11,895 research outputs found
Modern Approaches to Exact Diagonalization and Selected Configuration Interaction with the Adaptive Sampling CI Method.
Recent advances in selected configuration interaction methods have made them competitive with the most accurate techniques available and, hence, creating an increasingly powerful tool for solving quantum Hamiltonians. In this work, we build on recent advances from the adaptive sampling configuration interaction (ASCI) algorithm. We show that a useful paradigm for generating efficient selected CI/exact diagonalization algorithms is driven by fast sorting algorithms, much in the same way iterative diagonalization is based on the paradigm of matrix vector multiplication. We present several new algorithms for all parts of performing a selected CI, which includes new ASCI search, dynamic bit masking, fast orbital rotations, fast diagonal matrix elements, and residue arrays. The ASCI search algorithm can be used in several different modes, which includes an integral driven search and a coefficient driven search. The algorithms presented here are fast and scalable, and we find that because they are built on fast sorting algorithms they are more efficient than all other approaches we considered. After introducing these techniques, we present ASCI results applied to a large range of systems and basis sets to demonstrate the types of simulations that can be practically treated at the full-CI level with modern methods and hardware, presenting double- and triple-ζ benchmark data for the G1 data set. The largest of these calculations is Si2H6 which is a simulation of 34 electrons in 152 orbitals. We also present some preliminary results for fast deterministic perturbation theory simulations that use hash functions to maintain high efficiency for treating large basis sets
On the Benefit of Merging Suffix Array Intervals for Parallel Pattern Matching
We present parallel algorithms for exact and approximate pattern matching
with suffix arrays, using a CREW-PRAM with processors. Given a static text
of length , we first show how to compute the suffix array interval of a
given pattern of length in
time for . For approximate pattern matching with differences or
mismatches, we show how to compute all occurrences of a given pattern in
time, where is the size of the alphabet
and . The workhorse of our algorithms is a data structure
for merging suffix array intervals quickly: Given the suffix array intervals
for two patterns and , we present a data structure for computing the
interval of in sequential time, or in
parallel time. All our data structures are of size bits (in addition to
the suffix array)
BioSimulator.jl: Stochastic simulation in Julia
Biological systems with intertwined feedback loops pose a challenge to
mathematical modeling efforts. Moreover, rare events, such as mutation and
extinction, complicate system dynamics. Stochastic simulation algorithms are
useful in generating time-evolution trajectories for these systems because they
can adequately capture the influence of random fluctuations and quantify rare
events. We present a simple and flexible package, BioSimulator.jl, for
implementing the Gillespie algorithm, -leaping, and related stochastic
simulation algorithms. The objective of this work is to provide scientists
across domains with fast, user-friendly simulation tools. We used the
high-performance programming language Julia because of its emphasis on
scientific computing. Our software package implements a suite of stochastic
simulation algorithms based on Markov chain theory. We provide the ability to
(a) diagram Petri Nets describing interactions, (b) plot average trajectories
and attached standard deviations of each participating species over time, and
(c) generate frequency distributions of each species at a specified time.
BioSimulator.jl's interface allows users to build models programmatically
within Julia. A model is then passed to the simulate routine to generate
simulation data. The built-in tools allow one to visualize results and compute
summary statistics. Our examples highlight the broad applicability of our
software to systems of varying complexity from ecology, systems biology,
chemistry, and genetics. The user-friendly nature of BioSimulator.jl encourages
the use of stochastic simulation, minimizes tedious programming efforts, and
reduces errors during model specification.Comment: 27 pages, 5 figures, 3 table
Algebraic Methods in the Congested Clique
In this work, we use algebraic methods for studying distance computation and
subgraph detection tasks in the congested clique model. Specifically, we adapt
parallel matrix multiplication implementations to the congested clique,
obtaining an round matrix multiplication algorithm, where
is the exponent of matrix multiplication. In conjunction
with known techniques from centralised algorithmics, this gives significant
improvements over previous best upper bounds in the congested clique model. The
highlight results include:
-- triangle and 4-cycle counting in rounds, improving upon the
triangle detection algorithm of Dolev et al. [DISC 2012],
-- a -approximation of all-pairs shortest paths in
rounds, improving upon the -round -approximation algorithm of Nanongkai [STOC 2014], and
-- computing the girth in rounds, which is the first
non-trivial solution in this model.
In addition, we present a novel constant-round combinatorial algorithm for
detecting 4-cycles.Comment: This is work is a merger of arxiv:1412.2109 and arxiv:1412.266
Enhanced goal-oriented error assessment and computational strategies in adaptive reduced basis solver for stochastic problems
This work focuses on providing accurate low-cost approximations of stochastic ¿nite elements simulations in the framework of linear elasticity. In a previous work, an adaptive strategy was introduced as an improved Monte-Carlo method for multi-dimensional large stochastic problems. We provide here a complete analysis of the method including a new enhanced goal-oriented error estimator and estimates of CPU (computational processing unit) cost gain. Technical insights of these two topics are presented in details, and numerical examples show the interest of these new developments.Postprint (author's final draft
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