144 research outputs found
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
On SAT representations of XOR constraints
We study the representation of systems S of linear equations over the
two-element field (aka xor- or parity-constraints) via conjunctive normal forms
F (boolean clause-sets). First we consider the problem of finding an
"arc-consistent" representation ("AC"), meaning that unit-clause propagation
will fix all forced assignments for all possible instantiations of the
xor-variables. Our main negative result is that there is no polysize
AC-representation in general. On the positive side we show that finding such an
AC-representation is fixed-parameter tractable (fpt) in the number of
equations. Then we turn to a stronger criterion of representation, namely
propagation completeness ("PC") --- while AC only covers the variables of S,
now all the variables in F (the variables in S plus auxiliary variables) are
considered for PC. We show that the standard translation actually yields a PC
representation for one equation, but fails so for two equations (in fact
arbitrarily badly). We show that with a more intelligent translation we can
also easily compute a translation to PC for two equations. We conjecture that
computing a representation in PC is fpt in the number of equations.Comment: 39 pages; 2nd v. improved handling of acyclic systems, free-standing
proof of the transformation from AC-representations to monotone circuits,
improved wording and literature review; 3rd v. updated literature,
strengthened treatment of monotonisation, improved discussions; 4th v. update
of literature, discussions and formulations, more details and examples;
conference v. to appear LATA 201
Analysis of an exhaustive search algorithm in random graphs and the n^{c\log n} -asymptotics
We analyze the cost used by a naive exhaustive search algorithm for finding a
maximum independent set in random graphs under the usual G_{n,p} -model where
each possible edge appears independently with the same probability p. The
expected cost turns out to be of the less common asymptotic order n^{c\log n},
which we explore from several different perspectives. Also we collect many
instances where such an order appears, from algorithmics to analysis, from
probability to algebra. The limiting distribution of the cost required by the
algorithm under a purely idealized random model is proved to be normal. The
approach we develop is of some generality and is amenable for other graph
algorithms.Comment: 35 page
The history of degenerate (bipartite) extremal graph problems
This paper is a survey on Extremal Graph Theory, primarily focusing on the
case when one of the excluded graphs is bipartite. On one hand we give an
introduction to this field and also describe many important results, methods,
problems, and constructions.Comment: 97 pages, 11 figures, many problems. This is the preliminary version
of our survey presented in Erdos 100. In this version 2 only a citation was
complete
Sensitivity of a tonne-scale NEXT detector for neutrinoless double beta decay searches
The Neutrino Experiment with a Xenon TPC (NEXT) searches for the neutrinoless
double-beta decay of Xe-136 using high-pressure xenon gas TPCs with
electroluminescent amplification. A scaled-up version of this technology with
about 1 tonne of enriched xenon could reach in less than 5 years of operation a
sensitivity to the half-life of neutrinoless double-beta decay decay better
than 1E27 years, improving the current limits by at least one order of
magnitude. This prediction is based on a well-understood background model
dominated by radiogenic sources. The detector concept presented here represents
a first step on a compelling path towards sensitivity to the parameter space
defined by the inverted ordering of neutrino masses, and beyond.Comment: 22 pages, 11 figure
Homomorphic Secret Sharing for Low Degree Polynomials
Homomorphic secret sharing (HSS) allows clients to secret-share data to servers, who can then homomorphically evaluate public functions over the shares. A natural application is outsourced computation over private data. In this work, we present the first plain-model homomorphic secret sharing scheme that supports the evaluation of polynomials with degree higher than 2. Our construction relies on any degree- (multi-key) homomorphic encryption scheme and can evaluate degree- polynomials, for any polynomial number of inputs and any sub-logarithmic (in the security parameter) number of servers . At the heart of our work is a series of combinatorial arguments on how a polynomial can be split into several low-degree polynomials over the shares of the inputs, which we believe is of independent interest
Technical Design Report for the PANDA Solenoid and Dipole Spectrometer Magnets
This document is the Technical Design Report covering the two large
spectrometer magnets of the PANDA detector set-up. It shows the conceptual
design of the magnets and their anticipated performance. It precedes the tender
and procurement of the magnets and, hence, is subject to possible modifications
arising during this process.Comment: 10 pages, 14MB, accepted by FAIR STI in May 2009, editors: Inti
Lehmann (chair), Andrea Bersani, Yuri Lobanov, Jost Luehning, Jerzy Smyrski,
Technical Coordiantor: Lars Schmitt, Bernd Lewandowski (deputy),
Spokespersons: Ulrich Wiedner, Paola Gianotti (deputy
Feasibility studies of time-like proton electromagnetic form factors at PANDA at FAIR
Simulation results for future measurements of electromagnetic proton form
factors at \PANDA (FAIR) within the PandaRoot software framework are reported.
The statistical precision with which the proton form factors can be determined
is estimated. The signal channel is studied on the basis
of two different but consistent procedures. The suppression of the main
background channel, , is studied.
Furthermore, the background versus signal efficiency, statistical and
systematical uncertainties on the extracted proton form factors are evaluated
using two different procedures. The results are consistent with those of a
previous simulation study using an older, simplified framework. However, a
slightly better precision is achieved in the PandaRoot study in a large range
of momentum transfer, assuming the nominal beam conditions and detector
performance
Low-diffusion Xe-He gas mixtures for rare-event detection: Electroluminescence Yield
High pressure xenon Time Projection Chambers (TPC) based on secondary
scintillation (electroluminescence) signal amplification are being proposed for
rare event detection such as directional dark matter, double electron capture
and double beta decay detection. The discrimination of the rare event through
the topological signature of primary ionisation trails is a major asset for
this type of TPC when compared to single liquid or double-phase TPCs, limited
mainly by the high electron diffusion in pure xenon. Helium admixtures with
xenon can be an attractive solution to reduce the electron diffusion
significantly, improving the discrimination efficiency of these optical TPCs.
We have measured the electroluminescence (EL) yield of Xe-He mixtures, in the
range of 0 to 30% He and demonstrated the small impact on the EL yield of the
addition of helium to pure xenon. For a typical reduced electric field of 2.5
kV/cm/bar in the scintillation region, the EL yield is lowered by ~ 2%, 3%, 6%
and 10% for 10%, 15%, 20% and 30% of helium concentration, respectively. This
decrease is less than what has been obtained from the most recent simulation
framework in the literature. The impact of the addition of helium on EL
statistical fluctuations is negligible, within the experimental uncertainties.
The present results are an important benchmark for the simulation tools to be
applied to future optical TPCs based on Xe-He mixtures
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