Determination of the prime bound of a graph

Given a graph $G$, a subset $M$ of $V(G)$ is a module of $G$ if for each $v\in V(G)\setminus M$, $v$ is adjacent to all the elements of $M$ or to none of them. For instance, $V(G)$, $\emptyset$ and $\{v\}$ ($v\in V(G)$) are modules of $G$ called trivial. Given a graph $G$, $\omega_M(G)$ (respectively $\alpha_M(G)$) denotes the largest integer $m$ such that there is a module $M$ of $G$ which is a clique (respectively a stable) set in $G$ with $|M|=m$. A graph $G$ is prime if $|V(G)|\geq 4$ and if all its modules are trivial. The prime bound of $G$ is the smallest integer $p(G)$ such that there is a prime graph $H$ with $V(H)\supseteq V(G)$, $H[V(G)]=G$ and $|V(H)\setminus V(G)|=p(G)$. We establish the following. For every graph $G$ such that $\max(\alpha_M(G),\omega_M(G))\geq 2$ and $\log_2(\max(\alpha_M(G),\omega_M(G)))$ is not an integer, $p(G)=\lceil\log_2(\max(\alpha_M(G),\omega_M(G)))\rceil$. Then, we prove that for every graph $G$ such that $\max(\alpha_M(G),\omega_M(G))=2^k$ where $k\geq 1$, $p(G)=k$ or $k+1$. Moreover $p(G)=k+1$ if and only if $G$ or its complement admits $2^k$ isolated vertices. Lastly, we show that $p(G)=1$ for every non prime graph $G$ such that $|V(G)|\geq 4$ and $\alpha_M(G)=\omega_M(G)=1$.Comment: arXiv admin note: text overlap with arXiv:1110.293

3-uniform hypergraphs: modular decomposition and realization by tournaments

Let $H$ be a 3-uniform hypergraph. A tournament $T$ defined on $V(T)=V(H)$ is a realization of $H$ if the edges of $H$ are exactly the 3-element subsets of $V(T)$ that induce 3-cycles. We characterize the 3-uniform hypergraphs that admit realizations by using a suitable modular decomposition

A European survey on the detection and management of iron overload in transfusion-dependent patients with MDS

International audienceTo better understand the detection and management of iron overload in transfusion-dependent patients with myelodysplastic syndromes (MDS), a 15-min web- or paper-based survey was conducted among 338 European physicians from 27 countries. Respondents had a mean of 18 years of clinical experience. Forty-six percent and 27% of physicians noted that detecting and treating iron overload were either "very important" or "important," respectively. The main reason for not actively exploring iron overload was related to poor patient prognosis, while the main reasons for not initiating iron chelation therapy were poor patient prognosis and older patient age. Thirty-seven percent and 31% of physicians believed that treating iron overload in these patients was "very important" or "important," respectively. Ninety percent of physicians prescribed iron chelation therapy, and 38% of transfusion-dependent patients received iron chelation therapy. The key reasons for not initiating iron chelation therapy were related to poor patient prognosis (72%), patient age ≥85 years (50%), and comorbidities (34%). The views of these experienced MDS physicians reflect available international MDS treatment guidelines

Augmented reality for the virtual dissection of white matter pathways

Background: The human white matter pathway network is complex and of critical importance for functionality. Thus, learning and understanding white matter tract anatomy is important for the training of neuroscientists and neurosurgeons. The study aims to test and evaluate a new method for fiber dissection using augmented reality (AR) in a group which is experienced in cadaver white matter dissection courses and in vivo tractography. Methods: Fifteen neurosurgeons, neurolinguists, and neuroscientists participated in this questionnaire-based study. We presented five cases of patients with left-sided perisylvian gliomas who underwent awake craniotomy. Diffusion tensor imaging fiber tracking (DTI FT) was performed and the language-related networks were visualized separated in different tracts by color. Participants were able to virtually dissect the prepared DTI FTs using a spatial computer and AR goggles. The application was evaluated through a questionnaire with answers from 0 (minimum) to 10 (maximum). Results: Participants rated the overall experience of AR fiber dissection with a median of 8 points (mean ± standard deviation 8.5 ± 1.4). Usefulness for fiber dissection courses and education in general was rated with 8 (8.3 ± 1.4) and 8 (8.1 ± 1.5) points, respectively. Educational value was expected to be high for several target audiences (student: median 9, 8.6 ± 1.4; resident: 9, 8.5 ± 1.8; surgeon: 9, 8.2 ± 2.4; scientist: 8.5, 8.0 ± 2.4). Even clinical application of AR fiber dissection was expected to be of value with a median of 7 points (7.0 ± 2.5). Conclusion: The present evaluation of this first application of AR for fiber dissection shows a throughout positive evaluation for educational purposes

Impaired set-shifting from dorsal stream disconnection: Insights from a european series of right parietal lower-grade glioma resection

Awake surgery with cognitive monitoring has increasingly been implemented to preserve brain networks and functionality. More recently, not only surgery in the left but also in the right hemisphere, i.c., the parietal lobe, was associated with potential risk for deficits in cognitive functions, such as cognitive flexibility. In this explorative pilot study, we compare cognitive performance more than three months after surgery with baseline measurements and explore the association between cognitive decline and subcortical tracts that may have been severed during surgery in the right hemisphere. Twenty-two patients who underwent surgery for a right parietal low-grade glioma were assessed pre-and postoperatively using the Trail Making Test and the Stroop task to administer set-shifting abilities and inhibition. Volume measurements and lesion–symptom mapping analyses were performed on postoperative MRI scans. Careful interpretation of the results shows a change in TMT performance and not on the Stroop Task when the lateral part of the arcuate fasciculus is damaged, indicating that disconnection of the lateral part of the dorsal stream might be correlated specifically with impaired set-shifting and not with inhibition. More importantly, this study underlines the need for international concertation to allow larger studies to increase power and perform more detailed analyses

Natalizumab treatment shows low cumulative probabilities of confirmed disability worsening to EDSS milestones in the long-term setting.

Abstract Background Though the Expanded Disability Status Scale (EDSS) is commonly used to assess disability level in relapsing-remitting multiple sclerosis (RRMS), the criteria defining disability progression are used for patients with a wide range of baseline levels of disability in relatively short-term trials. As a result, not all EDSS changes carry the same weight in terms of future disability, and treatment benefits such as decreased risk of reaching particular disability milestones may not be reliably captured. The objectives of this analysis are to assess the probability of confirmed disability worsening to specific EDSS milestones (i.e., EDSS scores ≥3.0, ≥4.0, or ≥6.0) at 288 weeks in the Tysabri Observational Program (TOP) and to examine the impact of relapses occurring during natalizumab therapy in TOP patients who had received natalizumab for ≥24 months. Methods TOP is an ongoing, open-label, observational, prospective study of patients with RRMS in clinical practice. Enrolled patients were naive to natalizumab at treatment initiation or had received ≤3 doses at the time of enrollment. Intravenous natalizumab (300 mg) infusions were given every 4 weeks, and the EDSS was assessed at baseline and every 24 weeks during treatment. Results Of the 4161 patients enrolled in TOP with follow-up of at least 24 months, 3253 patients with available baseline EDSS scores had continued natalizumab treatment and 908 had discontinued (5.4% due to a reported lack of efficacy and 16.4% for other reasons) at the 24-month time point. Those who discontinued due to lack of efficacy had higher baseline EDSS scores (median 4.5 vs. 3.5), higher on-treatment relapse rates (0.82 vs. 0.23), and higher cumulative probabilities of EDSS worsening (16% vs. 9%) at 24 months than those completing therapy. Among 24-month completers, after approximately 5.5 years of natalizumab treatment, the cumulative probabilities of confirmed EDSS worsening by 1.0 and 2.0 points were 18.5% and 7.9%, respectively (24-week confirmation), and 13.5% and 5.3%, respectively (48-week confirmation). The risks of 24- and 48-week confirmed EDSS worsening were significantly higher in patients with on-treatment relapses than in those without relapses. An analysis of time to specific EDSS milestones showed that the probabilities of 48-week confirmed transition from EDSS scores of 0.0–2.0 to ≥3.0, 2.0–3.0 to ≥4.0, and 4.0–5.0 to ≥6.0 at week 288 in TOP were 11.1%, 11.8%, and 9.5%, respectively, with lower probabilities observed among patients without on-treatment relapses (8.1%, 8.4%, and 5.7%, respectively). Conclusions In TOP patients with a median (range) baseline EDSS score of 3.5 (0.0–9.5) who completed 24 months of natalizumab treatment, the rate of 48-week confirmed disability worsening events was below 15%; after approximately 5.5 years of natalizumab treatment, 86.5% and 94.7% of patients did not have EDSS score increases of ≥1.0 or ≥2.0 points, respectively. The presence of relapses was associated with higher rates of overall disability worsening. These results were confirmed by assessing transition to EDSS milestones. Lower rates of overall 48-week confirmed EDSS worsening and of transitioning from EDSS score 4.0–5.0 to ≥6.0 in the absence of relapses suggest that relapses remain a significant driver of disability worsening and that on-treatment relapses in natalizumab-treated patients are of prognostic importance

Energy Resolution Performance of the CMS Electromagnetic Calorimeter

The energy resolution performance of the CMS lead tungstate crystal electromagnetic calorimeter is presented. Measurements were made with an electron beam using a fully equipped supermodule of the calorimeter barrel. Results are given both for electrons incident on the centre of crystals and for electrons distributed uniformly over the calorimeter surface. The electron energy is reconstructed in matrices of 3 times 3 or 5 times 5 crystals centred on the crystal containing the maximum energy. Corrections for variations in the shower containment are applied in the case of uniform incidence. The resolution measured is consistent with the design goals