Enhanced sampling of multidimensional free-energy landscapes using adaptive biasing forces

We propose an adaptive biasing algorithm aimed at enhancing the sampling of multimodal measures by Langevin dynamics. The underlying idea consists in generalizing the standard adaptive biasing force method commonly used in conjunction with molecular dynamics to handle in a more effective fashion multidimensional reaction coordinates. The proposed approach is anticipated to be particularly useful for reaction coordinates, the components of which are weakly coupled, as illuminated in a mathematical analysis of the long-time convergence of the algorithm. The strength as well as the intrinsic limitation of the method are discussed and illustrated in two realistic test cases

Simulating Hamiltonian dynamics with a truncated Taylor series

We describe a simple, efficient method for simulating Hamiltonian dynamics on a quantum computer by approximating the truncated Taylor series of the evolution operator. Our method can simulate the time evolution of a wide variety of physical systems. As in another recent algorithm, the cost of our method depends only logarithmically on the inverse of the desired precision, which is optimal. However, we simplify the algorithm and its analysis by using a method for implementing linear combinations of unitary operations to directly apply the truncated Taylor series.Comment: 5 page

Intrinsic Frequency Analysis and Fast Algorithms

Intrinsic Frequency (IF) has recently been introduced as an ample signal processing method for analyzing carotid and aortic pulse pressure tracings. The IF method has also been introduced as an effective approach for the analysis of cardiovascular system dynamics. The physiological significance, convergence and accuracy of the IF algorithm has been established in prior works. In this paper, we show that the IF method could be derived by appropriate mathematical approximations from the Navier-Stokes and elasticity equations. We further introduce a fast algorithm for the IF method based on the mathematical analysis of this method. In particular, we demonstrate that the IF algorithm can be made faster, by a factor or more than 100 times, using a proper set of initial guesses based on the topology of the problem, fast analytical solution at each point iteration, and substituting the brute force algorithm with a pattern search method. Statistically, we observe that the algorithm presented in this article complies well with its brute-force counterpart. Furthermore, we will show that on a real dataset, the fast IF method can draw correlations between the extracted intrinsic frequency features and the infusion of certain drugs. In general, this paper aims at a mathematical analysis of the IF method to show its possible origins and also to present faster algorithms

FastSIR Algorithm: A Fast Algorithm for simulation of epidemic spread in large networks by using SIR compartment model

The epidemic spreading on arbitrary complex networks is studied in SIR (Susceptible Infected Recovered) compartment model. We propose our implementation of a Naive SIR algorithm for epidemic simulation spreading on networks that uses data structures efficiently to reduce running time. The Naive SIR algorithm models full epidemic dynamics and can be easily upgraded to parallel version. We also propose novel algorithm for epidemic simulation spreading on networks called the FastSIR algorithm that has better average case running time than the Naive SIR algorithm. The FastSIR algorithm uses novel approach to reduce average case running time by constant factor by using probability distributions of the number of infected nodes. Moreover, the FastSIR algorithm does not follow epidemic dynamics in time, but still captures all infection transfers. Furthermore, we also propose an efficient recursive method for calculating probability distributions of the number of infected nodes. Average case running time of both algorithms has also been derived and experimental analysis was made on five different empirical complex networks.Comment: 8 figure

Dynamic mode decomposition in vector-valued reproducing kernel Hilbert spaces for extracting dynamical structure among observables

Understanding nonlinear dynamical systems (NLDSs) is challenging in a variety of engineering and scientific fields. Dynamic mode decomposition (DMD), which is a numerical algorithm for the spectral analysis of Koopman operators, has been attracting attention as a way of obtaining global modal descriptions of NLDSs without requiring explicit prior knowledge. However, since existing DMD algorithms are in principle formulated based on the concatenation of scalar observables, it is not directly applicable to data with dependent structures among observables, which take, for example, the form of a sequence of graphs. In this paper, we formulate Koopman spectral analysis for NLDSs with structures among observables and propose an estimation algorithm for this problem. This method can extract and visualize the underlying low-dimensional global dynamics of NLDSs with structures among observables from data, which can be useful in understanding the underlying dynamics of such NLDSs. To this end, we first formulate the problem of estimating spectra of the Koopman operator defined in vector-valued reproducing kernel Hilbert spaces, and then develop an estimation procedure for this problem by reformulating tensor-based DMD. As a special case of our method, we propose the method named as Graph DMD, which is a numerical algorithm for Koopman spectral analysis of graph dynamical systems, using a sequence of adjacency matrices. We investigate the empirical performance of our method by using synthetic and real-world data.Comment: 34 pages with 4 figures, Published in Neural Networks, 201

Simulated Annealing Clusterization Algorithm for Studying the Multifragmentation

We present the details of the numerical realization of the recently advanced algorithm developed to identify the fragmentation in heavy ion reactions. This new algorithm is based on the Simulated Annealing method and is dubbed as Simulated Annealing Clusterization Algorithm [SACA]. We discuss the different parameters used in the Simulated Annealing method and present an economical set of the parameters which is based on the extensive analysis carried out for the central and peripheral collisions of Au-Au, Nb-Nb and Pb-Pb. These parameters are crucial for the success of the algorithm. Our set of optimized parameters gives the same results as the most conservative choice, but is very fast. We also discuss the nucleon and fragment exchange processes which are very important for the energy minimization and finally present the analysis of the reaction dynamics using the new algorithm. This algorithm is can be applied whenever one wants to identify which of a given number of constituents form bound objects.Comment: 36 pages, 15 figures, submitted to Journal of Computational Physic

Activation of effector immune cells promotes tumor stochastic extinction: A homotopy analysis approach

In this article we provide homotopy solutions of a cancer nonlinear model describing the dynamics of tumor cells in interaction with healthy and effector immune cells. We apply a semi-analytic technique for solving strongly nonlinear systems - the Step Homotopy Analysis Method (SHAM). This algorithm, based on a modification of the standard homotopy analysis method (HAM), allows to obtain a one-parameter family of explicit series solutions. By using the homotopy solutions, we first investigate the dynamical effect of the activation of the effector immune cells in the deterministic dynamics, showing that an increased activation makes the system to enter into chaotic dynamics via a period-doubling bifurcation scenario. Then, by adding demographic stochasticity into the homotopy solutions, we show, as a difference from the deterministic dynamics, that an increased activation of the immune cells facilitates cancer clearance involving tumor cells extinction and healthy cells persistence. Our results highlight the importance of therapies activating the effector immune cells at early stages of cancer progression

The Dynamic Exponent of the Two-Dimensional Ising Model and Monte Carlo Computation of the Sub-Dominant Eigenvalue of the Stochastic Matrix

We introduce a novel variance-reducing Monte Carlo algorithm for accurate determination of autocorrelation times. We apply this method to two-dimensional Ising systems with sizes up to $15 \times 15$, using single-spin flip dynamics, random site selection and transition probabilities according to the heat-bath method. From a finite-size scaling analysis of these autocorrelation times, the dynamical critical exponent $z$ is determined as $z=2.1665$ (12)