Statistical Mechanics of the Hyper Vertex Cover Problem

We introduce and study a new optimization problem called Hyper Vertex Cover. This problem is a generalization of the standard vertex cover to hypergraphs: one seeks a configuration of particles with minimal density such that every hyperedge of the hypergraph contains at least one particle. It can also be used in important practical tasks, such as the Group Testing procedures where one wants to detect defective items in a large group by pool testing. Using a Statistical Mechanics approach based on the cavity method, we study the phase diagram of the HVC problem, in the case of random regualr hypergraphs. Depending on the values of the variables and tests degrees different situations can occur: The HVC problem can be either in a replica symmetric phase, or in a one-step replica symmetry breaking one. In these two cases, we give explicit results on the minimal density of particles, and the structure of the phase space. These problems are thus in some sense simpler than the original vertex cover problem, where the need for a full replica symmetry breaking has prevented the derivation of exact results so far. Finally, we show that decimation procedures based on the belief propagation and the survey propagation algorithms provide very efficient strategies to solve large individual instances of the hyper vertex cover problem.Comment: Submitted to PR

msBP: An R package to perform Bayesian nonparametric inference using multiscale Bernstein polynomials mixtures

msBP is an R package that implements a new method to perform Bayesian multiscale nonparametric inference introduced by Canale and Dunson (2016). The method, based on mixtures of multiscale beta dictionary densities, overcomes the drawbacks of Pólya trees and inherits many of the advantages of Dirichlet process mixture models. The key idea is that an infinitely-deep binary tree is introduced, with a beta dictionary density assigned to each node of the tree. Using a multiscale stick-breaking characterization, stochastically decreasing weights are assigned to each node. The result is an infinite mixture model. The package msBP implements a series of basic functions to deal with this family of priors such as random densities and numbers generation, creation and manipulation of binary tree objects, and generic functions to plot and print the results. In addition, it implements the Gibbs samplers for posterior computation to perform multiscale density estimation and multiscale testing of group differences described in Canale and Dunson (2016)

Efficacy and safety of local lysozyme treatment in patients with oral mucositis after chemotherapy and radiotherapy

This observational clinical study was composed of two substudies: a non-comparative one (n = 166), testing only lysozyme-based compounds (LBCs), and a comparative substudy (n = 275), testing both LBCs and bicarbonate-based local compounds (BBCs) on the healing of oral mucositis during radio- or chemotherapy. The density of ulcerations has decreased significantly after the treatment with lysozyme in both substudies. The density of ulcerations in the radiotherapy group was lower in patients treated with LBCs compared to patients treated with BBCs (p < 0.001). In the chemotherapy group, reduction of ulceration density was similar with both LBCs and BBCs. The LBCs reduced pain intensity during the intake of solid food and speech more than BBCs in both patient cohorts (p < 0.05). In the radiotherapy cohort, pain intensity when consuming liquid foods was reduced more with LBCs than with BBCs (p < 0.05). No adverse events were recorded. This study demonstrates the advantages of treating oral mucositis during radiotherapy or chemotherapy with LBCs

Warming Up Density Functional Theory

Density functional theory (DFT) has become the most popular approach to electronic structure across disciplines, especially in material and chemical sciences. Last year, at least 30,000 papers used DFT to make useful predictions or give insight into an enormous diversity of scientific problems, ranging from battery development to solar cell efficiency and far beyond. The success of this field has been driven by usefully accurate approximations based on known exact conditions and careful testing and validation. In the last decade, applications of DFT in a new area, warm dense matter, have exploded. DFT is revolutionizing simulations of warm dense matter including applications in controlled fusion, planetary interiors, and other areas of high energy density physics. Over the past decade or so, molecular dynamics calculations driven by modern density functional theory have played a crucial role in bringing chemical realism to these applications, often (but not always) with excellent agreement with experiment. This chapter summarizes recent work from our group on density functional theory at non-zero temperatures, which we call thermal DFT. We explain the relevance of this work in the context of warm dense matter, and the importance of quantum chemistry to this regime. We illustrate many basic concepts on a simple model system, the asymmetric Hubbard dimer

Microstructural, Densitometric and Metabolic Variations in Bones from Rats with Normal or Altered Skeletal States

Background: High resolution μCT, and combined μPET/CT have emerged as non-invasive techniques to enhance or even replace dual energy X-ray absorptiometry (DXA) as the current preferred approach for fragility fracture risk assessment. The aim of this study was to assess the ability of µPET/CT imaging to differentiate changes in rat bone tissue density and microstructure induced by metabolic bone diseases more accurately than current available methods. Methods: Thirty three rats were divided into three groups of control, ovariectomy and vitamin-D deficiency. At the conclusion of the study, animals were subjected to glucose (18FDG) and sodium fluoride (Na18F) PET/CT scanning. Then, specimens were subjected to µCT imaging and tensile mechanical testing. Results: Compared to control, those allocated to ovariectomy and vitamin D deficiency groups showed 4% and 22% (significant) increase in 18FDG uptake values, respectively. DXA-based bone mineral density was higher in the vitamin D deficiency group when compared to the other groups (cortical bone), yet μCT-based apparent and mineral density results were not different between groups. DXA-based bone mineral density was lower in the ovariectomy group when compared to the other groups (cancellous bone); yet μCT-based mineral density results were not different between groups, and the μCT-based apparent density results were lower in the ovariectomy group compared to the other groups. Conclusion: PET and micro-CT provide an accurate three-dimensional measurement of the changes in bone tissue mineral density, as well as microstructure for cortical and cancellous bone and metabolic activity. As osteomalacia is characterized by impaired bone mineralization, the use of densitometric analyses may lead to misinterpretation of the condition as osteoporosis. In contrast, µCT alone and in combination with the PET component certainly provides an accurate three-dimensional measurement of the changes in both bone tissue mineral density, as well as microstructure for cortical and cancellous bone and metabolic activity

Tinjauan Kuat Geser Tanah Lempung Menggunakan Kapur Sebagai Bahan Stabilisasi Dengan Variasi Diameter Butiran Tanah

Based on the research results Wiqoyah (2003) Tanon soil is clay. Percentage sieve No. 200 clay is at 94.13%, liquid limit (LL) = 88.03%, the plasticity index (IP) = 49.44%. Based on the system of the American Association Of State Highway And Transportation Officials (AASHTO), clay Tanon included into the group of A-7-5, and based on the classification of the Unified Soil Classification System (USCS) belong to the group CH ie inorganic clay with high plasticity. Based on the research above example that stabilization with lime can improve soil conditions, but so far it is not known how the effect of variations in the diameter of grain to the stabilization of the land. In this study conducted an experiment using a variety of soil particle diameter is through sieve No. 4, through sieve No. 30 and sieve No. 50, this is done to determine whether the grain diameter variations affect the physical and mechanical properties of the clay soil. In this study, the test was conducted on the physical properties of the soil mix and test the DST (Direct Shear Test) with the addition of lime amounted to 2.5% and 5% of the weight of the sample. Results of testing the physical properties of the soil mixture obtained water content, density (specific gravity), the liquid limit and plasticity index fell, while the value of plastic limit and shrinkage limit rose. Results of soil testing mixtures classified according to AASHTO system, including a group of A-7-5, while according to the system USCS, clay + lime 2.5% into the group CH and clay + lime 5% belong to the group MH. Results of testing the mechanical properties of testing standards and testing Proctor DST (Direct Shear Test), from Proctor standard test showed a decrease in weight of dry volume and the largest decline occurred in the land passes No. 50 + lime 5% by volume dry weight values of 1.062 g / cm3, for optimum water content largest increase occurred in soil sieve No. 4 at the limestone addition of 5% with the results of the optimum water content of 32.46%. The test results DST (Direct Shear Test) increase, the biggest increase occurred in the soil through sieve No. 4 at the limestone addition of 5% with a value of shear stress (τ) 0.677 kg / cm2

Towards a clinical staging for bipolar disorder: defining patient subtypes based on functional outcome.

BACKGROUND: The functional outcome of Bipolar Disorder (BD) is highly variable. This variability has been attributed to multiple demographic, clinical and cognitive factors. The critical next step is to identify combinations of predictors that can be used to specify prognostic subtypes, thus providing a basis for a staging classification in BD. METHODS: Latent Class Analysis was applied to multiple predictors of functional outcome in a sample of 106 remitted adults with BD. RESULTS: We identified two subtypes of patients presenting "good" (n=50; 47.6%) and "poor" (n=56; 52.4%) outcome. Episode density, level of residual depressive symptoms, estimated verbal intelligence and inhibitory control emerged as the most significant predictors of subtype membership at the p<0.05 level. Their odds ratio (OR) and confidence interval (CI) with reference to the "good" outcome group were: episode density (OR=4.622, CI 1.592-13.418), level of residual depressive symptoms (OR=1.543, CI 1.210-1.969), estimated verbal intelligence (OR=0.969; CI 0.945-0.995), and inhibitory control (OR=0.771, CI 0.656-0.907). Age, age of onset and duration of illness were comparable between prognostic groups. LIMITATIONS: The longitudinal stability or evolution of the subtypes was not tested. CONCLUSIONS: Our findings provide the first empirically derived staging classification of BD based on two underlying dimensions, one for illness severity and another for cognitive function. This approach can be further developed by expanding the dimensions included and testing the reproducibility and prospective prognostic value of the emerging classes. Developing a disease staging system for BD will allow individualised treatment planning for patients and selection of more homogeneous patient groups for research purposes