The map equation

Many real-world networks are so large that we must simplify their structure before we can extract useful information about the systems they represent. As the tools for doing these simplifications proliferate within the network literature, researchers would benefit from some guidelines about which of the so-called community detection algorithms are most appropriate for the structures they are studying and the questions they are asking. Here we show that different methods highlight different aspects of a network's structure and that the the sort of information that we seek to extract about the system must guide us in our decision. For example, many community detection algorithms, including the popular modularity maximization approach, infer module assignments from an underlying model of the network formation process. However, we are not always as interested in how a system's network structure was formed, as we are in how a network's extant structure influences the system's behavior. To see how structure influences current behavior, we will recognize that links in a network induce movement across the network and result in system-wide interdependence. In doing so, we explicitly acknowledge that most networks carry flow. To highlight and simplify the network structure with respect to this flow, we use the map equation. We present an intuitive derivation of this flow-based and information-theoretic method and provide an interactive on-line application that anyone can use to explore the mechanics of the map equation. We also describe an algorithm and provide source code to efficiently decompose large weighted and directed networks based on the map equation.Comment: 9 pages and 3 figures, corrected typos. For associated Flash application, see http://www.tp.umu.se/~rosvall/livemod/mapequation

Patients with prostate cancer and androgen deprivation therapy have increased risk of fractures—a study from the Fractures and Fall Injuries in the Elderly Cohort (FRAILCO)

Summary Osteoporosis is a common complication of androgen deprivation therapy (ADT). In this large Swedish cohort study consisting of a total of nearly 180,000 older men, we found that those with prostate cancer and ADT have a significantly increased risk of future osteoporotic fractures. Introduction: Androgen deprivation therapy (ADT) in patients with prostate cancer is associated to increased risk of fractures. In this study, we investigated the relationship between ADT in patients with prostate cancer and the risk of incident fractures and non-skeletal fall injuries both compared to those without ADT and compared to patients without prostate cancer. Methods: We included 179,744 men (79.1 ± 7.9 years (mean ± SD)) from the Swedish registry to which national directories were linked in order to study associations regarding fractures, fall injuries, morbidity, mortality and medications. We identified 159,662 men without prostate cancer, 6954 with prostate cancer and current ADT and 13,128 men with prostate cancer without ADT. During a follow-up of approximately 270,300 patient-years, we identified 10,916 incident fractures including 4860 hip fractures. Results: In multivariable Cox regression analyses and compared to men without prostate cancer, those with prostate cancer and ADT had increased risk of any fracture (HR 95% CI 1.40 (1.28–1.53)), hip fracture (1.38 (1.20–1.58)) and MOF (1.44 (1.28–1.61)) but not of non-skeletal fall injury (1.01 (0.90–1.13)). Patients with prostate cancer without ADT did not have increased risk of any fracture (0.97 (0.90–1.05)), hip fracture (0.95 (0.84–1.07)), MOF (1.01 (0.92–1.12)) and had decreased risk of non-skeletal fall injury (0.84 (0.77–0.92)). Conclusions: Patients with prostate cancer and ADT is a fragile patient group with substantially increased risk of osteoporotic fractures both compared to patients without prostate cancer and compared to those with prostate cancer without ADT. We believe that this must be taken in consideration in all patients with prostate cancer already at the initiation of ADT

One step multiderivative methods for first order ordinary differential equations

A family of one-step multiderivative methods based on Padé approximants to the exponential function is developed. The methods are extrapolated and analysed for use in PECE mode. Error constants and stability intervals are calculated and the combinations compared with well known linear multi-step combinations and combinations using high accuracy Newton-Cotes quadrature formulas as correctors. w926020

Hip fracture risk and safety with alendronate treatment in the oldest-old

Background. There is high evidence for secondary prevention of fractures, including hip fracture, with alendronate treatment, but alendronate’s efficacy to prevent hip fractures in the oldest-old (≥80 years old), the population with the highest fracture risk, has not been studied. Objective. To investigate whether alendronate treatment amongst the oldest-old with prior fracture was related to decreased hip fracture rate and sustained safety. Methods. Using a national database of men and women undergoing a fall risk assessment at a Swedish healthcare facility, we identified 90 795 patients who were 80 years or older and had a prior fracture. Propensity score matching (four to one) was then used to identify 7844 controls to 1961 alendronate-treated patients. The risk of incident hip fracture was investigated with Cox models and the interaction between age and treatment was investigated using an interaction term. Results. The case and control groups were well balanced in regard to age, sex, anthropometrics and comorbidity. Alendronate treatment was associated with a decreased risk of hip fracture in crude (hazard ratio (HR) 0.62 (0.49–0.79), P < 0.001) and multivariable models (HR 0.66 (0.51–0.86), P < 0.01). Alendronate was related to reduced mortality risk (HR 0.88 (0.82–0.95) but increased risk of mild upper gastrointestinal symptoms (UGI) (HR 1.58 (1.12–2.24). The alendronate association did not change with age for hip fractures or mild UGI. Conclusion. In old patients with prior fracture, alendronate treatment reduces the risk of hip fracture with sustained safety, indicating that this treatment should be considered in these high-risk patient

Weighted maximal regularity estimates and solvability of non-smooth elliptic systems II

We continue the development, by reduction to a first order system for the conormal gradient, of $L^2$ \textit{a priori} estimates and solvability for boundary value problems of Dirichlet, regularity, Neumann type for divergence form second order, complex, elliptic systems. We work here on the unit ball and more generally its bi-Lipschitz images, assuming a Carleson condition as introduced by Dahlberg which measures the discrepancy of the coefficients to their boundary trace near the boundary. We sharpen our estimates by proving a general result concerning \textit{a priori} almost everywhere non-tangential convergence at the boundary. Also, compactness of the boundary yields more solvability results using Fredholm theory. Comparison between classes of solutions and uniqueness issues are discussed. As a consequence, we are able to solve a long standing regularity problem for real equations, which may not be true on the upper half-space, justifying \textit{a posteriori} a separate work on bounded domains.Comment: 76 pages, new abstract and few typos corrected. The second author has changed nam

Discovery of multiple Lorentzian components in the X-ray timing properties of the Narrow Line Seyfert 1 Ark 564

We present a power spectral analysis of a 100 ksec XMM-Newton observation of the narrow line Seyfert 1 galaxy Ark~564. When combined with earlier RXTE and ASCA observations, these data produce a power spectrum covering seven decades of frequency which is well described by a power law with two very clear breaks. This shape is unlike the power spectra of almost all other AGN observed so far, which have only one detected break, and resemble Galactic binary systems in a soft state. The power spectrum can also be well described by the sum of two Lorentzian-shaped components, the one at higher frequencies having a hard spectrum, similar to those seen in Galactic binary systems. Previously we have demonstrated that the lag of the hard band variations relative to the soft band in Ark 564 is dependent on variability time-scale, as seen in Galactic binary sources. Here we show that the time-scale dependence of the lags can be described well using the same two-Lorentzian model which describes the power spectrum, assuming that each Lorentzian component has a distinct time lag. Thus all X-ray timing evidence points strongly to two discrete, localised, regions as the origin of most of the variability. Similar behaviour is seen in Galactic X-ray binary systems in most states other than the soft state, i.e. in the low-hard and intermediate/very high states. Given the very high accretion rate of Ark 564 the closest analogy is with the very high (intermediate) state rather than the low-hard state. We therefore strengthen the comparison between AGN and Galactic binary sources beyond previous studies by extending it to the previously poorly studied very high accretion rate regime.Comment: 11 pages, 11 figures, accepted for publication in MNRA

Peptide microarray-based characterization of antibody responses to host proteins after bacille Calmette-Guerin vaccination

BACKGROUND: Bacille Calmette–Guérin (BCG) is the world’s most widely distributed vaccine, used against tuberculosis (TB), in cancer immunotherapy, and in autoimmune diseases due to its immunomodulatory properties. To date, the effect of BCG vaccination on antibody responses to host proteins has not been reported. High-content peptide microarrays (HCPM) offer a unique opportunity to gauge specific humoral immune responses. METHODS: The sera of BCG-vaccinated healthy adults were tested on a human HCPM platform (4953 randomly selected epitopes of human proteins) to detect specific immunoglobulin gamma (IgG) responses. Samples were obtained at 56, 112, and 252 days after vaccination. Immunohistology was performed on lymph node tissue from patients with TB lymphadenitis. Results were analysed with a combination of existing and novel statistical methods. RESULTS: IgG recognition of host peptides exhibited a peak at day 56 post BCG vaccination in all study subjects tested, which diminished over time. Primarily, IgG responses exhibited increased reactivity to ion transporters (sodium, calcium channels), cytokine receptors (interleukin 2 receptor β (IL2Rβ), fibroblast growth factor receptor 1 (FGFR1)), other cell surface receptors (inositol, somatostatin, angiopoeitin), ribonucleoprotein, and enzymes (tyrosine kinases, phospholipase) on day 56. There was decreased IgG reactivity to transforming growth factor-beta type 1 receptor (TGFβR1) and, in agreement with the peptide microarray findings, immunohistochemical analysis of TB-infected lymph node samples revealed an overexpression of TGFβR in granulomatous lesions. Moreover, the vesicular monoamine transporter (VMAT2) showed increased reactivity on days 112 and 252, but not on day 56 post-vaccination. IgG to interleukin 4 receptor (IL4R) showed increased reactivity at 112 days post-vaccination, while IgG to IL2Rβ and FGFR1 showed decreased reactivity on days 112 and 252 as compared to day 56 post BCG vaccination. CONCLUSIONS: BCG vaccination modifies the host’s immune landscape after 56 days, but this imprint changes over time. This may influence the establishment of immunological memory in BCG-vaccinated individuals