On the cardinality and complexity of the set of codings for self-similar sets with positive Lebesgue measure

Let λ1,…,λn be real numbers in (0,1) and p1,…,pn be points in Rd. Consider the collection of maps fj:Rd→Rd given by fj(x)=λjx+(1−λj)pj. It is a well known result that there exists a unique nonempty compact set Λ⊂Rd satisfying Λ=∪nj=1fj(Λ). Each x∈Λ has at least one coding, that is a sequence (ϵi)∞i=1 ∈{1,…,n}N that satisfies limN→∞fϵ1…fϵN(0)=x. We study the size and complexity of the set of codings of a generic x∈Λ when Λ has positive Lebesgue measure. In particular, we show that under certain natural conditions almost every x∈Λ has a continuum of codings. We also show that almost every x∈Λ has a universal coding. Our work makes no assumptions on the existence of holes in Λ and improves upon existing results when it is assumed Λ contains no holes.

On univoque points for self-similar sets

Let K⊆R be the unique attractor of an iterated function system. We consider the case where K is an interval and study those elements of K with a unique coding. We prove under mild conditions that the set of points with a unique coding can be identified with a subshift of finite type. As a consequence, we can show that the set of points with a unique coding is a graph-directed self-similar set in the sense of Mauldin and Williams (1988). The theory of Mauldin and Williams then provides a method by which we can explicitly calculate the Hausdorff dimension of this set. Our algorithm can be applied generically, and our result generalises the work of Daróczy, Kátai, Kallós, Komornik and de Vries.

Consent and the use of force: an examination of ‘intervention by invitation’ as a basis for US drone strikes in Pakistan, Somalia and Yemen

Drone strikes are becoming a key feature of the United States’ global military response to nonstate actors, and it has been widely adduced that these strikes have been carried out with the consent of the host states in which such non-state actors reside. This article examines the degree to which assertions of consent (or ‘intervention by invitation’), provided as a justification for drone strikes by the United States in Pakistan, Yemen and Somalia, can be said to accord with international law. First the article provides a broad sketch of the presence of consent in international law. It then analyses in detail the individual elements of consent as provided by Article 20 of the International Law Commission Draft Articles of State Responsibility. These require that consent should be ‘valid’, given by the legitimate government and expressed by an official empowered to do so. These elements will be dealt with individually, and each in turn will be applied to the cases of Pakistan, Yemen and Somalia. Finally, the article will examine the breadth of the exculpatory power of consent, and the extent to which it can preclude the wrongfulness of acts carried out in contravention of international law other than the prohibition of the use of force under Article 2(4) of the Charter of the United Nations.

Epstein-Barr virus: clinical and epidemiological revisits and genetic basis of oncogenesis

Epstein-Barr virus (EBV) is classified as a member in the order herpesvirales, family herpesviridae, subfamily gammaherpesvirinae and the genus lymphocytovirus. The virus is an exclusively human pathogen and thus also termed as human herpesvirus 4 (HHV4). It was the first oncogenic virus recognized and has been incriminated in the causation of tumors of both lymphatic and epithelial nature. It was reported in some previous studies that 95% of the population worldwide are serologically positive to the virus. Clinically, EBV primary infection is almost silent, persisting as a life-long asymptomatic latent infection in B cells although it may be responsible for a transient clinical syndrome called infectious mononucleosis. Following reactivation of the virus from latency due to immunocompromised status, EBV was found to be associated with several tumors. EBV linked to oncogenesis as detected in lymphoid tumors such as Burkitt's lymphoma (BL), Hodgkin's disease (HD), post-transplant lymphoproliferative disorders (PTLD) and T-cell lymphomas (e.g. Peripheral T-cell lymphomas; PTCL and Anaplastic large cell lymphomas; ALCL). It is also linked to epithelial tumors such as nasopharyngeal carcinoma (NPC), gastric carcinomas and oral hairy leukoplakia (OHL). In vitro, EBV many studies have demonstrated its ability to transform B cells into lymphoblastoid cell lines (LCLs). Despite these malignancies showing different clinical and epidemiological patterns when studied, genetic studies have suggested that these EBV- associated transformations were characterized generally by low level of virus gene expression with only the latent virus proteins (LVPs) upregulated in both tumors and LCLs. In this review, we summarize some clinical and epidemiological features of EBV- associated tumors. We also discuss how EBV latent genes may lead to oncogenesis in the different clinical malignancies

Arnold v. Britton: a ratio and two sets of obiter dicta

Arnold v Britton marks the final stage of the longstanding dispute as to the correct interpretation of a number of 99-year leases of chalets on a leisure park at Oxwich, in the Gower peninsula, near Swansea. The aspect of the case which has attracted most discussion has, understandably, been its main ratio: the proper way to construe a provision of a lease which arguably has an absurd result. This will be considered in this case-note. The judgment of the Supreme Court – particularly the judgment of Lord Neuberger PSC – does, however contain some observations on the possible reform of the law on service charges which are of interest to those engaged in this field. It also contains some obiter comments on ‘letting schemes’ which are – in the view of the present author – highly unorthodox. These three rather disparate issues which are raised by this case will be considered in turn. As they have little in common with each other, they will be considered as separate sections.

Moral uncertainty and permissibility: evaluating option sets

In this essay, we explore an issue of moral uncertainty: what we are permitted to do when we are unsure about which moral principles are correct. We develop a novel approach to this issue that incorporates important insights from previous work on moral uncertainty, while avoiding some of the difficulties that beset existing alternative approaches. Our approach is based on evaluating and choosing between option sets rather than particular conduct options. We show how our approach is particularly well-suited to address this issue of moral uncertainty with respect to agents that have credence in moral theories that are not fully consequentialist.

Inter-comparison of stratospheric mean-meridional circulation and eddy mixing among six reanalysis data sets

The stratospheric mean-meridional circulation (MMC) and eddy mixing are compared among six meteorological reanalysis data sets: NCEP-NCAR, NCEP-CFSR, ERA-40, ERA-Interim, JRA-25, and JRA-55 for the period 1979–2012. The reanalysis data sets produced using advanced systems (i.e., NCEP-CFSR, ERA-Interim, and JRA-55) generally reveal a weaker MMC in the Northern Hemisphere (NH) compared with those produced using older systems (i.e., NCEP/NCAR, ERA-40, and JRA-25). The mean mixing strength differs largely among the data products. In the NH lower stratosphere, the contribution of planetary-scale mixing is larger in the new data sets than in the old data sets, whereas that of small-scale mixing is weaker in the new data sets. Conventional data assimilation techniques introduce analysis increments without maintaining physical balance, which may have caused an overly strong MMC and spurious small-scale eddies in the old data sets. At the NH mid-latitudes, only ERA-Interim reveals a weakening MMC trend in the deep branch of the Brewer–Dobson circulation (BDC). The relative importance of the eddy mixing compared with the mean-meridional transport in the subtropical lower stratosphere shows increasing trends in ERA-Interim and JRA-55; this together with the weakened MMC in the deep branch may imply an increasing age-of-air (AoA) in the NH middle stratosphere in ERA-Interim. Overall, discrepancies between the different variables and trends therein as derived from the different reanalyses are still relatively large, suggesting that more investments in these products are needed in order to obtain a consolidated picture of observed changes in the BDC and the mechanisms that drive them.