18,109 research outputs found
A Novel Piecewise Linear Recursive Convolution Approach for Dispersive Media Using the Finite-Difference Time-Domain Method
Peer reviewedPublisher PD
Fast recursive filters for simulating nonlinear dynamic systems
A fast and accurate computational scheme for simulating nonlinear dynamic
systems is presented. The scheme assumes that the system can be represented by
a combination of components of only two different types: first-order low-pass
filters and static nonlinearities. The parameters of these filters and
nonlinearities may depend on system variables, and the topology of the system
may be complex, including feedback. Several examples taken from neuroscience
are given: phototransduction, photopigment bleaching, and spike generation
according to the Hodgkin-Huxley equations. The scheme uses two slightly
different forms of autoregressive filters, with an implicit delay of zero for
feedforward control and an implicit delay of half a sample distance for
feedback control. On a fairly complex model of the macaque retinal horizontal
cell it computes, for a given level of accuracy, 1-2 orders of magnitude faster
than 4th-order Runge-Kutta. The computational scheme has minimal memory
requirements, and is also suited for computation on a stream processor, such as
a GPU (Graphical Processing Unit).Comment: 20 pages, 8 figures, 1 table. A comparison with 4th-order Runge-Kutta
integration shows that the new algorithm is 1-2 orders of magnitude faster.
The paper is in press now at Neural Computatio
Recursive Program Optimization Through Inductive Synthesis Proof Transformation
The research described in this paper involved developing transformation techniques which increase the efficiency of the noriginal program, the source, by transforming its synthesis proof into one, the target, which yields a computationally more efficient algorithm. We describe a working proof transformation system which, by exploiting the duality between mathematical induction and recursion, employs the novel strategy of optimizing recursive programs by transforming inductive proofs. We compare and contrast this approach with the more traditional approaches to program transformation, and highlight the benefits of proof transformation with regards to search, correctness, automatability and generality
A computer algebra user interface manifesto
Many computer algebra systems have more than 1000 built-in functions, making
expertise difficult. Using mock dialog boxes, this article describes a proposed
interactive general-purpose wizard for organizing optional transformations and
allowing easy fine grain control over the form of the result even by amateurs.
This wizard integrates ideas including:
* flexible subexpression selection;
* complete control over the ordering of variables and commutative operands,
with well-chosen defaults;
* interleaving the choice of successively less main variables with applicable
function choices to provide detailed control without incurring a combinatorial
number of applicable alternatives at any one level;
* quick applicability tests to reduce the listing of inapplicable
transformations;
* using an organizing principle to order the alternatives in a helpful
manner;
* labeling quickly-computed alternatives in dialog boxes with a preview of
their results,
* using ellipsis elisions if necessary or helpful;
* allowing the user to retreat from a sequence of choices to explore other
branches of the tree of alternatives or to return quickly to branches already
visited;
* allowing the user to accumulate more than one of the alternative forms;
* integrating direct manipulation into the wizard; and
* supporting not only the usual input-result pair mode, but also the useful
alternative derivational and in situ replacement modes in a unified window.Comment: 38 pages, 12 figures, to be published in Communications in Computer
Algebr
Efficient Instantiation of Parameterised Boolean Equation Systems to Parity Games
Parameterised Boolean Equation Systems (PBESs) are sequences of Boolean fixed point equations with data variables, used for, e.g., verification of modal μ-calculus formulae for process algebraic specifications with data. Solving a PBES is usually done by instantiation to a Parity Game and then solving the game. Practical game solvers exist, but the instantiation step is the bottleneck. We enhance the instantiation in two steps. First, we transform the PBES to a Parameterised Parity Game (PPG), a PBES with each equation either conjunctive or disjunctive. Then we use LTSmin, that offers transition caching, efficient storage of states and both distributed and symbolic state space generation, for generating the game graph. To that end we define a language module for LTSmin, consisting of an encoding of variables with parameters into state vectors, a grouped transition relation and a dependency matrix to indicate the dependencies between parts of the state vector and transition groups. Benchmarks on some large case studies, show that the method speeds up the instantiation significantly and decreases memory usage drastically
A Typed Language for Truthful One-Dimensional Mechanism Design
We first introduce a very simple typed language for expressing allocation algorithms that allows automatic verification that an algorithm is monotonic and therefore truthful. The analysis of truthfulness is accomplished using a syntax-directed transformation which constructs a proof of monotonicity based on an exhaustive critical-value analysis of the algorithm. We then define a more high-level, general-purpose programming language with typical constructs, such as those for defining recursive functions, along with primitives that match allocation algorithm combinators found in the work of Mu'alem and Nisan [10]. We demonstrate how this language can be used to combine both primitive and user-defined combinators, allowing it to capture a collection of basic truthful allocation algorithms. In addition to demonstrating the value of programming language design techniques in application to a specific domain, this work suggests a blueprint for interactive tools that can be used to teach the simple principles of truthful mechanism desig
Unification and Matching on Compressed Terms
Term unification plays an important role in many areas of computer science,
especially in those related to logic. The universal mechanism of grammar-based
compression for terms, in particular the so-called Singleton Tree Grammars
(STG), have recently drawn considerable attention. Using STGs, terms of
exponential size and height can be represented in linear space. Furthermore,
the term representation by directed acyclic graphs (dags) can be efficiently
simulated. The present paper is the result of an investigation on term
unification and matching when the terms given as input are represented using
different compression mechanisms for terms such as dags and Singleton Tree
Grammars. We describe a polynomial time algorithm for context matching with
dags, when the number of different context variables is fixed for the problem.
For the same problem, NP-completeness is obtained when the terms are
represented using the more general formalism of Singleton Tree Grammars. For
first-order unification and matching polynomial time algorithms are presented,
each of them improving previous results for those problems.Comment: This paper is posted at the Computing Research Repository (CoRR) as
part of the process of submission to the journal ACM Transactions on
Computational Logic (TOCL)
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