On Equidomination in Graphs

A graph G=(V,E) is called equidominating if there exists a value t in IN and a weight function w : V -> IN such that the total weight of a subset D of V is equal to t if and only if D is a minimal dominating set. Further, w is called an equidominating function, t a target value and the pair (w,t) an equidominating structure. To decide whether a given graph is equidominating is referred to as the EQUIDOMINATION problem. First, we examine several results on standard graph classes and operations with respect to equidomination. Furthermore, we characterize hereditarily equidominating graphs. These are the graphs whose every induced subgraph is equidominating. For those graphs, we give a finite forbidden induced subgraph characterization and a structural decomposition. Using this decomposition, we state a polynomial time algorithm that recognizes hereditarily equidominating graphs. We introduce two parameterized versions of the EQUIDOMINATION problem: the k-EQUIDOMINATION problem and the TARGET-t EQUIDOMINATION problem. For k in IN, a graph is called k-equidominating if we can identify the minimal dominating sets using only weights from 1 to k. In other words, if an equidominating function with co-domain {1,...,k} exists. For t in IN, a graph is said to be target-t equidominating if there is an equidominating structure with target value t. For both parameterized problems we prove fixed-parameter tractability. The first step for this is to achieve the so-called pseudo class partition, which coarsens the twin partition. It is founded on the requirement that vertices from different blocks of the partition cannot have equal weights in any equidominating structure. Based on the pseudo class partition, we state an XP algorithm for the parameterized versions of the EQUIDOMINATION problem. The second step is the examination of three reduction rules - each of them concerning a specific type of block of the pseudo class partition - which we use to construct problem kernels. The sizes of the kernels are bounded by a function depending only on the respective parameter. By applying the XP algorithm to the kernels, we achieve FPT algorithms. The concept of equidomination was introduced nearly 40 years ago, but hardly any investigations exist. With this thesis, we want to fill that gap. We may lay the foundation for further research on equidomination

Evaluation of Concomitant Systemic Treatment in Older Adults With Head and Neck Squamous Cell Carcinoma Undergoing Definitive Radiotherapy

IMPORTANCE The number of older adults with head and neck squamous cell carcinoma (HNSCC) is increasing, and these patients are underrepresented in clinical trials. It is unclear whether the addition of chemotherapy or cetuximab to radiotherapy is associated with improved survival in older adults with HNSCC. OBJECTIVE To examine whether the addition of chemotherapy or cetuximab to definitive radiotherapy is associated with improved survival in patients with locoregionally advanced (LA) HNSCC. DESIGN, SETTING, AND PARTICIPANTS The Special Care Patterns for Elderly HNSCC Patients Undergoing Radiotherapy (SENIOR) study is an international, multicenter cohort study including older adults (≥65 years) with LA-HNSCCs of the oral cavity, oropharynx/hypopharynx, or larynx treated with definitive radiotherapy, either alone or with concomitant systemic treatment, between January 2005 and December 2019 at 12 academic centers in the US and Europe. Data analysis was conducted from June 4 to August 10, 2022. INTERVENTIONS All patients underwent definitive radiotherapy alone or with concomitant systemic treatment. MAIN OUTCOMES AND MEASURES The primary outcome was overall survival. Secondary outcomes included progression-free survival and locoregional failure rate. RESULTS Among the 1044 patients (734 men [70.3%]; median [IQR] age, 73 [69-78] years) included in this study, 234 patients (22.4%) were treated with radiotherapy alone and 810 patients (77.6%) received concomitant systemic treatment with chemotherapy (677 [64.8%]) or cetuximab (133 [12.7%]). Using inverse probability weighting to attribute for selection bias, chemoradiation was associated with longer overall survival than radiotherapy alone (hazard ratio [HR], 0.61; 95% CI, 0.48-0.77; P < .001), whereas cetuximab-based bioradiotherapy was not (HR, 0.94; 95% CI, 0.70-1.27; P = .70). Progression-free survival was also longer after the addition of chemotherapy (HR, 0.65; 95% CI, 0.52-0.81; P < .001), while the locoregional failure rate was not significantly different (subhazard ratio, 0.62; 95% CI, 0.30-1.26; P = .19). The survival benefit of the chemoradiation group was present in patients up to age 80 years (65-69 years: HR, 0.52; 95% CI, 0.33-0.82; 70-79 years: HR, 0.60; 95% CI, 0.43-0.85), but was absent in patients aged 80 years or older (HR, 0.89; 95% CI, 0.56-1.41). CONCLUSIONS AND RELEVANCE In this cohort study of older adults with LA- HNSCC, chemoradiation, but not cetuximab-based bioradiotherapy, was associated with longer survival compared with radiotherapy alone

Charge-dependent curvature-bias corrections using a pseudomass method

International audienceMomentum measurements for very high momentum charged particles, such as muons from electroweak vector boson decays, are particularly susceptible to charge-dependent curvature biases that arise from misalignments of tracking detectors. Low momentum charged particles used in alignment procedures have limited sensitivity to coherent displacements of such detectors, and therefore are unable to fully constrain these misalignments to the precision necessary for studies of electroweak physics. Additional approaches are therefore required to understand and correct for these effects. In this paper the curvature biases present at the LHCb detector are studied using the pseudomass method in proton-proton collision data recorded at centre of mass energy $\sqrt{s}=13$ TeV during 2016, 2017 and 2018. The biases are determined using $Z\to\mu^+\mu^-$ decays in intervals defined by the data-taking period, magnet polarity and muon direction. Correcting for these biases, which are typically at the $10^{-4}$ GeV$^{-1}$ level, improves the $Z\to\mu^+\mu^-$ mass resolution by roughly 20% and eliminates several pathological trends in the kinematic-dependence of the mean dimuon invariant mass

Observation of the Bc+→J/ψπ+π0B_c^+ \to J/\psi \pi^+ \pi^0 decay

International audienceThe first observation of the $B_c^+ \to J/\psi \pi^+ \pi^0$ decay is reported with high significance using proton-proton collision data, corresponding to an integrated luminosity of 9fb$^{-1}$, collected with the LHCb detector at centre-of-mass energies of 7, 8, and 13 TeV. The ratio of its branching fraction relative to the $B_c^+ \to J/\psi \pi^+$ channel is measured to be $$\frac{ {\cal{B}}( B_c^+ \to J/\psi \pi^+\pi^0 ) } { {\cal{B}}( B_c^+ \to J/\psi \pi^+ ) } = 2.80 \pm 0.15 \pm 0.11 \pm 0.16 \,,$$ where the first uncertainty is statistical, the second systematic and the third related to imprecise knowledge of the branching fractions for $B^+ \to J/\psi K^{*+}$ and $B^+ \to J/\psi K^+$ decays, which are used to determine the $\pi^0$ detection efficiency. The $\pi^+\pi^0$ mass spectrum is found to be consistent with the dominance of an intermediate $\rho^+$ contribution in accordance with a model based on QCD factorisation

Study of Bc+→χcπ+B_c^+ \rightarrow \chi_c \pi^+ decays

International audienceA study of $B_c^+ \rightarrow \chi_c \pi^+$ decays is reported using proton-proton collision data, collected with the LHCb detector at centre-of-mass energies of 7, 8, and 13 TeV, corresponding to an integrated luminosity of 9fb$^{-1}$. The decay $B_c^+ \rightarrow \chi_{c2} \pi^+$ is observed for the first time, with a significance exceeding seven standard deviations. The relative branching fraction with respect to the $B_c^+ \rightarrow J/\psi \pi^+$ decay is measured to be $$\frac{\mathcal{B}_{B_c^+ \rightarrow \chi_{c2} \pi^+}} {\mathcal{B}_{B_c^+ \rightarrow J/\psi \pi^+}} = 0.37 \pm 0.06 \pm 0.02 \pm 0.01 ,$$ where the first uncertainty is statistical, the second is systematic, and the third is due to the knowledge of the $\chi_c \rightarrow J/\psi \gamma$ branching fraction. No significant $B_c^+ \rightarrow \chi_{c1} \pi^+$ signal is observed and an upper limit for the relative branching fraction for the $B_c^+ \rightarrow \chi_{c1} \pi^+$ and $B_c^+ \rightarrow \chi_{c2} \pi^+$ decays of $$\frac{\mathcal{B}_{B_c^+ \rightarrow \chi_{c1} \pi^+}} {\mathcal{B}_{B_c^+ \rightarrow \chi_{c2} \pi^+}} < 0.49$$ is set at the 90% confidence level

Study of Bc+→χcπ+B_c^+ \rightarrow \chi_c \pi^+ decays

International audienceA study of $B_c^+ \rightarrow \chi_c \pi^+$ decays is reported using proton-proton collision data, collected with the LHCb detector at centre-of-mass energies of 7, 8, and 13 TeV, corresponding to an integrated luminosity of 9fb$^{-1}$. The decay $B_c^+ \rightarrow \chi_{c2} \pi^+$ is observed for the first time, with a significance exceeding seven standard deviations. The relative branching fraction with respect to the $B_c^+ \rightarrow J/\psi \pi^+$ decay is measured to be $$\frac{\mathcal{B}_{B_c^+ \rightarrow \chi_{c2} \pi^+}} {\mathcal{B}_{B_c^+ \rightarrow J/\psi \pi^+}} = 0.37 \pm 0.06 \pm 0.02 \pm 0.01 ,$$ where the first uncertainty is statistical, the second is systematic, and the third is due to the knowledge of the $\chi_c \rightarrow J/\psi \gamma$ branching fraction. No significant $B_c^+ \rightarrow \chi_{c1} \pi^+$ signal is observed and an upper limit for the relative branching fraction for the $B_c^+ \rightarrow \chi_{c1} \pi^+$ and $B_c^+ \rightarrow \chi_{c2} \pi^+$ decays of $$\frac{\mathcal{B}_{B_c^+ \rightarrow \chi_{c1} \pi^+}} {\mathcal{B}_{B_c^+ \rightarrow \chi_{c2} \pi^+}} < 0.49$$ is set at the 90% confidence level

Charge-dependent curvature-bias corrections using a pseudomass method

Momentum measurements for very high momentum charged particles, such as muons from electroweak vector boson decays, are particularly susceptible to charge-dependent curvature biases that arise from misalignments of tracking detectors. Low momentum charged particles used in alignment procedures have limited sensitivity to coherent displacements of such detectors, and therefore are unable to fully constrain these misalignments to the precision necessary for studies of electroweak physics. Additional approaches are therefore required to understand and correct for these effects. In this paper the curvature biases present at the LHCb detector are studied using the pseudomass method in proton-proton collision data recorded at centre of mass energy $\sqrt{s}=13$ TeV during 2016, 2017 and 2018. The biases are determined using $Z\to\mu^+\mu^-$ decays in intervals defined by the data-taking period, magnet polarity and muon direction. Correcting for these biases, which are typically at the $10^{-4}$ GeV$^{-1}$ level, improves the $Z\to\mu^+\mu^-$ mass resolution by roughly 20% and eliminates several pathological trends in the kinematic-dependence of the mean dimuon invariant mass

Charge-dependent curvature-bias corrections using a pseudomass method

International audienceMomentum measurements for very high momentum charged particles, such as muons from electroweak vector boson decays, are particularly susceptible to charge-dependent curvature biases that arise from misalignments of tracking detectors. Low momentum charged particles used in alignment procedures have limited sensitivity to coherent displacements of such detectors, and therefore are unable to fully constrain these misalignments to the precision necessary for studies of electroweak physics. Additional approaches are therefore required to understand and correct for these effects. In this paper the curvature biases present at the LHCb detector are studied using the pseudomass method in proton-proton collision data recorded at centre of mass energy $\sqrt{s}=13$ TeV during 2016, 2017 and 2018. The biases are determined using $Z\to\mu^+\mu^-$ decays in intervals defined by the data-taking period, magnet polarity and muon direction. Correcting for these biases, which are typically at the $10^{-4}$ GeV$^{-1}$ level, improves the $Z\to\mu^+\mu^-$ mass resolution by roughly 20% and eliminates several pathological trends in the kinematic-dependence of the mean dimuon invariant mass

Study of Bc+→χcπ+B_c^+ \rightarrow \chi_c \pi^+ decays

International audienceA study of $B_c^+ \rightarrow \chi_c \pi^+$ decays is reported using proton-proton collision data, collected with the LHCb detector at centre-of-mass energies of 7, 8, and 13 TeV, corresponding to an integrated luminosity of 9fb$^{-1}$. The decay $B_c^+ \rightarrow \chi_{c2} \pi^+$ is observed for the first time, with a significance exceeding seven standard deviations. The relative branching fraction with respect to the $B_c^+ \rightarrow J/\psi \pi^+$ decay is measured to be $$\frac{\mathcal{B}_{B_c^+ \rightarrow \chi_{c2} \pi^+}} {\mathcal{B}_{B_c^+ \rightarrow J/\psi \pi^+}} = 0.37 \pm 0.06 \pm 0.02 \pm 0.01 ,$$ where the first uncertainty is statistical, the second is systematic, and the third is due to the knowledge of the $\chi_c \rightarrow J/\psi \gamma$ branching fraction. No significant $B_c^+ \rightarrow \chi_{c1} \pi^+$ signal is observed and an upper limit for the relative branching fraction for the $B_c^+ \rightarrow \chi_{c1} \pi^+$ and $B_c^+ \rightarrow \chi_{c2} \pi^+$ decays of $$\frac{\mathcal{B}_{B_c^+ \rightarrow \chi_{c1} \pi^+}} {\mathcal{B}_{B_c^+ \rightarrow \chi_{c2} \pi^+}} < 0.49$$ is set at the 90% confidence level

Study of Bc+→χcπ+B_c^+ \rightarrow \chi_c \pi^+ decays

International audienceA study of $B_c^+ \rightarrow \chi_c \pi^+$ decays is reported using proton-proton collision data, collected with the LHCb detector at centre-of-mass energies of 7, 8, and 13 TeV, corresponding to an integrated luminosity of 9fb$^{-1}$. The decay $B_c^+ \rightarrow \chi_{c2} \pi^+$ is observed for the first time, with a significance exceeding seven standard deviations. The relative branching fraction with respect to the $B_c^+ \rightarrow J/\psi \pi^+$ decay is measured to be $$\frac{\mathcal{B}_{B_c^+ \rightarrow \chi_{c2} \pi^+}} {\mathcal{B}_{B_c^+ \rightarrow J/\psi \pi^+}} = 0.37 \pm 0.06 \pm 0.02 \pm 0.01 ,$$ where the first uncertainty is statistical, the second is systematic, and the third is due to the knowledge of the $\chi_c \rightarrow J/\psi \gamma$ branching fraction. No significant $B_c^+ \rightarrow \chi_{c1} \pi^+$ signal is observed and an upper limit for the relative branching fraction for the $B_c^+ \rightarrow \chi_{c1} \pi^+$ and $B_c^+ \rightarrow \chi_{c2} \pi^+$ decays of $$\frac{\mathcal{B}_{B_c^+ \rightarrow \chi_{c1} \pi^+}} {\mathcal{B}_{B_c^+ \rightarrow \chi_{c2} \pi^+}} < 0.49$$ is set at the 90% confidence level