In algorithms based on reference counting, a garbage-collection decision has to be made whenever a pointer x→ y is about to be destroyed. At this time, the node y may become dead even if y’s reference count is not zero. This is because y may belong to a piece of cyclic garbage. Some aggressive collection algorithms will put y on the list of potential garbage regardless of y’s reference count. L...

Abstra t. We solve vis ous Burger's equation using a fast and a urate algorithm referred to here as the redu tion algorithm for omputing near optimal rational approximations. Given a proper rational fun tion with n poles, the redu tion algorithm omputes (for a desired L ∞ -approximation error) a rational approximation of the same form, but with a (near) optimally small number m ≪ n of poles. Al...

In this lecture we use Azuma’s inequality to analyze the randomized Quicksort algorithm. Quicksort takes as input a set S of numbers, which can be assumed to be distinct without loss of generality, and sorts the set S as follows: it picks a pivot x ∈ S uniformly at random, then it partitions the set S as Sx = {y ∈ S | y > x}, and recursively sorts Sx . The fo...

This paper presents a new left-looking parallel sparse Cholesky fac,torization algorithm for shared-memory MIMD multiprocessors. The algorithm is particularly well-suited for vector supercomputers with multiple processors, such as the Cray Y-MP. The new algorithm uses supernodes in the Cholesky factor to improve performance by reducing indirect addressing and memory traffic. Earlier factorizati...

Recently, we developed and implemented the bond-propagation algorithm for calculating the partition function and correlation functions of random-bond Ising models in two dimensions Y. L. Loh and E. W. Carlson, Phys. Rev. Lett. 97, 227205 2006 . The algorithm is the fastest available for calculating these quantities near the percolation threshold. In this paper, we show how to extend the bond-pr...

FORWARD ALGORITHMS Two observations: • PAVA is efficient and generalizes to partial orders • Follow The Leader algorithms are common in practice Forward Algorithm: To predict at xt, imagine y′ t ∈ [0, 1], compute f∗ on {(x1, y1) . . . (xt−1, yt−1)} ∪ {(xt, y′ t)}, and play ŷt = f(xt). FORWARD ALGORITHM EXAMPLES • IR-Int: Compute f∗ on past data. Predict with average of f∗ at nearest xi. • Inter...

In this article, we try to construct an algorithm to compute the Heegaard Floer homology ĤF (Y ) for a 3-manifold Y . The method can also be used to compute the filtration coming from a knot K in Y .

So far, we’ve mainly been talking about learning algorithms that model p(y|x; θ), the conditional distribution of y given x. For instance, logistic regression modeled p(y|x; θ) as hθ(x) = g(θx) where g is the sigmoid function. In these notes, we’ll talk about a different type of learning algorithm. Consider a classification problem in which we want to learn to distinguish between elephants (y =...

So far, we’ve mainly been talking about learning algorithms that model p(y|x; θ), the conditional distribution of y given x. For instance, logistic regression modeled p(y|x; θ) as hθ(x) = g(θ T x) where g is the sigmoid function. In these notes, we’ll talk about a different type of learning algorithm. Consider a classification problem in which we want to learn to distinguish between elephants (...