Open problem: Tightness of maximum likelihood semidefinite relaxations

We have observed an interesting, yet unexplained, phenomenon: Semidefinite programming (SDP) based relaxations of maximum likelihood estimators (MLE) tend to be tight in recovery problems with noisy data, even when MLE cannot exactly recover the ground truth. Several results establish tightness of SDP based relaxations in the regime where exact recovery from MLE is possible. However, to the best of our knowledge, their tightness is not understood beyond this regime. As an illustrative example, we focus on the generalized Procrustes problem

Semidefinite Programming Approach for the Quadratic Assignment Problem with a Sparse Graph

The matching problem between two adjacency matrices can be formulated as the NP-hard quadratic assignment problem (QAP). Previous work on semidefinite programming (SDP) relaxations to the QAP have produced solutions that are often tight in practice, but such SDPs typically scale badly, involving matrix variables of dimension $n^2$ where n is the number of nodes. To achieve a speed up, we propose a further relaxation of the SDP involving a number of positive semidefinite matrices of dimension $\mathcal{O}(n)$ no greater than the number of edges in one of the graphs. The relaxation can be further strengthened by considering cliques in the graph, instead of edges. The dual problem of this novel relaxation has a natural three-block structure that can be solved via a convergent Augmented Direction Method of Multipliers (ADMM) in a distributed manner, where the most expensive step per iteration is computing the eigendecomposition of matrices of dimension $\mathcal{O}(n)$. The new SDP relaxation produces strong bounds on quadratic assignment problems where one of the graphs is sparse with reduced computational complexity and running times, and can be used in the context of nuclear magnetic resonance spectroscopy (NMR) to tackle the assignment problem.Comment: 31 page

Probing the gateway to superheavy nuclei in cranked relativistic Hartree-Bogoliubov theory

The cranked relativistic Hartree+Bogoliubov theory has been applied for a systematic study of the nuclei around 254No, the heaviest nuclei for which detailed spectroscopic data are available. The deformation, rotational response, pairing correlations, quasi-particle and other properties of these nuclei have been studied with different relativistic mean field (RMF) parametrizations. For the first time, the quasi-particle spectra of odd deformed nuclei have been calculated in a fully self-consistent way within the framework of the RMF theory. The energies of the spherical subshells, from which active deformed states of these nuclei emerge, are described with an accuracy better than 0.5 MeV for most of the subshells with the NL1 and NL3 parametrizations. However, for a few subshells the discrepancy reach 0.7-1.0 MeV. The implications of these results for the study of superheavy nuclei are discussed.Comment: 7 pages, 3 figures, Proceedings of the Conference on Frontiers of Nuclear Structure, Berkeley, California, July 29th - August 2nd, 2002, UC Berkeley, Clark Kerr Campus, in pres

A Computerized Constructionist Approach To Simulation And Modeling Pedagogy

A major limitation in traditional class lectures on simulation and modeling, that uses assignments, handouts, transparencies, and textbooks, is that students often are unable to appreciate the "experience" of simulating a real problem.  This limitation can be overcome by using an active real case study approach to allow students to simulate a real-time queuing problem through interactive visual simulation software (EXTEND®).  Actual raw data had been collected prior to the case assignment and students are taught to develop the simulation model, based on the actual raw data.  The intent is that by "doing" or "constructing" the simulation model from actual data, the students will understand better and remember

DNA methylation of ESR-1 and N-33 in colorectal mucosa of patients with Ulcerative Colitis (UC)

Introduction: Epigenetic marking such as DNA methylation influence gene transcription and chromosomal stability and may also be affected by environmental exposures. Few studies exist on alteration in DNA methylation profiles (genomic and gene specific methylation) in patients with Ulcerative Colitis (UC) and none assessing its relationship with lifestyle exposures. Aims & Methods: To assess genomic methylation and promoter methylation of the ESR-1 (oestrogen receptor - 1) and N-33 (tumour suppressor candidate-3) genes in the macroscopically normal mucosa of UC patients as well as to investigate effects of anthropometric and lifestyle exposures on DNA methylation. Sixty eight subjects were recruited (24 UC and 44 age and sex matched controls). Colorectal mucosal biopsies were obtained and DNA was extracted. Genomic DNA methylation was quantified using the tritium-labelled cytosine extension assay (3[H] dCTP) whilst gene specific methylation was quantified using the COBRA method. Results: The methylation level of both ESR-1 and N-33 genes were significantly higher in UC subjects compared with controls (7.9% vs 5.9%; p = 0.015 and 66% vs 9.3%; p < 0.001 respectively). There was no detectable difference in global DNA methylation between patients with UC and age and sex matched controls. No associations between indices of DNA methylation and anthropometric measures or smoking patterns were detected. Conclusions: For the first time, we have shown increased methylation in the promoter regions of the putative tumour suppressor gene N-33 in macroscopically normal mucosa of patients with UC. In addition, we have confirmed that methylation of ESR-1 promoter is higher in UC patients compared with age and sex matched controls. These findings suggests that, inactivation through methylation of the putative tumour suppressor genes N-33 and ESR-1, may not be associated with colorectal carcinogenesis in UC

Motives for adult participation in physical activity: type of activity, age, and gender

Background In recent years, there has been a decline in physical activity among adults. Motivation has been shown to be a crucial factor in maintaining physical activity. The purpose of this study was to examine whether motives for participation could accurately discriminate gender, age, and type of physical activity. Methods A quantitative, cross-sectional descriptive research design was employed. The Physical Activity and Leisure Motivation Scale (PALMS) was used to assess motives for physical activity in 1,360 adults (703 males, 657 females) who had been exercising regularly for at least six months. The PALMS consists of 40 items that constitute eight sub-scales (mastery, enjoyment, psychological condition, physical condition, appearance, others’ expectations, affiliation, competition/ego). Respondents were divided into two age groups (young adults aged 20 to 40 years and middle-aged adults 41 to 64 years) and five types of activity (individual racing sports plus bowls, team sports, racquet sports, martial arts, and exercise). Results The group discriminant function analyses revealed significant canonical functions correctly classifying the cases into gender (82%), age group (83%), team sport players 76%, individual racing sport plus bowls players 91%, racquet sport players 90%, exercisers 84%, and martial art players 91%. The competition/ego, appearance, physical condition, and mastery sub-scales contributed most to gender differences. Five sub-scales (mastery, psychological condition, others’ expectations, affiliation, and enjoyment) contributed most to the discriminant function for age. For type of activity, different sub-scales were the strongest contributors to the discriminant function for each type of PA. Conclusion The findings in this study suggest that strong and important motives for participation in physical activity are different across type of activity, age, and gender in adults. Understanding the motives that influence physical activity participation is critical for developing interventions to promote higher levels of involvement

Minimum target prices for production of direct acting antivirals and associated diagnostics to combat Hepatitis C Virus

Combinations of direct-acting antivirals (DAAs) can cure hepatitis C virus (HCV) in the majority of treatment-naïve patients. Mass treatment programs to cure HCV in developing countries are only feasible if the costs of treatment and laboratory diagnostics are very low. This analysis aimed to estimate minimum costs of DAA treatment and associated diagnostic monitoring. Clinical trials of HCV DAAs were reviewed to identify combinations with consistently high rates of sustained virological response across hepatitis C genotypes. For each DAA, molecular structures, doses, treatment duration, and components of retrosynthesis were used to estimate costs of large-scale, generic production. Manufacturing costs per gram of DAA were based upon treating at least 5 million patients per year and a 40% margin for formulation. Costs of diagnostic support were estimated based on published minimum prices of genotyping, HCV antigen tests plus full blood count/clinical chemistry tests. Predicted minimum costs for 12-week courses of combination DAAs with the most consistent efficacy results were: US$122 per person for sofosbuvir+daclatasvir; US$152 for sofosbuvir+ribavirin; US$192 for sofosbuvir+ledipasvir; and US$115 for MK-8742+MK-5172. Diagnostic testing costs were estimated at US$90 for genotyping US$34 for two HCV antigen tests and US$22 for two full blood count/clinical chemistry tests. Conclusions: Minimum costs of treatment and diagnostics to cure hepatitis C virus infection were estimated at US$171-360 per person without genotyping or US$261-450 per person with genotyping. These cost estimates assume that existing large-scale treatment programs can be established. (Hepatology 2015;61:1174–1182

Pengiraan Persentil Taburan Panjang Larian bagi Carta Kawalan Purata Bergerak Berpemberat Eksponen Multivariat

Prabhu dan Runger (1997) telah mengemukakan cadangan dalam pemilihan parameter-parameter untuk skema carta kawalan purata bergerak berpemberat eksponen multivariat (MEWMA). Walau bagaimanapun, cadangan tersebut hanya berdasarkan prestasi panjang larian purata (average run length - ARL). Oleh itu, dalam makalah ini, kami akan mengira nilai-nilai persentil untuk taburan panjang larian bagi pelbagai skema carta kawalan MEWMA yang dikemukakan oleh Prabhu dan Runger (1997). Persentil-persentil yang dikira akan membekalkan maklumat tambahan seperti kekerapan isyarat luar kawalan palsu yang awal (early false out of control signals), panjang larian median (median run length - MRL) dan kepencongan taburan panjang larian untuk sesuatu skema tertentu. Maklumat-maklumat tambahan ini mungkin berguna dalam membekalkan jurutera kawalan mutu pengetahuan mendalam dan lengkap tentang sesuatu skema carta kawalan MEWMA yang dipilih berdasarkan cadangan Prabhu dan Runger (1997)