75 research outputs found
Pairs of graphs with site and bond percolation critical probabilities in opposite orders
AbstractIn simulation studies in the physics literature, there is only one pair of graphs which have site and bond percolation critical probability estimates in the opposite order. We prove that this phenomenon does occur, by constructing an infinite collection of two-dimensional infinite graphs G(n) with the property. The construction will produce such a sequence of graphs in any dimension d⩾2
Equality of bond percolation critical exponents for pairs of dual lattices
For a certain class of two-dimensional lattices, lattice-dual pairs are shown
to have the same bond percolation critical exponents. A computational proof is
given for the martini lattice and its dual to illustrate the method. The result
is generalized to a class of lattices that allows the equality of bond
percolation critical exponents for lattice-dual pairs to be concluded without
performing the computations. The proof uses the substitution method, which
involves stochastic ordering of probability measures on partially ordered sets.
As a consequence, there is an infinite collection of infinite sets of
two-dimensional lattices, such that all lattices in a set have the same
critical exponents.Comment: 10 pages, 7 figure
Bond percolation critical probability bounds for three Archimedean lattices
Abstract Rigorous bounds for the bond percolation critical probability are determined for three Archimedean lattices: .7385 < pc ((3, 12 2 ) bond) < .7449, .6430 < pc((4, 6, 12) bond) < .7376, Consequently, the bond percolation critical probability of the (3, 12 2 ) lattice is strictly larger than those of the other ten Archimedean lattices. Thus, the (3, 12 2 ) bond percolation critical probability is possibly the largest of any vertex-transitive graph with bond percolation critical probability that is strictly less than one
The critical manifolds of inhomogeneous bond percolation on bow-tie and checkerboard lattices
We give a conditional derivation of the inhomogeneous critical percolation manifold of the bow-tie lattice with five different probabilities, a problem that does not appear at first to fall into any known solvable class. Although our argument is mathematically rigorous only on a region of the manifold, we conjecture that the formula is correct over its entire domain, and we provide a non-rigorous argument for this that employs the negative probability regime of the triangular lattice critical surface. We discuss how the rigorous portion of our result substantially broadens the range of lattices in the solvable class to include certain inhomogeneous and asymmetric bow-tie lattices, and that, if it could be put on a firm foundation, the negative probability portion of our method would extend this class to many further systems, including F Y Wu’s checkerboard formula for the square lattice. We conclude by showing that this latter problem can in fact be proved using a recent result of Grimmett and Manolescu for isoradial graphs, lending strong evidence in favor of our other conjectured results. This article is part of ‘Lattice models and integrability’, a special issue of Journal of Physics A: Mathematical and Theoretical in honour of F Y Wu's 80th birthday.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/98528/1/1751-8121_45_49_494005.pd
The Online Knapsack Problem with Departures
The online knapsack problem is a classic online resource allocation problem
in networking and operations research. Its basic version studies how to pack
online arriving items of different sizes and values into a capacity-limited
knapsack. In this paper, we study a general version that includes item
departures, while also considering multiple knapsacks and multi-dimensional
item sizes. We design a threshold-based online algorithm and prove that the
algorithm can achieve order-optimal competitive ratios. Beyond worst-case
performance guarantees, we also aim to achieve near-optimal average performance
under typical instances. Towards this goal, we propose a data-driven online
algorithm that learns within a policy-class that guarantees a worst-case
performance bound. In trace-driven experiments, we show that our data-driven
algorithm outperforms other benchmark algorithms in an application of online
knapsack to job scheduling for cloud computing
Design and construction of the MicroBooNE Cosmic Ray Tagger system
The MicroBooNE detector utilizes a liquid argon time projection chamber
(LArTPC) with an 85 t active mass to study neutrino interactions along the
Booster Neutrino Beam (BNB) at Fermilab. With a deployment location near ground
level, the detector records many cosmic muon tracks in each beam-related
detector trigger that can be misidentified as signals of interest. To reduce
these cosmogenic backgrounds, we have designed and constructed a TPC-external
Cosmic Ray Tagger (CRT). This sub-system was developed by the Laboratory for
High Energy Physics (LHEP), Albert Einstein center for fundamental physics,
University of Bern. The system utilizes plastic scintillation modules to
provide precise time and position information for TPC-traversing particles.
Successful matching of TPC tracks and CRT data will allow us to reduce
cosmogenic background and better characterize the light collection system and
LArTPC data using cosmic muons. In this paper we describe the design and
installation of the MicroBooNE CRT system and provide an overview of a series
of tests done to verify the proper operation of the system and its components
during installation, commissioning, and physics data-taking
Ionization Electron Signal Processing in Single Phase LArTPCs II. Data/Simulation Comparison and Performance in MicroBooNE
The single-phase liquid argon time projection chamber (LArTPC) provides a
large amount of detailed information in the form of fine-grained drifted
ionization charge from particle traces. To fully utilize this information, the
deposited charge must be accurately extracted from the raw digitized waveforms
via a robust signal processing chain. Enabled by the ultra-low noise levels
associated with cryogenic electronics in the MicroBooNE detector, the precise
extraction of ionization charge from the induction wire planes in a
single-phase LArTPC is qualitatively demonstrated on MicroBooNE data with event
display images, and quantitatively demonstrated via waveform-level and
track-level metrics. Improved performance of induction plane calorimetry is
demonstrated through the agreement of extracted ionization charge measurements
across different wire planes for various event topologies. In addition to the
comprehensive waveform-level comparison of data and simulation, a calibration
of the cryogenic electronics response is presented and solutions to various
MicroBooNE-specific TPC issues are discussed. This work presents an important
improvement in LArTPC signal processing, the foundation of reconstruction and
therefore physics analyses in MicroBooNE.Comment: 54 pages, 36 figures; the first part of this work can be found at
arXiv:1802.0870
Ionization Electron Signal Processing in Single Phase LArTPCs I. Algorithm Description and Quantitative Evaluation with MicroBooNE Simulation
We describe the concept and procedure of drifted-charge extraction developed
in the MicroBooNE experiment, a single-phase liquid argon time projection
chamber (LArTPC). This technique converts the raw digitized TPC waveform to the
number of ionization electrons passing through a wire plane at a given time. A
robust recovery of the number of ionization electrons from both induction and
collection anode wire planes will augment the 3D reconstruction, and is
particularly important for tomographic reconstruction algorithms. A number of
building blocks of the overall procedure are described. The performance of the
signal processing is quantitatively evaluated by comparing extracted charge
with the true charge through a detailed TPC detector simulation taking into
account position-dependent induced current inside a single wire region and
across multiple wires. Some areas for further improvement of the performance of
the charge extraction procedure are also discussed.Comment: 60 pages, 36 figures. The second part of this work can be found at
arXiv:1804.0258
A Deep Neural Network for Pixel-Level Electromagnetic Particle Identification in the MicroBooNE Liquid Argon Time Projection Chamber
We have developed a convolutional neural network (CNN) that can make a
pixel-level prediction of objects in image data recorded by a liquid argon time
projection chamber (LArTPC) for the first time. We describe the network design,
training techniques, and software tools developed to train this network. The
goal of this work is to develop a complete deep neural network based data
reconstruction chain for the MicroBooNE detector. We show the first
demonstration of a network's validity on real LArTPC data using MicroBooNE
collection plane images. The demonstration is performed for stopping muon and a
charged current neutral pion data samples
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