Besov priors for Bayesian inverse problems

We consider the inverse problem of estimating a function $u$ from noisy, possibly nonlinear, observations. We adopt a Bayesian approach to the problem. This approach has a long history for inversion, dating back to 1970, and has, over the last decade, gained importance as a practical tool. However most of the existing theory has been developed for Gaussian prior measures. Recently Lassas, Saksman and Siltanen (Inv. Prob. Imag. 2009) showed how to construct Besov prior measures, based on wavelet expansions with random coefficients, and used these prior measures to study linear inverse problems. In this paper we build on this development of Besov priors to include the case of nonlinear measurements. In doing so a key technical tool, established here, is a Fernique-like theorem for Besov measures. This theorem enables us to identify appropriate conditions on the forward solution operator which, when matched to properties of the prior Besov measure, imply the well-definedness and well-posedness of the posterior measure. We then consider the application of these results to the inverse problem of finding the diffusion coefficient of an elliptic partial differential equation, given noisy measurements of its solution.Comment: 18 page

Hierarchical Bayesian level set inversion

The level set approach has proven widely successful in the study of inverse problems for inter- faces, since its systematic development in the 1990s. Re- cently it has been employed in the context of Bayesian inversion, allowing for the quantification of uncertainty within the reconstruction of interfaces. However the Bayesian approach is very sensitive to the length and amplitude scales in the prior probabilistic model. This paper demonstrates how the scale-sensitivity can be cir- cumvented by means of a hierarchical approach, using a single scalar parameter. Together with careful con- sideration of the development of algorithms which en- code probability measure equivalences as the hierar- chical parameter is varied, this leads to well-defined Gibbs based MCMC methods found by alternating Metropolis-Hastings updates of the level set function and the hierarchical parameter. These methods demon- strably outperform non-hierarchical Bayesian level set methods

Herpes Simplex Virus Type 1 Clinical Isolates Respond to UL29-Targeted siRNA Swarm Treatment Independent of Their Acyclovir Sensitivity

Acyclovir is the drug of choice for the treatment of herpes simplex virus (HSV) infections. Acyclovir-resistant HSV strains may emerge, especially during long-term drug use, and subsequently cause difficult-to-treat exacerbations. Previously, we set up a novel treatment approach, based on enzymatically synthesized pools of siRNAs, or siRNA swarms. These swarms can cover kilobases-long target sequences, reducing the likelihood of resistance to treatment. Swarms targeting the UL29 essential gene of HSV-1 have demonstrated high efficacy against HSV-1 in vitro and in vivo. Here, we assessed the antiviral potential of a UL29 siRNA swarm against circulating strains of HSV-1, in comparison with acyclovir. All circulating strains were sensitive to both antivirals, with the half-maximal inhibitory concentrations (IC50) in the range of 350-1911 nM for acyclovir and 0.5-3 nM for the UL29 siRNA swarm. Additionally, we showed that an acyclovir-resistant HSV-1, devoid of thymidine kinase, is highly sensitive to UL29 siRNA treatment (IC50 1.0 nM; I-max 97%). Moreover, the detected minor variations in the RNAi target of the HSV strains had no effect on the potency or efficacy of UL29 siRNA swarm treatment. Our findings support the development of siRNA swarms for the treatment of HSV-1 infections, in order to circumvent any potential acyclovir resistance

Environmental friendly mobile radio networks: Approaches of the European OPERA-Net 2 project

International audienceReducing the overall environmental impact of mobile radio networks is a central factor in achieving improved mobile services whilst at the same time enabling a growing telecommunications industry in emerging markets. The OPERA-Net-2 (Optimising Power Efficiency in Mobile Radio Networks 2) project concentrates on this challenge, addressing both energy and material efficiencies of 3G, 4G and heterogeneous networks, while also considering the use of renewable energy sources. This paper presents an insight into the project after its first year and discusses research trends in `green communications networks' for the future

The determination of the distribution of collagenase in gastric cancer tissue by the peroxidase-labeled antibody method

胃癌が発育進展するとき,あるいは潰瘍が進行,治癒するときには病巣及び病巣周囲の間質結合織はそれに伴い崩壊する一方,増生もしてくる.この間質の変化は,結合織崩壊に働く因子と増生に働く因子の均衡によっている.結合織崩壊の因子の中で最も重要なものの一つとして,生理的条件下でcollagen分子を特異的に分解するcollagenaseがあげられる.浸潤しつつある癌の先進部では,癌細胞より分泌されたcollagenaseを主とする蛋白分解酵素が間質を破壊し,その間隙を癌細胞が拡がって行くと考えるのが妥当であろう.すでに胃癌浸潤とcollagenaseの関連について,胃癌組織各部のcollagenase活性を計測し,癌先進部で最も活性が高く,胃癌の進展にcollagenaseが関与しているとの報告がある.しかし,そのcollagenaseが胃癌細胞から分泌されているのかという最も興味ある疑問に答えることはできていない.著者はcollagenase抗体を作製し,免疫組織学的方法(酵素抗体法)を用いて,胃癌組織内におけるcollagenaseの局在を検索した.その結果collagenaseは間質側に多く存在するが,癌細胞内にも存在することを確認した.また胃癌を組織型別,深達度別,浸潤様式別等に分類し,各組織でのcollagenaseの局在を検索し,これらの結果や他の報告をも含めて,胃癌の進展にcollagenaseがどのように関与しているのか考察した.更には対照組織として正常ヒト皮膚,胃潰瘍,大腸癌を検討し,各組織におけるcollagenaseの局在と免疫学的組織特異性の有無も検討した.Collagenase plays an important role in the invasion of gastric cancer. However, it is not known if gastric cancer cells produce collagenase. In this study, anti-collagenase antibodies were generated by inoculation of collagenase, which was isolated and purified from normal human cultured skin tissue. The distribution of collagenase in gastric cancer tissue from 52 gastric cancer patients was analysed by the peroxidase-labeled antibody method. Collagenase existed on the surface of collagen fibers and in cell plasma of fibroblasts. Moreover, cancer cells themselves produced collagenase, as the cell plasma of cancer cells stained. The relation of the histological type and depth of invasion to positive staining of cancer cells was then analysed. Cancer cells of the differentiated type stained frequently, while positive staining was low in cases of early gastric cancer. The percentage of positive staining increased according to the advance of gastric cancer. The infiltrative growth pattern also changed the distribution of parechymal collagenase