Median problems in networks

The P-median problem is a classical location model par excellence . In this paper we, firstexamine the early origins of the problem, formulated independently by Louis Hakimi andCharles ReVelle, two of the fathers of the burgeoning multidisciplinary field of researchknown today as Facility Location Theory and Modelling. We then examine some of thetraditional heuristic and exact methods developed to solve the problem. In the third sectionwe analyze the impact of the model in the field. We end the paper by proposing new lines ofresearch related to such a classical problem.

The P-median problem in a changing network: The case of Barcelona

In this paper a p--median--like model is formulated to address theissue of locating new facilities when there is uncertainty. Severalpossible future scenarios with respect to demand and/or the travel times/distanceparameters are presented. The planner will want a strategy of positioning thatwill do as ``well as possible'' over the future scenarios. This paper presents a discrete location model formulation to address this P--Medianproblem under uncertainty. The model is applied to the location of firestations in Barcelona.

Comparing Random-based and k-Anonymity-Based Algorithms for Graph Anonymization

Recently, several anonymization algorithms have appeared for privacy preservation on graphs. Some of them are based on random-ization techniques and on k-anonymity concepts. We can use both of them to obtain an anonymized graph with a given k-anonymity value. In this paper we compare algorithms based on both techniques in orderto obtain an anonymized graph with a desired k-anonymity value. We want to analyze the complexity of these methods to generate anonymized graphs and the quality of the resulting graphs.

Assessment of letrozole and tamoxifen alone and in sequence for postmenopausal women with steroid hormone receptor-positive breast cancer: the BIG 1-98 randomised clinical trial at 8·1 years median follow-up.

BACKGROUND: Postmenopausal women with hormone receptor-positive early breast cancer have persistent, long-term risk of breast-cancer recurrence and death. Therefore, trials assessing endocrine therapies for this patient population need extended follow-up. We present an update of efficacy outcomes in the Breast International Group (BIG) 1-98 study at 8·1 years median follow-up. METHODS: BIG 1-98 is a randomised, phase 3, double-blind trial of postmenopausal women with hormone receptor-positive early breast cancer that compares 5 years of tamoxifen or letrozole monotherapy, or sequential treatment with 2 years of one of these drugs followed by 3 years of the other. Randomisation was done with permuted blocks, and stratified according to the two-arm or four-arm randomisation option, participating institution, and chemotherapy use. Patients, investigators, data managers, and medical reviewers were masked. The primary efficacy endpoint was disease-free survival (events were invasive breast cancer relapse, second primaries [contralateral breast and non-breast], or death without previous cancer event). Secondary endpoints were overall survival, distant recurrence-free interval (DRFI), and breast cancer-free interval (BCFI). The monotherapy comparison included patients randomly assigned to tamoxifen or letrozole for 5 years. In 2005, after a significant disease-free survival benefit was reported for letrozole as compared with tamoxifen, a protocol amendment facilitated the crossover to letrozole of patients who were still receiving tamoxifen alone; Cox models and Kaplan-Meier estimates with inverse probability of censoring weighting (IPCW) are used to account for selective crossover to letrozole of patients (n=619) in the tamoxifen arm. Comparison of sequential treatments to letrozole monotherapy included patients enrolled and randomly assigned to letrozole for 5 years, letrozole for 2 years followed by tamoxifen for 3 years, or tamoxifen for 2 years followed by letrozole for 3 years. Treatment has ended for all patients and detailed safety results for adverse events that occurred during the 5 years of treatment have been reported elsewhere. Follow-up is continuing for those enrolled in the four-arm option. BIG 1-98 is registered at clinicaltrials.govNCT00004205. FINDINGS: 8010 patients were included in the trial, with a median follow-up of 8·1 years (range 0-12·4). 2459 were randomly assigned to monotherapy with tamoxifen for 5 years and 2463 to monotherapy with letrozole for 5 years. In the four-arm option of the trial, 1546 were randomly assigned to letrozole for 5 years, 1548 to tamoxifen for 5 years, 1540 to letrozole for 2 years followed by tamoxifen for 3 years, and 1548 to tamoxifen for 2 years followed by letrozole for 3 years. At a median follow-up of 8·7 years from randomisation (range 0-12·4), letrozole monotherapy was significantly better than tamoxifen, whether by IPCW or intention-to-treat analysis (IPCW disease-free survival HR 0·82 [95% CI 0·74-0·92], overall survival HR 0·79 [0·69-0·90], DRFI HR 0·79 [0·68-0·92], BCFI HR 0·80 [0·70-0·92]; intention-to-treat disease-free survival HR 0·86 [0·78-0·96], overall survival HR 0·87 [0·77-0·999], DRFI HR 0·86 [0·74-0·998], BCFI HR 0·86 [0·76-0·98]). At a median follow-up of 8·0 years from randomisation (range 0-11·2) for the comparison of the sequential groups with letrozole monotherapy, there were no statistically significant differences in any of the four endpoints for either sequence. 8-year intention-to-treat estimates (each with SE ≤1·1%) for letrozole monotherapy, letrozole followed by tamoxifen, and tamoxifen followed by letrozole were 78·6%, 77·8%, 77·3% for disease-free survival; 87·5%, 87·7%, 85·9% for overall survival; 89·9%, 88·7%, 88·1% for DRFI; and 86·1%, 85·3%, 84·3% for BCFI. INTERPRETATION: For postmenopausal women with endocrine-responsive early breast cancer, a reduction in breast cancer recurrence and mortality is obtained by letrozole monotherapy when compared with tamoxifen montherapy. Sequential treatments involving tamoxifen and letrozole do not improve outcome compared with letrozole monotherapy, but might be useful strategies when considering an individual patient's risk of recurrence and treatment tolerability. FUNDING: Novartis, United States National Cancer Institute, International Breast Cancer Study Group.

90Yttrium-Ibritumomab Tiuxetan Consolidation of First Remission in Advanced-Stage Follicular Non-Hodgkin Lymphoma: Updated Results After a Median Follow-Up of 7.3 Years From the International, Randomized, Phase III First-Line Indolent Trial.

PURPOSE Updated results are presented after a median follow-up of 7.3 years from the phase III First-Line Indolent Trial of yttrium-90 ((90)Y) -ibritumomab tiuxetan in advanced-stage follicular lymphoma (FL) in first remission. PATIENTS AND METHODS Patients with CD20(+) stage III or IV FL with complete response (CR), unconfirmed CR (CRu), or partial response (PR) after first-line induction treatment were randomly assigned to (90)Y-ibritumomab consolidation therapy (rituximab 250 mg/m(2) days -7 and 0, then (90)Y-ibritumomab 14.8 MBq/kg day 0; maximum 1,184 MBq) or no further treatment (control). Primary end point was progression-free survival (PFS) from date of random assignment. Results For 409 patients available for analysis ((90)Y-ibritumomab, n = 207; control, n = 202), estimated 8-year overall PFS was 41% with (90)Y-ibritumomab versus 22% for control (hazard ratio [HR], 0.47; P < .001). For patients in CR/CRu after induction, 8-year PFS with (90)Y-ibritumomab was 48% versus 32% for control (HR, 0.61; P = .008), and for PR patients, it was 33% versus 10% (HR, 0.38; P < .001). For (90)Y-ibritumomab consolidation, median PFS was 4.1 years (v 1.1 years for control; P < .001). Median time to next treatment (TTNT) was 8.1 years for (90)Y-ibritumomab versus 3.0 years for control (P < .001) with approximately 80% response rates to second-line therapy in either arm, including autologous stem-cell transplantation. No unexpected toxicities emerged during long-term follow-up. Estimated between-group 8-year overall survival rates were similar. Annualized incidence rate of myelodysplastic syndrome/acute myeloblastic leukemia was 0.50% versus 0.07% in (90)Y-ibritumomab and control groups, respectively (P = .042). CONCLUSION (90)Y-ibritumomab consolidation after achieving PR or CR/CRu to induction confers 3-year benefit in median PFS with durable 19% PFS advantage at 8 years and improves TTNT by 5.1 years for patients with advanced FL.

Graph theory reveals dysconnected hubs in 22q11DS and altered nodal efficiency in patients with hallucinations.

Schizophrenia is postulated to be the prototypical dysconnection disorder, in which hallucinations are the core symptom. Due to high heterogeneity in methodology across studies and the clinical phenotype, it remains unclear whether the structural brain dysconnection is global or focal and if clinical symptoms result from this dysconnection. In the present work, we attempt to clarify this issue by studying a population considered as a homogeneous genetic sub-type of schizophrenia, namely the 22q11.2 deletion syndrome (22q11.2DS). Cerebral MRIs were acquired for 46 patients and 48 age and gender matched controls (aged 6-26, respectively mean age = 15.20 ± 4.53 and 15.28 ± 4.35 years old). Using the Connectome mapper pipeline (connectomics.org) that combines structural and diffusion MRI, we created a whole brain network for each individual. Graph theory was used to quantify the global and local properties of the brain network organization for each participant. A global degree loss of 6% was found in patients' networks along with an increased Characteristic Path Length. After identifying and comparing hubs, a significant loss of degree in patients' hubs was found in 58% of the hubs. Based on Allen's brain network model for hallucinations, we explored the association between local efficiency and symptom severity. Negative correlations were found in the Broca's area (p < 0.004), the Wernicke area (p < 0.023) and a positive correlation was found in the dorsolateral prefrontal cortex (DLPFC) (p < 0.014). In line with the dysconnection findings in schizophrenia, our results provide preliminary evidence for a targeted alteration in the brain network hubs' organization in individuals with a genetic risk for schizophrenia. The study of specific disorganization in language, speech and thought regulation networks sharing similar network properties may help to understand their role in the hallucination mechanism.