Random Bit Multilevel Algorithms for Stochastic Differential Equations

We study the approximation of expectations \E(f(X)) for solutions $X$ of SDEs and functionals $f \colon C([0,1],\R^r) \to \R$ by means of restricted Monte Carlo algorithms that may only use random bits instead of random numbers. We consider the worst case setting for functionals $f$ from the Lipschitz class w.r.t.\ the supremum norm. We construct a random bit multilevel Euler algorithm and establish upper bounds for its error and cost. Furthermore, we derive matching lower bounds, up to a logarithmic factor, that are valid for all random bit Monte Carlo algorithms, and we show that, for the given quadrature problem, random bit Monte Carlo algorithms are at least almost as powerful as general randomized algorithms

Random Bit Quadrature and Approximation of Distributions on Hilbert Spaces

We study the approximation of expectations \E(f(X)) for Gaussian random elements $X$ with values in a separable Hilbert space $H$ and Lipschitz continuous functionals $f \colon H \to \R$. We consider restricted Monte Carlo algorithms, which may only use random bits instead of random numbers. We determine the asymptotics (in some cases sharp up to multiplicative constants, in the other cases sharp up to logarithmic factors) of the corresponding $n$-th minimal error in terms of the decay of the eigenvalues of the covariance operator of $X$. It turns out that, within the margins from above, restricted Monte Carlo algorithms are not inferior to arbitrary Monte Carlo algorithms, and suitable random bit multilevel algorithms are optimal. The analysis of this problem leads to a variant of the quantization problem, namely, the optimal approximation of probability measures on $H$ by uniform distributions supported by a given, finite number of points. We determine the asymptotics (up to multiplicative constants) of the error of the best approximation for the one-dimensional standard normal distribution, for Gaussian measures as above, and for scalar autonomous SDEs

Comparison of Intravitreal Bevacizumab Upload Followed by a Dexamethasone Implant versus Dexamethasone Implant Monotherapy for Retinal Vein Occlusion with Macular Edema

Purpose: To compare the efficacy and safety of three intravitreal bevacizumab upload injections followed by a dexamethasone implant versus dexamethasone implant monotherapy in eyes with macular edema due to retinal vein occlusion. Methods: Sixty-four eyes of 64 patients were included in this prospective, consecutive, nonrandomized case series: group 1 consisted of 38 patients (22 with central retinal vein occlusion, CRVO, 16 with branch retinal vein occlusion, BRVO) treated using a dexamethasone implant (Ozurdex) alone; group 2 consisted of 26 patients (14 CRVO, 12 BRVO) treated with three consecutive intravitreal bevacizumab injections at monthly intervals followed by a dexamethasone implant. In case of recurrence, both cohorts received further dexamethasone implants. Preoperatively and monthly best corrected visual acuity (BCVA, ETDRS), central retinal thickness (Spectralis-OCT), intraocular pressure, and wide-angle fundus photodocumentation (Optomap) were performed. The primary clinical endpoint was BCVA at 6 months after initiation of therapy. Secondary endpoints were central retinal thickness and safety of the therapy applied. Results: In group 1, an increase in BCVA of 2.5 (+/- 1.6) letters in the CRVO and of 13.0 (+/- 3.2) letters in BRVO patients was seen after 6 months, in group 2 of 5.9 (+/- 0.4) letters (CRVO) and 3.8 (+/- 2.4) letters (BRVO), which was not statistically significant. When comparing the two treatment groups with respect to the type of vein occlusion, there was a significant advantage for BRVO patients for the dexamethasone implant monotherapy (BRVO patients in group 1, p = 0.005). Central retinal thickness showed a significant reduction after 6 months only in patients of group 1, both for CRVO (p = 0.01) and BRVO (p = 0.003). First recurrence after the first dexamethasone implant injection occurred after 3.8 months (mean) in CRVO and 3.5 months in BRVO patients (group 1), versus 3.2 and 3.7 months, respectively, in group 2. In group 1, 63.6% with CRVO and 50% with BRVO showed an increased intraocular pressure after treatment; in group 2, 57.1% with CRVO and 50.0% with BRVO, respectively. Conclusion: In CRVO, there was no difference between the two treatment strategies investigated. However, in BRVO, dexamethasone implant monotherapy was associated with better functional outcome. Copyright (C) 2012 S. Karger AG, Base

Role of brain imaging in disorders of brain-gut interaction: a Rome Working Team Report.

Imaging of the living human brain is a powerful tool to probe the interactions between brain, gut and microbiome in health and in disorders of brain-gut interactions, in particular IBS. While altered signals from the viscera contribute to clinical symptoms, the brain integrates these interoceptive signals with emotional, cognitive and memory related inputs in a non-linear fashion to produce symptoms. Tremendous progress has occurred in the development of new imaging techniques that look at structural, functional and metabolic properties of brain regions and networks. Standardisation in image acquisition and advances in computational approaches has made it possible to study large data sets of imaging studies, identify network properties and integrate them with non-imaging data. These approaches are beginning to generate brain signatures in IBS that share some features with those obtained in other often overlapping chronic pain disorders such as urological pelvic pain syndromes and vulvodynia, suggesting shared mechanisms. Despite this progress, the identification of preclinical vulnerability factors and outcome predictors has been slow. To overcome current obstacles, the creation of consortia and the generation of standardised multisite repositories for brain imaging and metadata from multisite studies are required

Characterization of protein-interaction networks in tumors

<p>Abstract</p> <p>Background</p> <p>Analyzing differential-gene-expression data in the context of protein-interaction networks (PINs) yields information on the functional cellular status. PINs can be formally represented as graphs, and approximating PINs as undirected graphs allows the network properties to be characterized using well-established graph measures.</p> <p>This paper outlines features of PINs derived from 29 studies on differential gene expression in cancer. For each study the number of differentially regulated genes was determined and used as a basis for PIN construction utilizing the Online Predicted Human Interaction Database.</p> <p>Results</p> <p>Graph measures calculated for the largest subgraph of a PIN for a given differential-gene-expression data set comprised properties reflecting the size, distribution, biological relevance, density, modularity, and cycles. The values of a distinct set of graph measures, namely <it>Closeness Centrality</it>, <it>Graph Diameter</it>, <it>Index of Aggregation</it>, <it>Assortative Mixing Coefficient</it>, <it>Connectivity</it>, <it>Sum of the Wiener Number</it>, <it>modified Vertex Distance Number</it>, and <it>Eigenvalues </it>differed clearly between PINs derived on the basis of differential gene expression data sets characterizing malignant tissue and PINs derived on the basis of randomly selected protein lists.</p> <p>Conclusion</p> <p>Cancer PINs representing differentially regulated genes are larger than those of randomly selected protein lists, indicating functional dependencies among protein lists that can be identified on the basis of transcriptomics experiments. However, the prevalence of hub proteins was not increased in the presence of cancer. Interpretation of such graphs in the context of robustness may yield novel therapies based on synthetic lethality that are more effective than focusing on single-action drugs for cancer treatment.</p

RNA chaperone activity and RNA-binding properties of the E. coli protein StpA

The E. coli protein StpA has RNA annealing and strand displacement activities and it promotes folding of RNAs by loosening their structures. To understand the mode of action of StpA, we analysed the relationship of its RNA chaperone activity to its RNA-binding properties. For acceleration of annealing of two short RNAs, StpA binds both molecules simultaneously, showing that annealing is promoted by crowding. StpA binds weakly to RNA with a preference for unstructured molecules. Binding of StpA to RNA is strongly dependent on the ionic strength, suggesting that the interactions are mainly electrostatic. A mutant variant of the protein, with a glycine to valine change in the nucleic-acid-binding domain, displays weaker RNA binding but higher RNA chaperone activity. This suggests that the RNA chaperone activity of StpA results from weak and transient interactions rather than from tight binding to RNA. We further discuss the role that structural disorder in proteins may play in chaperoning RNA folding, using bioinformatic sequence analysis tools, and provide evidence for the importance of conformational disorder and local structural preformation of chaperone nucleic-acid-binding sites