Showing papers by "William G. Macready published in 2007"

Processing relational database problems using analog processors

Abstract: Systems, methods and articles solve queries or database problems through the use of graphs. An association graph may be formed based on a query graph and a database graph. The association graph may be solved for a clique, providing the results to a query or problem and/or an indication of a level of responsiveness of the results. Thus, unlimited relaxation of constraint may be achieved. Analog processors such as quantum processors may be used to solve for the clique.

Graph embedding techniques

Abstract: Approaches to embedding source graphs into targets graphs in a computing system are disclosed. Such may be advantageously facilitate computation with computing systems that employ one or more analog processors, for example one or more quantum processors.

Using self‐dissimilarity to quantify complexity

Abstract: For many systems characterized as “complex” the patterns exhibited on different scales differ markedly from one another. For example, the biomass distribution in a human body “looks very different” depending on the scale at which one examines it. Conversely, the patterns at different scales in “simple” systems (e.g., gases, mountains, crystals) vary little from one scale to another. Accordingly, the degrees of self-dissimilarity between the patterns of a system at various scales constitute a complexity “signature” of that system. Here we present a novel quantification of self-dissimilarity. This signature can, if desired, incorporate a novel information-theoretic measure of the distance between probability distributions that we derive here. Whatever distance measure is chosen, our quantification of self-dissimilarity can be measured for many kinds of real-world data. This allows comparisons of the complexity signatures of wholly different kinds of systems (e.g., systems involving information density in a digital computer vs. species densities in a rain forest vs. capital density in an economy, etc.). Moreover, in contrast to many other suggested complexity measures, evaluating the self-dissimilarity of a system does not require one to already have a model of the system. These facts may allow self-dissimilarity signatures to be used as the underlying observational variables of an eventual overarching theory relating all complex systems. To illustrate self-dissimilarity, we present several numerical experiments. In particular, we show that the underlying structure of the logistic map is picked out by the self-dissimilarity signature of time series produced by that map. © 2007 Wiley Periodicals, Inc. Complexity 12: 77–85, 2007

Method and system for solving integer programming and discrete optimization problems using analog processors

Abstract: Discrete optimization problem are solved using an analog optimization device such as a quantum processor. Problems are solved using an objective function and at least one constraint corresponding to the discrete optimization problems. The objective function is converted into a first set of inputs and the at least one constraint is converted into a second set of inputs for the analog optimization device. A third set of inputs is generated which are indicative of at least one penalty coefficient. A final state of the analog optimization device corresponds to at least a portion of the solution to the discrete optimization problem.

Systems, devices, and methods for solving computational problems

Abstract: Systems, devices, and methods for using an analog processor to solve computational problems. A digital processor is configured to track computational problem processing requests received from a plurality of different users, and to track at least one of a status and a processing cost for each of the computational problem processing requests. An analog processor, for example a quantum processor, is operable to assist in producing one or more solutions to computational problems identified by the computational problem processing requests via a physical evolution.

Systems, methods and apparatus for protein folding simulation

Abstract: Analog processors such as quantum processors are employed to predict the native structures of proteins based on a primary structure of a protein. A target graph may be created of sufficient size to permit embedding of all possible native multi-dimensional topologies of the protein. At least one location in a target graph may be assigned to represent a respective amino acid forming the protein. An energy function is generated based assigned locations in the target graph. The energy function is mapped onto an analog processor, which is evolved from an initial state to a final state, the final state predicting a native structure of the protein.

Using self-dissimilarity to quantify complexity: Research Articles

Abstract: For many systems characterized as “complex” the patterns exhibited on different scales differ markedly from one another. For example, the biomass distribution in a human body “looks very different” depending on the scale at which one examines it. Conversely, the patterns at different scales in “simple” systems (e.g., gases, mountains, crystals) vary little from one scale to another. Accordingly, the degrees of self-dissimilarity between the patterns of a system at various scales constitute a complexity “signature” of that system. Here we present a novel quantification of self-dissimilarity. This signature can, if desired, incorporate a novel information-theoretic measure of the distance between probability distributions that we derive here. Whatever distance measure is chosen, our quantification of self-dissimilarity can be measured for many kinds of real-world data. This allows comparisons of the complexity signatures of wholly different kinds of systems (e.g., systems involving information density in a digital computer vs. species densities in a rain forest vs. capital density in an economy, etc.). Moreover, in contrast to many other suggested complexity measures, evaluating the self-dissimilarity of a system does not require one to already have a model of the system. These facts may allow self-dissimilarity signatures to be used as the underlying observational variables of an eventual overarching theory relating all complex systems. To illustrate self-dissimilarity, we present several numerical experiments. In particular, we show that the underlying structure of the logistic map is picked out by the self-dissimilarity signature of time series produced by that map. © 2007 Wiley Periodicals, Inc. Complexity 12: 77–85, 2007This paper was submitted as an invited paper resulting from the “Understanding Complex Systems” conference held at the University of Illinois-Urbana Champaign, May 2005.This article is a US Government work, and as such, is in the public domain in the United States of America.