonas aeruginosa dissociants has been described by a variational model of consumption and growth. The generalized entropy functional was used as the objective function. The model parameters include the requirements of the dissociants for the main nutrients: carbon, nitrogen, and phosphorus. The variational model was used to calculate the limiting regions and microbial community composition during stationary growth for different initial combinations of the resources as a function of the limiting resources. A correspondence between the experimental data and model calculations has been demonstrated. A possibility to control the community structure is discussed.     

A variational Bayesian mixture modelling framework for cluster analysis of gene-expression data

MOTIVATION: Accurate subcategorization of tumour types through gene-expression profiling requires analytical techniques that estimate the number of categories or clusters rigorously and reliably. Parametric mixture modelling provides a natural setting to address this problem. RESULTS: We compare a criterion for model selection that is derived from a variational Bayesian framework with a popular alternative based on the Bayesian information criterion. Using simulated data, we show that the variational Bayesian method is more accurate in finding the true number of clusters in situations that are relevant to current and future microarray studies. We also compare the two criteria using freely available tumour microarray datasets and show that the variational Bayesian method is more sensitive to capturing biologically relevant structure.     

A new approach of fitting biomass dynamics models to data

A non-traditional approach of fitting dynamic resource biomass models to data is developed in this paper. A variational adjoint technique is used for dynamic parameter estimation. In the variational formulation, a cost function measuring the distance between the model solution and the observations is minimized. The data assimilation method provides a novel and computationally efficient procedure for combining all available information, i.e., the data and the model in the analysis of a resource system. This technique will be used to analyze data for the North-east Arctic cod stock. Two alternative population growth models: the logistic and the Gompertz model are used for estimating parameters of simple bioeconomic models by the method of constrained least squares. Estimates of the parameters of the models dynamics are reasonable and can be accepted. The main inference from the work is that the average fishing mortality is found to be significantly above the maximum sustainable yield value.     

Physical models of biological information and adaptation

The bio-informational equivalence asserts that biological processes reduce to processes of information transfer. In this paper, that equivalence is treated as a metaphor with deeply anthropomorphic content of a sort that resists constitutive-analytical definition, including formulation within mathematical theories of information. It is argued that continuance of the metaphor, as a quasi-theoretical perspective in biology, must entail a methodological dislocation between biological and physical science. It is proposed that a general class of functions, drawn from classical physics, can serve to eliminate the anthropomorphism. Further considerations indicate that the concept of biological adaptation is central to the general applicability of the informational idea in biology; a non-anthropomorphic treatment of adaptive phenomena is suggested in terms of variational principles.     

Lyapunov exponents computation for hybrid neurons

Lyapunov exponents are a basic and powerful tool to characterise the long-term behaviour of dynamical systems. The computation of Lyapunov exponents for continuous time dynamical systems is straightforward whenever they are ruled by vector fields that are sufficiently smooth to admit a variational model. Hybrid neurons do not belong to this wide class of systems since they are intrinsically non-smooth owing to the impact and sometimes switching model used to describe the integrate-and-fire (I&F) mechanism. In this paper we show how a variational model can be defined also for this class of neurons by resorting to saltation matrices. This extension allows the computation of Lyapunov exponent spectrum of hybrid neurons and of networks made up of them through a standard numerical approach even in the case of neurons firing synchronously.     

Conformational analysis of stiff chiral polymers with end-constraints

We present a Lie-group-theoretic method for the kinematic and dynamic analysis of stiff chiral polymers with end constraints. The first is to determine the minimum energy conformations of stiff polymers with end constraints and the second is to perform normal mode analysis based on the determined minimum energy conformations. In this paper, we use concepts from the theory of Lie groups and principles of variational calculus to model such polymers as inextensible or extensible chiral elastic rods with coupling between stiffnesses. This method is general enough to include any stiffness and chirality parameters in the context of elastic filament models with the quadratic elastic potential energy function. As an application of this formulation, the analysis of DNA conformations is discussed. We demonstrate our method with examples of DNA conformations in which topological properties such as writhe, twist and linking number are calculated from the results of the proposed method. Given these minimum energy conformations, we describe how to perform the normal mode analysis. The results presented here build both on recent experimental work in which DNA mechanical properties have been measured and theoretical work in which the mechanics of non-chiral elastic rods has been studied.     

A 3d-fem Simulation of Highest Stress Lines in Mandible Fractures by Elastic Impact

In this article, the more usual mandible fracture areas are located by identifying the highest stress lines using a three-dimensional (tetrahedral) finite element method. By taking into account the temporomandibular contact and the inertia effects, the mathematical model is considered to be a dynamic Signorini's problem, that is, a dynamic variational inequality which is discretized in time following Newmark's method. So, in each time step a stationary variational inequality is solved by a penalty-duality algorithm. Finally, some numerical results obtained by simulating the more usual fractures in the human mandible are presented and compared with clinical experimental information.     

Structure-based modeling of energy transfer in photosynthesis

We provide a minimal model for a structure-based simulation of excitation energy transfer in pigment–protein complexes (PPCs). In our treatment, the PPC is assembled from its building blocks. The latter are defined such that electron exchange occurs only within, but not between these units. The variational principle is applied to investigate how the Coulomb interaction between building blocks changes the character of the electronic states of the PPC. In this way, the standard exciton Hamiltonian is obtained from first principles and a hierarchy of calculation schemes for the parameters of this Hamiltonian arises. Possible extensions of this approach are discussed concerning (i) the inclusion of dispersive site energy shifts and (ii) the inclusion of electron exchange between pigments. First results on electron exchange within the special pair of photosystem II of cyanobacteria and higher plants are presented and compared with earlier results on purple bacteria. In the last part of this mini-review, the coupling of electronic and nuclear degrees of freedom is considered. First, the standard exciton–vibrational Hamiltonian is parameterized with the help of a normal mode analysis of the PPC. Second, dynamical theories are discussed that exploit this Hamiltonian in the study of dissipative exciton motion.     

Bright solitary waves as charge transport in DNA: A variational approximation

Modeling energy and charge transfer in DNA has been a challenging issue because of many conformations DNA can take. Due to its simplicity, we propose a discrete variational approach to study the charge transfer mechanism in DNA based on the Holstein-Su-Schrieffer-Heeger model. It is shown that bright solitary waves may propagate through the DNA and the variational approximation provides explicit relations between experimental parameters and important characteristics of the waves such as amplitude, width, chirp and homogenous phase, and energy. Our analytical predictions are confirmed by intensive numerical simulations with a good accuracy.     

How different types of pattern formation mechanisms affect the evolution of form and development

Here we investigate how development and evolution can affect each other by exploring what kind of phenotypic variation is produced by different types of developmental mechanisms. A limited number of developmental mechanisms are capable of pattern formation in development. Two main types have been identified. In morphodynamic mechanisms, induction events and morphogenetic processes, such as simple growth, act at the same time. In morphostatic mechanisms, induction events happen before morphogenetic mechanisms, and thus growth cannot influence the induction of a pattern. We present a study of the variational properties of these developmental mechanisms that can help to understand how and why a developmental mechanism may become involved in the evolution and development of a particular morphological structure. Using existing models of pattern formation in teeth, an extensive simulation analysis of the phenotypic variation produced by different types of developmental mechanisms is performed. The studied properties include the amount and diversity of the phenotypic variation produced, the complexity of the phenotypic variation produced, and the relationship between phenotype and genotype. These variational properties are so different between different types of mechanisms that the relative involvement of these types of mechanisms in evolutionary innovation and in different stages of development can be estimated. In addition, type of mechanism affects the tempo and mode of morphological evolution. These results suggest that the basic principles by which development is organized can influence the likelihood of morphological evolution.     

A general probabilistic model for group independent component analysis and its estimation methods

Independent component analysis (ICA) has become an important tool for analyzing data from functional magnetic resonance imaging (fMRI) studies. ICA has been successfully applied to single-subject fMRI data. The extension of ICA to group inferences in neuroimaging studies, however, is challenging due to the unavailability of a prespecified group design matrix and the uncertainty in between-subjects variability in fMRI data. We present a general probabilistic ICA (PICA) model that can accommodate varying group structures of multisubject spatiotemporal processes. An advantage of the proposed model is that it can flexibly model various types of group structures in different underlying neural source signals and under different experimental conditions in fMRI studies. A maximum likelihood (ML) method is used for estimating this general group ICA model. We propose two expectation-maximization (EM) algorithms to obtain the ML estimates. The first method is an exact EM algorithm, which provides an exact E-step and an explicit noniterative M-step. The second method is a variational approximation EM algorithm, which is computationally more efficient than the exact EM. In simulation studies, we first compare the performance of the proposed general group PICA model and the existing probabilistic group ICA approach. We then compare the two proposed EM algorithms and show the variational approximation EM achieves comparable accuracy to the exact EM with significantly less computation time. An fMRI data example is used to illustrate application of the proposed methods.     

Isolating cost drivers in interstitial lung disease treatment using nonparametric Bayesian methods

Mixture modeling is a popular approach to accommodate overdispersion, skewness, and multimodality features that are very common for health care utilization data. However, mixture modeling tends to rely on subjective judgment regarding the appropriate number of mixture components or some hypothesis about how to cluster the data. In this work, we adopt a nonparametric, variational Bayesian approach to allow the model to select the number of components while estimating their parameters. Our model allows for a probabilistic classification of observations into clusters and simultaneous estimation of a Gaussian regression model within each cluster. When we apply this approach to data on patients with interstitial lung disease, we find distinct subgroups of patients with differences in means and variances of health care costs, health and treatment covariates, and relationships between covariates and costs. The subgroups identified are readily interpretable, suggesting that this nonparametric variational approach to inference can discover valid insights into the factors driving treatment costs. Moreover, the learning algorithm we employed is very fast and scalable, which should make the technique accessible for a broad range of applications.