18,646 research outputs found
A distributional limit law for the continued fraction digit sum
We consider the continued fraction digits as random variables measured with
respect to Lebesgue measure. The logarithmically scaled and normalized
fluctuation process of the digit sums converges strongly distributional to a
random variable uniformly distributed on the unit interval. For this process
normalized linearly we determine a large deviation asymptotic.Comment: 14 pages, 1 figur
Separated at Birth: Jet Maximization, Axis Minimization, and Stable Cone Finding
Jet finding is a type of optimization problem, where hadrons from a
high-energy collision event are grouped into jets based on a clustering
criterion. As three interesting examples, one can form a jet cluster that (1)
optimizes the overall jet four-vector, (2) optimizes the jet axis, or (3)
aligns the jet axis with the jet four-vector. In this paper, we show that these
three approaches to jet finding, despite being philosophically quite different,
can be regarded as descendants of a mother optimization problem. For the
special case of finding a single cone jet of fixed opening angle, the three
approaches are genuinely identical when defined appropriately, and the result
is a stable cone jet with the largest value of a quantity J. This relationship
is only approximate for cone jets in the rapidity-azimuth plane, as used at the
Large Hadron Collider, though the differences are mild for small radius jets.Comment: 7 pages, 2 tables; v2: references added; v3: small clarifications and
table 2 added to match journal versio
Is Determinism with regard to the Spheres of Law or Nature Consistent?
Probably the most important problem for lawyers is
the relationship between cases that confront them and the
rules of the legal order that they have to apply. Lawyers
want to know whether a certain case falls under a certain
rule or, more generally, to which set of cases a certain rule
has to be applied. If they are able to answer this question,
then those lawyers can tell you fairly precisely what the
content of a certain rule is
Energy cooperation between the EU and Switzerland Partners by destiny in search of a new model. IES Policy Paper Issue 2020/01 • January 2020
The gradual integration of EU energy policy has implications for the national energy policies of its neighbors. While members of the European Economic Area (EEA) and the Energy Community implement large parts of the EU’s energy acquis, other third countries are also affected. Switzerland—physically integrated in the European energy grid but lacking a formalized mechanism of regulatory adaptation with the EU—is an interesting case in this respect, not least because of its implications for a UK-EU relationship post-Brexit. Currently, an EU-Switzerland electricity agreement is being negotiated but its conclusion remains highly uncertain. This briefing paper highlights that either outcome—with or without an electricity agreement—has important implications for the Swiss energy transition, Swiss access to European bodies of energy policy-making, and Swiss renewable investors. Yet, even without an electricity agreement, interdependence between the Swiss and EU electricity systems will increase, creating pressure to find alternative forms of cooperation
Semi-Streaming Algorithms for Annotated Graph Streams
Considerable effort has been devoted to the development of streaming
algorithms for analyzing massive graphs. Unfortunately, many results have been
negative, establishing that a wide variety of problems require
space to solve. One of the few bright spots has been the development of
semi-streaming algorithms for a handful of graph problems -- these algorithms
use space .
In the annotated data streaming model of Chakrabarti et al., a
computationally limited client wants to compute some property of a massive
input, but lacks the resources to store even a small fraction of the input, and
hence cannot perform the desired computation locally. The client therefore
accesses a powerful but untrusted service provider, who not only performs the
requested computation, but also proves that the answer is correct.
We put forth the notion of semi-streaming algorithms for annotated graph
streams (semi-streaming annotation schemes for short). These are protocols in
which both the client's space usage and the length of the proof are . We give evidence that semi-streaming annotation schemes
represent a substantially more robust solution concept than does the standard
semi-streaming model. On the positive side, we give semi-streaming annotation
schemes for two dynamic graph problems that are intractable in the standard
model: (exactly) counting triangles, and (exactly) computing maximum matchings.
The former scheme answers a question of Cormode. On the negative side, we
identify for the first time two natural graph problems (connectivity and
bipartiteness in a certain edge update model) that can be solved in the
standard semi-streaming model, but cannot be solved by annotation schemes of
"sub-semi-streaming" cost. That is, these problems are just as hard in the
annotations model as they are in the standard model.Comment: This update includes some additional discussion of the results
proven. The result on counting triangles was previously included in an ECCC
technical report by Chakrabarti et al. available at
http://eccc.hpi-web.de/report/2013/180/. That report has been superseded by
this manuscript, and the CCC 2015 paper "Verifiable Stream Computation and
Arthur-Merlin Communication" by Chakrabarti et a
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