CRANKITE: a fast polypeptide backbone conformation sampler

Background: CRANKITE is a suite of programs for simulating backbone conformations of polypeptides and proteins. The core of the suite is an efficient Metropolis Monte Carlo sampler of backbone conformations in continuous three-dimensional space in atomic details. Methods: In contrast to other programs relying on local Metropolis moves in the space of dihedral angles, our sampler utilizes local crankshaft rotations of rigid peptide bonds in Cartesian space. Results: The sampler allows fast simulation and analysis of secondary structure formation and conformational changes for proteins of average length

Manifold Optimization Over the Set of Doubly Stochastic Matrices: A Second-Order Geometry

Convex optimization is a well-established research area with applications in almost all fields. Over the decades, multiple approaches have been proposed to solve convex programs. The development of interior-point methods allowed solving a more general set of convex programs known as semi-definite programs and second-order cone programs. However, it has been established that these methods are excessively slow for high dimensions, i.e., they suffer from the curse of dimensionality. On the other hand, optimization algorithms on manifold have shown great ability in finding solutions to nonconvex problems in reasonable time. This paper is interested in solving a subset of convex optimization using a different approach. The main idea behind Riemannian optimization is to view the constrained optimization problem as an unconstrained one over a restricted search space. The paper introduces three manifolds to solve convex programs under particular box constraints. The manifolds, called the doubly stochastic, symmetric and the definite multinomial manifolds, generalize the simplex also known as the multinomial manifold. The proposed manifolds and algorithms are well-adapted to solving convex programs in which the variable of interest is a multidimensional probability distribution function. Theoretical analysis and simulation results testify the efficiency of the proposed method over state of the art methods. In particular, they reveal that the proposed framework outperforms conventional generic and specialized solvers, especially in high dimensions

Simulation-based solution of stochastic mathematical programs with complementarity constraints: Sample-path analysis

We consider a class of stochastic mathematical programs with complementarity constraints, in which both the objective and the constraints involve limit functions or expectations that need to be estimated or approximated. Such programs can be used for modeling \\average" or steady-state behavior of complex stochastic systems. Recently, simulation-based methods have been successfully used for solving challenging stochastic optimization problems and equilibrium models. Here we broaden the applicability of so-called the sample-path method to include the solution of certain stochastic mathematical programs with equilibrium constraints. The convergence analysis of sample-path methods rely heavily on stability conditions. We first review necessary sensitivity results, then describe the method, and provide sufficient conditions for its almost-sure convergence. Alongside we provide a complementary sensitivity result for the corresponding deterministic problems. In addition, we also provide a unifying discussion on alternative set of sufficient conditions, derive a complementary result regarding the analysis of stochastic variational inequalities, and prove the equivalence of two different regularity conditions.simulation;mathematical programs with equilibrium constraints;stability;regularity conditions;sample-path methods;stochastic mathematical programs with complementarity constraints

Impact of using different models in practice - a case study with the simplified methods of ISO 13790 standard and detailed modelling programs

The updated ISO 13790 Standard is part of the new set of CEN Standards that supports the European Energy Performance of Buildings Directive (EPBD) requirement for a general framework for calculation of the energy consumption of buildings. The Standard sets out procedures for space heating and cooling energy calculations, allowing the use of three different methods: a simplified monthly quasi-steady state method, a simple-hourly method and detailed simulation. This paper examines the implications of allowing different methods to be used for assessing the energy usage. The research method used was to undertake a comparison of the various methods applied to a common building specification, with parametric analyses of variations in this specification. The paper discusses differences in results for heating and cooling requirements between the simplified methods and when a detailed simulation program (ESP-r) is used with constrained (according to the Standard) inputs and with a number of unconstrained inputs. The case where two different detailed simulation programs (ESP-r and EnergyPlus) are used in practice for the same building is also included and conclusions are drawn regarding the practical use of different detailed modelling programs against the simplified methods, as well as against each other

Unified Framework for Finite Element Assembly

At the heart of any finite element simulation is the assembly of matrices and vectors from discrete variational forms. We propose a general interface between problem-specific and general-purpose components of finite element programs. This interface is called Unified Form-assembly Code (UFC). A wide range of finite element problems is covered, including mixed finite elements and discontinuous Galerkin methods. We discuss how the UFC interface enables implementations of variational form evaluation to be independent of mesh and linear algebra components. UFC does not depend on any external libraries, and is released into the public domain

Tracking system study

A digital computer program was generated which mathematically describes an optimal estimator-controller technique as applied to the control of antenna tracking systems used by NASA. Simulation studies utilizing this program were conducted using the IBM 360/91 computer. The basic ideas of applying optimal estimator-controller techniques to antenna tracking systems are discussed. A survey of existing tracking methods is given along with shortcomings and inherent errors. It is explained how these errors can be considerably reduced if optimal estimation and control are used. The modified programs generated in this project are described and the simulation results are summarized. The new algorithms for direct synthesis and stabilization of the systems including nonlinearities, are presented

Effect of Sky Discretization for Shading Device Calculation on Building Energy Performance Simulations

The calculation of sunlit surfaces in a building has always been a relevant aspect in building energy simulation programs. Due to the high computational cost, some programs use algorithms for shading calculation for certain solar positions after discretization of hemispherical sky. The influence of the level of discretization on the estimation of incident direct radiation on building surfaces, as well as on the required computational times, are studied in this work. The direct solar energy on a window for a year, with simulation time steps of five minutes, has been simulated by using an algorithm based on Projection and Clipping Methods. A total of 6144 simulations have been carried out, varying window sizes, window orientations, typologies of shading devices, latitudes and discretization levels of the hemispherical sky. In terms of annual incident solar energy, the results show that maximum error values are about 5% for a low level of angular discretization. Errors up to 22% in hourly incident solar energy have been estimated for some of the configurations analysed. Furthermore, a great number of configurations show errors of shading factor on a window of up to 30%, which could be most relevant in studies of natural lighting. The study also shows that the improvement achieved by the most accurate discretization level implies an increase in computational cost of about 30 times

A review of the analytical simulation of aircraft crash dynamics

A large number of full scale tests of general aviation aircraft, helicopters, and one unique air-to-ground controlled impact of a transport aircraft were performed. Additionally, research was also conducted on seat dynamic performance, load-limiting seats, load limiting subfloor designs, and emergency-locator-transmitters (ELTs). Computer programs were developed to provide designers with methods for predicting accelerations, velocities, and displacements of collapsing structure and for estimating the human response to crash loads. The results of full scale aircraft and component tests were used to verify and guide the development of analytical simulation tools and to demonstrate impact load attenuating concepts. Analytical simulation of metal and composite aircraft crash dynamics are addressed. Finite element models are examined to determine their degree of corroboration by experimental data and to reveal deficiencies requiring further development

Simulation-Based Solution of Stochastic Mathematical Programs with Complementarity Constraints: Sample-Path Analysis

We consider a class of stochastic mathematical programs with complementarity constraints, in which both the objective and the constraints involve limit functions or expectations that need to be estimated or approximated.Such programs can be used for modeling average or steady-state behavior of complex stochastic systems.Recently, simulation-based methods have been successfully used for solving challenging stochastic optimization problems and equilibrium models.Here we broaden the applicability of so-called the sample-path method to include the solution of certain stochastic mathematical programs with equilibrium constraints.The convergence analysis of sample-path methods rely heavily on stability conditions.We first review necessary sensitivity results, then describe the method, and provide sufficient conditions for its almost-sure convergence.Alongside we provide a complementary sensitivity result for the corresponding deterministic problems.In addition, we also provide a unifying discussion on alternative set of sufficient conditions, derive a complementary result regarding the analysis of stochastic variational inequalities, and prove the equivalence of two different regularity conditions.stochastic processes;mathematics;stability;simulation;regulations;general equilibrium