15,305 research outputs found
Stanford Matrix Considered Harmful
This note argues about the validity of web-graph data used in the literature
Broadword Implementation of Parenthesis Queries
We continue the line of research started in "Broadword Implementation of
Rank/Select Queries" proposing broadword (a.k.a. SWAR, "SIMD Within A
Register") algorithms for finding matching closed parentheses and the k-th far
closed parenthesis. Our algorithms work in time O(log w) on a word of w bits,
and contain no branch and no test instruction. On 64-bit (and wider)
architectures, these algorithms make it possible to avoid costly tabulations,
while providing a very significant speedup with respect to for-loop
implementations
The Virasoro algebra and sectors with infinite statistical dimension
We show that the sectors with lowest weight , , j\in
{1/2}\ZZ of the local net of von Neumann algebras on the circle generated by
the Virasoro algebra with central charge c=1 have infinite statistical
dimension.Comment: 14 pages, minor changes, one reference adde
Fibonacci Binning
This note argues that when dot-plotting distributions typically found in
papers about web and social networks (degree distributions, component-size
distributions, etc.), and more generally distributions that have high
variability in their tail, an exponentially binned version should always be
plotted, too, and suggests Fibonacci binning as a visually appealing,
easy-to-use and practical choice
Supremum-Norm Convergence for Step-Asynchronous Successive Overrelaxation on M-matrices
Step-asynchronous successive overrelaxation updates the values contained in a
single vector using the usual Gau\ss-Seidel-like weighted rule, but arbitrarily
mixing old and new values, the only constraint being temporal coherence: you
cannot use a value before it has been computed. We show that given a
nonnegative real matrix , a and a vector such that , every iteration of
step-asynchronous successive overrelaxation for the problem , with , reduces geometrically the -norm of the current error by a factor that we can compute explicitly. Then,
we show that given a it is in principle always possible to
compute such a . This property makes it possible to estimate the
supremum norm of the absolute error at each iteration without any additional
hypothesis on , even when is so large that computing the product
is feasible, but estimating the supremum norm of
is not
An experimental exploration of Marsaglia's xorshift generators, scrambled
Marsaglia proposed recently xorshift generators as a class of very fast,
good-quality pseudorandom number generators. Subsequent analysis by Panneton
and L'Ecuyer has lowered the expectations raised by Marsaglia's paper, showing
several weaknesses of such generators, verified experimentally using the
TestU01 suite. Nonetheless, many of the weaknesses of xorshift generators fade
away if their result is scrambled by a non-linear operation (as originally
suggested by Marsaglia). In this paper we explore the space of possible
generators obtained by multiplying the result of a xorshift generator by a
suitable constant. We sample generators at 100 equispaced points of their state
space and obtain detailed statistics that lead us to choices of parameters that
improve on the current ones. We then explore for the first time the space of
high-dimensional xorshift generators, following another suggestion in
Marsaglia's paper, finding choices of parameters providing periods of length
and . The resulting generators are of extremely
high quality, faster than current similar alternatives, and generate
long-period sequences passing strong statistical tests using only eight logical
operations, one addition and one multiplication by a constant
On the representation theory of Virasoro Nets
We discuss various aspects of the representation theory of the local nets of
von Neumann algebras on the circle associated with positive energy
representations of the Virasoro algebra (Virasoro nets). In particular we
classify the local extensions of the Virasoro net for which the
restriction of the vacuum representation to the Virasoro subnet is a direct sum
of irreducible subrepresentations with finite statistical dimension (local
extensions of compact type). Moreover we prove that if the central charge
is in a certain subset of , including , and , the irreducible representation with lowest weight of the
corresponding Virasoro net has infinite statistical dimension. As a consequence
we show that if the central charge is in the above set and satisfies then the corresponding Virasoro net has no proper local extensions of
compact type.Comment: 34 page
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