Michael C. Sullivan

Balancing DRAM locality and parallelism in shared memory CMP systems

Modern memory systems rely on spatial locality to provide high bandwidth while minimizing memory device power and cost. The trend of increasing the number of cores that share memory, however, decreases apparent spatial locality because access streams from independent threads are interleaved. Memory access scheduling recovers only a fraction of the original locality because of buffering limits. We investigate new techniques to reduce inter-thread access interference. We propose to partition the internal memory banks between cores to isolate their access streams and eliminate locality interference. We implement this by extending the physical frame allocation algorithm of the OS such that physical frames mapped to the same DRAM bank can be exclusively allocated to a single thread. We compensate for the reduced bank-level parallelism of each thread by employing memory sub-ranking to effectively increase the number of independent banks. This combined approach, unlike memory bank partitioning or sub-ranking alone, simultaneously increases overall performance and significantly reduces memory power consumption.

Visually building Smale flows in S3

Abstract A Smale flow is a structurally stable flow with one-dimensional invariant sets. We use information from homology and template theory to construct, visualize and in some cases, classify, nonsingular Smale flows in the 3-sphere.

THE PRIME DECOMPOSITION OF KNOTTED PERIODIC ORBITS IN DYNAMICAL SYSTEMS

Templates are used to capture the knotting and linking patterns of periodic orbits of positive entropy flows in 3 dimensions. Here, we study the properties of various templates, especially whether or not there is a bound on the number of prime factors of the knot types of the periodic orbits. We will also see that determining whether two templates are different is highly nontrivial.

Prime Decomposition of Knots in Lorenz-like Templates

In [8] R.F. Williams showed that all knots in the Lorenz template are prime. His proof included the cases where any number of positive twists were added to one of the template’s branches. However [8] does give an example of a composite knot in a template with a single negative twist. Below we will show that in all the negative cases composite knots do exist, and give a mechanism for producing many examples. This problem was cited in a list of problems in dynamics in [1, problem 4.2].

Composite Knots in the Figure-8 Knot Complement Can Have Any Number of Prime Factors

Abstract We study an Anosov flow ∅ t in S 3 – \s{figure-8 knot\s}. Birman and Williams conjectured that the knot types of the periodic orbits of this flow could have at most two prime factors. Below, we give a geometric method for constructing knots in this flow with any number of prime factors.

An Invariant of Basic Sets of Smale Flows

We consider one-dimensional flows which arise as hyperbolic invariant sets of a smooth flow on a manifold. Included in our data is the twisting in the local stable and unstable manifolds. A topological invariant sensitive to this twisting is obtained.

Positive Braids with a Half Twist are Prime

We shall prove that a knot which can be represented by a positive braid with a half twist is prime. This is done by associating to each such braid a smooth branched 2-manifold with boundary and studying its intersection with a would-be cutting sphere.

A zeta function for flows with positive templates

Abstract A zeta function for a map f : M → M is a device for counting periodic orbits. For a topological flow however, there is not a clear meaning to the period of a closed orbit. We circumvent this for flows which have positive templates by counting the “twists” in the stable manifolds of the periodic orbits.

FACTORING FAMILIES OF POSITIVE KNOTS ON LORENZ-LIKE TEMPLATES

We show that for m and n positive, composite closed orbits realized on the Lorenz-like template L(m, n) have two prime factors, each a torus knot; and that composite closed orbits on L(-1, -1) have either two for three prime factors, two of which are torus knots.

Quantum Invariants of Templates

We define invariants for templates that appear in certain dynamical systems. Invariants are derived from certain bialgebras. Diagrammatic relations between projections of templates and the algebraic structures are used to define invariants. We also construct 3-manifolds via framed links associated to tamplate diagrams, so that any 3-manifold invariant can be used as a template invariant.