Automorphisms of real Lie algebras of dimension five or less

The Lie algebra version of the Krull-Schmidt Theorem is formulated and proved. This leads to a method for constructing the automorphisms of a direct sum of Lie algebras from the automorphisms of its indecomposable components. For finite-dimensional Lie algebras, there is a well-known algorithm for finding such components, so the theorem considerably simplifies the problem of classifying the automorphism groups. We illustrate this by classifying the automorphisms of all indecomposable real Lie algebras of dimension five or less. Our results are presented very concisely, in tabular form

Romania's evolving legal framework for private sector development

As the economies of Central and Eastern Europe move from central planning and state ownership to market-driven development of private sector activity, they are undertaking comprehensive change in the"rules of the game", the legal framework for economic activity. The authors analyze the evolving legal framework for private sector development in Romania. The government has worked intensively in the last two years to create a legal framework for a market economy. It has adopted not only a new constitution but also extensive new legislation covering real and intellectual property, companies, and foreign investment. It has revived the pre-war civil code as a basis for contract law, and is moving to modernize its bankruptcy code. The only area surveyed in which little legal reform has occurred is antimonopoly law. Challenges remain in both law and practice. The broad principles of private ownership, free market exchange, and equal treatment of public and private firms are well recognized and have been largely achieved. But a tendency towards centralized, bureaucratic control remains in excessive requirements for approval and uneconomic limits on certain activities. Moreover, implementation will take a long time because there is little or no institutional framework for enforcement and dispute resolution. Developing a body of regulation and case practice will take time.Environmental Economics&Policies,National Governance,Legal Products,Banks&Banking Reform,Real&Intellectual Property Law

The legal framework for private sector development in a transitional economy : the case of Poland

The economies of Central and Eastern Europe are in the midst of a historic transition from central planning and state ownership to development of a market-driven private sector. This transition requires comprehensive changes in"rules of the game"- including the legal framework for economic activity. A market economy presupposes a set of property rights and a system of laws or customs that allow the exchange of those rights. The legal framework in a market economy has at least three basic functions: defining the universe of property rights; setting the rules for entry into and exit from productive activities; and setting the rules of market exchange. These legal tasks are accomplished by areas of law such as: company, foreign investment, bankruptcy, contract and competition law. Poland has a rich legal tradition dating from pre-socialist times, which was suppressed but not eliminated during its forty years of socialism. This tradition is being revised as the country moves toward a private market economy. The current legal framework in Poland closely follows other continental jurisdictions and has a clear and reasonable internal logic. Many of the laws are old, but most are flexible enough to permit a wide range of modern, market-oriented activity. Property law, however, remains a"jungle". The wide discretion and general lack of precedent create tremendous legal uncertainty that is sure to hamper private sector development.Environmental Economics&Policies,Banks&Banking Reform,Municipal Housing and Land,Legal Products,Land and Real Estate Development

SHOULD I STAY OR SHOULD I GO: THE ROLE OF REFERRALS ON ONLINE COMMUNITY MEMBER TURNOVER AND TENURE

Communities are often faced with challenges associated with attracting and maintaining a membership base, which affects their ability to develop a pool of resources and ultimately impacts their sustainability. A potential resolution to this challenge lies in the members of the community referring non-members to the community – member referrals. While community joining has been acknowledged as important stage in the life cycle of community members; however, the way in which a member becomes aware of a community and its resulting influence on their engagement with the community has not been examined. This research-in-progress paper outlines the examination of the role of referrals on member turnover and tenure. Drawing upon theories of referrals from organizational behavior and marketing, the paper theorizes that referrals have the potential to facilitate the awareness of, and interest in, a community, which ultimately influences new members to return to, and stay, in a community

Hahahahaha, Duuuuude, Yeeessss!: A two-parameter characterization of stretchable words and the dynamics of mistypings and misspellings

Stretched words like \u27heellllp\u27 or \u27heyyyyy\u27 are a regular feature of spoken language, often used to emphasize or exaggerate the underlying meaning of the root word. While stretched words are rarely found in formal written language and dictionaries, they are prevalent within social media. In this paper, we examine the frequency distributions of \u27stretchable words\u27 found in roughly 100 billion tweets authored over an 8 year period. We introduce two central parameters, \u27balance\u27 and \u27stretch\u27, that capture their main characteristics, and explore their dynamics by creating visual tools we call \u27balance plots\u27 and \u27spelling trees\u27. We discuss how the tools and methods we develop here could be used to study the statistical patterns of mistypings and misspellings and be used as a basis for other linguistic research involving stretchable words, along with the potential applications in augmenting dictionaries, improving language processing, and in any area where sequence construction matters, such as genetics

Delivering services by building and running virtual organisations

Non peer reviewedPostprin

COVID-19 antibody testing: From hype to immunological reality

The potential role for serological tests in the current COVID-19 pandemic has generated very considerable recent interest across many sectors worldwide, inter alia pathologists seeking additional weapons for their armoury of diagnostic tests; epidemiologists seeking tools to gain seroprevalence data that will inform improved models of the spread of disease; research scientists seeking tools to study the natural history of COVID-19 disease; vaccine developers seeking tools to assess vaccine efficacy in clinical trials; and companies and governments seeking tools to aid return-to-work decision-making. However, much of the local debate to date has centred on questions surrounding whether regulatory approval processes are limiting access to serological tests, and has not paused to consider the intrinsically limiting impact of underlying fundamental biology and immunology on where and how different COVID-19 serological tests can usefully be deployed in the response to the current pandemic. We review, from an immunological perspective, recent experimental evidence on the time-dependency of adaptive immune responses following SARS-CoV-2 infection and the impact of this on the sensitivity and specificity of COVID-19 antibody tests made at different time points post infection. We interpret this scientific evidence in terms of mooted clinical applications for current COVID-19 antibody tests in identifying acute infections, in confirming recent or past infections at the individual and population level, and in detecting re-infection and protective immunity. We conclude with guidance on where current COVID-19 antibody tests can make a genuine impact in the pandemic

English verb regularization in books and tweets

The English language has evolved dramatically throughout its lifespan, to the extent that a modern speaker of Old English would be incomprehensible without translation. One concrete indicator of this process is the movement from irregular to regular (-ed) forms for the past tense of verbs. In this study we quantify the extent of verb regularization using two vastly disparate datasets: (1) Six years of published books scanned by Google (2003-2008), and (2) A decade of social media messages posted to Twitter (2008-2017). We find that the extent of verb regularization is greater on Twitter, taken as a whole, than in English Fiction books. Regularization is also greater for tweets geotagged in the United States relative to American English books, but the opposite is true for tweets geotagged in the United Kingdom relative to British English books. We also find interesting regional variations in regularization across counties in the United States. However, once differences in population are accounted for, we do not identify strong correlations with socio-demographic variables such as education or income