The Random Quadratic Assignment Problem

Optimal assignment of classes to classrooms \cite{dickey}, design of DNA microarrays \cite{carvalho}, cross species gene analysis \cite{kolar}, creation of hospital layouts cite{elshafei}, and assignment of components to locations on circuit boards \cite{steinberg} are a few of the many problems which have been formulated as a quadratic assignment problem (QAP). Originally formulated in 1957, the QAP is one of the most difficult of all combinatorial optimization problems. Here, we use statistical mechanical methods to study the asymptotic behavior of problems in which the entries of at least one of the two matrices that specify the problem are chosen from a random distribution $P$. Surprisingly, this case has not been studied before using statistical methods despite the fact that the QAP was first proposed over 50 years ago \cite{Koopmans}. We find simple forms for $C_{\rm min}$ and $C_{\rm max}$, the costs of the minimal and maximum solutions respectively. Notable features of our results are the symmetry of the results for $C_{\rm min}$ and $C_{\rm max}$ and the dependence on $P$ only through its mean and standard deviation, independent of the details of $P$. After the asymptotic cost is determined for a given QAP problem, one can straightforwardly calculate the asymptotic cost of a QAP problem specified with a different random distribution $P$

Role of genetic testing for inherited prostate cancer risk: Philadelphia prostate cancer consensus conference 2017

Purpose: Guidelines are limited for genetic testing for prostate cancer (PCA). The goal of this conference was to develop an expert consensus-dri

Age at first birth in women is genetically associated with increased risk of schizophrenia

Prof. Paunio on PGC:n jäsenPrevious studies have shown an increased risk for mental health problems in children born to both younger and older parents compared to children of average-aged parents. We previously used a novel design to reveal a latent mechanism of genetic association between schizophrenia and age at first birth in women (AFB). Here, we use independent data from the UK Biobank (N = 38,892) to replicate the finding of an association between predicted genetic risk of schizophrenia and AFB in women, and to estimate the genetic correlation between schizophrenia and AFB in women stratified into younger and older groups. We find evidence for an association between predicted genetic risk of schizophrenia and AFB in women (P-value = 1.12E-05), and we show genetic heterogeneity between younger and older AFB groups (P-value = 3.45E-03). The genetic correlation between schizophrenia and AFB in the younger AFB group is -0.16 (SE = 0.04) while that between schizophrenia and AFB in the older AFB group is 0.14 (SE = 0.08). Our results suggest that early, and perhaps also late, age at first birth in women is associated with increased genetic risk for schizophrenia in the UK Biobank sample. These findings contribute new insights into factors contributing to the complex bio-social risk architecture underpinning the association between parental age and offspring mental health.Peer reviewe

Factors Associated with Revision Surgery after Internal Fixation of Hip Fractures

Background: Femoral neck fractures are associated with high rates of revision surgery after management with internal fixation. Using data from the Fixation using Alternative Implants for the Treatment of Hip fractures (FAITH) trial evaluating methods of internal fixation in patients with femoral neck fractures, we investigated associations between baseline and surgical factors and the need for revision surgery to promote healing, relieve pain, treat infection or improve function over 24 months postsurgery. Additionally, we investigated factors associated with (1) hardware removal and (2) implant exchange from cancellous screws (CS) or sliding hip screw (SHS) to total hip arthroplasty, hemiarthroplasty, or another internal fixation device. Methods: We identified 15 potential factors a priori that may be associated with revision surgery, 7 with hardware removal, and 14 with implant exchange. We used multivariable Cox proportional hazards analyses in our investigation. Results: Factors associated with increased risk of revision surgery included: female sex, [hazard ratio (HR) 1.79, 95% confidence interval (CI) 1.25-2.50; P = 0.001], higher body mass index (fo

Recent advances in magnetic resonance microscopy to the physical structure characterization of carbonaceous and inorganic materials

Magnetic resonance microscopy (MRM) techniques have been employed to study the molecular architectures and properties of structural polymers, fossil fuels, microporous carbons and inorganic catalysts

Nondestructive NMR technique for moisture determination in radioactive materials.

This progress report focuses on experimental and computational studies used to evaluate nuclear magnetic resonance (NMR) spectroscopy and magnetic resonance imaging (MRI) for detecting, quantifying, and monitoring hydrogen and other magnetically active nuclei ({sup 3}H, {sup 3}He, {sup 239}Pu, {sup 241}Pu) in Spent nuclear fuels and packaging materials. The detection of moisture by using a toroid cavity NMR imager has been demonstrated in SiO{sub 2} and UO{sub 2} systems. The total moisture was quantified by means of {sup 1}H NMR detection of H{sub 2}O with a sensitivity of 100 ppm. In addition, an MRI technique that was used to determine the moisture distribution also enabled investigators to discriminate between bulk and stationary water sorbed on the particles. This imaging feature is unavailable in any other nondestructive assay (NDA) technique. Following the initial success of this program, the NMR detector volume was scaled up from the original design by a factor of 2000. The capacity of this detector exceeds the size specified by DOE-STD-3013-96

Nondestructive NMR technique for moisture determination in radioactive materials.

This progress report focuses on experimental and computational studies used to evaluate nuclear magnetic resonance (NMR) spectroscopy and magnetic resonance imaging (MRI) for detecting, quantifying, and monitoring hydrogen and other magnetically active nuclei ({sup 3}H, {sup 3}He, {sup 239}Pu, {sup 241}Pu) in Spent nuclear fuels and packaging materials. The detection of moisture by using a toroid cavity NMR imager has been demonstrated in SiO{sub 2} and UO{sub 2} systems. The total moisture was quantified by means of {sup 1}H NMR detection of H{sub 2}O with a sensitivity of 100 ppm. In addition, an MRI technique that was used to determine the moisture distribution also enabled investigators to discriminate between bulk and stationary water sorbed on the particles. This imaging feature is unavailable in any other nondestructive assay (NDA) technique. Following the initial success of this program, the NMR detector volume was scaled up from the original design by a factor of 2000. The capacity of this detector exceeds the size specified by DOE-STD-3013-96