On the Von Neumann Entropy of Graphs

The von Neumann entropy of a graph is a spectral complexity measure that has recently found applications in complex networks analysis and pattern recognition. Two variants of the von Neumann entropy exist based on the graph Laplacian and normalized graph Laplacian, respectively. Due to its computational complexity, previous works have proposed to approximate the von Neumann entropy, effectively reducing it to the computation of simple node degree statistics. Unfortunately, a number of issues surrounding the von Neumann entropy remain unsolved to date, including the interpretation of this spectral measure in terms of structural patterns, understanding the relation between its two variants, and evaluating the quality of the corresponding approximations. In this paper we aim to answer these questions by first analysing and comparing the quadratic approximations of the two variants and then performing an extensive set of experiments on both synthetic and real-world graphs. We find that 1) the two entropies lead to the emergence of similar structures, but with some significant differences; 2) the correlation between them ranges from weakly positive to strongly negative, depending on the topology of the underlying graph; 3) the quadratic approximations fail to capture the presence of non-trivial structural patterns that seem to influence the value of the exact entropies; 4) the quality of the approximations, as well as which variant of the von Neumann entropy is better approximated, depends on the topology of the underlying graph

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Friday, March 18, 2005, 20:50 EDT (8:50 PM EDT)CDCHAN-00224-2005-03-18-ADV-NThe Centers for Disease Control and Prevention (CDC) has learned of 11 cases of Serratia marcescens (S. marcescens) bacteremia from two states associated with magnesium sulfate solution manufactured by Pharmedium (Lake Forest, IL) that may have been intrinsically contaminated with S. marcescens. In March 2005, the New Jersey Department of Health and Senior Services (N JD H SS) was notified of a cluster of S. marcescens blood stream infections involving five patients hospitalized at a New Jersey health-care facility. All five patients developed sepsis caused by S. marcescens and had received intravenous magnesium sulfate manufactured by Pharmedium prior to illness onset. All patients responded to ciprofloxacin treatment, are well and have been discharged from the health-care facility. In an earlier outbreak in a California hospital in January 2005, 6 cases of S. marcescens bacteremia in cardiovascular surgery patients were identified, all of whom received magnesium sulfate manufactured by Pharmedium from a lot that differed from the implicated lot in New Jersey.The N JD H SS laboratory recovered S. marcescens from an opened bag of magnesium sulfate (1 gram in 5% dextrose and water; lot # 100504900049, expiration date 4/4/05) and an unopened bag of magnesium sulfate (1 gram in 5% dextrose and water; lot # 100504900049). The patient isolates and those obtained from the bags of magnesium sulfate solution had identical antibiotic susceptibility profiles. Molecular typing to determine relatedness of the isolates is being performed by the CDC. Pharmedium provides pharmaceutical products to hospitals nationwide. CDC is working with state health departments and the Food and Drug Administration to determine the magnitude of this outbreak. Testing of other product lots is underway to determine the extent of possible contamination. Individuals who are aware of cases of S. marcescens bacteremia occurring during or shortly after receipt of this product should contact their health department and CDC at 1 -800-893-0485.2005Serratia Infections, 2005BacteriaSerratia marcescen

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May 9, 2007, 11:15 EDT (11:15 AM EDT)CDCHAN-00259-07-05-09-ADV-NCDC is requesting that states report all cases of influenza-related pediatric mortality from the 2006-2007 influenza season.Since 2004, the Influenza-Associated Pediatric Mortality Surveillance System, part of the Nationally Notifiable Disease Surveillance System, has collected information on deaths among children due to laboratory-confirmed influenza, including the presence of other medical conditions and bacterial infections at the time of death. From October 1, 2006 through May 7, 2007, 55 deaths from influenza in children have been reported to CDC from 23 state health departments and two city health departments. Data on bacterial co-infections were reported for 51 cases; 20 (39%) had a bacterial co-infection, and 16/20 were infected with Staphylococcus aureus. While the number of pediatric influenza associated deaths is similar to that reported during the two previous years, there has been an increase in the number of deaths in which both influenza and pneumonia or bacteremia due to S. aureus were identified. Only one influenza and S. aureus co-infection was identified in 2004-2005, and 3 were identified in 2005-2006. Of the 16 children reported with S. aureus so far in 2006-2007, 11 children had methicillin-resistant (MRSA) isolated from a sterile site (9) or sputum (2), and 5 had methicillin-susceptible S.aureus isolated from a sterile site (3) or sputum (2). The median age of children with S. aureus co-infection was older than children without S.aureus co-infection (11 years versus 4 years, p<.01) Children with influenza and S. aureus co-infections were reported to be in good health before illness onset but progressed rapidly to severe illness. Influenza strains isolated from these children have not been different from common strains circulating in the community and the MRSA strains have been typical of those associated with MRSA skin infection outbreaks in the United States.Healthcare providers should be alerted to the possibility of bacterial co-infection among children with influenza, and request bacterial cultures when bacterial co-infection is suspected. Clinicians, clinical agencies and medical examiners are asked to contact their local or state health department as soon as possible when deaths among children due to laboratory-confirmed influenza are identified. CDC requests that all cases of pediatric influenza-associated deaths be reported promptly by state health departments to CDC through http://sdn.cdc.gov and that information about bacterial pathogens isolated from sterile sites and/or from sputum or endotracheal aspirates be completed on the Influenza-Associated Pediatric Mortality Surveillance System case report form. If the influenza death was complicated by S. aureus infection, please contact the clinical agency to determine if the S. aureus isolate is available. CDC is interested in receiving S. aureus isolates to better characterize those from fatal cases of influenza in children.2007Influenza-Associated Child Mortality, 2007Staphylococcus Infections, 2007VirusBacteriaInfluenza A virusInfluenza B virusStaphylococcus aureu

An \~{O}(n2)(n^2) Time Matrix Multiplication Algorithm

We show, for the input vectors $(a_0, a_1, ..., a_{n-1})$ and $(b_0, b_1, ..., b_{n-1})$, where $a_i$'s and $b_j$'s are real numbers, after \~{O}$(n)$ time preprocessing for each of them, the vector multiplication $(a_0, a_1, ..., a_{n-1})(b_0, b_1, ..., b_{n-1})^T$ can be computed in \~{O}$(1)$ time. This enables the matrix multiplication of two $n\times n$ matrices to be computed in \~{O}$(n^2)$ time.Comment: Version 11 and Version 12 section 2 laid the foundation of this algorithm but has a problem unresolved. This version corrects the problem in Version 11 and Section 2 of Version 1

Critique of Korean Multiculturalism as Viewed through Gendered Transnational Migration in Asia: The Case of Vietnamese Returnee Marriage Migrants

This article analyzes returnees from marriage migration by focusing on Vietnamese women from Cần Thơ and Hai Phòng who have been to South Korea for marriage migration. In contrast to prevalent concerns in South Korea about the possibility of child abduction by Vietnamese mothers/divorcees, the author found many deserted Korean Vietnamese children and their mothers in Vietnam through this research. There is also a growing number of Vietnamese return marriage migrants, women who came back to South Korea after their first divorce and return to Vietnam. The article emphasizes the complexities and multidirectional trajectories of marriage migration and highlights the agency of female migrants, whose contribution to family welfare and to development is often overshadowed by their status within the family