Layout of Graphs with Bounded Tree-Width

A \emph{queue layout} of a graph consists of a total order of the vertices, and a partition of the edges into \emph{queues}, such that no two edges in the same queue are nested. The minimum number of queues in a queue layout of a graph is its \emph{queue-number}. A \emph{three-dimensional (straight-line grid) drawing} of a graph represents the vertices by points in $\mathbb{Z}^3$ and the edges by non-crossing line-segments. This paper contributes three main results: (1) It is proved that the minimum volume of a certain type of three-dimensional drawing of a graph $G$ is closely related to the queue-number of $G$. In particular, if $G$ is an $n$-vertex member of a proper minor-closed family of graphs (such as a planar graph), then $G$ has a $O(1)\times O(1)\times O(n)$ drawing if and only if $G$ has O(1) queue-number. (2) It is proved that queue-number is bounded by tree-width, thus resolving an open problem due to Ganley and Heath (2001), and disproving a conjecture of Pemmaraju (1992). This result provides renewed hope for the positive resolution of a number of open problems in the theory of queue layouts. (3) It is proved that graphs of bounded tree-width have three-dimensional drawings with O(n) volume. This is the most general family of graphs known to admit three-dimensional drawings with O(n) volume. The proofs depend upon our results regarding \emph{track layouts} and \emph{tree-partitions} of graphs, which may be of independent interest.Comment: This is a revised version of a journal paper submitted in October 2002. This paper incorporates the following conference papers: (1) Dujmovic', Morin & Wood. Path-width and three-dimensional straight-line grid drawings of graphs (GD'02), LNCS 2528:42-53, Springer, 2002. (2) Wood. Queue layouts, tree-width, and three-dimensional graph drawing (FSTTCS'02), LNCS 2556:348--359, Springer, 2002. (3) Dujmovic' & Wood. Tree-partitions of $k$-trees with applications in graph layout (WG '03), LNCS 2880:205-217, 200

Planar projections of graphs

We introduce and study a new graph representation where vertices are embedded in three or more dimensions, and in which the edges are drawn on the projections onto the axis-parallel planes. We show that the complete graph on $n$ vertices has a representation in $\lceil \sqrt{n/2}+1 \rceil$ planes. In 3 dimensions, we show that there exist graphs with $6n-15$ edges that can be projected onto two orthogonal planes, and that this is best possible. Finally, we obtain bounds in terms of parameters such as geometric thickness and linear arboricity. Using such a bound, we show that every graph of maximum degree 5 has a plane-projectable representation in 3 dimensions.Comment: Accepted at CALDAM 202

Kappa free light chains is a valid tool in the diagnostics of MS: A large multicenter study

To validate kappa free light chain (KFLC) and lambda free light chain (LFLC) indices as a diagnostic biomarker in multiple sclerosis (MS).We performed a multicenter study including 745 patients from 18 centers (219 controls and 526 clinically isolated syndrome (CIS)/MS patients) with a known oligoclonal IgG band (OCB) status. KFLC and LFLC were measured in paired cerebrospinal fluid (CSF) and serum samples. Gaussian mixture modeling was used to define a cut-off for KFLC and LFLC indexes.The cut-off for the KFLC index was 6.6 (95% confidence interval (CI) = 5.2-138.1). The cut-off for the LFLC index was 6.9 (95% CI = 4.5-22.2). For CIS/MS patients, sensitivity of the KFLC index (0.88; 95% CI = 0.85-0.90) was higher than OCB (0.82; 95%CI = 0.79-0.85; p < 0.001), but specificity (0.83; 95% CI = 0.78-0.88) was lower (OCB = 0.92; 95% CI = 0.89-0.96; p < 0.001). Both sensitivity and specificity for the LFLC index were lower than OCB.Compared with OCB, the KFLC index is more sensitive but less specific for diagnosing CIS/MS. Lacking an elevated KFLC index is more powerful for excluding MS compared with OCB but the latter is more important for ruling in a diagnosis of CIS/MS

A Search for MeV to TeV Neutrinos from Fast Radio Bursts with IceCube

We present two searches for IceCube neutrino events coincident with 28 fast radio bursts (FRBs) and 1 repeating FRB. The first improves on a previous IceCube analysis - searching for spatial and temporal correlation of events with FRBs at energies greater than roughly 50 GeV - by increasing the effective area by an order of magnitude. The second is a search for temporal correlation of MeV neutrino events with FRBs. No significant correlation is found in either search; therefore, we set upper limits on the time-integrated neutrino flux emitted by FRBs for a range of emission timescales less than one day. These are the first limits on FRB neutrino emission at the MeV scale, and the limits set at higher energies are an order-of-magnitude improvement over those set by any neutrino telescope

Efficient propagation of systematic uncertainties from calibration to analysis with the SnowStorm method in IceCube

Efficient treatment of systematic uncertainties that depend on a large number of nuisance parameters is a persistent difficulty in particle physics and astrophysics experiments. Where low-level effects are not amenable to simple parameterization or re-weighting, analyses often rely on discrete simulation sets to quantify the effects of nuisance parameters on key analysis observables. Such methods may become computationally untenable for analyses requiring high statistics Monte Carlo with a large number of nuisance degrees of freedom, especially in cases where these degrees of freedom parameterize the shape of a continuous distribution. In this paper we present a method for treating systematic uncertainties in a computationally efficient and comprehensive manner using a single simulation set with multiple and continuously varied nuisance parameters. This method is demonstrated for the case of the depth-dependent effective dust distribution within the IceCube Neutrino Telescope

Search for sources of astrophysical neutrinos using seven years of icecube cascade events

Low-background searches for astrophysical neutrino sources anywhere in the sky can be performed using cascade events induced by neutrinos of all flavors interacting in IceCube with energies as low as ∼1 TeV. Previously we showed that, even with just two years of data, the resulting sensitivity to sources in the southern sky is competitive with IceCube and ANTARES analyses using muon tracks induced by charge current muon neutrino interactions - especially if the neutrino emission follows a soft energy spectrum or originates from an extended angular region. Here, we extend that work by adding five more years of data, significantly improving the cascade angular resolution, and including tests for point-like or diffuse Galactic emission to which this data set is particularly well suited. For many of the signal candidates considered, this analysis is the most sensitive of any experiment to date. No significant clustering was observed, and thus many of the resulting constraints are the most stringent to date. In this paper we will describe the improvements introduced in this analysis and discuss our results in the context of other recent work in neutrino astronomy

Combined sensitivity to the neutrino mass ordering with JUNO, the IceCube Upgrade, and PINGU

The ordering of the neutrino mass eigenstates is one of the fundamental open questions in neutrino physics. While current-generation neutrino oscillation experiments are able to produce moderate indications on this ordering, upcoming experiments of the next generation aim to provide conclusive evidence. In this paper we study the combined performance of the two future multi-purpose neutrino oscillation experiments JUNO and the IceCube Upgrade, which employ two very distinct and complementary routes toward the neutrino mass ordering. The approach pursued by the 20 kt medium-baseline reactor neutrino experiment JUNO consists of a careful investigation of the energy spectrum of oscillated νe produced by ten nuclear reactor cores. The IceCube Upgrade, on the other hand, which consists of seven additional densely instrumented strings deployed in the center of IceCube DeepCore, will observe large numbers of atmospheric neutrinos that have undergone oscillations affected by Earth matter. In a joint fit with both approaches, tension occurs between their preferred mass-squared differences Δm312=m32-m12 within the wrong mass ordering. In the case of JUNO and the IceCube Upgrade, this allows to exclude the wrong ordering at &gt;5σ on a timescale of 3-7 years - even under circumstances that are unfavorable to the experiments' individual sensitivities. For PINGU, a 26-string detector array designed as a potential low-energy extension to IceCube, the inverted ordering could be excluded within 1.5 years (3 years for the normal ordering) in a joint analysis

Design and performance of the first IceAct demonstrator at the South Pole

In this paper we describe the first results of IceAct, a compact imaging air-Cherenkov telescope operating in coincidence with the IceCube Neutrino Observatory (IceCube) at the geographic South Pole. An array of IceAct telescopes (referred to as the IceAct project) is under consideration as part of the IceCube-Gen2 extension to IceCube. Surface detectors in general will be a powerful tool in IceCube-Gen2 for distinguishing astrophysical neutrinos from the dominant backgrounds of cosmic-ray induced atmospheric muons and neutrinos: the IceTop array is already in place as part of IceCube, but has a high energy threshold. Although the duty cycle will be lower for the IceAct telescopes than the present IceTop tanks, the IceAct telescopes may prove to be more effective at lowering the detection threshold for air showers. Additionally, small imaging air-Cherenkov telescopes in combination with IceTop, the deep IceCube detector or other future detector systems might improve measurements of the composition of the cosmic ray energy spectrum. In this paper we present measurements of a first 7-pixel imaging air Cherenkov telescope demonstrator, proving the capability of this technology to measure air showers at the South Pole in coincidence with IceTop and the deep IceCube detector

Time-Integrated Neutrino Source Searches with 10 Years of IceCube Data.

This Letter presents the results from pointlike neutrino source searches using ten years of IceCube data collected between April 6, 2008 and July 10, 2018. We evaluate the significance of an astrophysical signal from a pointlike source looking for an excess of clustered neutrino events with energies typically above ∼1  TeV among the background of atmospheric muons and neutrinos. We perform a full-sky scan, a search within a selected source catalog, a catalog population study, and three stacked Galactic catalog searches. The most significant point in the northern hemisphere from scanning the sky is coincident with the Seyfert II galaxy NGC 1068, which was included in the source catalog search. The excess at the coordinates of NGC 1068 is inconsistent with background expectations at the level of 2.9σ after accounting for statistical trials from the entire catalog. The combination of this result along with excesses observed at the coordinates of three other sources, including TXS 0506+056, suggests that, collectively, correlations with sources in the northern catalog are inconsistent with background at 3.3σ significance. The southern catalog is consistent with background. These results, all based on searches for a cumulative neutrino signal integrated over the 10 years of available data, motivate further study of these and similar sources, including time-dependent analyses, multimessenger correlations, and the possibility of stronger evidence with coming upgrades to the detector

Neutrinos below 100 TeV from the southern sky employing refined veto techniques to IceCube data

Many Galactic sources of gamma rays, such as supernova remnants, are expected to produce neutrinos with a typical energy cutoff well below 100 TeV. For the IceCube Neutrino Observatory located at the South Pole, the southern sky, containing the inner part of the Galactic plane and the Galactic Center, is a particularly challenging region at these energies, because of the large background of atmospheric muons. In this paper, we present recent advancements in data selection strategies for track-like muon neutrino events with energies below 100 TeV from the southern sky. The strategies utilize the outer detector regions as veto and features of the signal pattern to reduce the background of atmospheric muons to a level which, for the first time, allows IceCube searching for point-like sources of neutrinos in the southern sky at energies between 100 GeV and several TeV in the muon neutrino charged current channel. No significant clustering of neutrinos above background expectation was observed in four years of data recorded with the completed IceCube detector. Upper limits on the neutrino flux for a number of spectral hypotheses are reported for a list of astrophysical objects in the southern hemisphere