2,863 research outputs found
The Fredholm index of locally compact band-dominated operators on
We establish a necessary and sufficient criterion for the Fredholmness of a
general locally compact band-dominated operator on and solve the
long-standing problem of computing its Fredholm index in terms of the limit
operators of . The results are applied to operators of convolution type with
almost periodic symbol
Geometry of the sample frequency spectrum and the perils of demographic inference
The sample frequency spectrum (SFS), which describes the distribution of
mutant alleles in a sample of DNA sequences, is a widely used summary statistic
in population genetics. The expected SFS has a strong dependence on the
historical population demography and this property is exploited by popular
statistical methods to infer complex demographic histories from DNA sequence
data. Most, if not all, of these inference methods exhibit pathological
behavior, however. Specifically, they often display runaway behavior in
optimization, where the inferred population sizes and epoch durations can
degenerate to 0 or diverge to infinity, and show undesirable sensitivity of the
inferred demography to perturbations in the data. The goal of this paper is to
provide theoretical insights into why such problems arise. To this end, we
characterize the geometry of the expected SFS for piecewise-constant
demographic histories and use our results to show that the aforementioned
pathological behavior of popular inference methods is intrinsic to the geometry
of the expected SFS. We provide explicit descriptions and visualizations for a
toy model with sample size 4, and generalize our intuition to arbitrary sample
sizes n using tools from convex and algebraic geometry. We also develop a
universal characterization result which shows that the expected SFS of a sample
of size n under an arbitrary population history can be recapitulated by a
piecewise-constant demography with only k(n) epochs, where k(n) is between n/2
and 2n-1. The set of expected SFS for piecewise-constant demographies with
fewer than k(n) epochs is open and non-convex, which causes the above phenomena
for inference from data.Comment: 21 pages, 5 figure
A multiprocessor based packet-switch: performance analysis of the communication infrastructure
The intra-chip communication infrastructures are receiving always more attention since they are becoming a crucial part in the development of current SoCs. Due to the high availability of pre-characterized hard-IP, the complexity of the design is moving toward global interconnections which are introducing always more constraints at each technology node. Power consumption, timing closure, bandwidth requirements, time to market, are some of the factors that are leading to the proposal of new solutions for next generation multi-million SoCs. The need of high programmable systems and the high gate-count availability is moving always more attention on multiprocessors systems (MP-SoC) and so an adequate solution must be found for the communication infrastructure. One of the most promising technologies is the Network-On-Chip (NoC) architecture, which seems to better fit with the new demanding complexity of such systems. Before starting to develop new solutions, it is crucial to fully understand if and when current bus architectures introduce strong limitations in the development of high speed systems. This article describes a case study of a multiprocessor based ethernet packet-switch application with a shared-bus communication infrastructure. This system aims to depict all the bottlenecks which a shared-bus introduces under heavy load. What emerges from this analysis is that, as expected, a shared-bus is not scalable and it strongly limits whole system performances. These results strengthen the hypothesis that new communication architectures (like the NoC) must be found
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