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Abstract. We consider n mobile sensors located on a line containing a barrier represented by a finite line segment. Sensors form a wireless sensor network and are able to move within the line. An intruder traversing the barrier can be detected only when it is within the sensing range of at least one sensor. The sensor network establishes barrier coverage of the segment if no intruder can penetrate the barrier from any direction in the plane without being detected. Starting from arbitrary initial positions of sensors on the line we are interested in finding final positions of sensors that establish barrier coverage and minimize the maximum distance traversed by any sensor. We distinguish several variants of the problem, based on (a) whether or not the sensors have identical ranges, (b) whether or not complete coverage is possible and (c) in the case when complete coverage is impossible, whether or not the maximal coverage is required to be contiguous. For the case of n sensors with identical range, when complete coverage is impossible, we give linear time optimal algorithms that achieve maximal coverage, both for the contiguous and non-contiguous case. When complete coverage is possible, we give an O(n 2 ) algorithm for an optimal solution, a linear time approximation scheme with approximation factor 2, and a (1 + ) PTAS. When the sensors have unequal ranges we show that a variation of the problem is NP-complete and identify some instances which can be solved with our algorithms for sensors with unequal ranges.

Addressing drug resistance is a core challenge in cancer research, but the degree of heterogeneity in resistance mechanisms in cancer is unclear. In this study, we conducted next-generation sequencing (NGS) of circulating tumor cells (CTC) from patients with advanced cancer to assess mechanisms of resistance to targeted therapy and reveal opportunities for precision medicine. Comparison of the genomic landscapes of CTCs and tissue metastases is complicated by challenges in comprehensive CTC genomic profiling and paired tissue acquisition, particularly in patients who progress after targeted therapy. Thus, we assessed by NGS somatic mutations and copy number alterations (CNA) in archived CTCs isolated from patients with metastatic breast cancer who were enrolled in concurrent clinical trials that collected and analyzed CTCs and metastatic tissues. In 76 individual and pooled informative CTCs from 12 patients, we observed 85% concordance in at least one or more prioritized somatic mutations and CNA between paired CTCs and tissue metastases. Potentially actionable genomic alterations were identified in tissue but not CTCs, and vice versa. CTC profiling identified diverse intra- and interpatient molecular mechanisms of endocrine therapy resistance, including loss of heterozygosity in individual CTCs. For example, in one patient, we observed CTCs that were either wild type for ( = 5/32), harbored the known activating p.Y537S mutation ( = 26/32), or harbored a novel p.A569S ( = 1/32). p.A569S was modestly activating, consistent with its presence as a minority circulating subclone. Our results demonstrate the feasibility and potential clinical utility of comprehensive profiling of archived fixed CTCs. Tissue and CTC genomic assessment are complementary, and precise combination therapies will likely be required for effective targeting in advanced breast cancer patients. These findings demonstrate the complementary nature of genomic profiling from paired tissue metastasis and circulating tumor cells from patients with metastatic breast cancer. .

Abstract. A set of sensors establishes barrier coverage of a given line segment if every point of the segment is within the sensing range of a sensor. Given a line segment I, n mobile sensors in arbitrary initial positions on the line (not necessarily inside I) and the sensing ranges of the sensors, we are interested in finding final positions of sensors which establish a barrier coverage of I so that the sum of the distances traveled by all sensors from initial to final positions is minimized. It is shown that the problem is NP complete even to approximate up to constant factor when the sensors may have different sensing ranges. When the sensors have an identical sensing range we give several efficient algorithms to calculate the final destinations so that the sensors either establish a barrier coverage or maximize the coverage of the segment if complete coverage is not feasible while at the same time the sum of the distances traveled by all sensors is minimized. Some open problems are also mentioned.

BackgroundFemale prisoners are at risk of acquiring sexually transmitted infections (STIs). There has been no previous study regarding the epidemiological status of STIs among female prisoners in Isfahan, central Iran.ObjectivesThe aim of this study was to investigate the prevalence and risk factors of the aforementioned infections among women incarcerated in the central prison, Isfahan, to determine appropriate prevention measures.Patients and MethodsIn a cross-sectional study, all of the 163 women incarcerated in the central prison, Isfahan in 2009, were voluntarily enrolled by the census method. After completing a checklist consisting of demographic, social, and risk factors, a 5ml blood sample was taken from each individual. The sera were analyzed for markers of the hepatitis B virus (HBV; HBsAg, HBsAb, HBcAb), hepatitis C virus (HCV; HCV antibodies), human immunodeficiency virus (HIV; HIV antibodies), and syphilis (RPR). Confirmatory tests were performed on HCV antibody-positive cases.ResultsThe mean age of the participants in the study was 34.54 ± 11.2 years old, 94.3% of these women were Iranian, and many of them had only a primary level of education. The prevalence of HBsAg, HBcAb, HBsAb, and HCV antibodies were; 1.2%, 7.4%, 12.9% and 7.4% respectively. No positive RPR or HIV antibodies were detected.ConclusionsA significant relationship was seen between the HCV antibody, drug injection and illegal sex in the women, and also between HBc-Ab and drug injection. Regular screening, educational programs, and facilitation of access to suitable treatment care should be widely implemented in the prison population. Testing for immunity against HBV should be considered on admission, and afterwards vaccination of all prisoners and an appropriate preventative approach should be applied.