2,000 research outputs found
Two-colorings with many monochromatic cliques in both colors
Color the edges of the n-vertex complete graph in red and blue, and suppose that red k-cliques are fewer than blue k-cliques. We show that the number of red k-cliques is always less than cknk, where ckâ(0, 1) is the unique root of the equation zk=(1-z)k+kz(1-z)k-1. On the other hand, we construct a coloring in which there are at least cknk-O(nk-1) red k-cliques and at least the same number of blue k-cliques. © 2013 Elsevier Inc
Two-Source Dispersers for Polylogarithmic Entropy and Improved Ramsey Graphs
In his 1947 paper that inaugurated the probabilistic method, Erd\H{o}s proved
the existence of -Ramsey graphs on vertices. Matching Erd\H{o}s'
result with a constructive proof is a central problem in combinatorics, that
has gained a significant attention in the literature. The state of the art
result was obtained in the celebrated paper by Barak, Rao, Shaltiel and
Wigderson [Ann. Math'12], who constructed a
-Ramsey graph, for some small universal
constant .
In this work, we significantly improve the result of Barak~\etal and
construct -Ramsey graphs, for some universal constant .
In the language of theoretical computer science, our work resolves the problem
of explicitly constructing two-source dispersers for polylogarithmic entropy
Full Scale Proton Beam Impact Testing of new CERN Collimators and Validation of a Numerical Approach for Future Operation
New collimators are being produced at CERN in the framework of a large
particle accelerator upgrade project to protect beam lines against stray
particles. Their movable jaws hold low density absorbers with tight geometric
requirements, while being able to withstand direct proton beam impacts. Such
events induce considerable thermo-mechanical loads, leading to complex
structural responses, which make the numerical analysis challenging. Hence, an
experiment has been developed to validate the jaw design under representative
conditions and to acquire online results to enhance the numerical models. Two
jaws have been impacted by high-intensity proton beams in a dedicated facility
at CERN and have recreated the worst possible scenario in future operation. The
analysis of online results coupled to post-irradiation examinations have
demonstrated that the jaw response remains in the elastic domain. However, they
have also highlighted how sensitive the jaw geometry is to its mounting support
inside the collimator. Proton beam impacts, as well as handling activities, may
alter the jaw flatness tolerance value by 70 m, whereas the
flatness tolerance requirement is 200 m. In spite of having validated
the jaw design for this application, the study points out numerical limitations
caused by the difficulties in describing complex geometries and boundary
conditions with such unprecedented requirements.Comment: 22 pages, 17 figures, Prepared for submission to JINS
Non locality, closing the detection loophole and communication complexity
It is shown that the detection loophole which arises when trying to rule out
local realistic theories as alternatives for quantum mechanics can be closed if
the detection efficiency is larger than
where is the dimension of the entangled system. Furthermore it is argued
that this exponential decrease of the detector efficiency required to close the
detection loophole is almost optimal. This argument is based on a close
connection that exists between closing the detection loophole and the amount of
classical communication required to simulate quantum correlation when the
detectors are perfect.Comment: 4 pages Latex, minor typos correcte
Mutation testing on an object-oriented framework: An experience report
This is the preprint version of the article - Copyright @ 2011 ElsevierContext
The increasing presence of Object-Oriented (OO) programs in industrial systems is progressively drawing the attention of mutation researchers toward this paradigm. However, while the number of research contributions in this topic is plentiful, the number of empirical results is still marginal and mostly provided by researchers rather than practitioners.
Objective
This article reports our experience using mutation testing to measure the effectiveness of an automated test data generator from a user perspective.
Method
In our study, we applied both traditional and class-level mutation operators to FaMa, an open source Java framework currently being used for research and commercial purposes. We also compared and contrasted our results with the data obtained from some motivating faults found in the literature and two real tools for the analysis of feature models, FaMa and SPLOT.
Results
Our results are summarized in a number of lessons learned supporting previous isolated results as well as new findings that hopefully will motivate further research in the field.
Conclusion
We conclude that mutation testing is an effective and affordable technique to measure the effectiveness of test mechanisms in OO systems. We found, however, several practical limitations in current tool support that should be addressed to facilitate the work of testers. We also missed specific techniques and tools to apply mutation testing at the system level.This work has been partially supported by the European Commission (FEDER) and Spanish Government under CICYT Project SETI (TIN2009-07366) and the Andalusian Government Projects ISABEL (TIC-2533) and THEOS (TIC-5906)
Synchronizing Automata on Quasi Eulerian Digraph
In 1964 \v{C}ern\'{y} conjectured that each -state synchronizing automaton
posesses a reset word of length at most . From the other side the best
known upper bound on the reset length (minimum length of reset words) is cubic
in . Thus the main problem here is to prove quadratic (in ) upper bounds.
Since 1964, this problem has been solved for few special classes of \sa. One of
this result is due to Kari \cite{Ka03} for automata with Eulerian digraphs. In
this paper we introduce a new approach to prove quadratic upper bounds and
explain it in terms of Markov chains and Perron-Frobenius theories. Using this
approach we obtain a quadratic upper bound for a generalization of Eulerian
automata.Comment: 8 pages, 1 figur
Testing Linear-Invariant Non-Linear Properties
We consider the task of testing properties of Boolean functions that are
invariant under linear transformations of the Boolean cube. Previous work in
property testing, including the linearity test and the test for Reed-Muller
codes, has mostly focused on such tasks for linear properties. The one
exception is a test due to Green for "triangle freeness": a function
f:\cube^{n}\to\cube satisfies this property if do not all
equal 1, for any pair x,y\in\cube^{n}.
Here we extend this test to a more systematic study of testing for
linear-invariant non-linear properties. We consider properties that are
described by a single forbidden pattern (and its linear transformations), i.e.,
a property is given by points v_{1},...,v_{k}\in\cube^{k} and
f:\cube^{n}\to\cube satisfies the property that if for all linear maps
L:\cube^{k}\to\cube^{n} it is the case that do
not all equal 1. We show that this property is testable if the underlying
matroid specified by is a graphic matroid. This extends
Green's result to an infinite class of new properties.
Our techniques extend those of Green and in particular we establish a link
between the notion of "1-complexity linear systems" of Green and Tao, and
graphic matroids, to derive the results.Comment: This is the full version; conference version appeared in the
proceedings of STACS 200
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Where Are My Intelligent Assistant's Mistakes? A Systematic Testing Approach
Intelligent assistants are handling increasingly critical tasks, but until now, end users have had no way to systematically assess where their assistants make mistakes. For some intelligent assistants, this is a serious problem: if the assistant is doing work that is important, such as assisting with qualitative research or monitoring an elderly parentâs safety, the user may pay a high cost for unnoticed mistakes. This paper addresses the problem with WYSIWYT/ML (What You See Is What You Test for Machine Learning), a human/computer partnership that enables end users to systematically test intelligent assistants. Our empirical evaluation shows that WYSIWYT/ML helped end users find assistantsâ mistakes significantly more effectively than ad hoc testing. Not only did it allow users to assess an assistantâs work on an average of 117 predictions in only 10 minutes, it also scaled to a much larger data set, assessing an assistantâs work on 623 out of 1,448 predictions using only the usersâ original 10 minutesâ testing effort
Chromatic number, clique subdivisions, and the conjectures of Haj\'os and Erd\H{o}s-Fajtlowicz
For a graph , let denote its chromatic number and
denote the order of the largest clique subdivision in . Let H(n) be the
maximum of over all -vertex graphs . A famous
conjecture of Haj\'os from 1961 states that for every
graph . That is, for all positive integers . This
conjecture was disproved by Catlin in 1979. Erd\H{o}s and Fajtlowicz further
showed by considering a random graph that for some
absolute constant . In 1981 they conjectured that this bound is tight up
to a constant factor in that there is some absolute constant such that
for all -vertex graphs . In this
paper we prove the Erd\H{o}s-Fajtlowicz conjecture. The main ingredient in our
proof, which might be of independent interest, is an estimate on the order of
the largest clique subdivision which one can find in every graph on
vertices with independence number .Comment: 14 page
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