Searching for network modules

When analyzing complex networks a key target is to uncover their modular structure, which means searching for a family of modules, namely node subsets spanning each a subnetwork more densely connected than the average. This work proposes a novel type of objective function for graph clustering, in the form of a multilinear polynomial whose coefficients are determined by network topology. It may be thought of as a potential function, to be maximized, taking its values on fuzzy clusterings or families of fuzzy subsets of nodes over which every node distributes a unit membership. When suitably parametrized, this potential is shown to attain its maximum when every node concentrates its all unit membership on some module. The output thus is a partition, while the original discrete optimization problem is turned into a continuous version allowing to conceive alternative search strategies. The instance of the problem being a pseudo-Boolean function assigning real-valued cluster scores to node subsets, modularity maximization is employed to exemplify a so-called quadratic form, in that the scores of singletons and pairs also fully determine the scores of larger clusters, while the resulting multilinear polynomial potential function has degree 2. After considering further quadratic instances, different from modularity and obtained by interpreting network topology in alternative manners, a greedy local-search strategy for the continuous framework is analytically compared with an existing greedy agglomerative procedure for the discrete case. Overlapping is finally discussed in terms of multiple runs, i.e. several local searches with different initializations.Comment: 10 page

Learning filter functions in regularisers by minimising quotients

Learning approaches have recently become very popular in the field of inverse problems. A large variety of methods has been established in recent years, ranging from bi-level learning to high-dimensional machine learning techniques. Most learning approaches, however, only aim at fitting parametrised models to favourable training data whilst ignoring misfit training data completely. In this paper, we follow up on the idea of learning parametrised regularisation functions by quotient minimisation as established in [3]. We extend the model therein to include higher-dimensional filter functions to be learned and allow for fit- and misfit-training data consisting of multiple functions. We first present results resembling behaviour of well-established derivative-based sparse regularisers like total variation or higher-order total variation in one-dimension. Our second and main contribution is the introduction of novel families of non-derivative-based regularisers. This is accomplished by learning favourable scales and geometric properties while at the same time avoiding unfavourable ones

Apparent non-canonical trans-splicing is generated by reverse transcriptase in vitro

Trans-splicing, the in vivo joining of two RNA molecules, is well characterized in several groups of simple organisms but was long thought absent from fungi, plants and mammals. However, recent bioinformatic analyses of expressed sequence tag (EST) databases suggested widespread trans-splicing in mammals^1-2^. Splicing, including the characterised trans-splicing systems, involves conserved sequences at the splice junctions. Our analysis of a yeast non-coding RNA revealed that around 30% of the products of reverse transcription lacked an internal region of 117 nt, suggesting that the RNA was spliced. The junction sequences lacked canonical splice-sites but were flanked by direct repeats, and further analyses indicated that the apparent splicing actually arose because reverse transcriptase can switch templates during transcription^3^. Many newly identified, apparently trans-spliced, RNAs lacked canonical splice sites but were flanked by short regions of homology, leading us to question their authenticity. Here we report that all reported categories of non-canonical splicing could be replicated using an in vitro reverse transcription system with highly purified RNA substrates. We observed the reproducible occurrence of ostensible trans-splicing, exon shuffling and sense-antisense fusions. The latter generate apparent antisense non-coding RNAs, which are also reported to be abundant in humans^4^. Different reverse transcriptases can generate different products of template switching, providing a simple diagnostic. Many reported examples of splicing in the absence of canonical splicing signals may be artefacts of cDNA preparation

Use of antihistamine medications during early pregnancy and selected birth defects: The National Birth Defects Prevention Study, 1997–2011

Background: It is estimated that approximately 10–15% of pregnant women report antihistamine use during pregnancy. Although antihistamines are generally considered safe during pregnancy, results from published studies are inconsistent. Methods: Using a case–control study design we analyzed 41,148 pregnancies (30,091 cases and 11,057 controls) from the National Birth Defects Prevention Study (1997–2011). Logistic regression models were used to estimate odds ratios (OR) and 95% confidence intervals for 64 birth defect groupings in relation to early pregnancy exposure to 14 distinct antihistamines. Models were adjusted for maternal age, race, parity, education level, prenatal care, folic acid use, smoking and alcohol use, and study site. Results: Approximately 13% of cases and controls were exposed to an antihistamine during early pregnancy. Analyses were restricted to those defects where more than five cases were exposed to the antihistamine of interest, generating 340 analyses which yielded 20 (5.9%) significant positive associations (adjusted ORs ranging from 1.21 to 4.34). Conclusions: Only a few of our findings were consistent with previous studies. There is a lack of strong evidence to conclude that birth defects are associated with exposure to antihistamines during early pregnancy

Hodge Theory on Metric Spaces

Hodge theory is a beautiful synthesis of geometry, topology, and analysis, which has been developed in the setting of Riemannian manifolds. On the other hand, spaces of images, which are important in the mathematical foundations of vision and pattern recognition, do not fit this framework. This motivates us to develop a version of Hodge theory on metric spaces with a probability measure. We believe that this constitutes a step towards understanding the geometry of vision. The appendix by Anthony Baker provides a separable, compact metric space with infinite dimensional \alpha-scale homology.Comment: appendix by Anthony W. Baker, 48 pages, AMS-LaTeX. v2: final version, to appear in Foundations of Computational Mathematics. Minor changes and addition

Nonlinear spectral image fusion

In this paper we demonstrate that the framework of nonlinear spectral decompositions based on total variation (TV) regularization is very well suited for image fusion as well as more general image manipulation tasks. The well-localized and edge-preserving spectral TV decomposition allows to select frequencies of a certain image to transfer particular features, such as wrinkles in a face, from one image to another. We illustrate the effectiveness of the proposed approach in several numerical experiments, including a comparison to the competing techniques of Poisson image editing, linear osmosis, wavelet fusion and Laplacian pyramid fusion. We conclude that the proposed spectral TV image decomposition framework is a valuable tool for semi- and fully-automatic image editing and fusion

Nonlocal similarity image filtering

Abstract. We exploit the recurrence of structures at different locations, orientations and scales in an image to perform denoising. While previous methods based on “nonlocal filtering ” identify corresponding patches only up to translations, we consider more general similarity transformations. Due to the additional computational burden, we break the problem down into two steps: First, we extract similarity invariant descriptors at each pixel location; second, we search for similar patches by matching descriptors. The descriptors used are inspired by scale-invariant feature transform (SIFT), whereas the similarity search is solved via the minimization of a cost function adapted from local denoising methods. Our method compares favorably with existing denoising algorithms as tested on several datasets.

Survival of children with trisomy 13 and trisomy 18: A multi-state population-based study

Trisomy 13 (T13) and trisomy 18 (T18) are among the most prevalent autosomal trisomies. Both are associated with a very high risk of mortality. Numerous instances, however, of long-term survival of children with T13 or T18 have prompted some clinicians to pursue aggressive treatment instead of the traditional approach of palliative care. The purpose of this study is to assess current mortality data for these conditions. This multi-state, population-based study examined data obtained from birth defect surveillance programs in nine states on live-born infants delivered during 1999–2007 with T13 or T18. Information on children’s vital status and selected maternal and infant risk factors were obtained using matched birth and death certificates and other data sources. The Kaplan–Meier method and Cox proportional hazards models were used to estimate age-specific survival probabilities and predictors of survival up to age five. There were 693 children with T13 and 1,113 children with T18 identified from the participating states. Among children with T13, 5-year survival was 9.7%; among children with T18, it was 12.3%. For both trisomies, gestational age was the strongest predictor of mortality. Females and children of non-Hispanic black mothers had the lowest mortality. Omphalocele and congenital heart defects were associated with an increased risk of death for children with T18 but not T13. This study found survival among children with T13 and T18 to be somewhat higher than those previously reported in the literature, consistent with recent studies reporting improved survival following more aggressive medical intervention for these children

Quantifying geocode location error using GIS methods

BACKGROUND: The Metropolitan Atlanta Congenital Defects Program (MACDP) collects maternal address information at the time of delivery for infants and fetuses with birth defects. These addresses have been geocoded by two independent agencies: (1) the Georgia Division of Public Health Office of Health Information and Policy (OHIP) and (2) a commercial vendor. Geographic information system (GIS) methods were used to quantify uncertainty in the two sets of geocodes using orthoimagery and tax parcel datasets. METHODS: We sampled 599 infants and fetuses with birth defects delivered during 1994–2002 with maternal residence in either Fulton or Gwinnett County. Tax parcel datasets were obtained from the tax assessor's offices of Fulton and Gwinnett County. High-resolution orthoimagery for these counties was acquired from the U.S. Geological Survey. For each of the 599 addresses we attempted to locate the tax parcel corresponding to the maternal address. If the tax parcel was identified the distance and the angle between the geocode and the residence were calculated. We used simulated data to characterize the impact of geocode location error. In each county 5,000 geocodes were generated and assigned their corresponding Census 2000 tract. Each geocode was then displaced at a random angle by a random distance drawn from the distribution of observed geocode location errors. The census tract of the displaced geocode was determined. We repeated this process 5,000 times and report the percentage of geocodes that resolved into incorrect census tracts. RESULTS: Median location error was less than 100 meters for both OHIP and commercial vendor geocodes; the distribution of angles appeared uniform. Median location error was approximately 35% larger in Gwinnett (a suburban county) relative to Fulton (a county with urban and suburban areas). Location error occasionally caused the simulated geocodes to be displaced into incorrect census tracts; the median percentage of geocodes resolving into incorrect census tracts ranged between 4.5% and 5.3%, depending upon the county and geocoding agency. CONCLUSION: Geocode location uncertainty can be estimated using tax parcel databases in a GIS. This approach is a viable alternative to global positioning system field validation of geocodes