A rigorous sequential update strategy for parallel kinetic Monte Carlo simulation

The kinetic Monte Carlo (kMC) method is used in many scientific fields in applications involving rare-event transitions. Due to its discrete stochastic nature, efforts to parallelize kMC approaches often produce unbalanced time evolutions requiring complex implementations to ensure correct statistics. In the context of parallel kMC, the sequential update technique has shown promise by generating high quality distributions with high relative efficiencies for short-range systems. In this work, we provide an extension of the sequential update method in a parallel context that rigorously obeys detailed balance, which guarantees exact equilibrium statistics for all parallelization settings. Our approach also preserves nonequilibrium dynamics with minimal error for many parallelization settings, and can be used to achieve highly precise sampling

Generalized Green Functions and current correlations in the TASEP

We study correlation functions of the totally asymmetric simple exclusion process (TASEP) in discrete time with backward sequential update. We prove a determinantal formula for the generalized Green function which describes transitions between positions of particles at different individual time moments. In particular, the generalized Green function defines a probability measure at staircase lines on the space-time plane. The marginals of this measure are the TASEP correlation functions in the space-time region not covered by the standard Green function approach. As an example, we calculate the current correlation function that is the joint probability distribution of times taken by selected particles to travel given distance. An asymptotic analysis shows that current fluctuations converge to the ${Airy}_2$ process.Comment: 46 pages, 3 figure

How Many Cooks Spoil the Soup?

In this work, we study the following basic question: "How much parallelism does a distributed task permit?" Our definition of parallelism (or symmetry) here is not in terms of speed, but in terms of identical roles that processes have at the same time in the execution. We initiate this study in population protocols, a very simple model that not only allows for a straightforward definition of what a role is, but also encloses the challenge of isolating the properties that are due to the protocol from those that are due to the adversary scheduler, who controls the interactions between the processes. We (i) give a partial characterization of the set of predicates on input assignments that can be stably computed with maximum symmetry, i.e., $\Theta(N_{min})$, where $N_{min}$ is the minimum multiplicity of a state in the initial configuration, and (ii) we turn our attention to the remaining predicates and prove a strong impossibility result for the parity predicate: the inherent symmetry of any protocol that stably computes it is upper bounded by a constant that depends on the size of the protocol.Comment: 19 page

A Tutorial on Advanced Dynamic Monte Carlo Methods for Systems with Discrete State Spaces

Advanced algorithms are necessary to obtain faster-than-real-time dynamic simulations in a number of different physical problems that are characterized by widely disparate time scales. Recent advanced dynamic Monte Carlo algorithms that preserve the dynamics of the model are described. These include the $n$-fold way algorithm, the Monte Carlo with Absorbing Markov Chains (MCAMC) algorithm, and the Projective Dynamics (PD) algorithm. To demonstrate the use of these algorithms, they are applied to some simplified models of dynamic physical systems. The models studied include a model for ion motion through a pore such as a biological ion channel and the metastable decay of the ferromagnetic Ising model. Non-trivial parallelization issues for these dynamic algorithms, which are in the class of parallel discrete event simulations, are discussed. Efforts are made to keep the article at an elementary level by concentrating on a simple model in each case that illustrates the use of the advanced dynamic Monte Carlo algorithm.Comment: 53 pages, 17 figure

Hardware implementation of non-bonded forces in molecular dynamics simulations

Molecular Dynamics is a computational method based on classical mechanics to describe the behavior of a molecular system. This method is used in biomolecular simulations, which are intended to contribute to the study and advance of nanotechnology, medicine, chemistry and biology. Software implementations of Molecular Dynamics simulations can spend most of time computing the non-bonded interactions. This work presents the design and implementation of an FPGA-based coprocessor that accelerates MD simulations by computing in parallel the non-bonded interactions, specifically, the van der Waals and the electrostatic interactions. These interactions are modeled as the Lennard-Jones 6-12 potential and the direct-space Ewald summation, respectively. In addition, this work introduces a novel variable transformation of the potential energy functions, and a novel interpolation method with pseudo-floating-point representation to compute the short-range forces. Also, it uses a combination of fixed-point and floating-point arithmetic to obtain the best of both representations. The FPGA coprocessor is a memory-mapped system connected to a host by PCI Express, and is provided with interruption capabilities to improve parallelization. Its main block is based on a single functional pipeline, and is connected via Avalon Bus to other peripherals such as the PCIe Hard-IP and the SG-DMA. It is implemented on an Altera¿s EP2AGX125EF35C4 device, can process 16k particles, and is configured to store up to 16 different types of particles. Simulations in a custom C-application for MD that only computes non-bonded forces become up to 12.5x faster using the FPGA coprocessor when considering 12500 atoms.PregradoINGENIERO(A) EN ELECTRÓNIC

Ultra-high-frequency piecewise-linear chaos using delayed feedback loops

We report on an ultra-high-frequency (> 1 GHz), piecewise-linear chaotic system designed from low-cost, commercially available electronic components. The system is composed of two electronic time-delayed feedback loops: A primary analog loop with a variable gain that produces multi-mode oscillations centered around 2 GHz and a secondary loop that switches the variable gain between two different values by means of a digital-like signal. We demonstrate experimentally and numerically that such an approach allows for the simultaneous generation of analog and digital chaos, where the digital chaos can be used to partition the system's attractor, forming the foundation for a symbolic dynamics with potential applications in noise-resilient communications and radar

Modular decomposition techniques for stored-logic digital filters

Digital filtering is an important signal processing technique whose theory is now well established. At present, however, there are no well-defined and systematic methods available for realising digital filters in hardware. This project aims to develop such methods which are general and technology independent, and adopts a systems and sub-systems design philosophy. The realisation problem is approached in a new way using concepts from finite-automata theory and implementing complete digital filter sections as stored-logic units. Two methods are introduced and developed. [Continues.