scholarly journals Symplectic Integration for Multivariate Dynamic Spline-Based Model of Deformable Linear Objects

2021 ◽  
Author(s):  
Alaa Khalifa ◽  
Gianluca Palli
Keyword(s):  
Integration Method ◽  
Robotic Manipulation ◽  
Model Parameters ◽  
Symplectic Method ◽  
Symplectic Integration ◽  
Symplectic Integrator ◽  
Computationally Efficient ◽  
Main Motivation ◽  
Surgical Sutures ◽  
Manipulation Process

Abstract Deformable Linear Objects (DLOs) such as ropes, cables, and surgical sutures have a wide variety of uses in automotive engineering, surgery, and electromechanical industries. Therefore, modeling of DLOs as well as a computationally efficient way to predict the DLO behavior are of great importance, in particular to enable robotic manipulation of DLOs. The main motivation of this work is to enable efficient pre- diction of the DLO behavior during robotic manipulation. In this paper, the DLO is modeled by a multivariate dynamic spline, while a symplectic integration method is used to solve the model iteratively by interpolating the DLO shape during the manipulation process. Comparisons between the symplectic, Runge-Kutta and Zhai integrators are reported. The presented results show the capabilities of the symplectic integrator to overcome other integration methods in predicting the DLO behavior. Moreover, the results obtained with different sets of model parameters integrated by means of the symplectic method are reported to show how they influence the DLO behavior estimation.

Nearly Exact Bayesian Estimation of Non-linear No-Arbitrage Term-Structure Models*

2021 ◽  
Author(s):  
Marcello Pericoli ◽  
Marco Taboga
Keyword(s):  
Bayesian Estimation ◽  
Term Structure ◽  
Broad Class ◽  
Model Parameters ◽  
State Variables ◽  
Computationally Efficient ◽  
Macroeconomic Factors ◽  
No Arbitrage ◽  
Term Structure Models ◽  
Non Linear

Abstract We propose a general method for the Bayesian estimation of a very broad class of non-linear no-arbitrage term-structure models. The main innovation we introduce is a computationally efficient method, based on deep learning techniques, for approximating no-arbitrage model-implied bond yields to any desired degree of accuracy. Once the pricing function is approximated, the posterior distribution of model parameters and unobservable state variables can be estimated by standard Markov Chain Monte Carlo methods. As an illustrative example, we apply the proposed techniques to the estimation of a shadow-rate model with a time-varying lower bound and unspanned macroeconomic factors.

scholarly journals Bayesian Inference of Species Trees using Diffusion Models

2020 ◽  
Vol 70 (1) ◽  
pp. 145-161 ◽  
Author(s):  
Marnus Stoltz ◽  
Boris Baeumer ◽  
Remco Bouckaert ◽  
Colin Fox ◽  
Gordon Hiscott ◽  
...  
Keyword(s):  
Bayesian Inference ◽  
Numerical Algorithms ◽  
Diffusion Models ◽  
Model Parameters ◽  
Data Sets ◽  
Species Trees ◽  
Computationally Efficient ◽  
Data Set ◽  
Snp Data ◽  
Binary Markers

Abstract We describe a new and computationally efficient Bayesian methodology for inferring species trees and demographics from unlinked binary markers. Likelihood calculations are carried out using diffusion models of allele frequency dynamics combined with novel numerical algorithms. The diffusion approach allows for analysis of data sets containing hundreds or thousands of individuals. The method, which we call Snapper, has been implemented as part of the BEAST2 package. We conducted simulation experiments to assess numerical error, computational requirements, and accuracy recovering known model parameters. A reanalysis of soybean SNP data demonstrates that the models implemented in Snapp and Snapper can be difficult to distinguish in practice, a characteristic which we tested with further simulations. We demonstrate the scale of analysis possible using a SNP data set sampled from 399 fresh water turtles in 41 populations. [Bayesian inference; diffusion models; multi-species coalescent; SNP data; species trees; spectral methods.]

Nanoparticle Mass Transfer From Lung Airways to Systemic Regions—Part II: Multi-Compartmental Modeling

2013 ◽  
Vol 135 (12) ◽  
Author(s):  
Arun V. Kolanjiyil ◽  
Clement Kleinstreuer
Keyword(s):  
Mass Transfer ◽  
Model Parameters ◽  
Computationally Efficient ◽  
Nanoparticle Deposition ◽  
Aerosol Dynamics ◽  
Multicompartmental Model ◽  
Quantitative Results ◽  
Species Extrapolation ◽  
Critical Insight ◽  
Lung Airways

This is the second article of a two-part paper, combining high-resolution computer simulation results of inhaled nanoparticle deposition in a human airway model (Kolanjiyil and Kleinstreuer, 2013, “Nanoparticle Mass Transfer From Lung Airways to Systemic Regions—Part I: Whole-Lung Aerosol Dynamics,” ASME J. Biomech. Eng., 135(12), p. 121003) with a new multicompartmental model for insoluble nanoparticle barrier mass transfer into systemic regions. Specifically, it allows for the prediction of temporal nanoparticle accumulation in the blood and lymphatic systems and in organs. The multicompartmental model parameters were determined from experimental retention and clearance data in rat lungs and then the validated model was applied to humans based on pharmacokinetic cross-species extrapolation. This hybrid simulator is a computationally efficient tool to predict the nanoparticle kinetics in the human body. The study provides critical insight into nanomaterial deposition and distribution from the lungs to systemic regions. The quantitative results are useful in diverse fields such as toxicology for exposure-risk analysis of ubiquitous nanomaterial and pharmacology for nanodrug development and targeting.

scholarly journals Application of a computationally efficient method to approximate gap model results with a probabilistic approach

2014 ◽  
Vol 7 (1) ◽  
pp. 1535-1600
Author(s):  
M. Scherstjanoi ◽  
J. O. Kaplan ◽  
H. Lischke
Keyword(s):  
Climate Change ◽  
Efficient Method ◽  
Tree Species ◽  
Forest Dynamics ◽  
Probabilistic Approach ◽  
Age Distribution ◽  
Change Scenario ◽  
Model Parameters ◽  
Computationally Efficient ◽  
Tree Species Composition

Abstract. To be able to simulate climate change effects on forest dynamics over the whole of Switzerland, we adapted the second generation DGVM LPJ-GUESS to the Alpine environment. We modified model functions, tuned model parameters, and implemented new tree species to represent the potential natural vegetation of Alpine landscapes. Furthermore, we increased the computational efficiency of the model to enable area-covering simulations in a fine resolution (1 km) sufficient for the complex topography of the Alps, which resulted in more than 32 000 simulation grid cells. To this aim, we applied the recently developed method GAPPARD (Scherstjanoi et al., 2013) to LPJ-GUESS. GAPPARD derives mean output values from a combination of simulation runs without disturbances and a patch age distribution defined by the disturbance frequency. With this computationally efficient method, that increased the model's speed by approximately the factor 8, we were able to faster detect shortcomings of LPJ-GUESS functions and parameters. We used the adapted LPJ-GUESS together with GAPPARD to assess the influence of one climate change scenario on dynamics of tree species composition and biomass throughout the 21st century in Switzerland. To allow for comparison with the original model, we additionally simulated forest dynamics along a north-south-transect through Switzerland. The results from this transect confirmed the high value of the GAPPARD method despite some limitations towards extreme climatic events. It allowed for the first time to obtain area-wide, detailed high resolution LPJ-GUESS simulation results for a large part of the Alpine region.

scholarly journals Efficient approximations for stationary single-channel Ca2+ nanodomains across length scales

2020 ◽  
Author(s):  
Y Chen ◽  
C Muratov ◽  
V Matveev
Keyword(s):  
Parameter Space ◽  
Single Channel ◽  
Asymptotic Series ◽  
Rational Functions ◽  
Great Accuracy ◽  
Model Parameters ◽  
Relevant Parameter ◽  
Buffer Concentration ◽  
Computationally Efficient ◽  
Wide Range

ABSTRACTWe consider the stationary solution for the Ca2+ concentration near a point Ca2+ source describing a single-channel Ca2+ nanodomain, in the presence of a single mobile Ca2+ buffer with one-to-one Ca2+ binding. We present computationally efficient approximants that estimate stationary single-channel Ca2+ nanodomains with great accuracy in broad regions of parameter space. The presented approximants have a functional form that combines rational and exponential functions, which is similar to that of the well-known Excess Buffer Approximation and the linear approximation, but with parameters estimated using two novel (to our knowledge) methods. One of the methods involves interpolation between the short-range Taylor series of the buffer concentration and its long-range asymptotic series in inverse powers of distance from the channel. Although this method has already been used to find Padé (rational-function) approximants to single-channel Ca2+ and buffer concentration, extending this method to interpolants combining exponential and rational functions improves accuracy in a significant fraction of the relevant parameter space. A second method is based on the variational approach, and involves a global minimization of an appropriate functional with respect to parameters of the chosen approximations. Extensive parameter sensitivity analysis is presented, comparing these two methods with previously developed approximants. Apart from increased accuracy, the strength of these approximants is that they can be extended to more realistic buffers with multiple binding sites characterized by cooperative Ca2+ binding, such as calmodulin and calretinin.STATEMENT OF SIGNIFICANCEMathematical and computational modeling plays an important role in the study of local Ca2+ signals underlying vesicle exocysosis, muscle contraction and other fundamental physiological processes. Closed-form approximations describing steady-state distribution of Ca2+ in the vicinity of an open Ca2+ channel have proved particularly useful for the qualitative modeling of local Ca2+ signals. We present simple and efficient approximants for the Ca2+ concentration in the presence of a mobile Ca2+ buffer, which achieve great accuracy over a wide range of model parameters. Such approximations provide an efficient method for estimating Ca2+ and buffer concentrations without resorting to numerical simulations, and allow to study the qualitative dependence of nanodomain Ca2+ distribution on the buffer’s Ca2+ binding properties and its diffusivity.

scholarly journals Joint Maximum Likelihood of Phylogeny and Ancestral States Is Not Consistent

2019 ◽  
Vol 36 (10) ◽  
pp. 2352-2357
Author(s):  
David A Shaw ◽  
Vu C Dinh ◽  
Frederick A Matsen
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Likelihood Estimation ◽  
Branch Length ◽  
Continuous Model ◽  
Model Parameters ◽  
Infinite Length ◽  
Computationally Efficient ◽  
Ancestral States ◽  
Joint Method

Abstract Maximum likelihood estimation in phylogenetics requires a means of handling unknown ancestral states. Classical maximum likelihood averages over these unknown intermediate states, leading to provably consistent estimation of the topology and continuous model parameters. Recently, a computationally efficient approach has been proposed to jointly maximize over these unknown states and phylogenetic parameters. Although this method of joint maximum likelihood estimation can obtain estimates more quickly, its properties as an estimator are not yet clear. In this article, we show that this method of jointly estimating phylogenetic parameters along with ancestral states is not consistent in general. We find a sizeable region of parameter space that generates data on a four-taxon tree for which this joint method estimates the internal branch length to be exactly zero, even in the limit of infinite-length sequences. More generally, we show that this joint method only estimates branch lengths correctly on a set of measure zero. We show empirically that branch length estimates are systematically biased downward, even for short branches.

Stochastic Multi-Symplectic Integrator for Stochastic Nonlinear Schrödinger Equation

2013 ◽  
Vol 14 (2) ◽  
pp. 393-411 ◽  
Author(s):  
Shanshan Jiang ◽  
Lijin Wang ◽  
Jialin Hong
Keyword(s):  
Solitary Wave ◽  
Recurrence Relation ◽  
Conservation Law ◽  
Numerical Experiments ◽  
Symplectic Structure ◽  
Symplectic Method ◽  
Symplectic Integrator ◽  
Discrete Energy ◽  
Nonlinear Schrödinger ◽  
Discrete Charge

AbstractIn this paper we propose stochastic multi-symplectic conservation law for stochastic Hamiltonian partial differential equations, and develop a stochastic multi-symplectic method for numerically solving a kind of stochastic nonlinear Schrödinger equations. It is shown that the stochastic multi-symplectic method preserves the multi-symplectic structure, the discrete charge conservation law, and deduces the recurrence relation of the discrete energy. Numerical experiments are performed to verify the good behaviors of the stochastic multi-symplectic method in cases of both solitary wave and collision.

scholarly journals Application of a computationally efficient method to approximate gap model results with a probabilistic approach

2014 ◽  
Vol 7 (4) ◽  
pp. 1543-1571 ◽  
Author(s):  
M. Scherstjanoi ◽  
J. O. Kaplan ◽  
H. Lischke
Keyword(s):  
Climate Change ◽  
Efficient Method ◽  
Tree Species ◽  
Forest Dynamics ◽  
Probabilistic Approach ◽  
Age Distribution ◽  
Model Parameters ◽  
Gap Model ◽  
Computationally Efficient ◽  
Dynamic Global Vegetation Model

Abstract. To be able to simulate climate change effects on forest dynamics over the whole of Switzerland, we adapted the second-generation DGVM (dynamic global vegetation model) LPJ-GUESS (Lund–Potsdam–Jena General Ecosystem Simulator) to the Alpine environment. We modified model functions, tuned model parameters, and implemented new tree species to represent the potential natural vegetation of Alpine landscapes. Furthermore, we increased the computational efficiency of the model to enable area-covering simulations in a fine resolution (1 km) sufficient for the complex topography of the Alps, which resulted in more than 32 000 simulation grid cells. To this aim, we applied the recently developed method GAPPARD (approximating GAP model results with a Probabilistic Approach to account for stand Replacing Disturbances) (Scherstjanoi et al., 2013) to LPJ-GUESS. GAPPARD derives mean output values from a combination of simulation runs without disturbances and a patch age distribution defined by the disturbance frequency. With this computationally efficient method, which increased the model's speed by approximately the factor 8, we were able to faster detect the shortcomings of LPJ-GUESS functions and parameters. We used the adapted LPJ-GUESS together with GAPPARD to assess the influence of one climate change scenario on dynamics of tree species composition and biomass throughout the 21st century in Switzerland. To allow for comparison with the original model, we additionally simulated forest dynamics along a north–south transect through Switzerland. The results from this transect confirmed the high value of the GAPPARD method despite some limitations towards extreme climatic events. It allowed for the first time to obtain area-wide, detailed high-resolution LPJ-GUESS simulation results for a large part of the Alpine region.

Feasible stock trajectories: a flexible and efficient sequential estimator for use in fisheries management procedures

2012 ◽  
Vol 69 (1) ◽  
pp. 161-177 ◽  
Author(s):  
Nokome Bentley ◽  
Adam D. Langley
Keyword(s):  
Fisheries Management ◽  
Probability Distributions ◽  
Sequential Estimation ◽  
Alternative Methods ◽  
Model Parameters ◽  
Computationally Efficient ◽  
Likelihood Functions ◽  
Management Procedure ◽  
Management Procedures ◽  
Stock Recruitment

We describe a sequential estimation approach designed to be used as part of a fisheries management procedure; it is computationally efficient and able to be applied to varying types, and extents, of data. The estimator maintains a pool of stock trajectories, each having a unique combination of model parameters (e.g., stock–recruitment steepness) sampled from prior probability distributions. Each year, for each trajectory, the values of variables (e.g., current biomass) are updated and tested against specified constraints. Constraints further determine the feasibility of the trajectories by defining likelihood functions for model variables, or combinations of variables, in particular years. Trajectories that fail to meet one or more of the constraints are discarded from the pool and replaced by new trajectories. Each year, stochastic forward projections of the trajectories in the pool are used to determine an optimal catch level. The flexibility and accuracy of the estimator is evaluated using the fishery for snapper, Pagrus auratus , off northern New Zealand as a case study. The sequential nature of the algorithm suggests alternative methods of presentation for understanding and explaining the fisheries estimation process. We provide recommendations for both the evaluation and operation of management procedures that employ the estimator.

POLYNOMIAL MAP FACTORIZATION OF SYMPLECTIC MAPS

2003 ◽  
Vol 14 (06) ◽  
pp. 847-854 ◽  
Author(s):  
GOVINDAN RANGARAJAN
Keyword(s):  
Integration Method ◽  
Symplectic Integration ◽  
Stability Studies ◽  
Symplectic Maps ◽  
Long Term Stability ◽  
Polynomial Map ◽  
Symplectic Map ◽  
Integration Algorithms ◽  
Three Degree Of Freedom

Long-term stability studies of nonlinear Hamiltonian systems require symplectic integration algorithms which are both fast and accurate. In this paper, we study a symplectic integration method wherein the symplectic map representing the Hamiltonian system is refactorized using polynomial symplectic maps. This method is analyzed for the three degree of freedom case. Finally, we apply this algorithm to study a large particle storage ring.

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